## Envision Math Common Core 5th Grade Answers Key Topic 13 Write and Interpret Numerical Expressions

enVision STEM Project: Food Chains and Food Webs
Do Research Use the Internet or other sources to find out more about food chains and food webs. Investigate the roles of producers, consumers, and decomposers. Explain how energy from sunlight is transferred to consumers.

Journal: Write a Report Include what you found. Also in your report:
• Draw a food web from an ecosystem near your home.
• Draw arrows on your food web to show how energy moves. Explain why the order is important.
• On one food chain of your food web, label each organism as a producer, consumer, or decomposer.

Review What You Know

Vocabulary

Choose the best term from the box. Write it on the blank.

• difference
• equation
• product
• sum
• quotient

Question 1.
The answer to a division problem is the ____.

The answer to a division problem is the  Quotient

Question 2.
The ____ of 5 and 7 is 12.

The sum of 5 and 7 is 12

Question 3.
To find the ___ between 16 and 4, you subtract.

To find the difference between 16 and 4, you subtract

Question 4.
A number sentence that shows two equivalent values is a(n) ____.

A number sentence that shows two equivalent values is an Equation

Mixed Review

Question 5.
648 ÷ 18

Question 6.
35 × 100

3500

Question 7.
47.15 + 92.9

140.05

Question 8.
$$\frac{1}{4}$$ + $$\frac{1}{4}$$ + $$\frac{1}{4}$$

1/4 + 1/4 + 1/4

1/2 + 1/4

3/4

Question 9.
3.4 – 2.7

0.7

Question 10.
1.9 + 7

8.9

Question 11.
3$$\frac{2}{5}$$ + $$\frac{1}{2}$$

3 2/5 + 1/2

17/5 + 1/2

39/10

Question 12.
75 ÷ $$\frac{1}{5}$$

75 ÷ 1/5

75 / 1/5

75 x 5

= 375

Question 13.
$3.75 +$2.49

$6.24 Question 14. 8$$\frac{5}{8}$$ – 1$$\frac{2}{8}$$ Answer: 8 5/8 – 1 2/8 69/8 – 10/8 59/8 Question 15. 31.8 × 2.3 Answer: 73.14 Question 16. 9 – 4.6 Answer: 4.4 Question 17. Jackson bought 2 tickets to the state fair. Each ticket cost$12. He spent $15 on rides and$8.50 on food. How much did Jackson spend in all?

Total cost of tickets = $12 x 2 =$24

Total money after spending $15 on rides =$24 + $15 =$39

Total money after spending $8.50 on food =$39 + $8.50 =$47.50

Total money spent =  $47.50 Question 18. A baker has 3 pounds of dried fruit. Each batch of a recipe she is making uses $$\frac{1}{2}$$ pound of the fruit. How many batches can she make? A. 9 batches B. 6 batches C. 2 batches D. 1$$\frac{1}{2}$$ batches Answer: B. 6 batches Multiplication Question 19. What equation comes next in the pattern below? Explain. 7 × 10 = 70 7 × 100 = 700 7 × 1,000 = 7,000 Answer: 7 × 10,000 = 70,000 pick a Project PROJECT 13A What’s been recovered from the wreck of the Atocha? Project: Write a Treasure Adventure Mystery Story PROJECT 13B Do you like to play games? Project: Design a Game Using Dominos PROJECT 13C What happens when a calculation is incorrect? Project: Program a Robot 3-ACT MATH PREVIEW Math Modeling Video Before watching the video, think: A conjecture is a statement someone believes is true based on observations. You can usually either prove or disprove a conjecture. Keep an eye out for the conjecture in this video. ### Lesson 13.1 Evaluate Expressions Activity Solve&Share Jordan and Annika are working on 15 + 12 ÷ 3 + 5. Jordan says the answer is 14 and Annika says the answer is 24. Who is right? Solve this problem any way you choose. Look Back! Construct Arguments Do you think two students, who made no computation errors, would get different values for this numerical expression? Explain. (4 × 35) + (36 × 8) Visual Learning Bridge Essential Question What Order Should You Use When You Evaluate an Expression? A. Jack evaluated [(7 × 2) – 3] ÷ 8 = 2 × 3. To avoid getting more than one answer, he used the order of operations given at the right. Parentheses, brackets, and braces are all used to group numbers in numerical expressions. Order of Operations 1. Evaluate inside parentheses (), brackets [ ], and braces {}. 2. Multiply and divide from left to right. 3. Add and subtract from left to right, B. Step 1 First, do the operations inside the parentheses. Then, evaluate the terms inside the brackets. C. Step 2 Next, multiply and divide in order from left to right. D. Step 3 Finally, add and subtract in order from left to right. 11 + 12 = 23 So, the value of the expression is 23. Convince Me! Construct Arguments Would the value of {2+[(15 – 3) – 6]} ÷ 2 change if the braces were removed? Explain. Guided Practice Do You Understand? Question 1. Explain the steps involved in evaluating the expression [(4 + 2) – 1] × 3. Answer: [(4 + 2) – 1] × 3 [(6) – 1] × 3 [5] × 3 15. Question 2. Would the value of (12 – 4) ÷ 4 + 1 change if the parentheses were removed? Explain. Answer: (12 – 4) ÷ 4 + 1 (8) ÷ 4 + 1 2 + 1 3. Do You Know How? In 3-6, use the order of operations to evaluate the expression. Question 3. [7 × (6 – 1)] + 100 Answer: [7 × (6 – 1)] + 100 [7 × (5)] + 100 [35] + 100 135 Question 4. 17 + 4 × 3 Answer: 17 + 4 × 3 17 + 12 29 Question 5. (8 + 1) + 9 × 7 Answer: (8 + 1) + 9 × 7 (9) + 9 × 7 (9) + 63 72 Question 6. {[(4 × 3) ÷ 2] + 3} × 6 Answer: {[(4 × 3) ÷ 2] + 3} × 6 {[(12) ÷ 2] + 3} × 6 {6 + 3} × 6 {9} × 6 54. Independent Practice Remember to evaluate inside parentheses, brackets, and braces first. Leveled Practice In 7-21, use the order of operations to evaluate the expression. Question 7. Answer: Question 8. Answer: Question 9. Answer: Question 10. 5 ÷ 5 + 4 × 12 Answer: 5 ÷ 5 + 4 × 12 1 + 4 × 12 1 + 48 49 Question 11. [6 – (3 × 2)] + 4 Answer: [6 – (3 × 2)] + 4 [6 – (6)] + 4 [0] + 4 4 Question 12. (4 × 8) ÷ 2 + 8 Answer: (4 × 8) ÷ 2 + 8 (32) ÷ 2 + 8 16 + 8 24 Question 13. (18 + 7) × (11 – 7) Answer: (18 + 7) × (11 – 7) (25) × (4) 100 Question 14. 2 + [4 + (5 × 6)] Answer: 2 + [4 + (5 × 6)] 2 + [4 + (30)] 2 + [34] 36 Question 15. (9 + 11) ÷ (5 + 4 + 1) Answer: (9 + 11) ÷ (5 + 4 + 1) (20) ÷ (10) 2 Question 16. 90 – 5 × 5 × 2 Answer: 90 – 5 × 5 × 2 90 – 50 40 Question 17. 120 – 40 ÷ 4 × 6 Answer: 120 – 40 ÷ 4 × 6 120 – 10 × 6 120 – 60 60 Question 18. 22 + (96 – 40) ÷ 8 Answer: 22 + (96 – 40) ÷ 8 22 + (56) ÷ 8 22 + 7 29 Question 19. (7.7 + 0.3) ÷ 0.1 × 4 Answer: (7.7 + 0.3) ÷ 0.1 × 4 (8) ÷ 0.1 × 4 80 x 4 320 Question 20. 32 ÷ (12 – 4) + 7 Answer: 32 ÷ (12 – 4) + 7 32 ÷ (8) + 7 4 + 7 11 Question 21. {8 × [1 + (20 – 6)} ÷ $$\frac{1}{2}$$ Answer: {8 × [1 + (20 – 6)} ÷ $$\frac{1}{2}$$ {8 × [1 + (20 – 6)} ÷ 1/2 {8 × [1 + (14)} ÷ 1/2 {8 × 15} ÷ 1/2 {120} ÷ 1/2 240. Problem Solving Question 22. Dan and his 4 friends want to share the cost of a meal equally. They order 2 large pizzas and 5 small drinks. If they leave a tip of$6.30, how much does each person pay?

Given,

They order 2 large pizzas and 5 small drinks.

They leave a tip of $6.30 So, (2 x 12) + (5 x 1.50) + 6.30 (24) + (7.50) + 6.30$37.8

Total Number of friends = 5

Each person have to pay = 37.8 ÷ 5

= $7.56 Question 23. Higher Order Thinking Use the operation signs +, -, ×, and ÷ once each in the expression below to make the number sentence true. Answer: Question 24. Be Precise Carlotta needs 12$$\frac{1}{2}$$ yards of ribbon for a project. She has 5$$\frac{1}{4}$$ yards of ribbon on one spool and 2$$\frac{1}{2}$$ yards on another spool. How much more ribbon does she need? Answer: Question 25. Theresa bought three containers of tennis balls at$2.98 each. She had a coupon for $1 off. Her mom paid for half of the remaining cost. How much did Theresa pay? Evaluate the expression [(3 × 2.98) – 1] ÷ 2. Answer: [(3 × 2.98) – 1] ÷ 2 [8.94 – 1] ÷ 2 [7.94] ÷ 2 3.97 Question 26. enVision®STEM Giraffes are herbivores, or plant eaters. A giraffe can eat up to 75 pounds of leaves each day. Write and evaluate an expression to find how many pounds of leaves 5 giraffes can eat in a week. Evaluate the expression in the parentheses first. Then subtract inside the brackets. Assessment Practice Question 27. Which expression has a value of 8? A. 11 – 6 – 3 B. 4 + 30 ÷ 6 C. (9 + 7) ÷ 2 D. 1 + 1 × (2 + 2) Answer: C. (9 + 7) ÷ 2 D. 1 + 1 × (2 + 2) Question 28. Using the order of operations, which operation should you perform last to evaluate this expression? (1 × 2.5) + (52 ÷ 13) +(6.7 – 5) – (98 + 8) A. Addition B. Subtraction C. Multiplication D. Division Answer: B. Subtraction ### Lesson 13.2 Write Numerical Expressions Activity Solve & Share A baker packages 12 cupcakes to a box. Sean orders 5 boxes for his sister’s graduation party and 3.5 boxes for the Variety Show party. Write an expression that shows the calculations you could use to find the number of cupcakes Sean orders. Model with Math You can write a numerical expression to model this situation. Look Back! Write a different expression to model Sean’s order. Evaluate both expressions to check that they are equivalent. How many cupcakes does Sean order? Visual Learning Bridge Essential Question How Can You Write a Numerical Expression to Record Calculations? A. The school auditorium has 546 seats on the main floor and 102 in the balcony. Every seat is filled for all of the Variety Show performances. Write an expression that shows the calculations you could use to determine how many tickets were sold. B. Think about how you would calculate the total number of tickets. Add 546 + 102 to find the total number of seats. Then multiply by the number of performances, 4. So, you need to write a numerical expression that represents: “Find 4 times the sum of 546 and 102.” C. Use numbers and symbols to write the numerical expression. The sum of 546 and 102: 546 + 102 4 times the sum: 4 × (546 + 102) Remember, parentheses show which calculation to do first. The expression 4 × (546 + 102) shows the calculations for the number of tickets sold. Convince Me! Reasoning Two students wrote different expressions to find the total number of tickets sold. Is their work correct? Explain. Guided Practice Do You Understand? Question 1. Why do some numerical expressions contain parentheses? Answer: Parentheses are symbols that group things together. This becomes very important in numerical expressions because operations inside parentheses are always completed first when evaluating the expression. Question 2. Show how to use a property to write an equivalent expression for 9 × (7 + 44). Can you use a different property to write another equivalent expression? Explain. Answer: Do You Know How? In 3-6, write a numerical expression for each calculation. Question 3. Add 8 and 7, and then multiply by 2. Answer: (8 + 7) x 2 Question 4. Find triple the difference between 44.75 and 22.8. Answer: 3 x (44.75 – 22.8) Question 5. Multiply 4 times $$\frac{7}{8}$$ and then add 12. Answer: (4 x 7/8) + 12 Question 6. Add 49 to the quotient of 125 and 5. Answer: 49 + (125 ÷ 5) Independent Practice In 7-11, write a numerical expression for each calculation. Question 7. Add 91, 129, and 16, and then divide by 44. Answer: (91 + 129 + 16) ÷ 44 Question 8. Find 8.5 times the difference between 77 and 13. Answer: 8.5 x (77 – 13) Question 9. Subtract 55 from the sum of 234 and 8. Answer: (234 + 8) – 55 Question 10. Multiply $$\frac{2}{3}$$ by 42, and then multiply that product by 10. Answer: ( 2/3 x 42 ) x 10 Question 11. Write an expression to show the calculations you could use to determine the total area of the rectangles at the right. Answer: 3 x ( 18 x 22 ) Problem Solving Question 12. Model with Math Ronnie’s Rentals charges$25 plus $15 per hour to rent a chain saw. David rented a chain saw for 5 hours. Write an expression to show how you could calculate the total amount David paid. Answer: 5 x (25 + 15) Question 13. Fourteen students bought their art teacher a new easel for$129 and a set of blank canvases for $46. Sales tax was$10.50. They shared the cost equally. Write an expression to show how you could calculate the amount each student paid.

[(129 + 46) + 10.50] ÷ 14

Question 14.
A-Z Vocabulary When evaluating an expression, why is it important to use the order of operations?

When evaluating an expression, it is important to use the order of operations. The order of operations is a set of rules for how to evaluate expressions. They make sure everyone gets the same answer.

Question 15.
A storage shed is shaped like a rectangular prism. The width is 8 yards, the height is 4 yards, and the volume is 288 cubic yards. Explain how to find the length of the storage shed.

Volume = Length x Breadth x Height

Length = Volume ÷ (Breadth x Height)

Length = 288 ÷ (8 x 4)

Length = 288 ÷ 32

Length = 9 yards

Question 16.
Higher Order Thinking Danielle has a third of the amount needed to pay for her choir trip expenses. Does the expression (77 + 106 +34) ÷ 3 show how you could calculate the amount of money Danielle has? Explain.

Yes.

The expression (77 + 106 +34) ÷ 3 show how I could calculate the amount of money Danielle has

(77 + 106 +34) ÷ 3

(217) ÷ 3

$72.3 Assessment Practice Question 17. Which expression represents the following phrase? Subtract 214 from 721 and then divide by 5. A. (721 ÷ 214) – 5 B. 721 – 214 ÷ 5 C. (721 ÷ 5) – 214 D. (721 – 214) ÷ 5 Answer: D. (721 – 214) ÷ 5 Question 18. What is the first step in evaluating this expression? 2 × (47 + 122) – 16 A. Multiply 2 and 47 B. Multiply 2 and 16 C. Add 47 and 122 D. Add 2 and 47 Answer: C. Add 47 and 122 ### Lesson 13.3 Interpret Numerical Expressions Solve & Share Mrs. Katz is planning her family’s trip to the museum. She made a list of the expenses. Then she wrote the following expression to show how she can calculate the total cost. 6 × (4.20 + 8 + 12 + 3.50) How many people do you think are in the family? How can you tell? Use Structure You can interpret the relationships in numerical expressions without doing any calculations. Look Back! While they are at the museum, the family decides to watch a movie about earthquakes for$2.75 per person. Jana and Kay disagree as to how they should adjust Mrs. Katz’s expression to find the total expenses for the trip. Jana says the expression should be 6 × (4.20 + 8 + 12 + 3.50) + 2.75. Kay says the expression should be 6 × (4.20 + 8 + 12 + 3.50 + 2.75). Who is correct? Explain.

Visual Learning Bridge

Essential Question
How Can You Interpret Numerical Expressions Without Evaluating Them?

A.
Jimmy’s clown costume requires $$\frac{7}{8}$$ + $$\frac{1}{2}$$ + 1$$\frac{3}{4}$$ yards of fabric.
His dad’s matching clown costume requires 3 × ($$\frac{7}{8}$$ + $$\frac{1}{2}$$ + 1$$\frac{3}{4}$$)) yards. How does the amount of fabric needed for the dad’s costume compare to the amount needed for Jimmy’s costume?

You can compare the expressions and solve the problem without doing any calculations.

B.
Interpret the part of each expression that is the same.
$$\frac{7}{8}$$ + $$\frac{1}{2}$$ + 1$$\frac{3}{4}$$

Both expressions contain the sum $$\frac{7}{8}$$ + $$\frac{1}{2}$$ + 1$$\frac{3}{4}$$. This is the amount of fabric needed for Jimmy’s costume.

C.
Interpret the part of each expression that is different.

Remember, multiplying by 3 means “3 times as much.”

The second expression shows that the sum is multiplied by 3. So, the dad’s costume requires 3 times as much fabric as Jimmy’s costume.

Convince Me! Reasoning The 7 students in a sewing class equally share the cost of fabric and other supplies. Last month, each student paid ($167.94 +$21.41) ÷ 7. This month, each student paid ($77.23 +$6.49) ÷ 7. Without doing any calculations, in which month did each student pay more? Explain.

In the last month each student paid more. Because the value is more compared to this month.

Guided Practice

Do You Understand?

Question 1.
The number of yards of fabric needed for Rob’s costume is . How does the amount of fabric needed for Rob’s costume compare to the amount needed for Jimmy’s costume? Explain.

Question 2.
Without doing any calculations, explain why the following number sentence is true.
14 + (413 × 7) > 6+ (413 × 7)

Do You Know How?

Without doing any calculations, describe how Expression A compares to Expression B.

Question 3.
A 8 × (41,516 – 987)
B 41,516 – 987

In 4 and 5, without doing any calculations, write >, <, or =.

Question 4.

Question 5.

Independent Practice

In 6 and 7, without doing any calculations, describe how Expression A compares to Expression B.

Question 6.
A (613 + 15,090) ÷ 4
B 613 + 15,090

Question 7.
A (418 × $$\frac{1}{4}$$1) + (418 × $$\frac{1}{2}$$)
B 418 × $$\frac{3}{4}$$

In 8-11, without doing any calculations, write >, <, or =.

Question 8.
(284 + 910) ÷ 30 img 73 (284 + 7,816) ÷ 30

(284 + 910) ÷ 30 < 73 (284 + 7,816) ÷ 30

Question 9.
$$\frac{1}{3}$$ × (5,366 – 117) img 735,366 – 117

$$\frac{1}{3}$$ × (5,366 – 117) < 735,366 – 117

Question 10.
71 +(13,888 – 4,296) img 73 70 + (13,888 – 4,296)

71 +(13,888 – 4,296) < 73 70 + (13,888 – 4,296)

Question 11.
15 × (3.6 + 9.44) img 73 (15 × 3.6) + (15 × 9.44)

15 × (3.6 + 9.44) < 73 (15 × 3.6) + (15 × 9.44)

Problem Solving

Question 12.
A four-story parking garage has spaces for 240 + 285 + 250 + 267 cars. While one floor is closed for repairs, the garage has spaces for 240 +250 + 267 cars. How many spaces are there on the floor that is closed? Explain.

240 + 285 + 250 + 267 > 240 +250 + 267

By comparing,

285 spaces are there on the floor that is closed

Question 13.
Use Structure Peter bought yards of ribbon. Marilyn bought yards of ribbon. Without doing any calculations, determine who bought more ribbon. Explain.

Marilyn bought more ribbon.

Question 14.
Brook’s score in a card game is 713 + 102 + 516. On her next turn, she draws one of the cards shown. Now her score is (713 + 102 + 516) ÷ 2. Which card did Brook draw? Explain.

Question 15.
Marta bought a 0.25-kilogram box of fish food. She uses 80 grams a week. Is one box of fish food enough for 4 weeks? Explain.

No. For 4 weeks, she needs 4 x 80 = 320 grams

But, she bought only 250 grams.

Question 16.
Higher Order Thinking How can you tell that (496 + 77 + 189) × 10 is twice as large as (496 + 77 + 189) × 5 without doing complicated calculations?

10 is twice 5. Hence, (496 + 77 + 189) × 10 is twice as large as (496 + 77 + 189) × 5

Assessment Practice

Question 17.
Which statement describes the expression (21 + 1.5) × 12 – 5?
A. The sum of 21 and 1.5 times the difference of 12 and 5
B. Five less than the sum of 21 and 1.5 multiplied by 12
C. Five less than the product of 12 and 1.5 added to 21
D. Subtract the product of 12 and 5 from the sum of 21. and 1.5

A. The sum of 21 and 1.5 times the difference of 12 and 5

### Lesson 13.4 Reasoning

Activity

Problem Solving

Solve & Share
The camp cook has 6 dozen eggs. He uses 18 eggs to bake some brownies. Then he uses twice as many eggs to make pancakes. How many eggs does the cook have left? Use reasoning to write and evaluate an expression that represents the problem.

Thinking Habits
• What do the numbers and symbols in the problem mean?
• How are the numbers or quantities related?
• How can I represent a word problem using pictures, numbers, or equations?

Look Back! Reasoning Explain how the numbers, symbols, and operations in your expression represent this problem.

Visual Learning Bridge

Essential Question How Can You Use Reasoning to Solve Problems?

A.
Rose has 3 albums for her soccer cards. She gets 7 more cards for each of her albums for her birthday. How many cards does Rose have in all?

What do I need to do to solve the problem?
I need to find how many cards, including Rose’s new cards, will be in each album. Then I need to multiply to find the number of cards in 3 albums.

You can use tools or draw a diagram to help solve the problem.

B.
How can I use reasoning to solve this problem?
I can
• identify the quantities I know.
• use mathematical properties, symbols, and operations to show relationships.
• use diagrams to help.

Here’s my thinking…

C.
I need to find how many cards Rose has in all.
I can use a diagram to show how the quantities in the problem are related. Then I can write an expression.
There are 22 cards in each of her 3 albums. She gets 7 more cards for each of her 3 albums.

3 × (22 + 7) = 3 × 29
= 87
Rose has 87 cards.

Convince Me! Reasoning How can you use the Distributive Property to write an expression equivalent to the one given above? Use reasoning to explain how you know the expressions are equivalent.

Guided Practice

Reasoning Todd has 4 baseball card albums like the one pictured. He lets his best friend Franco choose 5 cards from each album. How many cards does Todd have now?

Question 1.
Write an expression to represent the total number of cards in Todd’s albums before he gives some cards to Franco. Explain how your expression represents the quantities and the relationship between the quantities.

(4 x 42)

4 represents the number of card albums

42 represents the number of cards in each album

multiplication or ‘x’ gives the total number of cards in 4 albums.

Question 2.
Write an expression to represent the total number of cards in Todd’s albums after he gives some cards to Franco.

(4 x 42) – (4 x 5)

Question 3.
How many cards does Todd have after he gives some cards to Franco? Explain how you solved the problem.

(4 x 42) – (4 x 5)

168 – 20 = 148

Todd have 148 cards.

Independent Practice

Remember to think about the meaning of each number before solving the problem.

Reasoning
Brandon is filling a flower order for a banquet. He needs 3 large arrangements and 12 small arrangements. The large arrangements each contain 28 roses. The small arrangements each contain 16 roses. How many roses does Brandon need in all?

Question 4.
Write an expression to represent the total number of roses Brandon needs. You can use a diagram to help.

(3 x 28) + (12 x 16)

Question 5.
Explain how the numbers, symbols, and operations in your expression represent the problem.

the number represents the number of arrangements and number of roses

the operation represents multiplication and addition

symbols represent the separation between the large and small arrangements.

Question 6.
How many roses does Brandon need? Explain how you solved the problem.

(3 x 28) + (12 x 16)

84 + 192

276.

Problem Solving

Math Supplies
Ms. Kim is ordering sets of place-value blocks for the 3rd, 4th, and 5th graders. She wants one set for each student, and there are 6 sets of blocks in a carton. How many cartons should Ms. Kim order?

Question 7.
Make Sense and Persevere What information in the problem do you need?

Information related to 3rd, 4th, and 5th graders and the number of students.

Question 8.
Reasoning Does this problem require more than one operation? Does the order of the operations matter? Explain.

Yes.

As there are 6 sets of blocks are in each carton. We have to divide the whole by 6.

Question 9.
A model with Math Writes an expression to represent the number of cartons Ms. Kim needs to order. You can use a diagram to help.

Use reasoning to make sense of the relationship between the numbers.

Question 10.
Construct Arguments Did you use grouping symbols in your expression? If so, explain why they are needed.

Question 11.
Be Precise Find the total number of cartons Ms. Kim should order. Explain how you found the answer.

### Topic 13 Fluency Practice

Activity

Find a Match
Work with a partner. Point to a clue. Read the clue. Look below the clues to find a match. Write the clue letter in the box next to the match. Find a match for every clue.

Clues

Topic 13 Vocabulary Review

Word List

Glossary

Understand Vocabulary

Choose the best term from the Word List. Write it on the blank.

• braces
• brackets
• evaluate
• numerical expression
• order of operations
• parentheses
• variable

Question 1.
A set of rules that describes the order in which calculations are done is known as the ____

A set of rules that describes the order in which calculations are done is known as the order of operations

Question 2.
____ , ____ and _____ are symbols used in mathematical expressions to group numbers or variables.

braces, brackets, and parentheses are symbols used in mathematical expressions to group numbers or variables.

Question 3.
A(n) ____ is a mathematical phrase that contains numbers and at least one operation.

a numerical expression is a mathematical phrase that contains numbers and at least one operation.

For each term, give an example and a non-example.

Draw a line from each number in Column A to the correct value in Column B.

Use Vocabulary in Writing

Question 11.
Explain why the order of operations is important. Use at least three terms from the Word List in your explanation.

The order of operations is a rule that tells you the right order in which to solve different parts of a math problem. … Subtraction, multiplication, and division are all examples of operations. The order of operations is important because it guarantees that people can all read and solve a problem in the same way.

### Topic 13 ReTeaching

Set A
pages 537-540
Use the order of operations to evaluate 50 + (8 + 2) × (14 – 4).

Order of Operations
1. Calculate inside parentheses, brackets, and braces.
2. Multiply and divide from left to right.
3. Add and subtract from left to right.
Perform the operations inside the parentheses, brackets, and braces.
50 + (8 + 2) × (14 – 4) = 50 + 10 × 10
Multiply and divide in order from left to right.
50 + 10 × 10 = 50 + 100
Add and subtract in order from left to right.
50 + 100 = 150

Remember that if the parentheses are inside brackets or braces, perform the operations inside the parentheses first.

Evaluate each expression.

Question 1.
(78 + 47) ÷ 25

(78 + 47) ÷ 25

(125) ÷ 25

5

Question 2.
4 + 8 × 6 ÷ 2 + 3

4 + 8 × 6 ÷ 2 + 3

4 + 8 × 3 + 3

4 + 24 + 3

31

Question 3.
[(8 × 25) ÷ 5] + 120

[(8 × 25) ÷ 5] + 120

[200 ÷ 5] + 120

[40] + 120

160

Question 4.
312 × (40 + 60) ÷ 60

312 × (40 + 60) ÷ 60

312 × (100) ÷ 60

312 × (100) ÷ 60

312 x 5/3

520

Question 5.
80 – (0.4 + 0.2) × 10

80 – (0.4 + 0.2) × 10

80 – (0.6) × 10

80 – 6

74

Question 6.
(18 – 3) ÷ 5 + 4

(18 – 3) ÷ 5 + 4

(15) ÷ 5 + 4

3 + 4

7

Question 7.
8 × 5 + 7 × 3 – (10 – 5)

8 × 5 + 7 × 3 – (10 – 5)

8 × 5 + 7 × 3 – (5)

40 + 21 – (5)

61 – 5

56

Question 8.
22 – {[87 – 32) ÷ 5] × 2}

22 – {[87 – 32) ÷ 5] × 2}

22 – {55 ÷ 5] × 2}

22 – 11 × 2

0.

Set B
pages 541-544
Write a numerical expression for the phrase: “Subtract 15 from the product of 12 and 7”.
Think:
Difference → Subtraction (-)
Product → Multiplication (×)
Quotient → Division (÷)
Product of 12 and 7: 12 × 7
Subtract 15 from the product: (12 × 7) – 15
So, a numerical expression for the phrase is: (12 × 7) – 15.

Remember that you can use parentheses to show which calculation to do first. Write a numerical expression for each phrase.

Question 1.
Add 15 to the product of $$\frac{3}{4}$$ and 12.

(3/4 x 12) + 15

Question 2.
Find the difference of 29 and 13, and then divide by 2.

(29 – 13) ÷ 2

Question 3.
Add 1$$\frac{1}{2}$$ and $$\frac{3}{4}$$, and then subtract $$\frac{1}{3}$$.

( 1 1/2 + 3/4 ) – 1/3

Question 4.
Multiply 1.2 by 5 and then subtract 0.7.

( 1.2 x 5 ) – 0.7

Question 5.
Add the quotient of 120 and 3 to the product of 15 and 10.

(120 ÷ 3) + (15 x 10)

Set C
pages 545-548
The expressions below show how many miles each student ran this week. How does Alex’s distance compare to Kim’s distance?
Kim: (4 × 3$$\frac{1}{2}$$)
Alex: (4 × 3$$\frac{1}{2}$$) + 2$$\frac{1}{2}$$
What is the same about the expressions? Both contain the product 4 × 3$$\frac{1}{2}$$.
What is different about the expressions?
2$$\frac{1}{2}$$ is added in Alex’s expression.
So, Alex ran 2$$\frac{1}{2}$$ miles farther than Kim this week.

Remember that sometimes you can compare numerical expressions without doing any calculations.

Without doing any calculations, write >, <, or =

Question 1.
72 × (37 – 9) 69 × (37 – 9)

72 × (37 – 9)  > 69 × (37 – 9)

Question 2.
(144 ÷ 12) – 6 144 ÷ 12

(144 ÷ 12) – 6  <  144 ÷ 12

Question 3.
(4 + $$\frac{1}{2}$$ + 3) × 2 2 × (4 + $$\frac{1}{2}$$ + 3)

(4 + $$\frac{1}{2}$$ + 3) × 2 <  2 × (4 + $$\frac{1}{2}$$ + 3)

Question 4.
Describe how Expression A compares to Expression B.
A $3.99 + ($9.50 × 2)
B $9.50 × 2 Answer: Value of A is 3.99 more than Value of B Set D pages 549-552 Think about these questions to help you reason abstractly and quantitatively. Thinking Habits • What do the numbers and symbols in the problem mean? • How are the numbers or quantities related? • How can I represent a word problem using pictures, numbers, or equations? Remember that you can use diagrams to help solve problems. Question 1. Kerry has 5 metal and 3 wood paperweights in her collection. She has twice as many glass paperweights as metal paperweights. Write an expression to represent the total number of paperweights in her collection. Then find the total number of paperweights. Answer: Question 2. Reese had 327 baseball cards. Then he lost 8 of them and gave 15 of them to his brother. Write an expression to represent the number of baseball cards he has left. Then find how many baseball cards he has left. Answer: ### Topic 13 Assessment Practice Question 1. Which of the following is equal to 10? A. 2 × (45 ÷ 9) B. 24 – (7 × 3) C. 1 + (4 × 2) D. (2 × 25) × 5 Answer: A. 2 × (45 ÷ 9) Question 2. Select all of the expressions that are equal to 8 × 65. 3 + 5 × 60 8 × (60 + 5) 8 × (50 + 15) (8 + 60) × (8 + 5) (8 × 60) + (8 × 5) Answer: 8 × (60 + 5) 8 × (50 + 15) (8 × 60) + (8 × 5) Question 3. Which is the value of the expression 7 + (3 × 4) – 2? A. 38 B. 20 C. 17 D. 12 Answer: C.17 Question 4. Which expression represents the following calculation? Add 16 to the quotient of 72 and 8. A. (72 – 8) + 16 B. (72 ÷ 8) + 16 C. (16 + 72) ÷ 8 D. (16 + 72) + 8 Answer: B. (72 ÷ 8) + 16 Question 5. What is the value of (100 × 15) + (10 × 15)? Answer: (100 × 15) + (10 × 15) (1500) + (150) 1650 Question 6. Describe how the value of Expression A compares to the value of Expression B. A. 12 × (54 ÷ $$\frac{2}{5}$$) B. 54 ÷ $$\frac{2}{5}$$ Answer: Value of A is 12 times the value of B Question 7. Write >, <, or = in the circle to make the statement true. (368 × 19) – 24 img 95 (368 × 19) – 47 Answer: (368 × 19) – 24 < 95 (368 × 19) – 47 Question 8. Insert parentheses to make the statement true. 7 + 6 × 14 – 9 = 37 Answer: Question 9. Which expression represents the following calculation? Subtract 2 from the product of 7 and 3. A. (7 + 3) – 2 B. 7 × (3 – 2) C. (7 × 3) – 2 D. (7 × 2) – 3 Answer: C. (7 × 3) – 2 Question 10. What is the value of the expression (6 + 3) × 2? Answer: (6 + 3) × 2 9 × 2 18 Question 11. Evaluate the expression (6 + 12 ÷ 2) + 4. Show your work. Answer: (6 + 12 ÷ 2) + 4 (6 + 6) + 4 12 + 4 16 Question 12. Write >, <, or = in the circle to make the statement true. (249 + 1,078) × $$\frac{1}{3}$$ img 96 (249 + 1,078) ÷ 3 Answer: (249 + 1,078) × $$\frac{1}{3}$$ < 96 (249 + 1,078) ÷ 3 Question 13. Write an expression to find the product of 3 and 28 plus the product of 2 and 15. Then solve. Answer: (3 x 28) + (2 x 15) 84 + 30 114 Question 14. Evaluate the expression. 6 + (24 – 4) + 8 ÷ 2 A. What step do you perform first in evaluating this expression? B. What step do you perform second in evaluating this expression? C. What is the value of the expression? Answer: A. Subtraction 24-4 B. Division 8 ÷ 2 C. 30 Decorating Jackie is decorating her room. She wants to put a border around the ceiling. She will put wallpaper on one wall and paint the other three walls. Question 1. The drawing of Jackie’s Room shows the width of the room. The expression [13.2 – (2 × 2.8)] ÷2 represents the length of her room. Part A How much border does Jackie need to go around the entire ceiling of her room? Explain how you can tell from the expression. Part B. What is the length of Jackie’s room? Show the steps you use to evaluate the expression. Answer: Question 2. The Painted Walls drawing shows the three walls Jackie wants to paint. One wall is 2.8 meters long. The length of each of the other walls is the answer you found in Question 1, Part B. Answer: Part A Write an expression to represent how many square meters Jackie will paint. Part B Evaluate the expression you wrote in Part A to find how many square meters Jackie will paint. Show the steps you used to evaluate the expression. Answer: Question 3. The wall Jackie wants to wallpaper has two windows. The Wallpapered Wall drawing shows the lengths and widths of the wall and the windows. Each roll of wallpaper covers 0.8 square meter. Part A What does the expression 2 × (1.5 × 0.8) represent? What does the expression (2.8 × 2) – (2 × (1.5 × 0.8)] represent? Part B Write an expression to find how many rolls of wallpaper Jackie needs to buy. Show the steps you used to evaluate the expression. Answer: #### enVision Math Common Core Grade 5 Answer Key ## Envision Math Common Core Grade 5 Answer Key Topic 14 Graph Points on the Coordinate Plane ## Envision Math Common Core 5th Grade Answers Key Topic 14 Graph Points on the Coordinate Plane enVision STEM Project: Earth’s Rotation Do Research Use the Internet or other sources to find out more about Earth’s rotation. Investigate why it appears that the Sun is moving across the sky. Design a model to explain Earth’s day/night cycle. Compare Earth’s rotation to another planet’s rotation. Write a Report: Journal Include what you found. Also in your report: • Write a step-by-step procedure of how to use a ball and a flashlight to represent the day/night cycle. • Explain what happens if the ball rotates slowly. What happens if the ball rotates quickly? • Make up and solve problems for plotting points and using graphs to show relationships. Review What You Know A-Z Vocabulary Choose the best term from the Word List. Write it on the blank. • equation • factor • line plot • numerical expression • variable Question 1. A(n) ____ contains numbers and at least one operation. Answer: A(n) numerical expression contains numbers and at least one operation. Explanation: In the above-given question, given that, A(n) numerical expression contains numbers and at least one operation. for example: 8x + 4y. where x and y are variables. 8 and 4 are constants. Question 2. A letter or symbol that represents an unknown amount is a(n) ____. Answer: A letter or symbol that represents an unknown amount is a(n) variable. Explanation: In the above-given question, given that, A letter or symbol that represents an unknown amount is a(n) variable. for example: 8 + n = 12. a variable is a letter or symbol that represents a number(unknown quantity). Question 3. A number sentence that uses the = symbol is a(n) ____. Answer: A number sentence that uses the = symbol is a(n) equation. Explanation: In the above-given question, given that, A number sentence that uses the = symbol is a(n) equation. for example: 4 + 5 = 9. 8 – 2 = 6. Question 4. A display that shows Xs or dots above a number line is a(n) ___. Answer: A display that shows Xs or dots above a number line is a(n) line plot. Explanation: In the above-given question, given that, A display that shows Xs or dots above a number line is a(n) line plot. for example: x < 3. Evaluate Expressions Evaluate each numerical expression. Question 5. 3 × 4 × (10 – 7) ÷ 2 Answer: 3 x 4 x (10 – 7) / 2 = 12. Explanation: In the above-given question, given that, the equation is 3 x 4 x (10 – 7) / 2. 3 x 4 x (3)/3. 3 x 4 x 1. 3 x 4 = 12. 3 x 4 x (10 – 7) / 2 = 12. Question 6. (8 + 2) 6 – 4 Answer: (8 + 2) 6 – 4 = 12. Explanation: In the above-given question, given that, the equation is (8 + 2) 6 – 4. (6) 6 – 4. (6) 2. 6 x 2 = 12. (8 + 2) 6 – 4 = 12. Question 7. 8 + 2 × 6 – 4 Answer: 8 + 2 x 6 – 4 = 20. Explanation: In the above-given question, given that, the equation is 8 + 2 x 6 – 4. 10 x 6 – 4. 10 x 2 = 20. 8 + 2 x 6 – 4 = 20. Question 8. 40 ÷ 5 + 5 × (3 – 1) Answer: 40 / 5 + 5 x (3 – 1) = 18. Explanation: In the above-given question, given that, the equation is 40 / 5 + 5 x (3 – 1). 40 / 5 + 5 x (2). 8 + 5 x 2. 8 + 10 = 18. 40 / 5 + 5 x (3 – 1) = 18. Question 9. 15 ÷ 3 + 2 × 10 Answer: 15 / 3 + 2 x 10 = Explanation: In the above-given question, given that, the equation is 15 / 3 + 2 x 10. 5 + 2 x 10. 5 + 20. 25. 15 / 3 + 2 x 10 = 25. Question 10. 21 × (8 – 6) ÷ 14 Answer: 21 x (8 – 6) / 14 = 3. Explanation: In the above-given question, given that, the equation is 21 x (8 – 6) / 14. 21 x ( 2) / 14. 21 x 1/7. 21 / 7 = 3. 21 x (8 – 6) / 14 = 3. Write Expressions Write a numerical expression for each word phrase. Question 11. Three less than the product of eight and six Answer: Three less than the product of eight and six = 45. Explanation: In the above-given question, given that, three less than the product of eight and six. product of 6 and 8 is 48. 6 x 8 = 48. 48 – 3 = 45. Question 12. Thirteen more than the quotient of twenty divided by four Answer: Thirteen more than the quotient of twenty divided by four is 18. Explanation: In the above-given question, given that, thirteen more than the quotient of twenty divided by four is 18. 20 / 4 = 5. 5 + 13 = 18. so thirteen more than the quotient of twenty divided by four is 18. Question 13. Four times the difference between seven and two Answer: Four times the difference between seven and two is 20. Explanation: In the above-given question, given that, Four times the difference between seven and two is 20. 7 – 2 = 5. 4 x 5 = 20. so four times the difference between seven and two is 20. Compare Expressions Question 14. Use < or > to compare 13 × (54 + 28) and 13 × 54 + 28 without calculating. Explain your reasoning. Answer: 13 x (54 + 28) < 13 x 54 + 28. Explanation: In the above-given question, given that, the equation is 13 x (54 + 28). 13 x 82 = 1066. 13 x 54 + 28. 702 + 28 = 730. so 13 x (54 + 28) < 13 x 54 + 28. Pick a Project PROJECT 14A What does a city planner do? Project: Plan a City PROJECT 14B What are some of the oldest childhood games? Project: Make Your Own Game PROJECT 14C How can dogs help rescue people? Project: Write a Story of a Missing Hiker PROJECT 14D How can artists use grids in their work? Project: Draw a Picture Using a Grid ### Lesson 14.1 The Coordinate System Activity Solve&Share On the first grid, plot a point where two lines intersect. Name the location of the point. Plot and name another point. Work with a partner. Take turns describing the locations of the points on your first grid. Then plot the points your partner describes on your second grid. Compare your first grid with your partner’s second grid to see if they match. Use the grids below to solve this problem. You can use grid paper to graph ordered pairs. Show your work! Look Back! Construct Arguments Why does the order of the two numbers that name a point matter? Explain your thinking Visual Learning Bridge Essential Question How Do You Name a Point on a Coordinate Grid? A. A map shows the locations of landmarks and has guides for finding them. In a similar way, a coordinate grid is used to graph and name the locations of points in a plane. You can use ordered pairs to locate points on a coordinate grid. B. A coordinate grid has a horizontal x-axis and a vertical y-axis. The point at which the x-axis and y-axis intersect is called the origin. C. A point on the grid is named using an ordered pair of numbers. The first number, the x-coordinate, names the distance from the origin along the x-axis. The second number, the y-coordinate, names the distance from the origin along the y-axis. Convince Me! Reasoning in the example above, name the ordered pair for Point B if it is 3 units to the right of Point A. Tell how you decided Answer: The points are (3, 3). Explanation: In the above-given question, given that, the point B if it is 3 units to the right of point A. the point is (1, 3). on the x-axis, the point is 1. on the y-axis, the point is 3. so the point is (1,3). if it is 3 units to the right of point A. so the points are (3, 3). Guided Practice Do You Understand? Question 1. You are graphing Point E at (0,5). Do you move to the right zero units, or up zero units? Explain. Answer: We will move up to zero units. Explanation: In the above-given question, given that, the point is (0, 5). the point 0 on the x-axis. the point 5 on the y-axis. we have to move up zero units. so we will move up to zero units. Question 2. A-Z Vocabulary What ordered pair names the origin of any coordinate grid? Answer: The points (0, 0) names the origin of any coordinate grid. Explanation: In the above-given question, given that, the ordered pair names the origin of any coordinate grid. the points are (0, 0), (1, 1), (2, 2), (3, 3) and so on. the points (0, 0) names the origin of any coordinate grid. Question 3. Describe how to graph Point K at (5, 4). Answer: Point 5 on the x-axis and 4 on the y-axis. Explanation: In the above-given question, given that, the point k at (5, 4) on the co-ordinate axis. we have to move up zero units. point 5 is on the x-axis. point 4 is on the y-axis. point 5 on the x-axis and 4 on the y-axis. Do You Know How? In 4 and 5, write the ordered pair for each point. Use the grid. Question 4. B Answer: The ordered pairs are (3, 2), (1, 4), and (5, 3). Explanation: In the above-given question, given that, the points are A, B, C, and D. the points are (1, 4). 1 is on the x-axis. 4 is on the y-axis. the point is (3, 2). 3 is on the x-axis. 2 is on the y-axis. the point is (5, 3). 5 is on the x-axis. 3 is on the y-axis. so the ordered pairs are (3, 2), (1, 4), and (5, 3). Question 5. A Answer: In 6 and 7, name the point for each ordered pair on the grid above. Question 6. (5, 3) Answer: Point 5 moves up to 3 units. Explanation: In the above-given question, given that, point 5 is on the x-axis. point 3 is on the y-axis. so the point is (5, 3). point 5 moves up zero units. Question 7. (1, 4) Answer: Point 1 moves up to 4 units. Explanation: In the above-given question, given that, point 1 is on the x-axis. point 4 is on the y-axis. so the point is (1, 4). point 1 moves up to 4 units. Independent Practice In 8-13, write the ordered pair for each point. Use the grid. Question 8. T Answer: The ordered pair is (0, 5). Explanation: In the above-given question, given that, point 0 is on the origin. point 5 is on the y-axis. the ordered pair is (0, 5). so the ordered pair is (0, 5). Question 9. X Answer: The ordered pair is (4, 3). Explanation: In the above-given question, given that, point 4 is on the x-axis. point 3 is on the y-axis. the ordered pair is (4, 3). so the ordered pair is (4, 3). Question 10. Y Answer: The ordered pair is (1, 0). Explanation: In the above-given question, given that, point 1 is on the X-axis. point 0 is on the y-axis. the ordered pair is (1, 0). so the ordered pair is (1, 0). Question 11. W Answer: The ordered pair is (3, 3). Explanation: In the above-given question, given that, point 3 is on the x-axis. point 3 is on the y-axis. the ordered pair is (3, 3). so the ordered pair is (3, 3). Question 12. Z Answer: The ordered pair is (1, 4). Explanation: In the above-given question, given that, point 1 is on the x-axis. point 4 is on the y-axis. the ordered pair is (1, 4). so the ordered pair is (1, 4). Question 13. S Answer: The ordered pair is (5, 5). Explanation: In the above-given question, given that, point 5 is on the x-axis. point 5 is on the y-axis. the ordered pair is (5, 5). so the ordered pair is (5, 5). In 14-18, name the point for each ordered pair on the grid above. Question 14. (2, 2) Answer: The point is L. Explanation: In the above-given question, given that, the point is (2,2). 2 is on the x-axis. 2 is on the y-axis. so the point is 2. Question 15. (5, 4) Answer: The point is Q. Explanation: In the above-given question, given that, the point is (5, 4). 5 is on the x-axis. 4 is on the y-axis. so the point is Q. Question 16. (1, 5) Answer: The point is N. Explanation: In the above-given question, given that, the point is (1, 5). 1 is on the x-axis. 5 is on the y-axis. so the point is N. Question 17. (0, 3) Answer: The point is M. Explanation: In the above-given question, given that, the point is (0, 3). 0 is on the x-axis. 3 is on the y-axis. so the point is M. Question 18. (4, 0) Answer: The point is P. Explanation: In the above-given question, given that, the point is (4, 0). 4 is on the x-axis. 0 is on the y-axis. so the point is p. Problem Solving Question 19. Higher Order Thinking Describe to a friend how to find and name the ordered pair for Point R on the grid. Answer: The point is (4, 5). Explanation: In the above-given question, given that, the point is R. 4 is on the x-axis. 5 is on the y-axis. so the point is (4, 5). In 20-24, complete the table. List the point and ordered pair for each vertex of the pentagon at the right. Answer: The points are B, C, D, E, and F. Explanation: In the above-given question, given that, The point E is on the ordered pair (1, 1). the point D is on the ordered pair (1, 2). point C is on the ordered pair (1, 3). point B is on the ordered pair (2, 4). point F is on the ordered pair (3, 1). Question 25. Reasoning Why is the order important when naming or graphing the coordinates of a point? Answer: The order is important when naming or graphing the coordinates of a point. Explanation: In the above-given question, given that, the order is important because A is on the (3, 3). B is on the (2, 4). C is on the (1, 3). D is on the (1, 2). E is on the (1, 1). F is on the (3, 1). G is on the (5, 1). Question 26. How are the x-axis and the y-axis related on a coordinate grid? Answer: The x-axis and the y-axis are related. Explanation: In the above-given question, given that, the order is important because A is on the (3, 3). B is on the (2, 4). C is on the (1, 3). D is on the (1, 2). E is on the (1, 1). F is on the (3, 1). G is on the (5, 1). Assessment Practice Question 27. Which of the following points is located at (4, 2)? A. Point A B. Point M C. Point B D. Point P Answer: Option M is correct. Explanation: In the above-given question, given that, the point is (4, 2). 4 is located on the x-axis. 2 is located on the y-axis. so option M is correct. ### Lesson 14.2 Graph Data Using Ordered Pairs Activity Sole & Share Graph and label the point for each ordered pair below on the grid. Then connect the points with line segments to form a shape. What shape did you draw? Use Appropriate Tools You can graph points on a coordinate grid. Show your work! Answer: The shape formed is square. Explanation: In the above-given question, given that, the ordered pairs are (2, 1), (5, 1), (5, 4), and (2, 4). the point (2, 1) is on the A. the point (5, 1) is on the B. the point (5, 4) is on the C. the point (2, 4) is on the D. so the shape formed is square. Look Back! What tool could you use to help connect points A, B, C, and D? Explain. Visual Learning Bridge Essential Question How Do You Graph a Point on a Coordinate Grid? A. The table below shows the growth of a plant over a period of several days. Graph ordered pairs to show the plant’s growth. Let x be the number of days and let y be the height of the plant in centimeters. The ordered pairs are (1, 4), (3, 8), (5, 10), (7, 11), and (9, 14). B. Step 1 Graph the first point (1, 4). Start at (0, 0). Move 1 unit to the right along the x-axis. Then move 4 units up. C. Step 2 Plot the rest of the ordered pairs from the table. Use a ruler to connect the points. Convince Me! Reasoning Based on the data, about how tall was the plant on day 4? Day 8? Guided Practice Do You Understand? Question 1. Natalie is graphing Point T at (1,8). Should she move to the right 8 units or up 8 units? Explain. Answer: She moves 8 units up. Explanation: In the above-given question, given that, the point T at (1, 8). point 1 is on the x-axis. point 8 is on the y-axis. so she moves 8 units up. Question 2. Describe how to graph the point (c, d). Answer: Do You Know How? In 3-6, graph each point on the grid and label it with the appropriate letter. Question 3. E (1, 3) Answer: The point is E. Explanation: In the above-given question, given that, point 1 is on the x-axis. point 3 is on the y-axis. the ordered pair is (1, 3). so the point is E. Question 4. F (4, 4) Answer: The point is F. Explanation: In the above-given question, given that, point 4 is on the x-axis. point 4 is on the y-axis. the ordered pair is (4, 4). so the point is F. Question 5. G (5, 2) Answer: The point is G. Explanation: In the above-given question, given that, point 5 is on the x-axis. point 2 is on the y-axis. the ordered pair is (5, 2). so the point is G. Question 6. H (0, 2) Answer: The point is H. Explanation: In the above-given question, given that, point 0 is on the x-axis. point 2 is on the y-axis. the ordered pair is (0, 2). so the point is H. Independent Practice In 7-18, graph and label each point on the grid at the right. Question 7. J (2, 6) Answer: The point is J. Explanation: In the above-given question, given that, point 2 is on the x-axis. point 6 is on the y-axis. the ordered pair is (2, 6). so the point is J. Question 8. K (6, 2) Answer: The point is K. Explanation: In the above-given question, given that, point 6 is on the x-axis. point 2 is on the y-axis. the ordered pair is (6, 2). so the point is K. Question 9. L (4, 5) Answer: The point is L. Explanation: In the above-given question, given that, point 4 is on the x-axis. point 5 is on the y-axis. the ordered pair is (4, 5). so the point is L. Question 10. M (0, 8) Answer: The point is M. Explanation: In the above-given question, given that, point 0 is on the x-axis. point 8 is on the y-axis. the ordered pair is (0, 8). so the point is M. Question 11. N (3, 9) Answer: The point is N. Explanation: In the above-given question, given that, point 3 is on the x-axis. point 9 is on the y-axis. the ordered pair is (3, 9). so the point is N. Question 12. V (6, 6) Answer: The point is V. Explanation: In the above-given question, given that, point 6 is on the x-axis. point 6 is on the y-axis. the ordered pair is (6, 6). so the point is V. Question 13. P (1, 4) Answer: The point is P. Explanation: In the above-given question, given that, point 1 is on the x-axis. point 4 is on the y-axis. the ordered pair is (1, 4). so the point is P. Question 14. Q (5, 0) Answer: The point is Q. Explanation: In the above-given question, given that, point 5 is on the x-axis. point 0 is on the y-axis. the ordered pair is (5, 0). so the point is Q. Question 15. R (7, 3) Answer: The point is R. Explanation: In the above-given question, given that, point 7 is on the x-axis. point 3 is on the y-axis. the ordered pair is (7, 3). so the point is R. Question 16. S (7, 8) Answer: The point is S. Explanation: In the above-given question, given that, point 7 is on the x-axis. point 8 is on the y-axis. the ordered pair is (7, 8). so the point is S. Question 17. T (8, 1) Answer: The point is T. Explanation: In the above-given question, given that, point 8 is on the x-axis. point 1 is on the y-axis. the ordered pair is (8, 1). so the point is T. Question 18. U (3, 3) Answer: The point is E. Explanation: In the above-given question, given that, point 1 is on the x-axis. point 3 is on the y-axis. the ordered pair is (1, 3). so the point is E. Problem Solving Question 19. Reasoning How is graphing (0, 2) different from graphing (2,0)? Answer: (0, 2) is on the y-axis, and (2, 0) is on the x-axis. Explanation: In the above-given question, given that, the ordered pairs are (0, 2) and (2, 0). (0, 2) is 2 units up from the origin. (2, 0) is 2 units right from the origin. Question 20. Number Sense Shane took a test that had a total of 21 items. He got about of the items correct. About how many items did he get correct? Answer: Question 21. Higher Order Thinking Point C is located at (10, 3) and Point D is located at (4,3). What is the horizontal distance between the two points? Explain. Answer: The distance between the points is (6, 0). Explanation: In the above-given question, given that, point C is located at (10, 3). point D is located at (4, 3). 10 – 4 = 6. 3 – 3 = 0. so the distance between the points is (6, 0). Question 22. Laurel buys 3 balls of yarn. Each ball of yarn costs$4.75. She also buys 2 pairs of knitting needles. Each pair costs $5.75. She pays for her purchase with two 20-dollar bills. What is her change? Answer: The change is$14.25.

Explanation:
In the above-given question,
given that,
Laurel buys 3 balls of yarn.
Each ball of yarn costs $4.75. She also buys 2 pairs of knitting needles. Each pair costs$5.75.
3 x $4.75 =$14.25.
$5.75 x 2 =$11.5.
$14.25 +$11.5 = $25.75. 20 x 2 = 40 dollar bills. 40 – 25.75 =$14.25.

Question 23.
Graph the points below on the grid at the right.
A (2, 4) B (1, 2) C (2, 0) D (3, 0) E (4, 2) F (3, 4)

The points are (2, 4), (1, 2), (2, 0), (3, 0), (4, 2), and (3, 4).

Explanation:
In the above-given question,
given that,
The points are (2, 4), (1, 2), (2, 0), (3, 0), (4, 2), and (3, 4).
point 2 is on the x-axis.
point 4 is on the y-axis.
point 1 is on the x-axis.
point 2 is on the y-axis.
point 2 is on the x-axis.
point 0 is on the y-axis.
point 3 is on the x-axis.
point 4 is on the x-axis.
point 2 is on the y-axis.
point 3 is on the x-axis.
point 4 is on the y-axis.

Question 24.
Alejandro wants to connect the points to form a shape. What would be the most appropriate tool for him to use? Use the tool to connect the points.

The shape formed is the hexagon.

Explanation:
In the above-given question,
given that,
Alejandro wants to connect the points to form a shape.
points are (2, 4), (1, 2), (2, 0), (3, 0), (4, 2), and (3, 4).
point 2 is on the x-axis.
point 4 is on the y-axis.
point 1 is on the x-axis.
point 2 is on the y-axis.
point 2 is on the x-axis.
point 0 is on the y-axis.
point 3 is on the x-axis.
point 4 is on the x-axis.
point 2 is on the y-axis.
point 3 is on the x-axis.
point 4 is on the y-axis.
so the shape formed is the hexagon.

Assessment Practice

Question 25.
Talia draws a map of her neighborhood on a coordinate grid. Her map shows the school at S (1,6), her house at H (4,3), and the library at L (7,2). Graph and label each location on the grid at the right.

Points are (1, 6), (4, 3), and (7, 2).

Explanation:
In the above-given question,
given that,
Talia draws a map of her neighborhood on a coordinate grid.
Her map shows the school at S (1,6), her house at H (4,3), and the library at L (7,2).
point 1 is on the x-axis.
point 6 is on the y-axis.
point 4 is on the x-axis.
point 3 is on the y-axis.
point 7 is on the x-axis.
point 2 is on the y-axis.

### Lesson 14.3 Solve Problems Using Ordered Pairs

Activity

Solve&Share
The table below uses number patterns to describe changes in the width and length of a rectangle. Let x be the width and y be the length. Then plot each of the four ordered pairs in the table on the coordinate grid. What do you think the length is if the width is 5?

You can make a graph to help solve the problem. Show your work!

Look Back! Look for Relationships What pattern do the points form on your graph?

Visual Learning Bridge

Essential Question How Can You Use Ordered Pairs to Solve Problems?

A.
Both Ann and Bill earn the amount shown each week. Ann starts with no money, but Bill starts with $5. How much will Bill have when Ann has$30? Represent this situation using a table and a graph.

You know that when Ann has $0, Bill has$5.

B.
Make a table showing how much money Ann and Bill have after each week.

Let x = Ann’s earnings and y = Bill’s earnings.

C.
Plot the ordered pairs from the table. Draw a line to show the pattern. Extend your line to the point where the x-coordinate is 30. The corresponding y-coordinate is 35.

So, Bill has $35 when Ann has$30.

Convince Me! Look for Relationships What is the relationship between Bill’s earnings and Ann’s earnings?

Guided Practice

Do You Understand?

Question 1.
In the example on page 574, find another point on the line. What does this point represent?

Question 2.
Algebra In the example on page 574, write an equation to show the relationship between Ann’s earnings and Bill’s earnings. Remember to let x = Ann’s earnings and y = Bill’s earnings.

Let x = Ann’s earnings.
y = Bill’s earnings.

Explanation:
In the above-given question,
given that,
x + 5.
Ann has $30 and$35.
$30 + 5 =$35.

Do You Know How?

Write the missing coordinates and tell what the point represents.

Question 3.

The missing coordinates are (5, 200).

Explanation:
In the above-given question,
given that,
the points are (20, 800), (15, 600), (10, 400).
20 – 5 = 15.
15 – 5 = 10.
10 – 5 = 5.
800- 200 = 600.
600 – 200 = 400.
400 – 200 = 200.
so the missing coordinates are (5, 200).

Independent Practice

In 4 and 5, find the missing coordinates and tell what the point represents.

Question 4.

The missing coordinates are (900, 800).

Explanation:
In the above-given question,
given that,
the ordered pairs are (1500, 1200), (1200, 1000), (600, 600), and (300, 400).
on x-axis subtract 300.
1500 – 300 = 1200.
1200 – 300 = 900.
900 – 300 = 600.
600 – 300 = 300.
on y-axis subtract 200.
1200 – 200 = 1000.
1000 – 200 = 800.
800 – 200 = 600.
600 – 200 = 400.
so the missing coordinates are (900, 800).

Question 5.

The missing coordinates are (200, 150).

Explanation:
In the above-given question,
given that,
the ordered pairs are (600, 550), (500, 450), (400, 350), (300, 250), and (100, 50).
subtract 100 on x-axis.
subtract 100 on y-axis.
600 – 100 = 500.
500 – 100 = 400.
400 – 100 = 300.
300 – 100 = 200.
200 – 100 = 100.
so the missing coordinates are (200, 150).

Question 6.
For Exercise 5, find two other points on the line. Then graph and label them. Describe the relationship between deer sightings and elk sightings.

Problem Solving

In 7 and 8, use the table at the right.

Question 7.
Graph the points in the table on the grid at the right. Then draw a line through the points.

Time(h) is on the x-axis.
pages read is on the y-axis.

Explanation:
In the above-given question,
given that,
in 1 hour number of pages read is 20.
in 2 hours number of pages read is 40.
in 3 hours number of pages read is 60.
in 4 hours number of pages read is 80.
in 5 hours number of pages read is 100.

Question 8.
Look for Relationships If the pattern continues, how many pages will have been read after 6 hours? Extend your graph to solve.

The number of pages that will have been read after 6 hours = 120.

Explanation:
In the above-given question,
given that,
in 1 hour number of pages read is 20.
in 2 hours number of pages read is 40.
in 3 hours number of pages read is 60.
in 4 hours number of pages read is 80.
in 5 hours number of pages read is 100.
in 6 hours number of pages read is 120.

Question 9.
Higher Order Thinking Suppose you have a graph of speed that shows a lion can run four times as fast as a squirrel. Name an ordered pair that shows this relationship. What does this ordered pair represent?

The ordered pair represents (1, 4).

Explanation:
In the above-given question,
given that,
the lion can run four times as fast as a squirrel.
x + 4y.
x represents the speed of a squirrel.
y represents the speed of a lion.
so a lion can run four times as fast as a squirrel.

Question 10.
Number Sense Candace drives a total of 48 miles each day to get to work and back home. She works 5 days a week. Her car gets 21 miles per gallon of gas. About how many gallons of gas does she need to drive to work and back home each week?!

The number of gallons of gas does she need to drive to work = 48 gallons.

Explanation:
In the above-given question,
given that,
Candace drives a total of 48 miles each day to get to work and back home.
She works 5 days a week.
Her car gets 21 miles per gallon of gas.
48 x 5 = 240.
240 / 5 = 48.
so the number of gallons of gas does she need to drive to work.

Assessment Practice

Question 11.
What does the point (15, 4) represent on the graph at the right?

A. The ant crawled 15 meters in 19 seconds.
B. The ant crawled 15 meters in 4 seconds.
C. The ant crawled 4 meters in 19 seconds.
D. The ant crawled 4 meters in 15 seconds.

Option B is correct.

Explanation:
In the above-given question,
given that,
point (15, 4) is in the coordinate plane.
15 is on the x-axis.
4 is on the y-axis.
the ant crawled 15 meters in 4 seconds.
so option B is correct.

Question 12.
What does the point (20, 5) represent on the graph?
A. In 20 seconds, the ant crawled 5 centimeters.
B. In 20 seconds, the ant crawled 5 meters.
C. In 5 seconds, the ant crawled 20 meters.
D. In 5 seconds, the ant crawled 15 meters.

Option C is correct.

Explanation:
In the above-given question,
given that,
the point is (20, 5).
20 is on the x-axis.
5 is on the y-axis.
in 5 seconds the ant crawled 20 meters.
so option C is correct.

### Lesson 14.4 Reasoning

Activity

Problem Solving

Solve & Share
Six clowns apply for a circus job. The specific job requires the clown to have a clown shoe size less than 15 inches and to be shorter than 5 ft 8 in. tall.
How many clowns meet the size requirements for the job? Complete the graph below to help you decide.

Thinking Habits
• What do the numbers and symbols in the problem mean?
• How are the numbers or quantities related?
• How can I represent a word problem using pictures, numbers, or equations?

Look Back! Reasoning How can you use reasoning about the completed graph to find the number of clowns that meet the requirements? Explain.

Visual Learning Bridge

Essential Question How Can You Use Reasoning to Solve Mathematical Problems?

A.
In 1705, a ship sank in the ocean at the point shown. Every year the ocean currents moved the ship 1 mile east and 2 miles north. Where was the ship located after 4 years? Where was the ship located after 10 years? Tell how you decided.

What do I need to do to solve the problem?
I need to find the ship’s location after 4 years and after 10 years.

B.
How can I use reasoning to solve this problem?
I can
• use what I know about graphing points.
• graph ordered pairs.
• look for relationships in the coordinates.
• decide if my answer makes sense.

Here’s my thinking..

C.
I will use the graph to show the location each year for 4 years. Each point is 1 mile east and 2 miles north from the previous point.
After 4 years the ship was at (8, 14).
I see a pattern. The x-coordinate increases by 1, and the y-coordinate increases by 2:
(4, 6), (5, 8), (6, 10), (7, 12), (8, 14)

I can continue the pattern for another 6 years:
(9,16), (10, 18), (11, 20), (12, 22), (13, 24), (14, 26)
After 10 years, the ship was at (14, 26).

Convince Me! Make Sense and Persevere How could you decide if your answers make sense?

Guided Practice

Tanya marked a grid in her garden. She planted a rose bush at (3, 1). She moved 2 feet east and 1 foot north and planted the second rose bush. She continued planting rose bushes so that each bush is 2 feet east and 1 foot north of the previous bush.

Question 1.

The point is (3, 1), (5, 2), and (7, 3).

Explanation:
In the above-given question,
given that,
the point is (3, 1).
She moved 2 feet east and 1 foot north and planted the second rose bush.
3 + 2 = 5.
5 + 2 = 7.
1 + 1 = 2.
2 + 1 = 3.
so the points are (3, 1), (5, 2), and (7, 3).

Question 2.
Draw and label the locations of the first four bushes on the grid. Do Tanya’s 0 2 bushes lie on a straight line? How do you know?

The bushes lie in a straight line.

Explanation:
In the above-given question,
given that,
the point is (3, 1).
She moved 2 feet east and 1 foot north and planted the second rose bush.
3 + 2 = 5.
5 + 2 = 7.
1 + 1 = 2.
2 + 1 = 3.
so the points are (3, 1), (5, 2), and (7, 3).

Question 3.
What are the locations of the fifth and ninth rose bushes?

The locations of the fifth and ninth rose bushes are in a straight line.

Explanation:
In the above-given question,
given that,
the point is (3, 1).
She moved 2 feet east and 1 foot north and planted the second rose bush.
3 + 2 = 5.
5 + 2 = 7.
7 + 2 = 9.
1 + 1 = 2.
2 + 1 = 3.
3 + 1 = 4.
so the points are (3, 1), (5, 2), and (7, 3), (9, 4).

Independent Practice

Reasoning
A marching band uses a grid to determine the members’ positions. Juan starts at (2, 2). Every 15 seconds, he moves 4 yards east and 3 yards north.

Question 4.
How can you model this problem?

After 15 seconds Juan moves (6, 5).

Explanation:
In the above-given question,
given that,
A marching band uses a grid to determine the members’ positions.
Juan starts at (2, 2).
Every 15 seconds, he moves 4 yards east and 3 yards north.
2 + 4 = 6.
2 + 3 = 5.
so after 15 seconds Juan moves (6, 5).

Question 5.
Draw and label the locations of Juan’s first four positions. Do the points form a pattern? How can you tell?

Juan’s first four positions are (6, 5), (10, 8), (14, 11), and (18, 14).

Explanation:
In the above-given question,
given that,
A marching band uses a grid to determine the members’ positions.
Juan starts at (2, 2).
Every 15 seconds, he moves 4 yards east and 3 yards north.
2 + 4 = 6, 6 + 4 = 10, 10 + 4 = 14, and 14 + 4 = 18.
2 + 3 = 5, 5 + 3 = 8, 8 + 3 = 11, and 11 + 3 = 14.
so Juan’s first four positions are (6, 5), (10, 8), (14, 11), and (18, 14).

Question 6.
What will Juan’s location be after 60 seconds? 90 seconds? How does the coordinate grid help you reason about the locations?

Juan,s location be after 60 and 90 seconds are (14, 11), and (18, 14).

Explanation:
In the above-given question,
given that,
A marching band uses a grid to determine the members’ positions.
Juan starts at (2, 2).
Every 15 seconds, he moves 4 yards east and 3 yards north.
2 + 4 = 6, 6 + 4 = 10, 10 + 4 = 14, and 14 + 4 = 18.
2 + 3 = 5, 5 + 3 = 8, 8 + 3 = 11, and 11 + 3 = 14.
so Juan,s location be after 60 and 90 seconds are (14, 11), and (18, 14).

Problem Solving

Rozo Robot
A toy company is testing Rozo Robot. Rozo is 18 inches tall and weighs 2 pounds. The employees of the company marked a grid on the floor and set Rozo at (2,5). They programmed Rozo to walk 3 yards east and 4 yards north each minute. What will Rozo’s location be after 7 minutes?

Question 7.
Make Sense and Persevere Do you need all of the information given in the problem to solve the problem? Describe any information that is not needed.

Question 8.
Model with Math Label the graph and plot Rozo’s starting position. Then plot and label Rozo’s position at the end of each of the first 4 minutes.

Question 9.
Use Appropriate Tools What tool would you choose for drawing a line segment between points on a coordinate grid? Explain your thinking.

You can use the coordinate grid to reason about relationships between the points

Question 10.
Look for Relationships Describe the relationships between the coordinates of the points that represent Rozo’s locations.

Question 11.
Reasoning What will Rozo’s location be after 7 minutes? Explain how you determined your answer.

### Topic 14 Fluency Practice

Activity

Point & Tally

Find a partner. Get paper and a pencil. Each partner chooses light blue or dark blue.
At the same time, Partner 1 and Partner 2 each point to one of their black numbers. Both partners find the product of the two numbers.
The partner who chose the color where the product appears gets a tally mark. Work until one partner has seven tally marks.

Topic 14 Vocabulary Review

Glossary

Understand Vocabulary

Choose the best term from the Word List. Write it on the blank.

Word List
• coordinate grid
• ordered pair
• origin
• x-axis
• x-coordinate
• y-axis
• y-coordinate

Question 1.
The point where the axes of a coordinate grid intersect is the _____

The point where the axes of a coordinate grid intersect is the origin.

Explanation:
In the above-given question,
given that,
the point where the axes of a coordinate grid intersect is the origin.
for example:
(x, y) = (3, 2).

Question 2.
A(n) ____ names an exact location on a coordinate grid.

A(n) coordinate grid names an exact location on a coordinate grid.

Explanation:
In the above-given question,
given that,
A(n) coordinate grid names an exact location on a coordinate grid.
for example:
(2, 3) is on the coordinate plane.
2 is on the x-axis.
3 is on the y-axis.

Question 3.
The first number of an ordered pair describes the distance from the origin along the ____

The first number of an ordered pair describes the distance from the origin along with the ordered pair.

Explanation:
In the above-given question,
given that,
the first number of an ordered pair describes the distance from the origin along with the ordered pair.
for example:
(4, 5) 4 units on the x-axis.
5 units on the y-axis.

Question 4.
The second number of an ordered pair is the ______

The second number of an ordered pair is the y-coordinate.

Explanation:
In the above-given question,
given that,
the second number of an ordered pair is the y-coordinate.
for example:
In an ordered pair, the first number is always the x-coordinate.
the second number is the y-coordinate.

Question 5.
A ____ is formed by two number lines that intersect at a right angle.

A coordinate plane is formed by two number lines that intersect at a right angle.

Explanation:
In the above-given question,
given that,
A coordinate plane is formed by two number lines that intersect at a right angle.
for example:
x-axis = horizontal number line.
y-axis = vertical number line.
origin = where the number lines intersect.
the coordinates of the origin are (0, 0).

Draw a line from each lettered point in Column A to the ordered pair it represents.

Use Vocabulary in Writing

Question 12.
Why is the order of the coordinates important in an ordered pair? Use terms from the Word List in your explanation.

The order of the coordinates is important because it forms a shape, a straight line.

Explanation:
In the above-given question,
given that,
points are A(5, 2), B(1, 7), C(2, 3), D(0, 7), E(7, 1), and F(0, 6).
the points formed a shape.
so the order of the coordinates is important in an ordered pair.

### Topic 14 Reteaching

Set A
pages 565-568

What ordered pair names Point A?
Start at the origin. The x-coordinate is the horizontal distance along the x-axis. The y-coordinate is the vertical distance along the y-axis.

Point A is at (7, 3).

Remember to first find the x-coordinate. Then find the y-coordinate. Write the coordinates in (x, y) order.

Use the grid to answer the questions.

Question 1.
Which point is located at (9, 5)?

Point is located at (9, 5) is R.

Explanation:
In the above-given question,
given that,
point is (9, 5).
9 is on the x-axis.
5 is on the y-axis.
so the point is located at (9, 5) is R.

Question 2.
Which point is located at (2, 3)?

Point is located at (2, 3) is K.

Explanation:
In the above-given question,
given that,
the point is (2, 3).
2 is on the x-axis.
3 is on the y-axis.
so the point is located at (2, 3) is K.

Question 3.
What ordered pair names Point T ?

Point is located at (3, 4) is T.

Explanation:
In the above-given question,
given that,
the point is (3, 4).
3 is on the x-axis.
4 is on the y-axis.
so the point is located at (3, 4) is T.

Question 4.
What is the ordered pair for the origin?

Point is located at (0, 7).

Explanation:
In the above-given question,
given that,
the point is (0,7).
0 is on the x-axis.
7 is on the y-axis.
so the point is located at (0, 7) is the origin.

Set B
pages 569-572, 573-576
In the table, the x-coordinate is in the left column and the y-coordinate is in the right column. Use the table to plot the ordered pairs. Then draw a line to connect the points.

Remember that you can use a tool, such as a ruler, to draw a line to connect the points on the graph.

Question 1.
Use the table below to plot the ordered pairs. Then complete the graph by connecting the points.

The points are (2, 1), (4, 2), (6, 3), and (8, 4).

Explanation:
In the above-given question,
given that,
the points on the x-axis are 2, 4, 6, and 8.
the points on the y-axis are 1, 2, 3, and 4.
so the ordered pairs are (2, 1), (4, 2), (6, 3), and (8, 4).

Question 2.
Write two ordered pairs with x-coordinates greater than 10 that are on the line.

The two ordered pairs are (10, 5), and (12, 6).

Explanation:
In the above-given question,
given that,
the points on the x-axis are 2, 4, 6, and 8.
the points on the y-axis are 1, 2, 3, and 4.
2 + 2 = 4.
4 + 2 = 6.
6 + 2 = 8.
1 + 1 = 2.
2 + 1 = 3.
3 + 1 = 4.
4 + 1 = 5.
so the two ordered pairs are (10, 5), and (12, 6).

Set C
pages 577-580

Thinking Habits
• What do the numbers and symbols in the problem mean?
• How are the numbers or quantities related?
• How can I represent a word problem using pictures, numbers, or equations?

Remember that you can use a graph or a table to reason about and solve word problems.
A company uses the graph to show how many packages each truck driver delivers. How many packages will one truck driver deliver in a 7-hour day?

Question 1.

The number of packages each truck driver delivers in hours.

Explanation:
In the above-given question,
given that,
the number of packages each truck driver delivers in hours.
in 1 hour the number of packages is 15.
in 2 hours the number of packages is 30.
in 3 hours the number of packages is 45.
in 4 hours the number of packages is 60.

Question 2.
How can you find the number of packages a driver delivers in 3 hours?

The number of packages a driver delivers in 3 hours is 45.

Explanation:
In the above-given question,
given that,
the number of packages each truck driver delivers in hours.
in 1 hour the number of packages is 15.
in 2 hours the number of packages is 30.
in 3 hours the number of packages is 45.
in 4 hours the number of packages is 60.
so the number of packages a driver delivers in 3 hours is 45.

Question 3.
How many packages will one truck driver deliver in a 7-hour day?

The number of packages will one truck deliver in a 7-hour day is 105.

Explanation:
In the above-given question,
given that,
the number of packages each truck driver delivers in hours.
in 1 hour the number of packages is 15.
in 2 hours the number of packages is 30.
in 3 hours the number of packages is 45.
in 4 hours the number of packages is 60.
in 5 hours the number of packages is 75.
in 6 hours the number of packages is 90.
in 7 hours the number of packages is 105.

Question 4.
How can you find how many hours it will take for one truck driver to deliver 120 packages?

The number of hours is 8.

Explanation:
In the above-given question,
given that,
the number of packages each truck driver delivers in hours.
in 1 hour the number of packages is 15.
in 2 hours the number of packages is 30.
in 3 hours the number of packages is 45.
in 4 hours the number of packages is 60.
in 5 hours the number of packages is 75.
in 6 hours the number of packages is 90.
in 7 hours the number of packages is 105.

### Topic 14 Assessment Practice

Use the coordinate grid below to answer 1-4.

Question 1.
Which is the ordered pair for Point Y?
A. (4, 5)
B. (4, 9)
C. (7, 9)
D. (9, 4)

Option B is correct.

Explanation:
In the above-given question,
given that,
the point is (4, 9).
4 is on the x-axis.
9 is on the y-axis.
so option B is correct.

Question 2.
Which point is located at (5, 2) on the coordinate grid?
A. M
B. N
C. Q
D. P

Option B is correct.

Explanation:
In the above-given question,
given that,
the point is (5, 2).
5 is on the x-axis.
2 is on the y-axis.
so option B is correct.

Question 3.
What is the ordered pair for Point Z?

The ordered pair for point Z is (9, 1).

Explanation:
In the above-given question,
given that,
the point is (9, 1).
9 is on the x-axis.
1 is on the y-axis.
so the ordered pair for point Z is (9, 1).

Question 4.
What is the ordered pair for Point P?

The ordered pair for point P is (4, 5).

Explanation:
In the above-given question,
given that,
the point is (4, 5).
4 is on the x-axis.
5 is on the y-axis.
so the ordered pair for point P is (4, 5).

Question 5.
Each year, Ginny recorded the height of a tree growing in her front yard. The graph below shows her data.

What does the point (1, ?) represent?

The point (1, 5) represents the height in feet.

Explanation:
In the above-given question,
given that,
Ginny recorded the height of a tree growing in her front yard.
the points on the x-axis are 0, 1, 2, 3, and 4.
the points on the y-axis are 4, 5, 6, 7, and 8.
add the 1 on the x and y-axis.
so the point (1, 5) represents the height in feet.

Question 6.
Explain how to graph the point (6, 4) on a coordinate plane.

Point 6 is on the x-axis and 4 is on the y-axis.

Explanation:
In the above-given question,
given that,
the point is (6, 4).
point 6 is on the x-axis and 4 is on the y-axis.

Question 7.
Varsha draws a map of her neighborhood on a coordinate plane. Her map shows the park at P (3, 1), her house at H (5, 6), and the soccer field at S (2,4). Graph and label each location below.

The point is P(3, 1) is the park.
the point H(5, 6) is her house.
the point S(2, 4) is the soccer field.

Explanation:
In the above-given question,
given that,
Varsha draws a map of her neighborhood on a coordinate plane.
Her map shows the park at P (3, 1), her house at H (5, 6), and the soccer field at S (2,4).
the point is p(3, 1) is the park.
the point H(5, 6) is her house.
the point S(2, 4) is the soccer field.

Question 8.
Yesterday Billy earned $30 trimming hedges for Mrs. Gant. Today he will earn$10 an hour for weeding her garden. If he weeds her garden for 8 hours, how much in all will he earn working for Mrs. Gant?

A. $40 B.$ 80
C. $110 D.$ 120

Option B is correct.

Explanation:
In the above-given question,
given that,
Billy earned $30 trimming hedges for Mrs. Gant. Today he will earn$10 an hour for weeding her garden.
If he weeds her garden for 8 hours,
8 x $10 =$80.
so option B is correct.

Question 9.
How is graphing (0, 12) different from graphing (12, 0)?

(0, 12) is different from (12, 0).

Explanation:
In the above-given question,
given that,
the ordered pairs are (0, 12) and (12, 0).
(0, 12) is on the y-coordinate.
(12, 0) is on the x-coordinate.
so (0, 12) is different from (12, 0).

Question 10.
What ordered pair represents the point where the x-axis and y-axis intersect? What is the name of this point?

The ordered pair (0, 0) represents the point where the x-axis and y-axis intersect.

Explanation:
In the above-given question,
given that,
the ordered pair (0, 0) represents the origin.
the x-axis and y-axis intersect are called the origin.
so the ordered pair (0, 0) represents the point where the x-axis and y-axis intersect.

Question 11.
Three vertices of a rectangle are located at (1, 4), (1, 2), and (5, 2).
A. Graph and label each of the three vertices below.

B. What are the coordinates of the fourth vertex of the rectangle?

The coordinates of the fourth vertex of the rectangle are (5, 4).

Explanation:
In the above-given question,
given that,
three vertices of a rectangle are located at (1, 4), (1, 2), and (5, 2).
the other side is (5, 4).
for the rectangle, opposite sides are equal in length.
so the coordinates of the fourth vertex of the rectangle are (5, 4).

Digging for Dinosaur Bones
Omar’s mother is a paleontologist. She digs up and studies dinosaur bones. Omar is helping at the dig site.

Question 1.
The Dinosaur Bone Dig 1 grid shows the location of the tent and the triceratops skull Omar’s mother found.
Part A
What ordered pair names the location of the triceratops skull? Explain how you know.

Part B
omar found a leg bone at (4, 12). Graph this point on the coordinate grid and label it L. Explain how you located the point using the terms origin, x-coordinate, x-axis, y-coordinate, and y-axis.
Part C
Next, Omar dug 3 meters east and 1 meter south from the leg bone. Graph a point where Omar dug and label it A. What ordered pair names the point?

Part A: (6, 2).
Part B: (4, 12).
Part C: (7, 13).

Explanation:
In the above-given question,
given that,
Omar found a leg bone at (4, 12).
Omar dug 3 meters east and 1 meter south from the leg bone.
4 + 3 = 7.
12 + 1 = 13.
so part C is (7, 13).

Question 2.
Omar’s mother started at the triceratops skull. She kept moving east 1 meter and north 2 meters to dig for more dinosaur bones. Complete the table and the graph to find how far north she was when she was 11 meters east of the tent.

When she was 11 meters east of the tent, the far = 6.

Explanation:
In the above-given question,
given that,
Omar’s mother started at the triceratops skull.
She kept moving east 1 meter and north 2 meters to dig for more dinosaur bones.
(4, 12) is the ordered pair given?
4 + 1 = 5.
12 + 2 = 14.
(5, 14) is the ordered pair.
11 – 5 = 6.
so when was 11 meters east of the tent, the far is 6 meters.
Part A
Complete the table of ordered pairs.

Part B
Graph the points from the table in Part A on the coordinate grid in the Dinosaur Bone Dig 2 grid. Draw a line through the points. Extend the line past 11 meters east.
Part C
How far north was Omar’s mother when she was 11 meters east of the tent? Explain how to use the graph to solve and why your answer makes sense.

The ordered pairs are (6, 2), (7, 3), ( 8, 4), and (9, 5).

Explanation:
In the above-given question,
given that,
East of the tent in meters is given.
they are 6, 7, 8, and 9 meters are given.
the first ordered pair is (6, 2) is given.
so the ordered pairs are (7, 3), (8, 4), and (9, 5).
when she was 11 meters east of the tent is (11, 7).

## Envision Math Common Core 5th Grade Answers Key Topic 15 Algebra: Analyze Patterns and Relationships

Essential Questions: How can number patterns be analyzed and graphed? How can number patterns and graphs be used to solve problems?

enVision STEM Project: Analyze Patterns
Do Research Use the Internet or other sources to find patterns in cities and buildings in other parts of the world.

Journal: Write a Report Include what you found. Also in your report:
• Describe types of patterns found in nature.
• Describe types of patterns found in cities.
• Make a graph to show relationships between some of the patterns you found.

Review What You Know

A-Z Vocabulary

Choose the best term from the Word List. Write it on the blank.
• equation
• Expression
• variable
• evaluate
• ordered pair

Question 1.
A numerical _____ is a mathematical phrase that has numbers and at least one operation.

A numerical expression is a mathematical phrase that has numbers and at least one operation.

Explanation:
In the above-given question,
given that,
A numerical expression is a mathematical phrase that has numbers and at least one operation.
for example:
14 – 8 = 6.
21 – 5 + 2.
21 – 7 = 14.

Question 2.
A(n) _____ can be used to show the location of a point on the coordinate plane.

A(n) ordered pair can be used to show the location of a point on the coordinate plane.

Explanation:
In the above-given question,
given that,
A(n) ordered pair can be used to show the location of a point on the coordinate plane.
for example:
(1, 3) is an ordered pair.
1 is on the x-axis.
3 is on the y-axis.

Question 3.
The letter n in $10 × n is called a(n) ___ and is a quantity that can change. Answer: The letter n in$10 x n is called a(n) variable and is a quantity that can change.

Explanation:
In the above-given question,
given that,
The letter n in $10 x n is called a(n) variable and is a quantity that can change. for example: A factor can be a number, variable, term, or a longer expression. Expressions Write a numerical Expression for each calculation. Question 4. Add 230 and 54, and then divide by 7. Answer: 230 + 54 / 7. Explanation: In the above-given question, given that, Add 230 and 54, and then divide by 7. 230 + 54. 230 + 54 / 7. 284 / 7 = 40.5. Question 5. Subtract 37 from the product of 126 and 4. Answer: 37 – 126 x 4 = 467. Explanation: In the above-given question, given that, Subtract 37 from the product of 126 and 4. 126 x 4 – 37. 504 – 37. 467. Solve Equations Solve each equation. Question 6. 7,200 + x = 13,000 Answer: X = 5800. Explanation: In the above-given question, given that, the equation is 7200 + x = 13000. 7200 + x = 13000. 13000 – 7200 = x. x = 5800. Question 7. 6,000 = 20 × g Answer: G = 300. Explanation: In the above-given question, given that, the equation is 6000 = 20 x g. 6000 = 20 x g. g = 6000/ 20. g = 300. Question 8. 105 + 45 = w × 3 Answer: W = 50. Explanation: In the above-given question, given that, the equation is 105 + 45 = w x 3. 150 = w x 3. w = 150 / 3. w = 50. Question 9. 38 + 42 = 480 ÷ b Answer: B = 6. Explanation: In the above-given question, given that, the equation is 38 + 42 = 480 ÷ b. 80 = 480 / b. b = 480 / 80. b = 6. Question 10. Janine has 85 hockey cards in one book and 105 hockey cards in another book. The hockey cards come in packages of 5 cards. If Janine bought all of her hockey cards in packages, how many packages did she buy? A. 21 packages B. 38 packages C. 190 packages D. 195 packages Answer: Option D is correct. Explanation: In the above-given question, given that, Janine has 85 hockey cards in one book and 105 hockey cards in another book. The hockey cards come in packages of 5 cards. 85 + 105 = 190. 190 + 5 = 195. so option D is correct. Evaluate Expressions Question 11. Explain how to evaluate the Expression 9 + (45 × 2) ÷ 10. Answer: 9 + (45 x 2) / 10 = 18 Explanation: In the above-given question, given that, 9 + (45 x 2) / 10. 9 + (90) / 10. 9 + 9. 18. 9 + (45 x 2) / 10 = 18. Pick a Project PROJECT 15A How are piano keys arranged on a keyboard? Project: Learn More About Keyboards PROJECT 15B Why is it important to protect gopher tortoises? Project: Use Information to Write Problems PROJECT 15C How can you use patterns to make art? Project: Create a Work of String Art 3-ACT MATH PREVIEW Math Modeling Video Speed Stacks Before watching the video, think: Stacking cups is a lot less messy when they’re empty. ### Lesson 15.1 Numerical Patterns Activity Solve & Share Emma has$100 in her savings account. Jorge has $50 in his savings account. They each put$10 in their accounts at the end of each week. Complete the tables to see how much each of them has saved after 5 weeks. What patterns do you notice?

Emma has $150 and Jorge has$100 after 5 weeks.

Explanation:
In the above-given question,
given that,
Emma has $100 in her savings account. Jorge has$50 in his savings account.
They each put $10 in their accounts at the end of each week. 100 + 10 = 110, 110 + 10 = 120, 120 + 10 = 130, 130 + 10 = 140, and 140 + 10 = 150. 50 + 10 = 60, 60 + 10 = 70, 70 + 10 = 80, 80 + 10 = 90, 90 + 10 = 100. so Emma has$150 and Jorge has $100 after 5 weeks. Look for Relationships to see what is alike and what is different in the two tables. Answer: Both of them saved an equal amount of money that is$50.

Explanation:
In the above-given question,
given that,
Emma has $100 in her savings account. Jorge has$50 in his savings account.
They each put $10 in their accounts at the end of each week. 100 + 10 = 110, 110 + 10 = 120, 120 + 10 = 130, 130 + 10 = 140, and 140 + 10 = 150. 50 + 10 = 60, 60 + 10 = 70, 70 + 10 = 80, 80 + 10 = 90, 90 + 10 = 100. so both of them saved an equal amount of money that is$50.

Look Back! If the savings patterns continue, will Jorge ever have as much saved as Emma? Explain.

Visual Learning Bridge

Essential Question How Can You Solve Problems Involving Numerical Patterns?

A.
Lindsey has a sage plant that is 3.5 inches tall. She also has a rosemary plant that is 5.2 inches tall. Both plants grow 1.5 inches taller each week. How tall will the plants be after 5 weeks? What is the relationship between the heights of the plants?

You can create tables to help identify relationships between corresponding terms in the number sequences.

B.
You can use the rule “add 1.5” to complete the tables.

Convince Me! Reasoning If the patterns continue, how can you tell that the rosemary plant will always be taller than the sage plant?

Guided Practice

Do You Understand?

Question 1.
Anthony says, “The pattern is that the sage plant is always 1.7 inches shorter than the rosemary plant.” Do you agree? Explain.

Yes, I will agree.

Explanation:
In the above-given question,
given that,
Lindsey has a sage plant that is 3.5 inches tall.
She also has a rosemary plant that is 5.2 inches tall.
Both plants grow 1.5 inches taller each week.
5.2 – 3.5 = 1.7.
so I will agree.

Question 2.
How does making tables help you identify relationships between terms in patterns?

The difference for every pattern is 1.7.

Explanation:
In the above-given question,
given that,
Lindsey has a sage plant that is 3.5 inches tall.
She also has a rosemary plant that is 5.2 inches tall.
Both plants grow 1.5 inches taller each week.
5.2 – 3.5 = 1.7.
so the difference for every pattern is 1.7.

Do You Know How?

Question 3.
If the plants continue to grow 1.5 inches each week, how tall will each plant be after 10 weeks?

After 10 weeks each plant will be 18.5.

Explanation:
In the above-given question,
given that,
if the plants continue to grow 1.5 inches each week.
11 + 1.5 = 12.5.
12.5 + 1.5 = 14.0.
14.0 + 1.5 = 15.5.
15.5 + 1.5 = 17.0.
17.0 + 1.5 = 18.5.

Question 4.
If the plants continue to grow 1.5 inches each week, how tall will each plant be after 15 weeks?

After 15 weeks each plant will be 26.0.

Explanation:
In the above-given question,
given that,
if the plants continue to grow 1.5 inches each week.
18.5 + 1.5 = 20.0.
20.0 + 1.5 = 21.5.
21.5 + 1.5 = 23.0.
23.0 + 1.5 = 24.5.
24.5 + 1.5 = 26.0.

Independent Practice

In 5-7, use the rule “add $0.50” to help you. Question 5. Tim and Jill each have a piggy bank. Tim starts with$1.25 in his bank and puts in $0.50 each week. Jill starts with$2.75 in her bank and also puts in $0.50 each week. Complete the table to show how much money each has saved after five weeks. Answer: Tim saved$3.75 and Jill saved $5.25. Explanation: In the above-given question, given that, Tim and Jill each have a piggy bank. Tim starts with$1.25 in his bank and puts in $0.50 each week. Jill starts with$2.75 in her bank and also puts in $0.50 each week. 1.25 + 0.50 = 1.75. 1.75 + 0.50 = 2.25. 2.25 + 0.50 = 2.75. 2.75 + 0.50 = 3.25. 3.25 + 0.50 = 3.75. 2.75 + 0.50 = 3.25. 3.25 + 0.50 = 3.75. 3.75 + 0.50 = 4.25. 4.25 + 0.50 = 4.75. 4.75 + 0.50 = 5.25. Question 6. What relationship do you notice between the amount Tim has saved and the amount Jill has saved each week? Answer: Tim has saved$3.75 and Jill saved $5.25. Explanation: In the above-given question, given that, Tim and Jill each have a piggy bank. Tim starts with$1.25 in his bank and puts in $0.50 each week. Jill starts with$2.75 in her bank and also puts in $0.50 each week. 1.25 + 0.50 = 1.75. 1.75 + 0.50 = 2.25. 2.25 + 0.50 = 2.75. 2.75 + 0.50 = 3.25. 3.25 + 0.50 = 3.75. 2.75 + 0.50 = 3.25. 3.25 + 0.50 = 3.75. 3.75 + 0.50 = 4.25. 4.25 + 0.50 = 4.75. 4.75 + 0.50 = 5.25. Question 7. If Tim and Jill continue saving in this way, how much will each have saved after 10 weeks? Explain how you decided. Answer: Tim saves$6.25 and Jill saves $7.75. Explanation: In the above-given question, given that, Tim and Jill each have a piggy bank. Tim starts with$1.25 in his bank and puts in $0.50 each week. Jill starts with$2.75 in her bank and also puts in $0.50 each week. 3.75 + 0.50 = 4.25. 4.25 + 0.50 = 4.75. 4.75 + 0.50 = 5.25. 5.25 + 0.50 = 5.75. 5.75 + 0.50 = 6.25. 5.25 + 0.50 = 5.75. 5.75 + 0.50 = 6.25. 6.25 + 0.50 = 6.75. 6.75 + 0.50 = 7.25. 7.25 + 0.50 = 7.75. Problem Solving For 8-10, use the table. Question 8. enVision® STEM Bur oak and hickory trees are deciduous, which means that they lose their leaves seasonally. A bur oak is 25$$\frac{1}{2}$$ feet tall and grows 1$$\frac{1}{2}$$ feet each year. A hickory is 30 feet tall and grows 1$$\frac{1}{2}$$ feet each year. Complete the chart to show the heights of the two trees each year for five years. Answer: The heights of the two trees each year for five years = 32 and 37.5. Explanation: In the above-given question, given that, Bur oak and hickory trees are deciduous, which means that they lose their leaves seasonally. A bur oak is 25$$\frac{1}{2}$$ feet tall and grows 1$$\frac{1}{2}$$ feet each year. A hickory is 30 feet tall and grows 1$$\frac{1}{2}$$ feet each year. 25(1/2) = 51/2 = 25.5. 3/2 = 1.5. 25.5 + 1.5 = 27.0. 27.0 + 1.5 = 28.5. 28.5 + 1.5 = 30. 30 + 1.5 = 31.5. 31.5 + 1.5 = 32. 30 + 1.5 = 31.5. 31.5 + 1.5 = 33. 33 + 1.5 = 34.5. 34.5 + 1.5 = 36.0. 36.0 + 1.5 = 37.5. Question 9. If each tree continues to grow 1$$\frac{1}{2}$$ feet each year, how tall will each tree be after 15 years? Answer: The height of each tree after 15 years = 39.5 and 45.0. Explanation: In the above-given question, given that, A bur oak is 25$$\frac{1}{2}$$ feet tall and grows 1$$\frac{1}{2}$$ feet each year. Hickory is 30 feet tall and grows 1$$\frac{1}{2}$$ feet each year. 32 + 1.5 = 33.5. 33.5 + 1.5 = 35.0. 35.0 + 1.5 = 36.5. 36.5 + 1.5 = 38.0. 38.0 + 1.5 = 39.5. 37.5 + 1.5 = 39.0. 39.0 + 1.5 = 40.5. 40.5 + 1.5 = 42.0. 42.0 + 1.5 = 43.5. 43.5 + 1.5 = 45.0. Question 10. Higher Order Thinking What relationship do you notice between the height of the bur oak and the height of the hickory each year? Explain. Answer: Question 11. Reasoning Each small square on the chessboard is the same size. The length of a side of a small square is 2 inches. What is the area of the chessboard? Explain. Answer: The area of the chessboard = 4 sq in. Explanation: In the above-given question, given that, Each small square on the chessboard is the same size. The length of a side of a small square is 2 inches. area of the square = side x side. area of the square and area of the chessboard is the same. area = s x s. s = 2 inches. area = 2 x 2. area = 4 sq in. so the area of the chessboard = 4 sq in. Assessment Practice Question 12. Jessica has saved$50. She will add $25 to her savings each week. Ron has saved$40 and will add $25 to his savings each week. How much will each person have saved after 5 weeks? A. Jessica:$275; Ron: $225 B. Jessica:$250; Ron: $240 C. Jessica:$175; Ron: $165 D. Jessica:$165; Ron: $175 Answer: Option C is correct. Explanation: In the above-given question, given that, Jessica has saved$50.
She will add $25 to her savings each week. Ron has saved$40 and will add $25 to his savings each week.$50 + $25 =$75.
$25 x 5 =$125.
$125 +$50 = $175.$40 + $25 =$65.
$65 +$100 = $165. Question 13. Which of the following statements are true? Jessica has always saved$25 more than Ron.
Jessica has always saved $10 more than Ron. Ron has always saved$25 less than Jessica.
Ron has always saved $10 less than Jessica Answer: Option B is correct. Explanation: In the above-given question, given that, Jessica has saved$50.
She will add $25 to her savings each week. Ron has saved$40 and will add $25 to his savings each week.$175 – $165 =$10.
so option B is correct.

### Lesson 15.2 More Numerical Patterns

Activity

Solve & Share
During summer vacation, Julie read 45 pages each day. Her brother Bret read 15 pages each day. Complete the tables to show how many pages each of them read after 5 days. What relationship do you notice between the terms in each pattern?

The number of pages each of them read after 5 days = 105 and 75.

Explanation:
In the above-given question,
given that,
During summer vacation, Julie read 45 pages each day.
Her brother Bret read 15 pages each day.
45 + 15 = 60.
60 + 15 = 75.
75 + 15 = 90.
90 + 15 = 105.
105 + 15 = 125.
15 + 15 = 30.
30 + 15 = 45.
45 + 15 = 60.
60 + 15 = 75.

Look Back! Reasoning Explain why this relationship Exists between the terms.

Visual Learning Bridge

Essential Question
How Can You Identify Relationships Between Patterns?

A.
Jack is training for a race. Each week, he runs 30 miles and bikes 120 miles. He created a table to record his progress. How many total miles will he run and bike after 5 weeks? Can you identify any relationship between the miles run and the miles biked?

B.
Since jack runs 30 miles each week, add 30 to find the nExt term for the total miles run. Add 120 to find each term in the pattern for the total number of miles biked.

C.
Compare the corresponding terms in the patterns:
30 × 4 = 120
60 × 4 = 240
90 × 4 = 360
120 × 4 = 480
150 × 4 = 600
So, the total number of miles biked is always 4 times the total number of miles run.

Convince Me! Generalize Do you think the relationship between the corresponding terms in the table Jack created will always be true? Explain.

The relationship between the corresponding terms in the table Jack created will always be true.

Explanation:
In the above-given question,
given that,
Jack is training for a race.
Each week, he runs 30 miles and bikes 120 miles.
He created a table to record his progress.
30 × 4 = 120.
60 × 4 = 240.
90 × 4 = 360.
120 × 4 = 480.
150 × 4 = 600.
so the relationship between the corresponding terms in the table Jack created will always be true.

Guided Practice

Do You Understand?

In 1-3, use the table on page 598.

Question 1.
Neko says that the relationship between the terms is that the number of miles run is $$\frac{1}{4}$$ the number of miles biked. Do you agree? Explain.

Yes, it is true.

Explanation:
In the above-given question,
given that,
the number of miles run is 1/4 the number of miles biked.
Jack is training for a race.
Each week, he runs 30 miles and bikes 120 miles.
He created a table to record his progress.
30 × 4 = 120.
60 × 4 = 240.
90 × 4 = 360.
120 × 4 = 480.
150 × 4 = 600.
So it is true.

Question 2.
How many total miles will Jack have run and biked after 10 weeks? 15 weeks?

The number of miles will Jack have run and biked after 10 weeks and 15 weeks = 1200 and 1800.

Explanation:
In the above-given question,
given that,
180 x 4 = 720.
210 x 4 = 840.
240 x 4 = 960.
270 x 4 = 1080.
300 x 4 = 1200.
330 x 4 = 1320.
360 x 4 = 1440.
390 x 4 = 1560.
420 x 4 = 1680.
450 x 4 = 1800.
so the number of miles Will Jack have run and biked after 10 weeks and 15 weeks = 1200 and 1800.

Question 3.
Miguel says that he can use multiplication to find the terms in the patterns. Do you agree? Explain.

Yes, Miguel says that he can use multiplication to find the terms in the patterns.

Explanation:
In the above-given question,
given that,
180 x 4 = 720.
210 x 4 = 840.
240 x 4 = 960.
270 x 4 = 1080.
300 x 4 = 1200.
330 x 4 = 1320.
360 x 4 = 1440.
390 x 4 = 1560.
420 x 4 = 1680.
450 x 4 = 1800.
Independent Practice

Question 4.
Maria and Henry are each starting a savings account. Maria puts $250 into her account each month. Henry puts$125 into his account each month. How much money will each of them have saved after 6 months? Complete the table to solve.

The money will each of them have saved after 6 months =

Explanation:
In the above-given question,
given that,
Maria and Henry are each starting a savings account.
Maria puts $250 into her account each month. Henry puts$125 into his account each month.

Question 5.
What relationship do you notice between the total amount Maria has saved after each month and the total amount Henry has saved after each month?

Question 6.
If Maria and Henry continue saving this way for a full year, how much more will Maria have saved than Henry?

Problem Solving

Question 7.
Sheila and Patrick are making a table to compare gallons, quarts, and pints. Use the rule “add 4” to complete the column for the number of quarts. Then use the rule “add 8” to complete the column for the number of pints.

Question 8.
Patrick has a 12-gallon fish tank at home. How many quarts of water will fill his fish tank? How many pints?

Question 9.
Look for Relationships What relationship do you notice between the number of quarts and the number of pints?

Question 10.
Higher Order Thinking At their family’s pizzeria, Dan makes 8 pizzas in the first hour they are open and 6 pizzas each hour after that. Susan makes 12 pizzas in the first hour and 6 pizzas each hour after that. If the pizzeria is open for 6 hours, how many pizzas will they make in all? Complete the table using the rule “add 6” to help you.

Question 11.
Look for Relationships Compare the total number of pizzas made by each person after each hour. What relationship do you notice?

Assessment Practice

Question 12.
Mike and Sarah are packing boxes at a factory. Mike packs 30 boxes each hour. Sarah packs 15 boxes each hour. How many boxes will each person have packed after an 8-hour shift?
A. Mike: 38 boxes; Sarah: 23 boxes
B. Mike: 86 boxes; Sarah: 71 boxes
C. Mike: 120 boxes; Sarah: 240 boxes
D. Mike: 240 boxes; Sarah: 120 boxes

Question 13.
Which of the following are true statements about the number of boxes Mike and Sarah have packed after each hour?
Mike has always packed a total of 15 more boxes than Sarah.
Mike has always packed twice as many boxes as Sarah.
Sarah has always packed twice as many boxes as Mike.
Sarah has always packed half as many boxes as Mike.

### Lesson 15.3 Analyze and Graph Relationships

Activity

Solve & Share
A bakery can fit either 6 regular muffins or 4 jumbo muffins in each box. Each box will contain either regular or jumbo muffins. Complete the table to show how many of each muffin will fit in 2, 3, or 4 boxes. Then generate ordered pairs and graph them.

Find rules that describe the relationships between the number of boxes and the number of muffins.

Look Back! Look for Relationships The bakery can fit 12 mini-muffins in a box. How many mini-muffins will fit in 4 boxes? Without Extending the table, what relationship do you notice between the number of mini-muffins and the number of boxes?

Visual Learning Bridge

Essential Question How Can You Generate and Graph Numerical Patterns?

You can look for a relationship between the corresponding terms in the patterns.

A.
Jill earns $5 per hour babysitting. Robin earns$15 per hour teaching ice skating lessons. The girls made a table using the rule “Add 5” to show Jill’s earnings and the rule “Add 15” to show Robin’s earnings. Complete the table, compare their earnings, and graph the ordered pairs of the corresponding terms.

B.
Compare the numbers in Jill’s and Robin’s sequences.
Each sequence begins with zero. Then each term in Robin’s pattern is 3 times as great as the corresponding term in Jill’s pattern.
Generate ordered pairs from the total amount Jill and Robin have earned after each hour.
(0, 0), (5, 15), (10,30), (15,45), (20,60)

C.
Graph the ordered pairs.

Convince Me! Make Sense and Persevere What does the point (0,0) represent?

Guided Practice

Do You Understand?

Question 1.
In the Example on page 602, what ordered pair would you write for how much Jill and Robin have each earned after 5 hours?

Question 2.
Ben says that the relationship is that Jill earns $$\frac{1}{3}$$ as much as Robin. Do you agree? Explain.

Do You Know How?

Sam and Eric record the total number of miles they walk in one week. Sam walks 2 miles each day. Eric walks 4 miles each day.

Question 3.
What ordered pair represents the number of miles each has walked in all after 7 days?

Question 4.
What relationship do you notice between the total number of miles Sam and Eric have each walked?

Independent Practice

Question 5.
Megan and Scott go fishing while at camp. Megan catches 3 fish in the first hour and 4 fish each hour after that. Scott catches 5 fish in the first hour and 4 fish each hour after that. Complete the table to show the total number of fish each has caught after each hour.

Question 6.
What ordered pair represents the total number of fish they each caught after 4 hours?

Question 7.
What relationship do you notice between the total number of fish each has caught after each hour?

Question 8.
Graph the ordered pairs of the total number of fish each has caught after each hour.

Question 9.
The pattern continues until Scott’s total is 29 fish. What ordered pair represents the total number of fish they each caught when Scott’s total is 29 fish?

Problem Solving

Question 10.
The Snack Shack made a table to track the amount of money from sales of frozen yogurt and fruit cups for four hours. What are the missing values in the table?

Question 11.
Use Structure If sales continue in the same manner, what ordered pair would represent the money from sales of yogurt and fruit cups at 1 P.M.? Explain how you know.

Question 12.
Graph the ordered pairs for the money from sales of yogurt and fruit cups from 9 A.M. to 1 P.M.

Question 13.
A-Z Vocabulary Write two number sequences. Then, circle corresponding terms in the two sequences.

Question 14.
Higher Order Thinking Pedro runs 2$$\frac{1}{2}$$ miles each day for 5 days. Melissa runs 4 miles each day for 5 days. How many more miles will Melissa run in 5 days than Pedro? Make a table to help you.

Assessment Practice

Question 15.
Every month, Leonard pays $240 for a car payment. He spends$60 each month for a gym membership. Write an ordered pair to represent how much Leonard spends in 12 months for car payments and the gym membership.

Question 16.
What relationship do you notice between how much Leonard spends in 12 months on car payments and the gym membership?

### Lesson 15.4 Make Sense and Persevere

Activity

Solve & Share
Val is planning a bowling-and-pizza party. Including herself, there will be no more than 10 guests. Val wonders which bowling alley offers the less Expensive party plan.
Complete the tables for Leonard’s Lanes and Southside Bowl. On the same grid, graph the ordered pairs in each table. Use a different color for the values in each table. Which bowling alley would be less Expensive? Explain how you know.

Leonard’s Lanes
Bowling and Pizza: $25 plus$10 per person

Southside Bowl
Bowling and Pizza: $15 per person Guests 1 2 3 4 5 6 7 Thinking Habits Think about these questions to help you make sense and persevere. • What do I need to find? • What do I know? • What else can I try if I get stuck? • How can I check that my solution makes sense? Look Back! Make Sense and Persevere How did the graph help you answer the question? Visual Learning Bridge Essential Question How Can You Make Sense of a Problem Question and Persevere in Solving It? A. Make Sense of the Problem On Aiden’s farm, there are 12 acres of soybeans and 8 acres of corn. Aiden plans to replace his other crops with more acres of soybeans and corn. Will his farm ever have the same number of acres of soybeans and corn? Explain. You can make sense of the problem by answering these questions. What do you know? What are you asked to find? B. How can I make sense of and solve this problem? I can • choose and implement an appropriate strategy. • use ordered pairs to make graphs. • identify and analyze patterns. • check that my work and answer make sense. Here’s my thinking… C. For each crop, I can write a rule, make a table, and plot the ordered pairs. Then I can see if the number of acres is ever the same. Soybeans Rule: Start at 12 and add 3. Corn Rule: Start at 8 and add 4. Where the lines intersect, at 4 years, Aiden’s farm has 24 acres of each crop. Convince Me! Make Sense and Persevere How can you check your work? Does your answer make sense? Explain. Guided Practice Mindy has already saved$20 and plans to save $8 each month. Georgette has no money saved yet but plans to save$5 each month. Will the girls ever have saved the same amount? Explain.

Question 1.
Write a rule and complete each table.
Rule: _______
Rule: _______

Question 2.
On the same grid, graph the ordered pairs in each table.

Question 3.
Explain whether the girls will ever have the same amount of money saved.

Independent Practice

Make Sense and Persevere
O’Brien’s Landscaping pays employees $15 plus$12 per lawn. Carter’s Landscaping pays $25 plus$10 per lawn. Which company pays more? Explain.

Question 4.
Write a rule and complete each table.
Rule: _______
Rule: _______

Question 5.
On the grid, graph the ordered pairs in each table. Explain which company pays more.

Problem Solving

Track-a-Thon
Jordan is running in a track-a-thon to raise money for charity. Who will make a larger donation, Aunt Meg or Grandma Diane? Explain.

Question 6.
Make Sense and Persevere How can you use tables and a graph to solve the problem?

Question 7.
Use Appropriate Tools For each pledge, write a rule and complete the table.
Rule: ________

Rule: ________

When you make sense and persevere, you choose and implement an appropriate strategy

Question 8.
Use Appropriate Tools On the grid, graph the ordered pairs in each table.

Question 9.
Reasoning Explain whose donation will be greater.

### Topic 15 Fluency Practice

Activity

Solve each problem. Follow problems with an answer of 72,072 to shade a path from START to FINISH. You can only move up, down, right, or left.

Topic 15 Vocabulary Review

Glossory

Word List
• coordinate grid
• corresponding terms
• number sequence
• ordered pair • origin
• x-axis
• x-coordinate
• y-axis
• y-coordinate

Understand Vocabulary
Write always, sometimes, or never on each blank.

Question 1.
Corresponding terms are ____ in the same position in a pair of number sequences.

Question 2.
An ordered pair can ____ be plotted on the origin of a coordinate grid.

Question 3.
The origin is ____ any other location on a coordinate grid besides (0,0).

Question 4.
Two number lines that form a coordinate grid _____ intersect at a right angle.

Question 5.
The second number of an ordered pair ____ describes the distance to the right or left of the origin.

In 6-8, use the lists of numbers below.

Use Vocabulary in Writing

Question 9.
Explain how to identify corresponding terms in two number sequences. Use terms from the Word List in your Explanation.

### Topic 15 ReTeaching

Set A pages 593-596
Maria has $4. She will save$10 each week. Stephen has $9 and will also save$10 each week.
Maria uses the rule “add 10” to create tables to see how much each will have saved after each week. What relationship do you notice between the corresponding terms?

After each week, Stephen has $5 more saved than Maria. Or, Maria’s savings are always$5 less than Stephen’s savings.

Remember to compare corresponding terms to see if there is a relationship.

Question 1.
Two groups of students went hiking. After 1 hour, Group A hiked 1$$\frac{1}{2}$$ miles and Group B hiked 2$$\frac{1}{2}$$ miles. After that, each group hiked 2 miles each hour. Complete the tables to show how far each group had hiked after 3 hours.

Question 2.
What relationship do you notice between the corresponding terms?

Set B
pages 597-600
Each week, Andre lifts weights twice and runs 4 times. Andre uses the rules “add 2” and “add 4” to complete the table. What relationship do you notice between the corresponding terms?

The number of times Andre went running is always 2 times the number of times he lifted weights.

Question 1.
A garden center sells 15 trees and 45 shrubs each day for one week. Complete the table to show how many trees and shrubs in all were sold in 4 days. Use the rules “add 15″ and “add “45” to help you.

Question 2.
What is the relationship between the corresponding terms of the sequences?

Set C
pages 601-604
Kelly uses 3 pounds of nuts and 2 pounds of cereal to make each batch of trail mix. The chart shows how many total pounds of each she will need for 4 batches. Graph ordered pairs of the corresponding terms. What does the point (12, 8) represent?

The chart and graph both represent the problem. The point (12,8) shows that when Kelly uses 12 pounds of nuts, she will use 8 pounds of cereal.

Remember to make ordered pairs from corresponding terms.

Question 1.
Lauren has $6 and saves$5 each week. Derrick has $3 and saves$5 each week. How much will each have saved after 4 weeks? Use the rule “add 5” to complete the table.

Question 2.
What does the point (26, 23) represent?

Question 3.
What is the relationship between the corresponding terms?

Set D
pages 605-608

Thinking Habits
• What do I need to find?
• What do I know?
• What else can I try if I get stuck?
• How can I check that my solution makes sense?

Remember that you can use patterns, tables, and graphs to represent and solve problems.

Question 1.
Sam starts with 5 stamps and buys 10 more each month. Pat starts with 9 stamps and buys 9 more each month. Complete the table using the rules “add 10” and “add 9”.

Question 2.
Make a graph from the data in the tables. Will Sam ever have more stamps than Pat?

### Topic 15 Assessment Practice

Question 1.
Liz and Fareed each start a new savings account. Liz starts her account with $75. Fareed starts his account with$100. Each month, both save another $50. A. Complete the table to show the total amount each has saved after each month. Use the rule “add 50”. B. Select all the ordered pairs that represent amounts Liz and Fareed have each saved. (50, 75) (75, 100) (125, 150) (150, 200) (275, 300) C. Describe the relationship between the amount each person has saved after each month. Answer: Question 2. There are 16 pawns and 2 kings in each chess set. A. Complete the table to show how many pawns and kings in all are in different numbers of chess sets. Use the rules “add 16″ and “add 2”. B. Use the total number of pawns and kings to form ordered pairs. Graph the ordered pairs below. C. What would the ordered pair (96, 12) represent? Answer: Question 3. Luis kept track of the heights of his basil and chive plants. His basil plant was 15$$\frac{1}{2}$$cm tall and grew 1$$\frac{1}{2}$$ cm each week. His chive plant was 18$$\frac{1}{2}$$ cm tall and grew $$\frac{1}{2}$$ cm each week. A. Complete the table to show the heights of each plant after each week. Use the rules “add 1$$\frac{1}{2}$$” and “add 1$$\frac{1}{2}$$“. B. Will the basil plant ever be taller than the chive plant? If so, when? C. How does the table in A help you answer the question in B? Answer: Question 4. Bonnie’s Bakery makes 12 cakes and 36 muffins each hour. A. Complete the table to show how many cakes and muffins in all the bakery has made after each hour. Use the rules “add 12” and “add 36”. B. Miles says “the total number of muffins made is always 24 more than the total number of cakes made.” Do you agree? Explain your reasoning. C. Bonnie wants to graph this information. What ordered pair represents the total number of each item made after 6 hours? A. (36,12) B. (18,42) C. (60, 180) D. (72, 216) Answer: ### Topic 15 Performance Task Butterfly Patterns Use the Butterflies picture to Explore patterns. Question 1. Jessie and Jason use their cell phones to take pictures of butterflies. Jessie had 3 pictures of butterflies stored in her cell phone and Jason had 1 picture in his. On Saturday, they each took a picture of 1 butterfly every hour. Part A How many butterfly wings are in each photo collection after 3 hours? Complete the table. Part B What is the relationship between the corresponding terms of the two patterns in Part A? Part C Write rules for the number of butterfly wings in Jessie’s pictures and in Jason’s pictures. Answer: Question 2. Compare the number of wings to the number of legs in different numbers of butterflies. Part A Complete the table. Part B What is the relationship between the number of wings and the number of legs you found in Part A? Answer: Question 3. Tomika has no pictures of butterflies in her cell phone, but Kyle has 3 pictures in his. On Saturday, Tomika takes 2 pictures of butterflies every hour and Kyle takes 1 picture every hour. Answer the following to find whether or not their collections of butterfly pictures will ever have the same number of wings. Part A Write a rule and complete the Tomika’s Pictures table. Part B Write a rule and complete the Kyle’s Pictures table. Part C Graph the ordered pairs from Part A and Part B on the same coordinate grid and draw lines through each set. Part D Will Tomika and Kyle ever have the same number of wings in their pictures? Explain. Answer: #### enVision Math Common Core Grade 5 Answer Key ## Envision Math Common Core Grade 5 Answer Key Topic 16 Geometric Measurement: Classify Two-Dimensional Figures ## Envision Math Common Core 5th Grade Answers Key Topic 16 Geometric Measurement: Classify Two-Dimensional Figures enVision STEM Project: Ecosystems Do Research Use the Internet or other sources to learn more about ecosystems. Look for examples of changes that living organisms might cause. List three different ecosystems and describe any changes that humans might have made to each one. Journal: Write a Report Include what you found. Also in your report: • Compare two ecosystems. List 10 living things and 5 non-living things you might find in each one. • Think about changes that can occur in an ecosystem. Are the changes positive or negative? Why? • Use two-dimensional shapes to make a map or diagram of an ecosystem. Review What You Know A-Z Vocabulary Choose the best term from the box. Write it on the blank. • degree • polygon • line segment • quadrilateral • parallel • vertex • perimeter Question 1. A ___ is a polygon with four sides. Answer: A quadrilateral is a polygon with four sides. Explanation: In the above-given question, given that, A quadrilateral is a polygon with four sides. for example: square is a quadrilateral. square has four sides of equal length. square has four internal right angles. so a quadrilateral is a polygon with four sides. Question 2. The point where two sides of a polygon intersect is a ___ Answer: The point where two sides of a polygon intersect is a vertex. Explanation: In the above-given question, given that, the point where two sides of a polygon intersect is a vertex. for example: triangle is a polygon. a polygon with three sides is a triangle. we name a triangle by its three vertices. so the point where two sides of a polygon intersect is a vertex. Question 3. The distance between ____ sides of a polygon is always the same. Answer: The distance between parallel sides of a polygon is always the same. Explanation: In the above-given question, given that, the distance between the number of sides of a polygon is always the same. for example: the rectangle is a polygon. the rectangle has opposite sides that are equal. so the distance between parallel sides of a polygon is always the same. Question 4. The ____ is a unit of measure for angles. Answer: A degree is a unit of measure for angles. Explanation: In the above-given question, given that, a degree is a unit of measure for angles. for example: a circle is divided into 360 equal degrees. so that a right angle is 90 degrees. so the degree is a unit of measure for angles. Decimals Find each answer. Question 5. 2.75 + 9.08 Answer: 2.75 + 9.08 = 11.83. Explanation: In the above-given question, given that, addition of two numbers. the numbers are 2.75 and 9.08. 2.75 + 9.08. 11.83. Question 6. 17.6 – 3.08 Answer: 17.6 – 3.08 = 14.52. Explanation: In the above-given question, given that, subtraction of two numbers. the numbers are 17.6 and 3.08. 17.6 – 3.08. 14.52. Question 7. 83.2 × 0.1 Answer: 83.2 x 0.1 = 8.32. Explanation: In the above-given question, given that, multiplication of two numbers. the numbers are 83.2 and 0.1. 83.2 x 0.1. 8.32. Question 8. 24.27 × 103 Answer: 24.27 x 1000 = 24270. Explanation: In the above-given question, given that, multiplication of two numbers. the numbers are 24.27 and 10 x 10 x 10. 10 x 10 x 10 = 1000. 24.27 x 1000 = 24270. Fractions Find each answer. Question 9. 3$$\frac{2}{3}$$ + 6$$\frac{9}{10}$$ Answer: 3(2/3) + 6(9/10) = 7.2. Explanation: In the above-given question, given that, addition of two numbers. the numbers are 3(2/3) and 6(9/10). 2/3 = 0.6. 9/10 = 0.9. 3(0.6) + 6(0.9). 1.8 + 5.4 = 7.2. 3(2/3) + 6(9/10) = 7.2. Question 10. 8$$\frac{1}{2}$$ – 4$$\frac{4}{5}$$ Answer: 8(1/2) – 4(4/5) = 0.8. Explanation: In the above-given question, given that, subtraction of two numbers. the numbers are 8(1/2) and 4(4/5). 1/2 = 0.5. 4/5 = 0.8. 8(0.5) – 4(0.8). 4 – 3.2 = 0.8. 8(1/2) – 4(4/5) = 0.8. Question 11. 8 ÷ $$\frac{1}{2}$$ Answer: 8 ÷ $$\frac{1}{2}$$ = 16. Explanation: In the above-given question, given that, division of two numbers. the numbers are 8 and 1/2. 8 / 0.5. 16. 8 ÷ $$\frac{1}{2}$$ = 16. Question 12. $$\frac{1}{3}$$ ÷ 6 Answer: $$\frac{1}{3}$$ ÷ 6 = 0.05. Explanation: In the above-given question, given that, division of two numbers. the numbers are 6 and 1/3. 1/3 = 0.3. 0.3 / 6 = 0.05. $$\frac{1}{3}$$ ÷ 6 = 0.05. Write an Equation Question 13. Louisa drew a polygon with six sides of equal length. If the perimeter of Louisa’s polygon is 95.4 centimeters, how long is each side? Use an equation to solve. Answer: The length of each side = 15.9 cm. Explanation: In the above-given question, given that, If the perimeter of Louisa’s polygon is 95.4 centimeters. a polygon with 6 sides is called a hexagon. perimeter of hexagon = 6a. where a = side. p = 6 a. 95.4 = 6 a. a = 95.4 / 6. a = 15.9 cm. so the length of each side = 15.9 cm. Question 14. The area of a rectangle is 112 square inches. If the length of the rectangle is 16 inches, what is the width of the rectangle? Use an equation to solve. Answer: The width of the rectangle is = 7 in. Explanation: In the above-given question, given that, The area of a rectangle is 112 square inches. If the length of the rectangle is 16 inches. area of the rectangle = l x w. where l = length and w = width. 112 = 16 x w. 112 /16 = w. w = 7. so the width of the rectangle = 7 in. Pick a Project PROJECT 16A Where can you find a pyramid? Project: Build a Pyramid PROJECT 16B How do blueprints use different shapes? Project: Draw a Blueprint PROJECT 16C What shapes make up a map? Project: Hunt for Shapes in a Map PROJECT 16D What does the Florida flag look like? Project: Design a Flag Answer: The Florida flag looks like a cross mark. Explanation: In the above-given question, given that, in the flag, has the cross mark. the cross mark is inside the flag. so the Florida flag looks like a cross mark. cross mark indicates it is not correct. ### Lesson 16.1 Classify Triangles Solve & Share One triangle is shown below. Draw five more triangles with different properties. Next to each triangle, list its properties such as 2 equal sides, 1 right angle, 3 acute angles, and so on. Work with a partner to solve this problem. In a triangle, angles will be either acute, right, or obtuse. Look Back! Reasoning What are some different ways you can put triangles into categories? Explain. Answer: They are acute, obtuse, equilateral, right triangles. Explanation: In the above-given question, given that, the equilateral triangle has all the sides equal length. an acute triangle is a trigon with three sides and three angles each less than 90 degrees. an obtuse triangle will have one and only one obtuse angle. the other two angles are acute angles. a right triangle is a triangle in which one angle is a right angle. an isosceles triangle has at least two sides of the same length. so the triangles are acute, obtuse, equilateral, right triangles. Visual Learning Bridge Essential Question How Can You Classify Triangles? A. Triangles can be classified by the lengths of their sides. Equilateral triangle All sides are the same length. Isosceles triangle At least two sides are the same length. Scalene triangle No sides are the same length Can you tell if the sides of a triangle are the same length without measuring them? The total measure of all the angles in a triangle is 180°. B. Triangles can also be classified by the measures of their angles. Right triangle One angle is a right angle. Acute triangle All three angles are acute angles. Obtuse triangle One angle is an obtuse angle. Convince Me! Construct Arguments Can you draw an equilateral right triangle? Explain using precise mathematical language. To justify a mathematical argument, you must use precise mathematical language and ideas to explain your thinking Answer: Yes, we can draw an equilateral right triangle. Explanation: In the above-given question, given that, we can draw an equilateral triangle with 90 degrees. right angle means it has 90 degrees. an equilateral triangle has all the sides are equal. so we can draw an equilateral right triangle. Guided Practices Do You Understand? Question 1. Can a right triangle have an obtuse angle? Why or why not? Answer: No, the right triangle has an obtuse angle. Explanation: In the above-given question, given that, the right triangle cannot be an obtuse angle. since a right-angled triangle has one right angle, the other two angles are acute. therefore, an obtuse-angled triangle can never have a right angle. the side opposite the obtuse angle in a triangle is the longest. so the right triangle is not an obtuse angle. Question 2. Can an equilateral triangle have only two sides of equal length? Why or why not? Answer: No, an equilateral triangle has only two sides of equal length. Explanation: In the above-given question, given that, an equilateral triangle has all three sides are equal. if only two sides are equal in length, then it is an isosceles triangle. so the equilateral triangle does not have only two sides of equal length. Do You Know How? In 3 and 4, classify each triangle by its sides and then by its angles. Question 3. Answer: The triangle is an equilateral triangle. Explanation: In the above-given question, given that, the three angles are equal. the three sides are equal sides. an equilateral triangle has all the sides are equal. so the triangle is an equilateral triangle. Question 4. Answer: The triangle is an isosceles triangle. Explanation: In the above-given question, given that, the two sides have an equal length. they are 7 inches. the other side is 9.9 in. an isosceles triangle has only two sides are equal. so the above triangle is an isosceles triangle. Independent Practice In 5-10, classify each triangle by its sides and then by its angles. Question 5. Answer: The above triangle is an acute-angle triangle. Explanation: In the above-given question, given that, the two sides and the two sides have the same length. they are 75 degrees and 6 in. the other side has a different side length. acute angle triangle has two equal lengths. so the above triangle is an acute-angled triangle. Question 6. Answer: The triangle is a scalene triangle. Explanation: In the above-given question, given that, the triangle has three sides. the three sides have three different lengths. a scalene triangle has different lengths. so the above-given triangle is a scalene triangle. Think about what you need to compare to classify the triangle correctly. Question 7. Answer: The triangle is an equilateral triangle. Explanation: In the above-given question, given that, the triangle has the 3 equal sides and three equal angles. 60 + 60 + 60 = 180. an equilateral triangle has all three sides equal in length. so the above triangle is an equilateral triangle. Question 8. Answer: The triangle is an obtuse-angled triangle. Explanation: In the above-given question, given that, the triangle has 2 equal sides. obtuse-angled triangle has only two equal side lengths. so the triangle is an obtuse-angled triangle. Question 9. Answer: The triangle is a scalene triangle. Explanation: In the above-given question, given that, the triangle has three different side lengths. the side lengths are 6m, 10m, and 8m. a scalene triangle has three different side lengths. so the triangle is a scalene triangle. Question 10. Answer: The triangle is an isosceles triangle. Explanation: In the above-given question, given that, the triangle has two different side lengths. they are 12 cm and 6.5 cm. an isosceles triangle has the two sides equal. so the triangle is an isosceles triangle. Problem Solving Question 11. The Louvre Pyramid serves as an entrance to the Louvre Museum in Paris. The base of the pyramid is 35 meters long and the sides are 32 meters long. Classify the triangle on the front of the Louvre Pyramid by the lengths of its sides and the measures of its angles. Answer: The Louvre triangle is in the shape of an isosceles triangle. Explanation: In the above-given question, given that, The Louvre Pyramid serves as an entrance to the Louvre Museum in Paris. The base of the pyramid is 35 meters long and the sides are 32 meters long. an isosceles triangle has two equal side lengths. the other side is a difference in length. so the Louvre triangle is in the shape of an isosceles triangle. Question 12. A pizza is divided into twelve equal slices. Glenn and Ben each ate $$\frac{1}{6}$$ of the pizza on Monday. The next day Ben ate $$\frac{1}{2}$$ of the pizza that was left over. How many slices of the original pizza remain? Explain your reasoning. Answer: The number of slices of the original pizza remains = 2 pieces. Explanation: In the above-given question, given that, A pizza is divided into twelve equal slices. Glenn and Ben each ate $$\frac{1}{6}$$ of the pizza on Monday. The next day Ben ate $$\frac{1}{2}$$ of the pizza that was leftover. 1/6 + 1/2. 1/6 = 0.16. 1/2 = 0.5. 0.16 + 0.5 = 0.66. so the number of slices of the original pizza remains = 2 pieces. Question 13. During a sale at the bookstore, books sold for$3 and magazines sold for $2.50. Jan spent$16 and bought a total of 6 books and magazines. How many of each did she buy?

The number of each did she buy = $17. Explanation: In the above-given question, given that, During a sale at the bookstore, books sold for$3, and magazines sold for $2.50. Jan spent$16 and bought a total of 6 books and magazines.
6 x 3 = $18. 6 x$2.50 = $15.$18 + $15 = 33.$33 – $16 =$17.
so the number of each did she buy = $17. Question 14. Higher Order Thinking The measures of two angles of a triangle are 23° and 67°. Is the triangle acute, right, or obtuse? Use geometric terms in your explanation. Answer: The triangle is an acute-angled triangle. Explanation: In the above-given question, given that, The measures of two angles of a triangle are 23° and 67°. the triangles have two different angles. they are 23° and 67°. so the triangle is an acute-angled triangle. Question 15. Make Sense and Persevere An animal shelter houses dogs, cats, and rabbits. There are 126 animals at the shelter. Of the animals, $$\frac{1}{3}$$ are cats. Three fourths of the remaining animals are dogs. How many of the animals are rabbits? Show your work. Answer: The number of animals is rabbits = 21. Explanation: In the above-given question, given that, An animal shelter houses dogs, cats, and rabbits. There are 126 animals at the shelter. Of the animals, $$\frac{1}{3}$$ are cats. Three-fourths of the remaining animals are dogs. 1/3 = 0.3. 3/4 = 0.75. 0.3 + 0.75 = 1.05. so the number of animals is rabbits = 21. Assessment Practice Question 16. Two sides of a triangle measure 5 inches and 6 inches. Jason says the triangle must be scalene. Is Jason correct? Explain. Answer: No, Jason is not correct. Explanation: In the above-given question, given that, Two sides of a triangle measure 5 inches and 6 inches. a scalene triangle has all three sides have different lengths. an isosceles triangle has the two sides are equal. so Jason is not correct. ### Lesson 16.2 Classify Quadrilaterals Solve & Share Draw any length line segment that will fit in the space below. The line segment can go in any direction, but it must be straight. Draw another line segment of any length that is parallel to the first one. Connect the ends of each line segment with line segments to make a closed four-sided figure. What does your shape look like? Can you classify it? Discuss your ideas with a partner. Answer: The shape looks like is a rectangle. Explanation: In the above-given question, given that, the line segment has 5 cm in length. the other line segment has the same 2 cm in length. so the lines joined is formed a rectangle. the rectangle has two opposite sides that are equal. the rectangle has the area = length x width. so the shape looks like a rectangle. You can use reasoning to find the differences and similarities between shapes when classifying quadrilaterals. Show your work! Look Back! Reasoning How can you draw a quadrilateral different from the one above? Describe what you can change and why it changes the quadrilateral. Answer: The quadrilateral formed is square. Explanation: In the above-given question, given that, the line segment is increased by 3 cm. 5 – 2 = 3. so it has 4 equal side lengths. area of the square = 4 s. where S = sides. so the quadrilateral formed is square. Visual Learning Bridge Essential Question What Are Some Properties of Quadrilaterals? A. Categories of quadrilaterals are classified by their properties. • How many pairs of opposite sides are parallel? • Which sides have equal lengths? • How many right angles are there? Think about the questions below when you are classifying quadrilaterals. B. A trapezoid has one pair of parallel sides. A parallelogram has two pairs of opposite sides parallel and equal in length. C. A rectangle has four right angles. A rhombus has all sides the same length. D. A square has all sides the same length. A square has four right angles. Convince Me! Generalize How is a parallelogram different from a rhombus? How are they similar? Guided Practice Do You Understand? Question 1. A-Z Vocabulary How are a square and a rhombus alike? Answer: Yes, a square and a rhombus have four equal sides. Explanation: In the above-given question, given that, the square has four sides of the same length. square has four right angles. rhombus has all sides the same length. so the square and a rhombus have four equal sides. Question 2. Vocabulary How is a trapezoid different from a parallelogram? Answer: Yes, both of them are different. Explanation: In the above-given question, given that, a trapezoid has one pair of parallel sides. a parallelogram has two pairs of opposite sides and is equal in length. so both of them are different. Do You Know How? In 3-6, use as many names as possible to identify each polygon. Tell which name is most specific. Use the questions at the top of page 626 to help you classify the quadrilaterals. Question 3. Answer: The quadrilateral is a square. Explanation: In the above-given question, given that, the quadrilateral has 4 equal sides. four right angles. so the square has 4 equal sides. so the quadrilateral is a square. Question 4. Answer: The quadrilateral is a rectangle. Explanation: In the above-given question, given that, the quadrilateral has opposite equal sides. four right angles. so the rectangle has opposite equal sides. so the quadrilateral is a rectangle. Question 5. Answer: The quadrilateral is a rhombus. Explanation: In the above-given question, given that, the quadrilateral has 4 equal sides. so the rhombus has 4 equal sides. so the quadrilateral is a rhombus. Question 6. Answer: The quadrilateral is a parallelogram. Explanation: In the above-given question, given that, the quadrilateral has opposite sides are equal. four right angles. so the rectangle has opposite equal sides. so the quadrilateral is a parallelogram. Independent Practice Question 7. Identify the polygon using as many names as possible. Answer: The polygon is a square and rhombus. Explanation: In the above-given question, given that, the polygon has 4 equal sides. the polygon has 4 equal angles. so the polygon is a square and rhombus. Question 8. Identify the polygon using as many names as possible. Answer: The polygon is a quadrilateral and trapezoid. Explanation: In the above-given question, given that, the polygon has 4 different sides. the polygon has one right angle. so the polygon is a quadrilateral and trapezoid. Question 9. Why is a square also a rectangle? Answer: Yes, a square is also a rectangle. Explanation: In the above-given question, given that, the square has 4 equal right angles. the rectangle has 4 equal right angles. so square and rectangle are the same. so the square is also a rectangle. Question 10. Which special quadrilateral is both a rectangle and a rhombus? Explain how you know. Answer: The special quadrilateral is a square. Explanation: In the above-given question, given that, the square is a rectangle. square has 4 equal right angles. rectangle also has 4 equal right angles. rhombus also has 4 equal right angles. so the special quadrilateral is a square. Problem Solving Question 11. Each time Sophie makes a cut to a polygon, she can make a new type of polygon. What kind of polygon is left if Sophie cuts off the top of the isosceles triangle shown? Answer: The polygon formed is a trapezoid. Explanation: In the above-given question, given that, Each time Sophie makes a cut to a polygon, she can make a new type of polygon. the polygon is an isosceles triangle. after Sophie makes a cut to a polygon. so the polygon formed is a trapezoid. Question 12. Number Sense Donald’s car gets about 30 miles per gallon. About how many miles can Donald drive on 9.2 gallons of gas? At$3.15 a gallon, about how much would that amount of gas cost?

The amount of gas cost = $869.4 miles. Explanation: In the above-given question, given that, Donald’s car gets about 30 miles per gallon. 9.2 x 30 = 276 miles. 276 x$3.15 = $869.4 miles. so the amount of gas cost =$869.4 miles.

Question 13.
Is it possible to draw a quadrilateral that is not a rectangle but has at least one right angle? Explain.

Yes, it is possible to draw a quadrilateral that is not a rectangle.

Explanation:
In the above-given question,
given that,
the square is also a quadrilateral.
square has 4 equal right angles.
square has 4 equal side lengths.
so it is possible to draw a quadrilateral that is not a rectangle.

Question 14.
The area of a quadrilateral is 8.4 square feet. Find two decimals that give a product close to 8.4.

The two decimals are 2.1 and 4.0.

Explanation:
In the above-given question,
given that,
the area of a quadrilateral is 8.4 square feet.
area = l x w.
where l = 2.1 and w = 4.0.
area = 2.1 x 4.0.
area = 8.4.
so the two decimals are 2.1 and 4.0.

Question 15.
Be Precise Suppose you cut a square into two identical triangles. What type of triangles will you make?

The triangle I make is the isosceles triangle.

Explanation:
In the above-given question,
given that,
Suppose you cut a square into two identical triangles.
an isosceles triangle has the two sides equal.
the triangle formed is the isosceles triangle.
so the triangle I can make is an isosceles triangle.

Question 16.
Higher Order Thinking A parallelogram has four sides that are the same length. Is it a square? Explain how you know.

What do you know about the sides of a parallelogram?

Assessment Practice

Question 17.
Which quadrilateral could have side lengths 1 m, 5 m, 1 m, 5 m?
A. square
B. rectangle
C. trapezoid
D. rhombus

Option B is the correct answer.

Explanation:
In the above-given question,
given that,
the quadrilateral could have side lengths 1 m, 5 m, 1 m, and 5 m.
the rectangle has the opposite sides equal.
so option B is the correct answer.

Question 18.
Which of the following statements is NOT true?
A. A rectangle is also a parallelogram.
B. A trapezoid is also a quadrilateral.
C. A rhombus is also a rectangle.
D. A square is also a rectangle.

Option C is the correct answer.

Explanation:
In the above-given question,
given that,
a rectangle is also a parallelogram.
a trapezoid is also a quadrilateral.
a square is also a rectangle.
a rhombus is not a rectangle.
rhombus has all four equal sides.
so option C is the correct answer.

### Lesson 16.3 Continue to Classify Quadrilaterals

Solve & Share
Look at the quadrilaterals below. In the table, write the letters for all the figures that are trapezoids. Then do the same with each of the other quadrilaterals. Work with a partner to solve this problem.

You can classify quadrilaterals that have more than one property. Show your work!

List the letter of each figure in each group.

The number of trapezoids is Q, R, S, U, and O.
parallelograms are L, M, and N.
the rectangle is G.
the rhombus is V.

Explanation:
In the above-given question,
given that,
the number of trapezoids is Q, R, S, U, and O.
parallelograms are L, M, and N.
the rectangle is G.
the rhombus is V.

Look Back! Construct Arguments which quadrilateral had the most figures listed? Explain why this group had the most.

Visual Learning Bridge

Essential Question
How Are Special Quadrilaterals Related to Each Other?

A.
This Venn diagram shows how special quadrilaterals are related to each other.

How can you use the Venn diagram to describe other ways to classify a square? What does the diagram show about how a trapezoid relates to other special quadrilaterals?

B.
Each circle in the Venn diagram shows a category of quadrilateral.
Items in overlapping sections of the Venn diagram belong to more than one group.
“Square” is in more than one circle in the Venn diagram.

A square is also a rectangle, rhombus, parallelogram, and quadrilateral.

C.
In the diagram, the circle for trapezoids does not intersect with any other circles. This shows that a trapezoid is also a quadrilateral, but never a parallelogram, rectangle, rhombus, or square.

Convince Me! Construct Arguments When can a rectangle be a rhombus? Can a rhombus be a rectangle? Explain using examples.

Guided Practice

Do You Understand?

Question 1.
Explain how the Venn diagram on page 630 shows that every rectangle is a parallelogram.

Yes, every rectangle is a parallelogram.

Explanation:
In the above-given question,
given that,
square is a rectangle, parallelogram, rhombus, and quadrilateral.
square is also a rectangle.
square has 4 equal right angles.
a rectangle has 4 equal right angles.
so every rectangle is a parallelogram.

Question 2.
How are a rectangle and a rhombus alike?

The rectangle and rhombus are alike when they have 4 equal right angles.

Explanation:
In the above-given question,
given that,
square is a rectangle, parallelogram, rhombus, and quadrilateral.
square is also a rectangle.
square has 4 equal right angles.
a rectangle has 4 equal right angles.
so every rectangle is a parallelogram.
rhombus also have 4 equal right angles.
so the rectangle and rhombus are alike.

Do You Know How?

In 3-6, tell whether each statement is true or false. If false, explain.

Question 3.
All rectangles are squares.

Yes, all rectangles are squares.

Explanation:
In the above-given question,
given that,
the square is a rectangle.
square has 4 equal right angles.
rectangles have 4 equal right angles.
so all rectangles are squares.

Question 4.
Every rhombus is a parallelogram.

Yes, the rhombus is a parallelogram.

Explanation:
In the above-given question,
given that,
a rhombus has 4 equal sides lengths.
rhombus has 4 equal right angles.
a parallelogram has opposite sides equal.
so the rhombus is a parallelogram.

Question 5.
Parallelograms are special rectangles.

Parallelograms are special rectangles.

Explanation:
In the above-given question,
given that,
rectangles have two opposite side lengths.
the parallelogram has two opposite side lengths.
so parallelograms are special rectangles.

Question 6.
A trapezoid can be a square.

No, the trapezoid cannot be a square.

Explanation:
In the above-given question,
given that,
the square has 4 sides.
trapezoid also has 4 sides.
square has all sides equal.
a trapezoid has all sides not equal.
so trapezoid is not a square.

Independent Practice

In 7-10, write whether each statement is true or false. If false, explain why.

Question 7.
All rhombuses are rectangles.

False.

Explanation:
In the above-given question,
given that,
a rhombus has 4 equal side lengths.
rectangles have 2 opposite side lengths.
so the statement is not correct.

Question 8.

Yes, the trapezoid is a quadrilateral.

Explanation:
In the above-given question,
given that,
the trapezoid is also a quadrilateral but never a parallelogram, rectangle, rhombus, or square.
so the trapezoid is a quadrilateral.

Question 9.
Rhombuses are special parallelograms.

Yes, the rhombus is a special parallelogram.

Explanation:
In the above-given question,
given that,
a rhombus has 4 equal sides.
parallelograms have 4 sides.
so rhombus is a special parallelogram.

Question 10.

The statement is not correct.

Explanation:
In the above-given question,
given that,
rectangles have two opposite side lengths.
the quadrilateral has two opposite side lengths.
so the statement is not correct.

Question 11.
What properties does the shape have? Why is it not a parallelogram?

The shape formed is a rhombus.

Explanation:
In the above-given question,
given that,
the shape formed is a rhombus.
rhombus has 4 equal side lengths.
rhombus has 4 equal right angles.
so the shape formed is a rhombus.

Question 12.
Why is a square also a rhombus?

Yes, a square is also a rhombus.

Explanation:
In the above-given question,
given that,
a square has 4 equal sides.
square has 4 equal right angles.
rhombus has 4 equal sides.
rhombus has 4 equal right angles.
so the square is also a rhombus.

Problem Solving

Question 13.
Construct Arguments Draw a quadrilateral with one pair of parallel sides and two right angles. Explain why this figure is a trapezoid.

Yes, it is a trapezoid.

Explanation:
In the above-given question,
given that,
a trapezoid has one pair of parallel sides and two right angles.
a quadrilateral with one pair of parallel sides and two right angles.
so the figure formed is a trapezoid.

Question 14.
A reflecting pool is shaped like a rhombus with a side length of 6 meters. What is the perimeter of the pool? Explain how you found your answer.

The perimeter of the pool is

Explanation:
In the above-given question,
given that,
A reflecting pool is shaped like a rhombus with a side length of 6 meters.
the perimeter of rhombus = 6 a.
where a = sides.
perimeter = 6 x 6.
perimeter = 36 sq m.
so the perimeter of the pool is 36 sq m.

Question 15.
A bakery sold 31 bagels in the first hour of business and 42 bagels in the second hour. If the bakery had 246 bagels to start with, how many bagels were left after the second hour?
img 42.7

The number of bagels was left after the second hour = 3.36 bagels.

Explanation:
In the above-given question,
given that,
A bakery sold 31 bagels in the first hour of business and 42 bagels in the second hour.
42 + 31 = 73.
246/73 = 3.36.
so the number of bagels were left after the second hour = 3.36 bagels.

Question 16.
Higher Order Thinking Ann says the figure below is a square. Pablo says that it is a parallelogram. Felix says that it is a rectangle. Can they all be right? Explain.

Ann was correct.

Explanation:
In the above-given question,
given that,
the figure has 4 equal sides.
the figures have 4 equal angles.
the above figure is a square.
so Ann was correct.

Assessment Practice

Question 17.
Below is the Venn diagram of quadrilaterals.

Part A
Are rhombuses also rectangles? Explain.
Part B
What are all of the names that describe a rhombus?

Squares and rectangles describe a rhombus.

Explanation:
In the above-given question,
given that,
rhombuses, squares, and rectangles are over-linked with each other.
square has 4 equal side lengths.
square has 4 equal right angles.
rectangles have 2 opposite equal sides.
rhombus has 4 equal side lengths.
so squares and rectangles describe a rhombus.

### Lesson 16.4 Construct Arguments

Activity

Problem Solving

Solve & Share
Alfie thinks that if he cuts a parallelogram along a diagonal, he will get two triangles that have the same shape and size. Is he correct? Solve this problem any way you choose. Construct a math argument to justify your answer.

The two triangles are Scalene triangles.

Explanation:
In the above-given question,
given that,
Alfie thinks that if he cuts a parallelogram along a diagonal.
he will get two triangles that have the same shape and size.
the triangles formed are scalene triangles.
a scalene triangle has 3 different side lengths.

Thinking Habits
• How can I use numbers, objects, drawings, or actions to justify my argument?
• Am I using numbers and symbols correctly?
• Is my explanation clear and complete?
• Can I use a counterexample in my argument?

Look Back! Construct Arguments Suppose you cut along a diagonal of a rhombus, a rectangle, or a square. Would you get two triangles that have the same shape and size? Construct an argument to justify your answer.

Visual Learning Bridge

Essential Question How Can You Construct Arguments?

A.
Anika says, “If I draw a diagonal in a parallelogram, I will always form two right triangles.” Is she correct? Construct a math argument to justify your answer.

You can construct an argument using what you know about triangles and quadrilaterals.

What do I need to do to solve the problem?
I need to examine several cases, including special parallelograms. Then I need to state my conclusion and write a good argument to justify it.

Here’s my thinking..

B.
How can I construct an argument?
I can
• use math to explain my reasoning
• use the correct words and symbols.
• give a complete explanation.
• use a counterexample in my argument.

C.
Anika is incorrect. The triangles are right triangles only when the parallelogram is a rectangle or square. Rectangles and squares have four right angles. So, each triangle formed by drawing a diagonal will have a right angle and be a right triangle. But if the parallelogram does not have right angles, each triangle will not have a right angle.

Convince Me! Construct Arguments How can counterexamples be helpful in constructing an argument?

Guided Practice

Jamal says, “Two equilateral triangles that are the same size can be joined to make a rhombus.”

Question 1.
What is the definition of an equilateral triangle? What is the definition of a rhombus?

Yes, two equilateral triangles that are the same size can be joined to make a rhombus.

Explanation:
In the above-given question,
given that,
an equilateral triangle has all three sides has an equal length.
rhombus has all 4 sides are equal.
rhombus has all 4 equal right angles.
so the two equilateral triangles that are the same size can be joined to make a rhombus.

Question 2.
How could knowing these definitions help in constructing your argument?

Question 3.

Yes, Jamal was correct.

Explanation:
In the above-given question,
given that,
an equilateral triangle has all three sides has an equal length.
rhombus has all 4 sides are equal.
rhombus has all 4 equal right angles.
so the two equilateral triangles that are the same size can be joined to make a rhombus.

Independent Practice

Construct Arguments
Lauren says, “If I draw a diagonal in a trapezoid, neither of the triangles formed will have a right angle.”

Stuck? Answering this question might help. Have I interpreted all word meanings correctly?

Question 4.
What is the definition of a trapezoid?

The trapezoid is a quadrilateral with one pair of parallel sides.

Explanation:
In the above-given question,
given that,
the trapezoid is a quadrilateral with one pair of parallel sides.
area of trapezoid = 1/2(a + b) h.
where a and b are the bases.
h is the height.

Question 5.
Draw examples of a diagonal in a trapezoid.

The shape formed is a triangle.

Explanation:
In the above-given question,
given that,
if the trapezoid is divided into two equal halves.
we can get the two triangles.
so the shape formed is a triangle.

Question 6.
How can you use a drawing to construct an argument?

Question 7.

Problem Solving

Flag Making
Mr. Herrera’s class is studying quadrilaterals. The class worked in groups, and each group made a “quadrilateral flag.”

Question 8.
Construct Arguments Which flags show parallelograms? Construct a math argument to justify your answer.

Flag 1 shows a parallelogram.

Explanation:
In the above-given question,
given that,
Mr. Herrera’s class is studying quadrilaterals.
The class worked in groups, and each group made a “quadrilateral flag.
in 1st flag there are parallelograms.
so flag 1 shows a parallelogram.

Question 9.
Reasoning Explain how you would classify the quadrilaterals on the green flag and the blue flag.

Question 10.
Critique Reasoning Marcia’s group made the red flag. Bev’s group made the orange flag. Both girls say their flag shows all rectangles. Critique the reasoning of both girls and explain who is correct.

Question 11.
Make Sense and Persevere Does it make sense for this quadrilateral to be on any of the flags?

### Topic 16 Fluency Practice

Activity

Point & Tally

Find a partner. Get paper and a pencil. Each partner chooses light blue or dark blue.
At the same time, Partner 1 and Partner 2 each point to one of their black numbers. Both partners find the product of the two numbers.
The partner who chose the color where the product appears gets a tally mark. Work until one partner has seven tally marks.

Topic 16 Vocabulary Review

Understand Vocabulary

Word List
• acute triangle
• equilateral triangle
• isosceles triangle
• obtuse triangle
• parallelogram
• rectangle
• rhombus
• right triangle
• scalene triangle
• square
• trapezoid

Choose the best term from the Word List. Write it on the blank.

Question 1.
A 3-sided polygon with at least two sides the same length is a(n) _____

A 3-sided polygon with at least two sides of the same length is a(n) is an equilateral triangle.

Explanation:
In the above-given question,
given that,
a 3-sided polygon with at least two sides of the same length is a(n) is an equilateral triangle.
for example:
an equilateral triangle has three sides that are all the same length and three angles that all measure 60 degrees.

Question 2.
A polygon with one pair of parallel sides is a(n) ____

A polygon with one pair of parallel sides is a(n) is a trapezium.

Explanation:
In the above-given question,
given that,
a polygon with one pair of parallel sides is a(n) is a trapezium.
for example:
if the polygon has one pair of parallel sides is a trapezoid.

Question 3.
A(n) ____ has four right angles and all four sides the same length.

A(n) rhombus has four right angles and all four sides the same length.

Explanation:
In the above-given question,
given that,
a(n) rhombus has four right angles and all four sides the same length.
for example:
a rhombus is a parallelogram with 4 sides of equal length.
area of rhombus = 6 a.
where a = sides.

Question 4.
All three sides of a(n) ____ are different lengths.

All three sides of a(n) are scalene triangle are different lengths.

Explanation:
In the above-given question,
given that,
All three sides of a(n) are scalene triangle are different lengths.
for example:
a scalene triangle is a triangle in which all three sides have different lengths.

Question 5.
The measure of each of the three angles in a(n) ____ is less than 90°

The measure of each of the three angles in a(n) acute angle triangle is less than 90°.

Explanation:
In the above-given question,
given that,
the measure of each of the three angles in a(n) acute angle triangle is less than 90°.
for example:
an acute angle triangle has three angles that each measure less than 90 degrees.

Question 6.
A rectangle is a special type of ____

A rectangle is a special type of parallelogram.

Explanation:
In the above-given question,
given that,
a rectangle is a special type of parallelogram.
for example:
a rectangle is a special case of a parallelogram in which each pair of adjacent sides is perpendicular.

For each of these terms, draw an example and a non-example.

An obtuse triangle is an isosceles triangle.
Rhombus with no right angle is a quadrilateral.
An isosceles right triangle is two equal sides.

Explanation:
In the above-given question,
given that,
An obtuse triangle is an isosceles triangle.
Rhombus with no right angle is a quadrilateral.
An isosceles right triangle is two equal sides.

Use Vocabulary in Writing

Question 10.
Alana claims that not all 4-sided polygons with 2 pairs of equal sides are parallelograms. Is Alana correct? Use terms from the Word List in your answer.

No, she is not correct.

Explanation:
In the above-given question,
given that,
Alana claims that not all 4-sided polygons with 2 pairs of equal sides are parallelograms.
2 pairs of equal sides are not parallelograms.
so she was not correct.

### Topic 16 Reteaching

Set A
pages 621-624
Classify the triangle by the measures of its angles and the lengths of its sides.
Since one of the angles is right, this is a right triangle. Since two of the sides are the same length, this is an isosceles triangle.

It is a right, isosceles triangle.

Remember that right, obtuse, and acute describe the angles of a triangle. Equilateral, scalene, and isosceles describe the sides of a triangle.

Classify each triangle by the measures of its angles and the lengths of its sides.

Question 1.

The triangle is an equilateral triangle.

Explanation:
In the above-given question,
given that,
the triangles have 3 equal sides and three equal angles.
so the triangle is an equilateral triangle.

Question 2.

The triangle is a scalene triangle.

Explanation:
In the above-given question,
given that,
the triangle has 3 different sides.
they are 3 in, 5 in, and 4 in.
the three side lengths are different.
so the triangle is a scalene triangle.

Question 3.

The triangle is an isosceles triangle.

Explanation:
In the above-given question,
given that,
the triangle has 2 sides of equal length.
they are 8cm and 8 cm.
so the triangle is an isosceles triangle.

Question 4.

The triangle is a scalene triangle.

Explanation:
In the above-given question,
given that,
the triangle has 3 different sides.
they are 16.4 cm, 16 cm, and 10 cm.
so the triangle is a scalene triangle.

Set B
pages 625-628

Quadrilaterals are classified by their properties.
A trapezoid has one pair of parallel sides.

A parallelogram has two pairs of equal parallel sides.

A rectangle is a parallelogram with 4 right angles.

A rhombus is a parallelogram with 4 equal sides.

A square is a parallelogram with 4 right angles and 4 equal sides.

Remember that some quadrilaterals can be identified by more than one name.

Identify each quadrilateral. Describe each quadrilateral by as many names as possible.

Question 1.

Explanation:
In the above-given question,
given that,
the polygon has 4 right angles.
the polygon with 4 right angles is a rectangle.
so the quadrilateral is a rectangle.

Question 2.

Explanation:
In the above-given question,
given that,
the polygon has 4 equal sides.
rhombus is a parallelogram with 4 equal sides.
so the quadrilateral is a rhombus.

Question 3.

The polygon is a trapezoid.

Explanation:
In the above-given question,
given that,
a trapezoid has one pair of parallel sides.
so the polygon is a trapezoid.

Question 4.

The polygon is a square.

Explanation:
In the above-given question,
given that,
the quadrilateral has 4 equal sides and 4 equal angles.
a square is a parallelogram with 4 right angles and 4 equal sides.
so the polygon is a square.

Set C
pages 629-632
This Venn diagram shows how special quadrilaterals are related to each other.

Remember that each circle of the Venn diagram shows a subgroup of quadrilaterals.

Tell whether each statement is true or false.

Question 1.
All squares are rectangles.

True.

Explanation:
In the above-given question,
given that,
all squares are rectangles.
square is a rectangle.
area of the square = 4s.

Question 2.
Every parallelogram is a rectangle.

False.

Explanation:
In the above-given question,
given that,
a rectangle is a parallelogram.
but every parallelogram is a rectangle.
so the statement is false.

Question 3.
Rhombuses are special parallelograms.

True.

Explanation:
In the above-given question,
given that,
rhombuses are special parallelograms.
rhombus is a special parallelogram.
area of the rhombus = 4 a.

Question 4.

False.

Explanation:
In the above-given question,
given that,
a trapezoid is not a quadrilateral.
so the above statement is false.

Set D
pages 633-636

Thinking Habits
• How can I use numbers, objects, drawings, or actions to justify my argument?
• Am I using numbers and symbols correctly?
• Is my explanation clear and complete?
• Can I use a counterexample in my argument?

Remember that using definitions of geometric figures can help you construct arguments. Malcolm says, “The sum of the angle measures in any rectangle is 180°.”

Question 1.
What is the definition of a rectangle?

A rectangle is a parallelogram with 4 right angles.

Explanation:
In the above-given question,
given that,
a rectangle is a parallelogram with 4 right angles.
area of the rectangles = length x width.

Question 2.
Draw a picture of a rectangle and label its angles.

A rectangle is a parallelogram with 4 right angles.

Explanation:
In the above-given question,
given that,
a rectangle is a parallelogram with 4 right angles.
area of the rectangles = length x width.

Question 3.

### Topic 16 Assessment Practice

Question 1.
Which of the following correctly describes the triangles? Select all that apply.

Both triangles have a right angle.
Only one triangle is a right triangle.
Only one triangle has an acute angle.
Both triangles have an obtuse angle.
Both triangles have at least two acute angles.

Only one triangle is a right triangle.
only one triangle has an acute angle.

Explanation:
In the above-given question,
given that,
there are two triangles.
they have only one triangle is a right triangle.
only one triangle has an acute angle.

Question 2.
Which statement is true?
A. Trapezoids are parallelograms.
B. A square is always a rectangle.
C. A rectangle is always a square.
D. A rhombus is a trapezoid.

Option B is correct.

Explanation:
In the above-given question,
given that,
a square is always a rectangle.
square has 4 equal right angles.
the rectangle has 4 equal right angles.

Question 3.
Select all the shapes that are parallelograms.

Option 4 is correct.

Explanation:
In the above-given question,
given that,
the shapes are hexagon, rectangle, trapezoid, and parallelogram.
so option 4 is correct.

Question 4.
The necklace charm shown has one pair of m parallel sides. What type of quadrilateral is the charm? Explain.

The charm is in the shape of a trapezoid.

Explanation:
In the above-given question,
given that,
The necklace charm shown has one pair of m parallel sides.
a trapezoid has one pair of parallel sides.
the above charm has one pair of parallel sides.
so the charm is in the shape of a trapezoid.

Question 5.
Identify the figure below using as many names as possible.

The figure is a rhombus.

Explanation:
In the above-given question,
given that,
the square has 4 equal sides and 4 equal angles.
rhombus has 4 equal sides.
so the figure is a rhombus.

Question 6.
Claim 1: A square is a rectangle because it has 4 right angles.
Claim 2: A square is a rhombus because it has 4 equal sides.
Which claim is correct? Explain.

Yes, both of them are correct.

Explanation:
In the above-given question,
given that,
a square is a rectangle because it has 4 right angles.
a square is a rhombus because it has 4 equal sides.
so both of them are correct.

Assessment Practice

Question 7.
Look at the rhombus and square below.

A. How are the two figures the same?
B. How are the two figures different?

They are the same when they have 4 equal sides.
They are different when they have 4 equal right angles.

Explanation:
In the above-given question,
given that,
a square is a rectangle because it has 4 right angles.
a square is a rhombus because it has 4 equal sides.
they are the same when they have 4 equal sides.
they are different when they have 4 equal right angles.

Question 8.
Identify the figure below using as many names as possible.

The polygon is a trapezoid.

Explanation:
In the above-given question,
given that,
the figure has 4 different sides.
so the polygon is a trapezoid.

Question 9.
Identify the figure below using as many names as possible.

The polygon is a parallelogram.

Explanation:
In the above-given question,
given that,
the figure has opposite sides equal lengths.
parallelogram also has the opposite sides equal lengths.
so the polygon is a parallelogram.

Question 10.
What shape has two pairs of opposite sides that are parallel and has all sides of equal length but does NOT have four right angles?
A. Square
B. Rectangle
C. Rhombus
D. Trapezoid

Option C is correct.

Explanation:
In the above-given question,
given that,
rhombus has two pairs of opposite sides that are parallel.
all sides of equal length but do not have 4 right angles.
so option C is correct.

Question 11.
Use the Venn diagram. Are rhombuses always, sometimes, or never also parallelograms? Explain.

Rhombuses are always a parallelogram.

Explanation:
In the above-given question,
given that,
rhombuses are parallelograms.
rhombus is a parallelogram with 4 equal sides.
area of the rhombus = 4 a.
where a = side.
so rhombuses are always a parallelogram.

Question 12.
Describe triangle HJK in terms of its sides and angles.

The triangle is an isosceles triangle.

Explanation:
In the above-given question,
given that,
triangle HJK is an isosceles triangle.
an isosceles triangle has 2 sides equal.
so the triangle HJK is an isosceles triangle.

Geometry in Art
Artists often use triangles and quadrilaterals in their pictures.

Question 1.
Use the Poster to answer the following questions.
Part A
Classify Triangle 1 in the Poster by its angles and by its sides.

The triangle is a scalene triangle.

Explanation:
In the above-given question,
given that,
triangle 1 is a scalene triangle.
a scalene triangle has three different sides.

Part B
What are all of the names you can use to describe Shape 2 in the Poster?

Shape 2 is a parallelogram.

Explanation:
In the above-given question,
given that,
shape 2 is a parallelogram.
a parallelogram has two pairs of equal parallel sides.
shape 2 is a parallelogram.

Part C
Triangles 3 and 4 are identical. They are joined in the Poster to form a square. Construct a math argument to show why Triangles 3 and 4 are isosceles right triangles.
Part D
If Triangle 3 is joined with another triangle that is the same size and shape, do the two triangles always form a square? Construct a math argument to explain your reasoning.
Part E
What are the measures of the angles of Triangle 3? Note that two angles in an isosceles triangle always have the same measure. Explain.

Triangle 3 is a rhombus.

Explanation:
In the above-given question,
given that,
triangle 3 is a rhombus.
in the rhombus, there are 2 equilateral triangles.
triangles 3 and 4 are equilateral triangles.
so triangle 3 is a rhombus.

Question 2.
Classify the triangles and quadrilaterals in the Houses drawing to answer the following questions.
Part A
Are all the triangles shown in the design isosceles? Are they all equilateral? Construct a math argument, using properties, to explain why or why not.

Yes, the triangles are equilateral and isosceles triangle.

Explanation:
In the above-given question,
given that,
there are equilateral and isosceles triangles.
an equilateral triangle has all the 3 sides are equal.
an isosceles triangle has only two sides that are equal.
so the triangles are both equilateral and isosceles triangle.

Part B
All of the quadrilaterals in the Houses drawing are rectangles. Does that mean all of the quadrilaterals are parallelograms? Does that mean all are squares? Construct a math argument, using properties, to explain your reasoning.

Yes, all of the quadrilaterals in the house drawing are rectangles.

Explanation:
In the above-given question,
given that,
all of the quadrilaterals in the house drawing are rectangles.
all squares are rectangles.
so all of the quadrilaterals in the house drawing are rectangles.

## Envision Math Common Core Grade K Answers Key Topic 10 Compose and Decompose Numbers 11 to 19

Essential Question: How can composing and decomposing numbers from 11 to 19 into ten ones and some further ones help you understand place value?

envision STEM Project: Sunlight and Earth’s Surface
Directions Read the character speech bubbles to students. Find Out! Have students find out how sunlight affects Earth’s surface. Say: Talk to friends and relatives about sunlight and how it affects Earth. Journal: Make a Poster Have students make a poster that shows 3 things sunlight does for Earth. Have them draw a sun with 16 rays. Then have them write an equation for parts of 16.

Review What You Know

Question 1.

Explanation:
I circled the group that has 16 leafs.

Question 2.

Explanation:
I circled the group that has 20 leafs.

Question 3.

Explanation:
I circled the group that has less number of leafs.

Question 4.

Explanation:
There are 13 leafs in the above picture so, I wrote the number 13.

Question 5.

Explanation:
There are 17 leafs in the above picture so, I wrote the number 137

Question 6.

Explanation:
There are 15 leafs in the above picture so, I wrote the number 15.

Directions Have students: 1 draw a circle around the group with 16; 2 draw a circle around the group with 20; 3 draw a circle around the group that is less than the other group; 4-6 count the leaves, and then write the number to tell how many.

Pick a Project

A

B

Directions Say: You will choose one of these projects. Look at picture A. Think about this question: How great is the great outdoors? If you choose Project A, you will tell a camping story. Look at picture B. Think about this question: What do mice like to eat? If you choose Project B, you will make a mouse poster.

C

D

Directions Say: You will choose one of these projects. Look at picture C. Think about this question: What do you like to collect? If you choose Project C, you will make a sticker book. Look at picture D. Think about this question: What is in a granola bar? If you choose Project D, you will make a snack-time drawing.

### Lesson 10.1 Make 11, 12, and 13

Solve & Share

Explanation:
I filled the ten-frame with counters and kept 2 counters outside the frame.
The equation that matches with the number of counters is 10+2=12.

Directions Say: Use counters to fill the ten-frame. Put 1, 2, or 3 counters outside of the ten-frame. Draw all of the counters. What equation can you write to tell how many counters there are in all?

Visual Learning Bridge

Guided Practice

Question 1.

Directions 1 Have students write an equation to match the number of blocks shown. Then have them tell how the picture and equation show 10 ones and some more ones.

Question 2.

Explanation:
The equation that matches the number of blocks is 10+1=11.
The equation tells us that there are 10 ones and 1 more one.

Question 3.

Explanation:
The equation that matches the number of blocks is 10+3=13.
The equation tells us that there are 10 ones and 3 more ones.

Question 4.

Explanation:
I drew 12 counterss to match with the equation 10+2=12
The equation tells us that there are 10 ones and 2 more ones.

Question 5.

Explanation:
I drew 13 counters to match with the equation 10+3=13
The equation tells us that there are 10 ones and 3 more ones.

Directions Have students: 2 and 3 write an equation to match the number of blocks shown. Then have them tell how the picture and equation show 10 ones and some more ones; 4 and 5 draw blocks to match the equation. Then have them tell how the picture and equation show 10 ones and some more ones.

Independent Practice

Question 6.

Explanation:
I drew 13 counters to match with the equation 10+3=13
The equation tells us that there are 10 ones and 3 more ones.

Question 7.

Explanation:
I drew 11 counters to match with the equation 10+1=11
The equation tells us that there are 10 ones and 1 more one.

Question 8.

Explanation:
I drew 12 counters to match with the equation 10+2=12
The missing number is 2
The equation tells us that there are 10 ones and 2 more ones.

Question 9.

Explanation:
I drew 13 counters to match with the equation 10+3=13
The missing number is 3
The equation tells us that there are 10 ones and 3 more ones.

Directions Have students: 6 draw counters and write an equation to show how to make 13. Then have them tell how the picture and equation show 10 ones and some more ones; 7 draw counters and write an equation to show how to make 11. Then have them tell how the picture and equation show 10 ones and some more ones. 8 Algebra Have students draw counters to find the missing number. Then have them tell how the picture and equation show 10 ones and some more ones. 9 Higher Order Thinking Have students draw counters to find the missing number. Then have them tell how the picture and equation show 10 ones and some more ones.

### Lesson 10.2 Make 14, 15 and 16

Solve & Share

Explanation:
I drew 15 counters to match with the equation 10+5=15
The equation tells us that there are 10 ones and 5 more ones.

Directions Say: Put 15 counters in the double ten-frame to show 10 ones and some more ones. Then complete the equation to match the counters.

Visual Learning Bridge

Guided Practice

Question 1.

Directions 1 Have students write an equation to match the counters. Then have them tell how the picture and equation show 10 ones and some more ones.

Question 2.

Explanation:
I drew 15 counters to match with the equation 10+5=15
The equation tells us that there are 10 ones and 5 more ones.

Question 3.

Explanation:
I drew 16 counters to match with the equation 10+6=16
The equation tells us that there are 10 ones and 6 more ones.

Question 4.

Explanation:
I drew 14 counters to match with the equation 10+4=14
The equation tells us that there are 10 ones and 4 more ones.

Question 5.

Explanation:
I drew 15 counters to match with the equation 10+5=15
The equation tells us that there are 10 ones and 5 more ones.

Directions Have students: 2-3 write an equation to match the counters. Then have them tell how the picture and equation show 10 ones and some more ones; 4-5 draw counters to match the equation. Then have them tell how the picture and equation show 10 ones and some more ones.

Independent Practice

Question 6.

Explanation:
I drew 16 counters to match with the equation 10+6=16
The equation tells us that there are 10 ones and 6 more ones.

Question 7.

Explanation:
I drew 14 counters to match with the equation 10+4=14
The equation tells us that there are 10 ones and 4 more ones.

Question 8.

Explanation:
The equation 10+5=15 tells us that there are 10 ones and 5 more ones.

Question 9.

Explanation:
I drew 16 counters to match with the equation 10+6=16
The missing number is 6
The equation tells us that there are 10 ones and 6 more ones.

Directions Have students: 6 draw counters and write an equation to show how to make 16. Then have them tell how the picture and equation show 10 ones and some more ones; 7 draw counters and write an equation to show how to make 14. Then have them tell how the picture and equation show 10 ones and some more ones, 8 Number Sense Have students write an equation to show 15 as 10 ones and some more ones. 9 Higher Order Thinking Have students draw counters to find the missing number in the equation. Then have them tell how the picture and equation show 10 ones and some more ones.

### Lesson 10.3 Make 17, 18, and 19

Solve & Share

Explanation:
I drew 18 counters to match with the equation 10+8=18
The equation tells us that there are 10 ones and 8 more ones.

Directions Say: Jada made 10 prizes for the school carnival. She makes 8 more. Use counters to show how many prizes Jada made in all. Then write an equation to match the counters, and tell how the counters and equation show 10 ones and some more ones.

Visual Learning Bridge

Guided Practice

Question 1.

Directions 1 Have students complete the equation to match the counters. Then have them tell how the picture and equation show 10 ones and some more ones.

Question 2.

Explanation:
I counted the number of counters, there are 19 counters.
So, i wrote the equation 10+9=19
The equation tells us that there are 10 ones and 9 more ones.

Question 3.

Explanation:
I counted the number of counters, there are 18 counters.
So, i wrote the equation 10+8=18
The equation tells us that there are 10 ones and 8 more ones.

Question 4.

Explanation:
I counted the number of cubes, there are 17 cubes
So, i wrote the equation 10+7=17
The equation tells us that there are 10 ones and 7 more ones.

Question 5.

Explanation:
I counted the number of cubes, there are 19 cubes
So, i wrote the equation 10+9=19
The equation tells us that there are 10 ones and 9 more ones.

Directions Have students 2 and 3 write an equation to match the counters. Then have them tell how the picture and equation show 10 ones and some more ones; 4 and 5 complete the equation to match the cubes. Then have them tell how the picture and equation show 10 ones and some more ones.

Independent Practice

Question 6.

Explanation:
I drew 18 counters to match with the equation 10+8=18
The equation tells us that there are 10 ones and 8 more ones.

Question 7.

Explanation:
I drew 17 counters to match with the equation 10+7=17
The equation tells us that there are 10 ones and 7 more ones.

Question 8.

Explanation:
I drew 19 counters to match with the equation 10+9=19
The equation tells us that there are 10 ones and 9 more ones.

Question 9.

Explanation:
I drew 19 counters to match with the equation 10+9=19
The missing number is 9
The equation tells us that there are 10 ones and 9 more ones.

Directions Have students: 6 draw counters, and then write an equation to show how to make 18. Then have them tell how the picture and equation show 10 ones and some more ones; 7 draw counters, and then write an equation to show how to make 19. Then have them tell how the picture and equation show 10 ones and some more ones; 8 draw counters, and then write an equation to show how to make 17. Then have them tell how the picture and equation show 10 ones and some more ones. 9 Higher Order Thinking Have students draw counters to find the missing number in the equation. Then have them tell how the picture and equation show 10 ones and some more ones.

### Lesson 10.4 Find Parts of 11, 12 and 13

Solve & Share

Explanation:
13 means 10+3
I drew 13 counters to match with the equation 13=10+3
The equation tells us that there are 10 ones and 3 more ones.

Directions Say: 13 students wait for the train. There are only 10 seats in each train car. How many students will have to ride in a second car? Use counters to show your work. Then tell how the counters and equation show 10 ones and some more ones.

Visual Learning Bridge

Guided Practice

Question 1.

Directions 1 Have students use counters to show 11, draw them in the double ten-frame, and complete the equation to match the picture. Then have them tell how the picture and equation show 10 ones and some more ones.

Question 2.

Explanation:
13 means 10+3
I drew 13 counters to match with the equation 13=10+3
The equation tells us that there are 10 ones and 3 more ones.

Question 3.

Explanation:
There are 10 cubes and 2 more cubes.So, the missing numbers in the equation are 10 and 2
The equation tells us that there are 10 ones and 2 more ones.

Question 4.

Explanation:
I drew 11 counters to match with the equation 1=10+1
The equation tells us that there are 10 ones and 1 more one.

Directions Have students: 2 use counters to show 13, draw them in the double ten-frame, and complete the equation to match the picture. Then have them tell how the picture and equation show 10 ones and some more ones; 3 look at the picture of 12 cubes, and complete the equation to match the picture. Then have them tell how the picture and equation show 10 ones and some more ones; 4 draw counters to match the equation. Then have them tell how the picture and equation show 10 ones and some more ones.

Independent Practice

Question 5.

Explanation:
12 means 10+2
I drew 12 counters to match with the equation 12=10+2
The equation tells us that there are 10 ones and 2 more ones.

Question 6.

Explanation:
13 means 10+3
I counted the number of cunes, there are 13 cubes.13=10+3
The equation tells us that there are 10 ones and 3 more ones.

Question 7.

Explanation:
I drew 11 counters to match with the equation 11=10+1 and 10+1=11.
The equation tells us that there are 10 ones and 1 more ones.

Directions Have students: 5 draw counters to make 12, and complete the equation to match the picture. Then have them tell how the picture and equation show 10 ones and some more ones; 6 color the cubes blue and red to make 13, and complete the equation to match the picture. Then have them tell how the picture and equation show 10 ones and some more ones. 7 Higher Order Thinking Have students draw counters to show 11 and write two equations to match the picture. Then have them tell how the picture and equations show 10 ones and some more ones.

### Lesson 10.5 Find Parts of 14, 15, and 16

Solve & Share

Explanation:
14 means 10+4
I drew 14 counters to match with the equation 14=10+4
The equation tells us that there are 10 ones and 4 more ones.

Directions Say: 14 students go to the zoo. The first bus takes 10 students. The rest of the students go on a second bus. Use counters to describe this situation. Then complete the equation to match the counters and tell how the counters and equation show 10 ones and some more ones.

Visual Learning Bridge

Guided Practice

Question 1.

Directions 1 Have students use counters to show 15, draw them in the double ten-frame, and complete the equation to match the picture. Then have them tell how the picture and equation show 10 ones and some more ones.

Question 2.

Explanation:
14 means 10+4
I drew 14 counters to match with the equation 14=10+4
The equation tells us that there are 10 ones and 4 more ones.

Question 3.

Explanation:
16 means 10+6
I counted the number of cubes, there are 16 cubes.So, the equation is 16=10+6
The equation tells us that there are 10 ones and 6 more ones.

Question 4.

Explanation:
I drew 15 counters to match with the equation 15=10+5
The equation tells us that there are 10 ones and 5 more ones.

Directions Have students: 2 use counters to show 14, draw them in the double ten-frame, and complete the equation to match the picture. Then have them tell how the picture and equation show 10 ones and some more ones; 3 look at the picture of 16 cubes, and complete the equation to match the picture. Then have them tell how the picture and equation show 10 ones and some more ones; 4 draw counters to match the equation. Then have them tell how the picture and equation show 10 ones and some more ones.

Independent Practice

Question 5.

Explanation:
I drew 16 counters to match with the equation 16=10+6
The equation tells us that there are 10 ones and 6 more ones.

Question 6.

Explanation:
14=10+4
I colored 14 cubes to match with the equation 14=10+4
The equation tells us that there are 10 ones and 4 more ones.

Question 7.

Explanation:
I drew 16 counters to match with the equation 16=10+6 or 10+6=16
The equation tells us that there are 10 ones and 6 more ones.

Directions Have students 5 draw counters to match the equation. Then have them tell how the picture and equation show 10 ones and some more ones. 6 color the cubes blue and red to show 14, complete the equation to match the picture, and tell how the picture and equation show 10 ones and some more ones. 7 Higher Order Thinking Have students use counters to show 16, draw them in the double ten-frame, and complete two equations to match the picture. Then have them tell how the picture and equations show 10 ones and some more ones.

### Lesson 10.6 Find Parts of 17, 18 and 19

Solve & Share

Explanation:
I colored 10 boxes blue and the remaining 8 boxes red,
The equation is 10+8=18
The equation tells us that there are 10 ones and 5 more ones.

Directions Say: How can these 18 boxes be split into ten ones and some more ones? Use 2 different color crayons to color the boxes to show your work. Then write an equation to match the picture.

Visual Learning Bridge

Guided Practice

Question 1.

Directions 1 Have students color 10 cubes blue to show 10 ones, and then draw 10 blue cubes in the top ten-frame. Have them color the remaining cubes in the train red to show more ones, count them, and then draw red cubes in the bottom ten-frame. Then have them write an equation to match the pictures.

Question 2.

Explanation:
I colored 10 squares blue to show 10 ones, and then drew 10 blue squares in the top ten-frame.Then i colored the remaining cubes in the train red to show more ones, counted them, and then drew 9 red squares in the bottom ten-frame. Then i wrote the equation 19=10+9 to match the pictures.

Question 3.

Explanation:
I colored 10 squares blue to show 10 ones, and then drew 10 blue squares in the top ten-frame.Then i colored the remaining cubes in the train red to show more ones, counted them, and then drew 7 red squares in the bottom ten-frame. Then i wrote the equation 19=10+7 to match the pictures.

Question 4.

Explanation:
I counted the above counters, there are 18 counters.So, the equation is 18=10+8
The equation tells us that there are 10 ones an d8 more ones.

Directions Have students: 2 and 3 color 10 squares blue to show 10 ones, and then draw 10 blue squares in the top ten-frame. Have them color the remaining cubes in the train red to show more ones, count them, and then draw red squares in the bottom ten-frame. Then have them write an equation to match the pictures; 4 complete the equation to match the counters. Then have them tell how the picture and equation show 10 ones and some more ones.

Independent Practice

Question 5.

Explanation:
I counted the above counters, there are 17 counters.So, the equation is 17=10+7
The equation tells us that there are 10 ones and 7 more ones.

Question 6.

Explanation:
I counted the above counters, there are 19 counters.So, the equation is 19=10+9
The equation tells us that there are 10 ones and 9 more ones.

Question 7.

Explanation:
I drew 18 counters to match with the equation 18=10+8 or 10+8=18
The equation tells us that there are 10 ones and 8 more ones.

Directions 5 and 6 Have students complete the equation to match the counters. Then have them tell how the picture and equation show 10 ones and some more ones. 7 Higher Order Thinking Have students use counters to show 18, draw them in the double ten-frame, and write two equations to match the picture. Then have them tell how the picture and equations show 10 ones and some more ones.

### Lesson 10.7 Look For and Use Structure

Problem Solving

Solve & Share

Explanation:
I kept 2 counters in the red five-frame. Used a red crayon and wrote the number 2 that tells how many counters are in the red frame. I kept the same number of counters in the blue five-frame. Used a blue crayon and write the number that tells how many counters are in the blue frames.
The red nmber is smaller by ten then the blue number,
The pattern is 2,12.

Directions Say: Put some counters in the red five-frame. Use a red crayon and write the number that tells how many counters are in the red frame. Put the same number of counters in the blue five-frame. Use a blue crayon and write the number that tells how many counters are in the blue frames. Show the numbers to a partner. Compare your answers and look for patterns. How is your blue number like your red number? How is it different?

Visual Learning Bridge

Guided Practice

Question 1.

Directions 1 Have students find the number with the blue box around it, and then color the number that is 10 greater than the number in the blue box. Have them write an equation to show how the teen number they colored is composed of 10 ones and some more ones. Then have students explain how they decided what parts to add to make the teen number.

Independent Practice

Question 2.

Explanation:
I found the number with the blue box around it, it is 7 and then colored the number that is 10 greater than the number in the blue box which is 17.Then wrote an 10+7=17 equation to show how the teen number i colored is composed of 10 ones and 7 more ones.

Question 3.

Explanation:
I found the number with the blue box around it, it is 8 and then colored the number that is 10 greater than the number in the blue box which is 18.Then wrote an 10+8=18 equation to show how the teen number i colored is composed of 10 ones and 8 more ones.

Question 4.

Explanation:
I found the number with the blue box around it, it is 9 and then colored the number that is 10 greater than the number in the blue box which is 19.Then wrote an 10+9=19 equation to show how the teen number i colored is composed of 10 ones and 9 more ones.

Question 5.

Explanation:
The missing numbers in the pattern are 10 and 3.
The equaation is 10+3=13.

Directions Have students: 2-4 find the number with the blue box around it, and color the number that is 10 greater than the number in the blue box. Then have them write an equation to show how the teen number they colored is composed of 10 ones and some more ones; 5 complete the equation to continue the pattern, and then explain the pattern they made.

Problem Solving

Directions Read the problem to students. Then have them use multiple problem-solving methods to solve the problem. Say: Mr. Shepard’s class will exchange cards at a holiday party. There are 16 students in the class. The store sells cards in packs of 10. Alex already has 6 cards. Marta already has 7 cards. How many cards will Alex and Marta have after they each buy one pack of cards? 6 Use Structure How can the number chart help you solve the problem? Write the equations for the number of cards Alex and Marto will have. 7 Generalize After you find the number of cards Alex will have, is it easier to find the number of cards Marta will have? 8 Explain Tell a friend why your answers are correct. Then tell the friend about the pattern you see in the number chart and how the equations show 10 ones and some more ones.

### Topic 10 Fluency Practice

Find a Match

Activity

Question 1.

Explanation:
The clues are 2+3=5=4+1=O, 4-2=2=1+1=G, 5-2=3=4-1=H
I solved the addition and subtraction problems in the above picture and with the help of the clues i found the word HOG.

Question 2.

Explanation:
The clues are 2-1=1=5-4=W, 2+2=1+3=4=C, 1-1=0=0+0=O
I solved the addition and subtraction problems in the above picture and with the help of the clues i found the word COW.

Directions 1 and 2 Have students find a partner. Have them point to a clue in the top row, and then solve the addition or subtraction problem. Then have them look at the clues in the bottom row to find a match, and then write the clue letter above the match. Have students find a match for every clue.

Topic 10 Vocabulary Review

Question 1.

Question 2.

Directions Understand Vocabulary Have students: 1 complete the drawing and the equation to show how many more counters are needed to make 15; 2 complete the drawing and the equation to show how many more counters are needed to make 19.

### Topic 10 Reteaching

Set A

Question 1.

Explanation:
There are 13 cubres in the above picture.
The equation that matches with the image is 10+3=13
The equation tells us that there are 10 ones and 3 more ones.

Set B

Question 2.

Explanation:
I drew 6 more counters to show 16,
The equation 10+6=16 tells us that there are 10 ones and 6 more ones.

Directions Have students: 1 write an equation to match the blocks. Then have them tell how the picture and equation show 10 ones and some more ones; 2 draw counters to show 16, and then write an equation to match the picture. Then tell how the picture and equation show 10 ones and some more ones.

Set C

Question 3.

Explanation:
I drew 17 counters to match with the equation 10+7=17
The equation 10+7=17 tells us that there are 10 ones and 7 more ones.

Set D

Question 4.

Explanation:
I drew 11 counters to match with the equation 10+1=11
The equation tells us that there are 10 ones and 1 more ones.

Directions Have students: 3 draw counters to match the equation. Then have them tell how the picture and equation show 10 ones and some more ones; 4 draw counters to make 11, and then complete the equation to match the picture. Then have them tell how the picture and equation show 10 ones and some more ones.

Set E

Question 5.

Explanation:
I drew 14 counters to match with the equation 10+4=14
The missing numbers in the equation are 10 and 4.
The equation tells us that there are 10 ones and 4 more ones.

Set F

Question 6.

Explanation:
I found the number with the blue box around it, it is 8 and then colored the number that is 10 greater than the number in the blue box which is 18.Then wrote an 10+8=18 equation to show how the teen number i colored is composed of 10 ones and 8 more ones.

Directions Have students: 5 use counters to show 14, draw them in the double ten-frame, and complete the equation to match the picture. Then have them tell how the picture and equation show 10 ones and some more ones; 6 find the number with the blue box around it, and color the number that is 10 greater than the number in the blue box. Then have them write an equation to match, and then tell how the equation shows 10 ones and some more ones.

Set G

Question 7.

Explanation:
I colored 10 cubes blue in the train to show 10 ones, and then drew 10 blue cubes in the top ten-frame.Then colored the remaining 8 cubes in the train red to show 8 more ones, I counted them, and then draw the same number of red cubes in the bottom ten-frame. Then I wrote an equation 18= 10 + 8  to match the pictures.

Directions Have students: 7 color 10 cubes blue in the train to show 10 ones, and then draw 10 blue cubes in the top ten-frame. Have them color the remaining cubes in the train red to show more ones, count them, and then draw the same number of red cubes in the bottom ten-frame. Then have them write an equation to match the pictures.

### Topic 10 Assessment Practice

Question 1.

A. 15 = 10 + 5
B. 14 = 10 + 4
C. 13 = 10 + 3
D. 12 = 10 + 2

Explanation:
Option A is correct as there are 15 counters in the above ten frames which tell that there are 10 ones and 5 more ones.

Question 2.

A. 10 and 6
B. 10 and 7
C. 10 and 8
D. 10 and 9

Explanation:
Option C is correct as there are 18 counters in the above ten frames which tell that there are 10 ones and 8 more ones.

Question 3.
A 10 and 0
B 10 and 1
C 10 and 2
D 10 and 3

Explanation:
Option C is correct as there are 12 counters in the above ten frames which tell that there are 10 ones and 2 more ones.

Directions Have students mark the best answer. 1 Say: Mason uses counters in ten-frames to count his marbles. Which equation matches the picture and shows how many marbles Mason has? 2 Say: Sarah counts the number of counters and gets 18. Which two numbers add to 18? Use the equation and double ten-frame for help. 3 Say: Cole has 12 toy trucks. How can Cole split up his trucks into ten ones and some more ones?

Question 4.

Explanation:
I found the number with the blue box around it, it is 4 and then colored the number that is 10 greater than the number in the blue box which is 14.Then wrote an 10+4=14 equation to show how the teen number i colored is composed of 10 ones and 4 more ones.

Question 5.

Explanation:
I drew 3 more counters to match with the equation 13 = 10 + 3
The equation tells that there are 10 ones and 3 more ones.

Directions Have students: 4 find the number with the blue box around it, and then color the number that is 10 greater than the number in the blue box. Then have them write an equation that shows how the teen number they colored is composed of ten and some more ones; 5 draw counters to make 13, and then complete the equation to match the picture.

### Topic 10 Assessment Practice

Question 6.

Explanation:
I drew 6 more counters to match with the equation 16 = 10 + 6
The equation tells that there are 10 ones and 6 more ones.

Question 7.

Explanation:
I colored 10 cubes blue in the train to show 10 ones, and then drew 10 blue cubes in the top ten-frame.Then colored the remaining 9 cubes in the train red to show 9 more ones, I counted them, and then draw the same number of red cubes in the bottom ten-frame. Then I wrote an equation 18= 10 + 9  to match the pictures

Directions Have students: 6 listen to this story: Gabby has 16 counters. She wants to put her counters into a double ten-frame in order to decompose 16 into tens and ones. Draw counters to match Gabby’s equation. 7 color 10 cubes blue to show 10 ones, and then draw 10 blue cubes in the top ten-frame. Have them color the remaining cubes in the train red to show more ones, count them, and then draw the same number of red cubes in the bottom ten-frame. Then have them write an equation to match the pictures.

Question 8.

Explanation:
In the first double ten-frame there are 13 counters, i matched it with the equation 13=10+3
In the Second double ten-frame there are 1 counters, i matched it with the equation 17=10+7
In the third double ten-frame there are 1 counters, i matched it with the equation 11=10+1
In the forth double ten-frame there are 1 counters, i matched it with the equation 14=10+4

Directions 8 Have students choose the equation that matches each double ten-frame.

Question 1.

Explanation:
There are 12 marbles in the above ten frame.
I wrote the euqation 10+2=12 to match with the picture.
The equation tll that there are 10 ones and 2 mor eones.

Question 2.

Explanation:
I drew 8 more marbles to match with the equation 18 = 10 + 8
The equation tells that there are 10 ones and 8 more ones.

Question 3.

Explanation:
I drew 17 yellow marbles to match with the equation 17 = 10 + 7
The equation tells that there are 10 ones and 7 more ones.

Directions Mason’s Marbles Say: Mason collects many different kinds of marbles. He uses ten-frames to help count his marbles. Have students: 1 write the equation to show how many purple marbles Mason has; 2 draw red marbles in the second ten-frame to show 18 red marbles in all, and then complete the equation. Have them tell how the picture and equation show 10 ones and some more ones; 3 draw 17 yellow marbles in the double ten-frame, and then write two equations to match their drawing.

Question 4.

Explanation:
I drew 13 green marbles to match with the equation 13 = 10 + 3
The equation tells that there are 10 ones and 3 more ones.

Question 5.

Explanation:
I found the number with the blue box around it, it is 4 and then colored the number that is 10 greater than the number in the blue box which is 14.Then wrote an 10+4=14 equation to show how the teen number i colored is composed of 10 ones and 4 more ones.

Directions 4 Have students look at the equation Mason wrote to show how many green marbles he has, and then draw the marbles in the double ten-frame to show the number. Have them tell how the picture shows 10 ones and some more ones. 5 Say: Mason put his striped marbles in a five-frame. Then he buys 10 more striped marbles. Have students write the number to tell how many striped marbles Mason had at first, and then color the part of the number chart to show how many striped marbles he has now. Then have them write an equation and ask them to explain how the picture and equation show 10 ones and some more ones.

## Envision Math Common Core Grade K Answers Key Topic 9 Count Numbers to 20

Essential Question: How can numbers to 20 be counted, read, written, and pictured to tell how many?

enVision STEM Project: What Can We Get From Plants?
Directions Read the character speech bubbles to students. Find Out! Have students find out ways plants impact and change their environment. Say: Talk to friends and relatives about what plants do for the environment. Ask them how humans and animals use things in the environment, such as plants, to meet their needs. Journal: Make a Poster Have students make a poster. Ask them to draw some ways that plants can provide food and shelter for animals and humans. Finally, have students draw an orange tree with 15 oranges.

Review What You Know

Question 1.

Explanation:
I circled the equation that shows the addition.
The symbol plus (+) means addition.

Question 2.

Explanation:
I circled the symbol minus(-).

Question 3.

Explanation:
I circled the number 3 as it is the difference between 7 and 4.

Question 4.

Explanation:
There are 10 counters in the above question.SO, i circled 10.

Question 5.

Explanation:
There are 5 red counters and 3 yellow counters.The addition equation of the above counters is 5+3=8.

Directions Have students: 1 draw a circle around the equation that shows addition; 2 draw a circle around the minus sign; 3 draw a circle around the difference; 4 draw a circle around the correct number of counters shown; count the red counters, 5 count the yellow counters, and then write the equation to find the sum.

Pick a Project

A

B

C

Directions Say: You will choose one of these projects. Look at picture A. Think about this question: Can you count all these gum balls? If you choose Project A, you will play a counting game to 20. Look at picture B. Think about this question: What is your favorite sport? If you choose Project B, you will tell a sports story using numbers. Look a picture C. Think about this question: What kinds of fish make good pets? If you choose this project, you will make a model of a fish tank.

Math Modeling

Fresh From the Farm

3-Act Math Preview

Directions Read the robot’s speech bubble to students. Generate Interest Ask students what vegetables they enjoy most. Say: What vegetables might be used to make a salad? What vegetable do you like? Have your class decide which vegetables they would buy for a salad.

### Lesson 9.1 Count, Read, and Write 11 and 12

Solve & Share

Explanation:
There are 12 toy cars with Carlos.I put counters in 10 frame to show the number of counters.
Directions Say: Carlos has a collection of toy cars. How can Carlos show the number of cars he has? Use counters and put them together in two different ways so they can be counted easily. Draw your counters to show one of your ways.

Visual Learning Bridge

Guided Practice

Question 1.

Explanation:
I practiced writing the number 11.

Question 2.

Explanation:
I practiced writing the number 12.

Directions 1 and 2 Have students count the cars in each group, and then practice writing the number that tells how many.

Question 3.

Explanation:
I counted the number of toys, there are 11 toys.So, I drew counters for the number 11 and practiced it.

Question 4.

Explanation:
I counted the number of toys, there are 12 toys.So, I drew counters for the number 12 and practiced it.

Question 5.

Explanation:
I counted the number of toys, there are 12 toys.So, I drew counters for the number 12 and practiced it.

Question 6.

Explanation:
I counted the number of toys, there are 11 toys.So, I drew counters for the number 11.Then i wrote the number that comes after 11 that is 12.

Directions 3-5 Have students count the toys in each group, use counters to show how many, and then practice writing the number that tells how many. 6 Number Sense Have students count the train cars, write the number to tell how many, and then write the number that comes after it.

Independent Practice

Question 7.

Explanation:
I drew counters for the number 12 using ten frames.

Question 8.

Explanation:
I drew counters for the number 11 using ten frames.

Question 9.

Explanation:
There are 12 toys in the above question.So, i practiced writing the number 12.

Question 10.

Explanation:
I drew 11 toy cars and practiced writing the number 11.

Directions 7-8 Have students use counters to make the number and draw circles to show how many. 9 Have students count the toys, and then practice writing the number that tells how many. 10 Higher Order Thinking Have students draw 11 toys, and then practice writing the number that tells how many.

### Lesson 9.2 Count, Read, and Write 13 m, and 15

Solve & Share

Explanation:
Carlos collected leaves, There are 14  leaves.SO, i drew counters in tenframes for the number 14.

Directions Say: Carlos collected leaves to put in a scrapbook. How can Carlos show the number of leaves he collected? Use counters, and then draw them to show one way.

Visual Learning Bridge

Guided Practice

Question 1.

Explanation:
I practiced writing the number 13.

Question 2.

Explanation:
I practiced writing the number 14.

Directions 1 and 2 Have students count the leaves in each group, and then practice writing the number that tells how many.

Question 3.

Explanation:
There are 15 leaves in the above picture, I drew counters for number 15 in ten frames.
I practiced writing the number 15.

Question 4.

Explanation:
There are 15 leaves in the above picture, I drew counters for number 15 in ten frames.
I practiced writing the number 15.

Question 5.

Explanation:
There are 14 leaves in the above picture.
I practiced writing the number 14.

Question 6.

Explanation:
There are 13 leaves in the above picture, I practiced writing the number 13.

Directions 3-4 Have students count the leaves in each group, use counters to show how many, and then practice writing the number that tells how many. 5 Have students count the leaves, and then practice writing the number that tells how many. 6 envision STEM Say: Trees use their leaves to turn sunlight into food. Have students count the green leaves, and then practice writing the number that tells how many.

Independent Practice

Question 7.

Explanation:
There are 14 leaves in the above picture, I practiced writing the number 14.

Question 8.

Explanation:
I drew counters for the number 13 using ten frame.

Question 9.

Explanation:
I drew counters for the number 15 using ten frame.

Question 10.

Explanation:
I drew 14 leaves in a ten frame and practiced writing the number 14.

Directions 7 Have students count the leaves, and then practice writing the number that tells how many. 8-9 Have students use counters to make the number and use a ten-frame or draw circles to show how many. 10 Higher Order Thinking Have students draw 14 leaves, and then practice writing the number that tells how many.

### Lesson 9.3 Count, Read, and Write 16 and 17

Solve & Share

Directions Say: Jada has a collection of piggy banks. She displays her piggy banks in 2 rows, as shown on the page. Count the piggy banks and use red cubes to show how many in all. Then use blue cubes to show another way to display the same number of piggy banks. Draw the cubes to show your answer.

Visual Learning Bridge

Guided Practice

Question 1.

Question 2.

Directions 1 and 2 Have students count the piggy banks in each group, use cubes to show how many, and then practice writing the number that tells how many.

Question 3.

Question 4.

Question 5.

Directions 3-5 Have students count the stuffed animals in each group, use cubes to show how many, and then practice writing the number that tells how many.

Independent Practice

Question 6.

Question 7.

Question 8.

Question 9.

Directions 6-7 Have students count the stuffed animals in each group, and then practice writing the number that tells how many, 8 Have students use counters to make the number and use ten-frames or draw circles to show how many. 9 Higher Order Thinking Have students draw 17 balls, and then practice writing the number that tells how many.

### Lesson 9.4 Count, Read, and Write 18, 19, and 20

Solve & Share

Explanation:
I used the above given counters and drew the bird stickers in the frame.
There are 18 bird stickers with carlos.

Directions Say: Carlos has a collection of bird stickers in his sticker album. How can Carlos show the number of bird stickers he has? Use counters, and then draw them to show one way.

Visual Learning Bridge

Guided Practice

Question 1.

Explanation:
I practiced writing the number 19.

Question 2.

Explanation:
I practiced writing the number 20.

Directions 1 and 2 Have students count the counters showing how many red and blue bird stickers Carlos has in his collection, and then practice writing the number.

Question 3.

Explanation:
I practiced writing the number 18.

Question 4.

Explanation:
I drew counters for the number 19 in the ten frames.

Question 5.

Explanation:
I drew counters for the number 20 in the ten frames.

Question 6.

Explanation:
I counted the above given stickers, there are 18 stickers.So, i practiced writing number 18.

Directions 3 Have students count the counters showing how many yellow bird stickers Carlos has in his collection, and then practice writing the number. 4-5 Have students use counters to make each number and draw counters in the ten-frames to show how many. 6 Have students count the stickers, and then practice writing the number that tells how many.

Independent Practice

Question 7.

Explanation:
I counted the above given stickers, there are 20 stickers.So, i practiced writing number 20.

Question 8.

Explanation:
I counted the above given stickers, there are 18 stickers.So, i practiced writing number 18.

Question 9.

Explanation:
I drew counters in ten frames for the number 19.

Question 10.

Explanation:
I drew 20 bug stickers and practiced writing the number 20.

Directions 7 and 8 Have students count the stickers in each group, and then practice writing the number that tells how many. 9 Have students use counters to make the number and draw circles to show how many. 10 Higher Order Thinking Have students draw 20 bug stickers, and then practice writing the number that tells how many.

### Lesson 9.5 Count Forward from Any Number to 20

Solve & Share

Explanation:
I drew 12 counters on the double ten frame, I put one more counter and wrote the number 13, and I put 1 more counter and wrote the number 14.The numers get larger as i count.

Directions Say: Put 12 counters on the double ten-frame. Write the number to tell how many. Put I more counter on the double ten-frame, and then write the number. Repeat using I more counter. What do you notice about the numbers? Do they get larger or smaller as you count?

Visual Learning Bridge

Guided Practice

Question 1.

Explanation:
I Counted forward by 1s from the blue number 15 to the stop sign 20.I wrote the number i counted, they are 15, 16, 17, 18, 19, 20.

Directions 1 Have students find the blue number on the number chart, count forward until they reach the stop sign, and then write each number they counted.

Question 2.

Explanation:
I Counted forward by 1s from the blue number 3 to the stop sign 8.I wrote the number i counted, they are 3, 4, 5, 6, 7, 8.

Question 3.

Explanation:
I Counted forward by 1s from the blue number 11 to the stop sign 16.I wrote the number i counted, they are 11, 12, 13, 14, 15, 16.

Question 4.

Explanation:
I Counted forward by 1s from the blue number 13 to the stop sign 18.I wrote the number i counted, they are 13, 14, 15, 16, 17, 18.

Directions 2-4 Have students find the blue number on the number chart, count forward until they reach the stop sign, and then write each number they counted.

Independent Practice

Question 5.

Explanation:
I Counted forward by 1s from the blue number 7 to the stop sign 12.I wrote the number i counted, they are 7, 8, 9, 10, 11, 12.

Question 6.

Explanation:
I Counted forward by 1s from the blue number 10 to the stop sign 15.I wrote the number i counted, they are 10, 11, 12, 13, 14, 14.

Question 7.

Explanation:
I Counted forward by 1s from the blue number 25 to the stop sign 17.I wrote the number i counted, they are 12, 13, 14, 15, 16, 17.

Question 8.

Explanation:
I choosed a number 10 from number chart.I Counted forward by 1s from the number 10 to the stop sign 15.I wrote the number i counted, they are 10, 11, 12, 13, 14, 15.

Directions 5-7 Have students start at the blue number and count forward, and then write each number they counted. Have students use the number chart at the top of the page, if needed, 8 Higher Order Thinking Have students pick a number between 1 and 15, and write it on the first line. Have them count forward, and then write each number they counted.

### Lesson 9.6 Count to Find How Many

Solve & Share

Explanation:
I drew counters to show the number of cherries Dainel and Jada has.I drew 13 and 11 strawberries below their ten frames.I can tell my drawings are correct by counting them by 1s.

Directions Say: Daniel has 13 cherries on a tray. Jada has 11 cherries on a tray. How can you show this? Use counters to show the cherries on the trays, and then draw the pictures. How can you tell that your drawings are correct?

Visual Learning Bridge

Guided Practice

Question 1.

Explanation:
I counted upon by 1s the number of strawberries in both the trays and circled the tray that  has 6 strawberries in it.

Question 2.

Explanation:
I counted upon by 1s the number of strawberries in both the trays and circled the tray that  has 9 strawberries in it.

Directions Have students count to find how many. Then: 1 draw a circle around the tray with 6 strawberries; 2 draw a circle around the tray with 9 strawberries.

Question 3.

Explanation:
I counted upon by 1s the number of strawberries in both the trays and circled the tray that  has 18 strawberries in it.

Question 4.

Explanation:
I counted upon by 1s the number of bugs in all the sets and circled the set that has 15 bugs.

Question 5.

Explanation:
I counted upon by 1s and circled the sets of bananas that has 4 bananas in it.

Question 6.

Explanation:
I counted the bugs by 1s, there are 12 bugs in the group and i drew 8 more bugs in another group so that their will be 20 bugs in all.

Directions Have students count to find how many. Then: 3 draw a circle around the tray with 18 strawberries; 4 draw a circle around the groups with 15 bugs; 5 draw a circle around the groups with 4 bananas. 6 Algebra Have students count the bugs in the group, and then draw another group of bugs so that there are 20 bugs in all.

Independent Practice

Question 7.

Explanation:
I counted by 1s and circled the tray of oranges that has 6 oranges in it.

Question 8.

Explanation:
I counted by 1s and circled the flower that has 8 petals in it.

Question 9.

Explanation:
I counted the number of stars in each flag and circled that flags which has 10 stars in them.

Question 10.

Explanation:
I drew 19 strawberries in the above trays in 2 ways that is in ten frame way and random way.

Directions Have students count to find how many. Then 7 draw a circle around the tray with 6 oranges; 8 draw a circle around the flower with 8 petals; 9 draw a circle around the flags with 10 stars. 10 Higher Order Thinking Have students draw 19 strawberries in two different ways.

### Lesson 9.7 Reasoning

Problem Solving

Solve & Share

Explanation:
I counted the number of spaces in the carton by 1s and i found that there are 12 spaces to put eggs in them.Therefore I circled the number 12.

Directions Say: Carlos wants to put some or all of the eggs in the carton. Draw a circle around all the numbers that tell how many eggs he could put in the carton. Explain why there could be more than one answer.

Visual Learning Bridge

Guided Practice

Question 1.

Explanation:
I counted the number of cows, there are 9 cows outside the barn in the farm.If there are 1 or more cows inside the barn then their will be either 10, 11 or 12 cows in all.

Directions 1 Say: There are more than 8 cows on a farm. Some cows are outside the barn. 1 or more cows are inside the barn. Count the cows that are outside of the barn, and then draw a circle around the numbers that tell how many cows there could be in all.

Independent Practice

Question 2.

Explanation:
I counted the number of horses, there are 13 horses outside the stable.If there are 0, 1, or 2 horses are inside the stable.Then their could be 13, 14 or 15 horses in all.So, i circled the numbers 13, 14 and 15.

Question 3.

Explanation:
I counted the number of dogs, there are 17 dogs playing in the park.If 1 or 2 dogs rest at the dog house then their could be 18 or 19 dogs in all.So, i circled 18 and 19.

Question 4.

Explantion:
I counted the numbe rof fishes in the tank, there are 10 fishes in the tank.If the fish tank can hold 15 fishes then i can add 5 more fishes to the tank.So, I circled the number 5.

Directions Say: 2 There is 1 more than 12 horses outside the stable. 0, 1, or 2 horses are inside the stable. Draw a circle around the number of horses outside the stable, and then draw a circle around the numbers that tell how many horses there could be in all. 3 There is 1 more than 16 dogs playing in the park. 1 or 2 dogs are resting in a doghouse. Draw a circle around the numbers that tell how many dogs there could be in all. 4 The fish tank can hold up to 15 fish. Count the fish in the tank, and then draw a circle around the numbers that tell how many more fish could fit in the tank.

Problem Solving

Directions Read the problem to students. Then have them use multiple problem-solving methods to solve the problem. Say: Alex lives on a farm with so many cats that they are hard to count. Sometimes the cats are outside and sometimes they hide in the shed. Alex knows that the number of cats is greater than 11. There are less than 15 cats on the farm. How can Alex find out the number of cats that could be on his farm? 5 Reasoning What numbers do you know from the problem? Mark an X on the numbers that do NOT fit the clues. Draw a circle around the numbers that tell the number of cats that could be on the farm. 6 Model How can you show a word problem using pictures? Draw a picture of the cats on Alex’s farm. Remember that some may hide inside the shed. 7 Explain Is your drawing complete? Tell a friend how your drawing shows the number of cats on Alex’s farm.

### Topic 9 Fluency Practice

Question 1.

Explanation:
I colored the boxes that has the sum or difference that is equal to 4.

Question 2.

Explanation:
In the above question i could see the letter “F” after coloring the boxes that has the sum or difference equal to 4.

Directions Have students: 1 color each box that has a sum or difference that is equal to 4; 2 write the letter they see.

Topic 9 Vocabulary Review

Question 1.

Explanation:
I read the number above and circled the number 16.

Question 2.

Explanation:
I read the number above and circled the number 12.

Question 3.

Explanation:
I wrote the number 18(eighteen).

Question 4.

Explanation:
I drew 11 counters using ten frames an dwrote the number 11.

Question 5.

Explanation:
I counted 14 cubles and then circled them.

Question 6.

Explanation:
I wrote the number 12(Twelve).

Directions Understand Vocabulary Have students: 1 draw a circle around the number sixteen; 2 draw a circle around the number twelve; 3 write the number eighteen; 4 draw eleven counters in the box, and then write the number; 5 draw a circle around fourteen cubes; 6 write the number twenty.

### Topic 9 Reteaching

Set A

Question 1.

Explanation:
I counted the number of stars, there are 17 stars.So, I wrote the number 17 in the blank.

Question 2.

Explanation:
I counted the number of suns, there are 18 suns.So, I wrote the number 18 in the blank.

Set B

Question 3.

Explanation:
I found the blue number 9 on the number chart, counted forward until I reach the stop sign 11.I counted the number 9, 10, 11.So, I wrote the numbers 10 and 11 in the blanks.

Directions Have students: 1 and 2 count the objects in each group, and then write the number to tell how many; 3 find the blue number on the number chart, count forward until they reach the stop sign, and then write each number they counted.

Set C

Question 4.

Explanation:
I counted the number of bugs and I circled the group that contains 15 bugs.

Set D

Question 5.

Explanation:
I counted the number of bunnies.There are 10 bunnies resting in the grass.If there are 2 or 3 bunnies playing behind the bush then their will be 12 or 13 bunnies in all.

Directions Have students: 4 draw a circle around the group with 15 bugs; 5 listen to the story and use reasoning to find the answer. Some bunnies are resting in the grass. 2 or 3 bunnies are playing behind the bush. Count the bunnies in the grass, and then draw a circle around the numbers that show how many bunnies there could be in all.

Question 1.

Explanation:
I counted the numbe rof birds, there are 16 birds in the question.So, I circled Option.D 16.

Question 2.

Explanation:
I counted the number of objects, there are 11 objects in option.C. So, I circled it.
Option.C shows 11.

Question 3.

Explanation:
I counted the number of bees,there are 14 bees outside the beehive.If there are 1 or more bees inside the beehive then their would be 15, 16 or 17 bees in all.

Directions Have students mark the best answer. 1 Which number tells how many? 2 Which shows 11 ? 3 Have students listen to the story, and then mark all the possible answers. There are some bees outside of the beehive. 1 or more bees are inside the beehive. Count the bees outside of the beehive, and then mark three numbers that tell how many bees there could be in all.

Question 4.

Explanation:
I counted the number of leaves, there are 12 leaves.So, i wrote 12 in the blank.

Question 5.

Explanation:
I counted the bugs.I circled that group of bugs that have 15 bugs in the group.

Question 6.

Explanation:
I drew 18 marbles and wrote the number 18 in the blank.

Question 7.

Explanation:
I found the blue number 16 on the number chart, counted forward until I reach the stop sign 16.I counted the number 16, 17, 18.So, I wrote the numbers 17 and 18 in the blanks.

Directions Have students: 4 count the leaves, and then write the number to tell how many; 5 draw a circle around the group that shows 15 ladybugs; 6 draw eighteen marbles, and then write the number to tell how many; 7 find the blue number on the number chart, count forward until they reach the stop sign, and then write each number they counted.

Question 1.

Explanation:
I counted the numbe rof heart shapes in the above image, there are 15 heart shapes.So, i wrote the number 15 in the blank.

Question 2.

Explanation:
I counted the number of smilee faces in the above image, there are 15 smilee faces.So, i wrote the number 17 in the blank.

Directions Sadie’s Stickers Say: Sadie puts many stickers in her notebook. How many of each type of sticker is there? Have students: 1 count the number of heart stickers, and then write the number to tell how many; 2 count the number of smiley face stickers, and then write the number to tell how many.

Question 3.

Explanation:
I circled the group of stickers that Sadie should use to decorate a picture frame and i drew the stickers in different way in the box beside.

Question 4.

Explanation:
Sadie gets a sticker for feeding her dog every day. She has fed her dog for 10 days.Sadie have in 2 more days two more stickers.Count forward by 1s from 10 for 2times, one after 10 is 11 and one after 11 is 12.So, i wrote 11, 12 in the blanks.

Question 5.

Explanation:
Sadie puts 18 stickers on the front of a card. She puts 1 or more stickers on the back of a card.
Count forward by 1s from 18 for 2times, one after 18 is 19 and one after 19 is 20.So, i circled 19 and 20.

Directions 3 Say: Sadie wants to use Ih stickers to decorate a picture frame. Have students draw a circle around the group of stickers that she should use, and then draw a different way to show 14 stickers. 4 Say: Sadie gets a sticker for feeding her dog every day. She has fed her dog for 10 days. How many stickers will Sadie have in 2 more days? Have students count forward by 2 more days to find the answer, and then write each number they counted. 5 Say: Sadie puts 18 stickers on the front of a card. She puts 1 or more stickers on the back of a card. Have students draw a circle around the numbers that show how many stickers there could be in all. Have students explain their answer.

## Envision Math Common Core Grade K Answers Key Topic 11 Count Numbers to 100

Essential Question
How can numbers to 100 be counted using a hundred chart?

enVision’STEM Project: Ant Colonies
Directions Read the character speech bubbles to students. Find Out! Have students find out how ants live and work together in colonies. Say: Talk to friends and relatives about ant colonies. Ask about the different jobs ants in a colony might have that help them survive. Journal: Make a Poster Have students make a poster. Have them draw an ant colony with 5 groups of ants. There should be 10 ants in each group. Then have them count by tens to find how many ants there are in all. Hove students use a hundred chart to practice counting by tens to 50.

Review what You Know

Question 1.

Explanation:
I drew a circle around the number ninteen.

Question 2.

Explanation:
I circled 10+6 as 10+6=16
I drew a circle around the addition expression that makes 16.

Question 3.

Explanation:
I circled 10+8 as 10+8=18
I drew a circle around the addition expression that makes 18.

Question 4.

Explanation:
There are 7 objects in the first set and 6 objects in the second set.So, the wrote the numbers 7, 6 in the blanks and i circled 7 as it is greater than 6.

Question 5.

Explanation:
There are 5 objects in the first set and 8 objects in the second set.So, the wrote the numbers 5, 8 in the blanks and i circled  as it is greater than 5.

Question 6.

Explanation:
There are 4 objects in the first set and 10 objects in the second set.So, the wrote the numbers 4, 10 in the blanks and i circled 10 as it is greater than 4.

Directions Have students: 1 draw a circle around the number nineteen; 2 draw a circle around the addition expression that makes 16; 3 draw a circle around the addition expression that makes 18; 4-6 count each set of objects, write the numbers to tell how many, and then draw a circle around the number that is greater than the other number.

Pick a project

A

B

C

Directions Say: You will choose one of these projects. Look at picture A. Think about this question. What if you had more than two legs? If you choose Project A, you will make o model of a centipede. Look at picture B. Think about this question: Is there any math in dancing? If you choose Project B, you wilt create a numbers dance. Look at picture C. Think about this question: Where can you find a moonstone? If you choose Project C, you wilt collect and count treasures.

3-ACT MATH PREVIEW

Math Modeling

Stack Up

Directions Read the robot’s speech bubble to students. Generate Interest Ask students about their experience stacking blocks. Say: What’s the tallest block tower you have built? How many blocks was it? Give students a chance to practice building block towers and observe how many blocks tall they are.

### Lesson 11.1 Count Using Patterns to 30

Directions Say: Count forward from 1 to 30. Count aloud and point to each number as you say it. What patterns do you see or hear when you count to 30 using the numbers on the chart? Color the boxes that show a pattern you find

Visual Learning Bridge

Guided Practice

Explanation:
I counted forward from 1 to 10, circled the number in the top row and the part of the number in the bottom row that sound alike: twenty-ONE‘ twenty-TWO, twenty-THREE, twenty-FOUR twenty-FIVE, twenty-SIX.

Directions Have students: 1 count forward from 1 to 10. Count aloud and point to each number as it is said. Have them listen to the following numbers in the bottom row, and then draw a circle around the number in the top row and the part of the number in the bottom row that sound alike: twenty-ONE‘ twenty-TWO, twenty-THREE, twenty-FOUR twenty-FIVE, twenty-SIX. 2 listen to the pattern, and then use crayons to color the numbers that they hear: 16, 17, 18, 19.

Explanation:
I colored the numbers that i heard they are 16, 17, 18, 19.
I can see and hear the pattern of counting by ones.

Explanation:
3) I colored the numbers that i heard they are 1, 2, 3, 4, 5.
4) I colored the numbers that i heard they are 25, 26, 27, 28.
I can see and hear the pattern of counting by ones.

Explanation:
5) I colored the numbers that i heard they are 4, 14, 24.
6) I colored the numbers that i heard they are 16, 17, 18, 19.
I can see and hear the pattern of counting by ones and by tens.

Directions Have students listen to the count, color the numbers they hear, and then tell what pattern they see or hear: 3 1, 2, 3, 4, 5; 4 25, 26, 27, 28; 5 4, 14, 24; 6 16, 17, 18, 19.

Independent Practice

Explanation:
7) I colored the numbers that i heard they are 7, 17, 27.
8) I colored the numbers that i heard they are 21, 22, 23, 24, 25.
I can see and hear the pattern of counting by ones and tens.

Explanation:
I colored the numbers that i heard they are 13, 14, 15, 16, 17, 18 and circled the next number in the pattern that is 19.
I can see and hear the pattern of counting by ones.

Directions Have students listen to the count, color the numbers they hear, and then tell what pattern they see or hear: 7 7, 17, 27; 8 21,22, 23, 24, 25. 9 Higher Order Thinking Have students listen to the count, color the numbers they hear, and then tell what pattern they hear: 13, 14, 15, 16, 17, 18. Then have them draw a circle around the next number in the pattern.

### Lesson 11.2 Count by Ones and by Tens to 50

Solve & Share

Directions Say : Work with a partner. Count forward from 1 to 50. One partner points to each number in the first row while the other partner counts aloud each number. Change jobs for every row. Watch students go through all 5 rows. Say: Now, one partner will cover some numbers on the board using counters. The other partner will name the hidden numbers. Play 3 times, and then color the numbers that are the hardest to remember.

Visual Learning Bridge

Guided Practice

Explanation:
I counted the numbers in the middle row beginning with 31 and ending with 39, and drew a circle around the part of the number that sounds the same that is 3tens(thirty)
I read the numbers in the first column and drew a circle around the number 1(ones)  that i hear in each number.

Directions Have students: 1 count aloud the numbers in the top row and point to each number as it is said. Then have them count aloud the numbers in the middle row beginning with 31 and ending with 39, and draw a circle around the part of the number that sounds the same; 2 read the numbers in the first column. Draw a circle around the number that you hear in each number.

Explanation:
3)I found green number 20 and started counting up till 30 and colored the numbers green that has twenty as part of the number.
4)I found the red number 39 and started counting up till 49 and colored the numbers red.
5)I found the yellow number 33 amd started counting up till the next red number, colored the numbers yellow.
6)I found the blue number 20 and drew a circle around the parts of the numbers in the column that are the same.
7)I used counters to cover 3 numbers on the chart they are 14, 15, 16.

Directions Have students: 3 find the green number on the chart, and then begin counting forward by ones up to 30. Say: Color green all the numbers that have “twenty” as part of the number, 4 Find the red number and begin counting forward by ones and stop when they get to 49. Say: Color red all the numbers you counted; 5 find the yellow number. Then have them count forward by ones until they get to the red number. Say: What numbers did you count? Color them yellow, 6 find the blue number. Then draw a circle around the parts of the numbers in the column that are the same; 7 use counters to cover 3 numbers on the chart. Say: Show your chart to a friend, and ask them to tell you which numbers are hiding.

Independent Practice

Explanation:
8)I started counting stars around the first circle at the arrow, crossed the number 10, counted all stars around all the circles and marked the last number of stars after each circle, they are 20, 30, 40, 50.
9)I colored the number 14 and colored 14 numbe rof stars in the below.

Directions 8 Have students begin counting stars around the first circle at the arrow, and continue clockwise around the circle until they have counted all the stars. Say: When you finish counting one circle, cross off the last number you said in your count on the chart. Have students continue counting the stars around the circles, crossing off the last number they said in each circle, until they reach the end of the stars. 9 Higher Order Thinking Say: Color one number in the chart. Now count that same number of stars below. Color each star to show how many you counted.

### Lesson 11.3 Count by Tens to 100

Solve & Share

Directions Say: Color all the boxes of the numbers that have a zero as you count them aloud. Tell how you know which numbers to count. Count forward by tens beginning at 30 and going to 100. Point to the numbers as you count them aloud to a partner. Now begin at 60. Count forward by tens to 100. Mark each number with an X as you say it to your partner.

Visual Learning Bridge

Guided Practice

Question 1.

Explanation:
I circled 30.
I drew a circle around the decade number that comes before 40 but after 20 that is 30.

Question 2.

Explanation:
I circled 70.
I circled the decade number that is missing from this pattern: 60, 80, 90, 100 that is 70.

Directions Have students: 1 draw a circle around the decade number that comes before 40 but after 20; 2 circle the decade number that is missing from this pattern: 60, 80, 90, 100.

Question 3.

Explanation:
I circled 40, 60, 80, 90.
I circled the missing numbers in the following pattern: ten, twenty, thirty, ___, fifty, __ seventy, ____, ___, one hundred they are 40, 60, 80, 90.

Question 4.

Explanation:
I counted by tens, there are 30 cubes in the above image.
I circled 30.

Question 5.

Explanation:
I counted by tens, there are 70 cubes in the above image.
I circled 70.

Question 6.

Explanation:
I counted by tens, there are 80 cubes in the above image.
I circled 80.

Directions Have students: 3 draw a circle around the missing numbers in the following pattern: ten, twenty, thirty, ___, fifty, __ seventy, ____, ___, one hundred; 4-6 count the cubes by tens, and then draw a circle around the number that tells how many.

Independent Practice

Question 7.

Explanation:
I counted by tens, there are 60 cubes in the above image.
I circled 60.

Question 8.

Explanation:
I counted by tens, there are 100 cubes in the above image.
I circled 100.

Question 9.

Explanation:
If i start counting forward by tens from 40, the next tens are 50, 60, 70, 80, 90 and 100.
Therefore i circled the numbers by tens from 40 to 100.

Question 10.

Explanation:
There are 10 decade numbers in the number chart.They are 10, 20, 30, 40, 50, 60, 70, 80, 90 and 100.

Directions 7-8 Have students count the cubes, and then draw a circle around the number that tells how many. 9 Say: If you start with 40, how would you count to 100 by tens? Circle the numbers you count. 10 Higher Order Thinking Have students look at the hundred chart and read the decade numbers. Say: How many decade numbers are there in the chart? Write the number.

### Lesson 11.14 Count by Ones to 100

Solve & Share

Directions Say: Count forward from the yellow number. Stop at the red number. Tell how many numbers you counted aloud. Color the boxes of the numbers you counted aloud to show your work. Have students repeat the same steps for the blue to green sequence of squares, and for the orange to purple sequence of squares.

Visual Learning Bridge

Guided practice

Question 1.

Explanation:
I colored the boxes of the numbers, starting at the yellow box 42 and ending at the red box 60.

Question 2.

Explanation:
I colored the boxes of the numbers, starting at the yellow box 7 and ending at the red box 22.

Directions 1 and 2 Have students color the boxes of the numbers as they count aloud, starting at the yellow box and ending at the red box.

Question 3.

Explanation:
I colored the boxes of the numbers, starting at the yellow box 34 and ending at the red box 55.

Question 4.

Explanation:
I colored the boxes of the numbers, starting at the yellow box 79 and ending at the red box 100.

Question 5.

Explanation:
I colored the boxes of the numbers, starting at the yellow box 1 and ending at the red box 28.

Question 6.

Explanation:
I colored the boxes of the numbers, starting at the yellow box 56 and ending at the red box 76.

Directions 3-6 Have students color the boxes of the numbers as they count aloud, starting at the yellow box and ending at the red box.

Question 7.

Explanation:
I colored the boxes of the numbers, starting at the yellow box 12 and ending at the red box 33.

Question 8.

Explanation:
I colored the boxes of the numbers, starting at the yellow box 63 and ending at the red box 85.

Question 9.

Explanation:
I colored the boxes of the numbers, starting at the yellow box 47 and ending at the red box 64.

Question 10.

Explanation:
I colored the box of the missing number: 79, 80, 81,83, 84, 85, 86, 87, 88 that is 82.
I circled the numbers in the chart that are I more and I less than the missing number they are 81 and 83.

Directions 7-9 Have students color the boxes of the numbers as they count aloud, starting at the yellow box and ending at the red box. 10 Higher Order Thinking Have students listen to the count, and then color the box of the missing number: 79, 80, 81,83, 8*4, 85, 86, 87, 88. Say: Circle the numbers in the chart that are I more and I less than the missing number.

### Lesson 11.5 Look For and Use Structure

Problem Sharing

Solve & Share

Directions Say: Carlos looks at the chart. He knows 21 comes just after 20. Draw a circle around the numbers that come just after each decade number. How do you know you are correct? What patterns do you see?

Visual Learning Bridge

Guided Practice

Question 1.

Explanation:
I circled the numbers that i counted from 7 to 9.They are 7, 8 , 9.

Question 2.

Explanation:
I circled the numbers that i counted by tens from 10 to 30, they are 10, 20, 30.

Directions Have students 1 count forward by ones, beginning at 7 and going to 9. Have them circle the counted numbers. Then 2 count forward by tens, beginning at 10 and going to 30. Have them circle the counted numbers.

Independent Practice

Question 3.

Explanation:
The numbers that come after 65 if we count by 1s are 66, 67, 68
I circled the set of numbers 66, 67, 68 as they are the missing numers in the above number chart.

Question 4.

Explanation:
The numbers that come before 44 if we count by 1s are 41, 42, 43.
I circled the set of numbers 41, 42, 43 as they are the missing numers in the above number chart.

Question 5.

Explanation:
The numbers that come after 39 if we count by 10s are 40, 50, 60.
I circled the set of numbers 40, 50, 60 as they are the missing numers in the above number chart.

Question 6.

Explanation:
The numbers that come after 29 if we count by 1s are 30, 31, 32
I circled the set of numbers 30, 31, 32 as they are the missing numers in the above number chart.

Directions 3-6 Have students count forward, and then draw a circle around the row that shows the missing set of numbers.

Problem Solving

Explanation:
7)I counted up 18 squares, Used yellow crayon to make a path to show how i counted, and then i drew a circle around the number 25 where i ended.
8)If i counted by ones the would say 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25.
9)If i start counting at 10 and count up 17 squares, i would land on the number 27.No, there is no different way to count other than counting by 1s or 10s.

Directions Read the problem aloud. Then have students use multiple problem-solving methods to solve the problem. Say: Start at 7 and count up 18 squares in any way you choose. Use your yellow crayon to make a path to show how you counted, and then draw a circle around the number where you ended. 7 Be Precise How many tens are in 18? 8 Use Structure What numbers would you say if you only counted by ones? 9 Generalize Start at 10 and count up 17 squares. On what number did you land? Would there be a different way to count that would solve the problem?

### Topic 11 Fluency Practice Activity

Question 1.

Explanation:
2+2=4=3+1=B
3-1=2=4-2=I
4+1=5=2+3=G
By solving the addition and subraction statements i found the word BIG with the clues given.

Question 2.

Explanation:
5-5=0=3-3=C
4-3=1=5-4=A
0+3=3=1+2=T
By solving the addition and subraction statements i found the word CAT with the clues given.

Directions 1 and 2 Have students find a partner. Have them point to a clue in the top row, and then solve the addition or subtraction problem in the clue. Then have them look at the clues in the bottom row to find a match, and then write the clue letter above the match. Have students find a match for every clue.

Topic 11 Vocabulary Review

Explanation:
1)I drew a circle around the part of the number in the orange column that is 3 ones
2)I drew a circle around the part of the number in the blue column that shows the pattern of 8 ones
3)I colored the decade numbers red.

Directions Understand Vocabulary Have students: 1 draw a circle around the part of the number in the orange column that is 3 ones. 2 draw a circle around the part of the number in the blue column that shows the pattern of 8 ones; 3 color the decade numbers red.

### Topic 11 Reteaching

Set A

Question 1.

Explanation:
I drew a circle around the numbers in the top row and the part of the number in the bottom row that sound the same.

Set B

Question 2.

Explanation:
I counted by 10s, there are 80 cubes in the above image.
So, I circled 80.

Directions Have students: 1 count aloud the numbers in the top row. Then have them count aloud the numbers in the bottom row and draw a circle around the number in the top row and the part of the number in the bottom row that sound the same; 2 count by tens, and then draw a circle around the number that tells how many.

Set C

Question 3.

Explanation:
I colored the boxes of the numbers, starting at the yellow box 69 and ending at the red box 80.

Set D

Question 4.

Explanation:
I counted forward by 10s from 66, the next decades are 76, 86, 96.
So, i circled the set of missing numbers 76, 86, 96.

Directions Have students: 3 color the boxes of the numbers as they count aloud by ones, starting at the yellow box and ending at the red box; 4 count forward, and then draw a circle around the row that shows the missing set of numbers.

### Topic 11 Assessment Practice

Question 1.

Explanation:
I counted by 10s, there are 70 cubes in the above image.
So, I circled option(B) 70.

Question 2.

Explanation:
I counted by 1s, there are 58 beads in the above image.
So, I circled option(C) 58.

Question 3.

Explanation:
I counted by 10s, After 70, the numbers are 80, 90, 100.
So, I circled option(A) 80, 90, 100.

Directions Have students mark the best answer. 1 Which number tells how many cubes? 2 Count the beads by ones. Which number tells how many? 3 Which set of numbers shows the set of missing numbers in the number chart?

Question 4.

Explanation:
I number that is just before the yellow numbers is 22.So, i circled Option(A).

Question 5.

Explanation:
I started counting at 61 and drew a circle around the part of the number that sounds the same to show the pattern that is sixty, and then draw a circle around the column that has decade numbers 60, 70, 80, 90, 100.

Question 6.

Explanation:
I colored the boxes of the numbers, starting at the yellow box 77 and ending at the red box 94.

Question 7.

Explanation:
I counted by ones to write the missing numbers in the top row they are 16, 20, and then drew a circle around each of the missing numbers in the remaining rows they are 22, 30, 33, 39, 40, 41, 47, 48, 55, 56.

Directions Have students: 4 look at the numbers that are shaded yellow and choose the number that is counted just before the first yellow number. 5 look at the row beginning with 61. Count each number aloud. Have them draw a circle around the part of the number that sounds the same to show the pattern, and then draw a circle around the column that has decade numbers; 6 color the boxes of the numbers as they count by ones, starting at the yellow box and ending at the red box, and then explain any patterns they might see or hear; 7 count by ones to write the missing numbers in the top row, and then draw a circle around each of the missing numbers in the remaining rows.

Question 1.

Explanation:
If we count by 1s the number that comes after 18 is 19.SO, i circled 19.
Therefore, the missing number that tells how many grapes Keisha has is 19.

Question 2.

Explanation:
I counted the almonds above by 10s, there are 50 almonds.
So, i circled 50.
Therefore, the number that tells how many almonds that Liam and his friends share for their snack is 50.

Directions School Snacks Say: It’s snack time for the Kindergarten class! 1 Say: Keisha puts a grape on the hundred chart to show how many grapes she has in her snack bag. Have students look at the numbers that come just before and just after the grape, and then at the numbers that are just above and just below it. Have them draw a circle around the missing number that tells how many grapes Keisha has. 2 Have students count the almonds that Liam and his friends share for their snack. Have them draw a circle around the number that tells how many. If needed, students can use the hundred chart to help.

Question 3.

Explanation:
I counted by 1s, there are 16 crackers.So, I coloreed the number 16.
If each friend has I cracker then the crackers left over are 16-10=6.So, i colored 6.

Explanation:
I started at 64 on the number chart and made a path to show how to count up 18 i colored the number boxes from 64 to 81 then i drew a circle around the number where i stopped that is 82.

Directions 3 Say: Chen brings crackers for snack time for his table of 10 friends. Look at the crackers he brings. Have students count the crackers and color that number on the number chart. Say: How many crackers are left over if each friend has I cracker? Color that number on the chart. How do you know you are right? 4 Say: Zoe counts the cherries that she gives to her friends. She puts cherries on the number chart for the last three numbers that she counts. Have students find the cherries in the chart. Then have them look at the numbers to the right of the chart, and then draw a circle around the set of missing numbers to show how Zoe counted the cherries. 5 Say: Ty has 64 raisins in one bag. He has 18 raisins in another bag. Help Ty count his raisins. Have students start at 64 on the number chart and make a path to show how to count up 18 in any way they choose. Then have them draw a circle around the number where they stopped, and then explain how they counted up.

## Envision Math Common Core Grade K Answers Key Topic 13 Analyze, Compare, and Create Shapes

Essential Question:
How can solid figures be named, described, compared, and composed?

enVision STEM Project: How Do Objects Move? Directions Read the character speech bubbles to students. Find Out! Have students observe and describe how objects move using the terms roll, stack, and slide. Say: Objects move in different ways. Talk to your friends and relatives about everyday objects that are cones, cylinders, spheres, or cubes. Ask them how each one moves and whether they roll, stack, or slide. Journal: Make a Poster Have students make a poster that shows everyday objects that are cones, cylinders, spheres, and cubes, and then tell how each one moves.
When a force pushes or pulls the object, the object will move in the direction of the force. Then the force can make things move, change shape or change their speed. Some forces are direct and happen when two things touch (like a foot kicking a ball)
Objects move in different ways. The motion of an object might be circular, curved, back-and-forth so on.
The object which has a curved surface that is all circular objects can roll.
Examples: Ball, lemon, orange, apple, football, etc.
The object which has a flat surface can slide.
Example: Rubber, laptop, duster, book, plate, etc.
POSTER:

Review What You Know

Directions Have students: 1 draw a circle around the triangie; 2 draw a circle around the shapes that are the same shape. 3 draw a circle around the circle; 4 – 6 draw a circle around the square;
Question 1.

Question 2.

Question 3.

Question 4.

Question 5.

Question 6.

Pick a Project

Directions Say: You will choose one of these projects. Look at picture A. Think about this question: Have you eaten any circles or squares lately? If you choose Project A, you will make a kitchen shops poster. Look at picture B. Think about this question: Do you enjoy puppet shows? If you choose Project B, you will create a puppet show. Look at picture C. Think about this question: How would you describe the shapes in this quilt? If you choose Project C, you will design a patchwork quilt.

Project : A
POSTER :

Project : B
puppets are loved by young children for different reasons at different times in their lives. “Puppets have enduring appeal. Children can express these emotions too without upsetting anyone. Their puppet character is the one to feel these emotions. Playing with the emotions of the puppets helps to develop the characteristics of sympathy and empathy too. Children also experience this kind of expression when engaging in symbolic play. So in play schools puppet shows plays a vital role.
Materials required to play puppet show.
Paper ,glue, scissors, cardboards, markers etc.,
Use your scraps to make eyebrows, and lips.
Cut out lots of pieces. You can create lots of characters.
Use other paper with different colors and patterns to make clothing for your puppet.
Once the preparation is done with desired characters suitable for the story, by using our fingers, strings or holding sticks puppet show can be shown to the students.
POSTER:

Project : C
Patch work quilt
The quilt consists of Triangle, Square and Circle all these are in one rectangular quilt
3-ACT MATH PREVIEW

Math Modeling
Pieced Together

Directions Read the robot’s speech bubble to students. Generate Interest Ask students about their experience with shapes. Say: Can you use smaller rectangles to make a Targer one? Can you use triangles to make a rectangle? Give students a chance to practice making shapes out of smaller shapes.
I can … model with math using 2-D shapes to solve a problem.

### Lesson 13.1 Analyze and Compare Two Dimensional (2-D) Shapes

Solve & Share
Directions Say: Emily wants to figure out which shapes are behind the door. The mystery shapes that are behind the door have only 4 vertices (corners). Use the shapes shown above the door to help you decide which shapes are behind the door. Draw the shapes that match the clue on the door. How many shapes did you draw? Write that number next to the door. Now mark an X on the shapes that are NOT behind the door. Count those shapes and write the number. Look at the two numbers you wrote. Circle the number that is greater than the other number. If the numbers are the same, circle both numbers. Name the shapes that are behind the door.

I can … analyze and compare 2-D shapes

Visual Learning Bridge

Guided Practice

Directions Have students listen to the clues, mark an X on the shapes that do NOT fit the clues, draw a circle around the shape that the clues describe, and then tell how the shapes they marked with an X are different from the shape they drew a circle around. 1 I have 4 sides. I do NOT have 4 sides that are the same length. What shape am I? 2 I do NOT have 4 sides. I do NOT have any vertices. What shape am I?
The shape which is marked with X is triangle as it has only 3 sides and 3 vertices.
The shape which is marked with circle is square and rectangle as they have 4 sides and 4 vertices.
The object with 4 sides is rectangle.
The object without 4 sides and vertices is circle.

Question 1.

Question 2.

Directions Have students listen to the clues, mark an X on the shapes that do NOT fit the clues, draw a circle around the shape that the clues describe, and then tell how the shapes they marked with an X are similar to the shape they drew a circle around. 3 Number Sense I am NOT round. I have less than 4 sides. What shape am I? 4 I am NOT a rectangle. I have o sides. What shape am I? 5 I have 4 vertices. I am a special kind of rectangle because all my sides are the same length. What shape am I?
The shape which is not round and less than 4 sides is triangle. So students can mark X

The shape which is not a rectangle and no sides is circle. So students can draw circle around the shape easily.

The shape with special kind of rectangle and 4 vertices of same length is square.

Question 3.

Question 4.

Question 5.

Independent Practice

Directions Have students listen to the clues, mark an X on the shapes that do NOT fit the clues, draw a circle around the shape that the clues describe, and then tell how the shapes they marked with an X are different from the shape they drew a circle around. 6 All of my sides are NOT the same length. I have 3 vertices. What shape am I? 7 I have 4 sides. I am the same shape as a classroom door. What shape am I? 8 Have students listen to the clues, and then draw the shape the clues describe: I have more than 3 sides. The number of vertices I have is less than 5. All of my sides are the same length. What shape am I? 9 Higher Order Thinking Have students draw a shape with 4 sides and 4 vertices that is NOT a square or rectangle, and then explain why it is not. 10 Higher Order Thinking Have students draw a circle around the rectangles. Have them color all the squares, and then explain how the shapes are both similar and different from one another.
Question 6.

The shape with 3 different sides and 3 vertices is triangle.

Question 7.

4 sides and same as the shape of class door is rectangle.

Question 8.
The shape which has more than 3 sides less than 5 vertices and all side sare of same length is square.

Question 9.
A shape with 4 sides and 4 vertices that is not a square or rectangle,

Question 10.

### Lesson 13.2 Analyze and Compare Three Dimensional (3-D) Shapes

Solve & Share
Directions Say: Jackson wants to find a solid figure. The solid figure has more than one flat side and it rolls. Color the solid figures that match the description. Then count them. How many are there? How many shapes do you see in all?

I can…. analyze and compare 3-D shapes.

Visual Learning Bridge

Guided Practice

Directions Have students: 1 look at the stacked solid figures on the left, and then draw a circle around the other solid figures that stack; 2 look at the rolling solid figure on the left, and then draw a circle around the other solid figures that roll.
Question 1.

Question 2.

Directions Have students: 3 look at the sliding solid figure on the left, and then draw a circle around the other solid figures that slide; 4 look at the stacked solid figures on the left, and then draw a circle around the other solid figures that can stack on top of the cubes; 5 draw a circle around the solid figure that rolls and stacks; 6 draw a circle around the solid figures that slide and roll; 7 draw a circle around the solid figures that stack and slide. 8 en Vision® STEM Have students draw a circle around the solid figure that does NOT stack or slide. Then ask them what would cause a sphere to roll.
Question 3.

Question 4.

Question 5.

Question 6.

Question 7.

Question 8.

Independent Practice

Directions Have students: 9 look at the rolling object on the left, and then draw a circle around the other objects that roll; 10 look at the sliding object on the left, and then draw a circle around the other objects that slide. 11 Higher Order Thinking Have students draw 2 solid figures that can stack on each other. 12 Higher Order Thinking Have students draw a circle around the cube, and then explain why the other solid is NOT a cube.
Question 9.

Question 10.

Question 11.

Question 12.

Explanation:
Blue color solid figure is Cube, all side are of equal lengths and height is of same length, Red color solid figure is NOT Cube, because of the sides are of NOT same lengths

### Lesson 13.3 Compare 2-D and 3-D Shapes

Solve & Share
Directions Say: Jackson needs to find a circle that is a flat surface of a solid figure. Which of these solids has a flat circle as part of the figure? Draw a circle around each solid figure that has a flat circle part. Mark an X on the solid figures that do NOT have a flat circle part. How many shapes in all are there on the page? How many shapes did you circle? Without counting, how many shapes have an X? Count the shapes with an X to check your answer.

I can… analyze and compare 2-D and 3-D shapes.

10 shapes in all are there on the page
5 shapes circled
5 shapes marked X

Visual Learning Bridge

Guided Practice

Directions Have students: 1 and 2 look at the shape on the left, and then draw a circle around the solid figures that have a flat surface with that shape.
Question 1.

Question 2.

Directions 3 Vocabulary Have students draw the flat surface of the solid figures that have circles around them. 4-6 Have students look at the shape on the left, and then draw a circle around the solid figures that have a flat surface with that shape.
Question 3.

Question 4.

Question 5.

Question 6.

Independent Practice

Directions Have students: 7 and 8 look at the shape on the left, and then draw a circle around the objects that have a flat surface with that shape. 9 Higher Order Thinking Have students look at the solid figures that have a circle around them, and then draw the shape of the flat surfaces of these solid figures.
Question 7.

Question 8.

Question 9.

### Lesson 13.4 Problem Solving

Make Sense and Persevere
Solve & Share
Directions Say: Jackson wants to put flat shapes behind Door I and solid figures behind Door 2. Draw a line from each shape to the correct door to show how he should sort the shapes. Count all the shapes on the shelves. Then cover one door. Count the number of shapes that are behind the door you can see. Without counting tell how many shapes you think are behind the other door. Then count to check your answer.
I can … make sense of problems about shapes.

10 shapes on the shelves

5 the shapes behind door 1

5 the shapes behind door 2

Visual Learning Bridge

Guided Practice

Directions Have students listen to the clues, mark an X on the shapes that do NOT fit the clues, and then draw a circle around the shape that the clues describe. Have students name the shape, and then explain their answers. 1 I am a solid figure. I can roll. I have only a flat surface. What shape am I? Explain which clues helped you solve the mystery. 2 I am a solid figure. I can roll. I can also stack. What shape am I? Explain which clues helped you solve the mystery.
Question 1.

Question 2.

Independent Practice

Directions Have students listen to the clues, mark an X on the shapes that do NOT fit the clues, and then draw a circle around the shape that the clues describe. Have students name the shape, and then explain their answers. 3 I am a solid figure. I can stack and slide. I have 6 flat surfaces. What shape am I? 4 I am a solid figure. I can slide. I have only I flat surface. What shape am I? 5 I am a solid figure. I can roll. I do NOT have any flat surfaces. What shape am I? 6 I am a flat shape. I have 4 sides. All of my sides are the same length. What shape am I? 7 I am a flat shape. I do NOT have any straight sides. What shape am I? 8 lam a solid figure. I can roll. I have 2 flat surfaces. What shape am I?
Question 3.

Cube

Question 4.

Cone

Question 5.

Sphere

Question 6.

Square

Question 7.

Circle

Question 8.

Cylinder

Problem solving

Directions Read the problem to students. Then have them use multiple problem-solving methods to solve the problem. Have students look at the shape at the top of the page. Say: Emily’s teacher teaches the class a game. They have to give a classmate clues about the mystery shape. What clues can Emily give about this shape? 9 Make Sense What is the shape? What makes it special? 10 Be Precise What clues can you give about the shape? Think about how it looks, and whether or not it can roll, stock, or slide. 11 Explain What if your classmate gives you the wrong answer? Can you give more clues to help him or her?
Question.

10 . Answer : it is a solid figure with 2 flat surfaces up and down and it can roll. Water Bottle

11. Answer : it looks like coca cola tin cool drink tin shape

### Lesson 13.5 Make 2-D Shapes from Other 2-D Shapes

Directions Say: Emily has 4 triangles. She thinks she can use them to make other 2-D shapes by matching the sides exactly AND by connecting the 4 triangle shapes by their sides only. Use 4 yellow triangles like the ones Emily is holding. Make as many different shapes as you can using all 4 triangles. As you make each shape, tell what shape you made or describe it and tell where the triangles are. Then draw all four triangles on your page to show your favorite shape.

I can … make 2-D shapes using other 2-D shapes.

FISH

Visual Learning Bridge

Guided Practice

Directions 1 Have students use the pattern block shown to cover the shape, draw the lines, and then write the number that tells how many pattern blocks to use.
Question 1.

Directions 2-3 Have students use the pattern block shown to cover the shape, draw the lines, and then write the number that tells how many pattern blocks to use. 4 Have students use the pattern blocks shown to create the fish, and then write the number that tells how many of each pattern block to use.
Question 2.

Question 3.

Question 4.

Independent Practice

Directions 5 and 6 Have students use the pattern block shown to cover the shape, draw the lines, and then write the number that tells how many pattern blocks to use. 7 and 8 Have students use the pattern block shown to create a 2-D shape, draw the shape, and then write the number of pattern blocks used. 9 Higher Order Thinking Have students use pattern blocks to create a picture, and then draw it in the space.
Question 5.

Question 6.

Question 7.

Question 8.

Question 9.

### Lesson 13.6 Build 2-D Shapes

Solve & Share
Directions Say: Use yarn, string, or pipe cleaners to build a circle. Then use yarn, string, pipe cleaners, or straws to build a shape that is NOT a circle, and then tell what shape you built. Explain how the shapes you built are different from one another

I can …build 2-D shapes that match given attributes.

Visual Learning Bridge

Guided Practice

Directions Provide students with yarn, pipe cleaners, or straws to make each shape. Students should attach the shapes they make with materials to the page. Have students draw or build: 1 a square; 2 a shape that is NOT a square.
Question 1.

Question 2.

Directions Provide students with yarn, pipe cleaners, or straws to make each shape. Students should attach the shapes they make with materials to the page. Have students draw or build: 3 a rectangle; 4 a shape that is NOT a rectangle; 5 a triangle; 6 a shape that is NOT a triangle.
Question 3.

Question 4.

Question 5.

Question 6.

Independent Practice

Directions Have students: 7 draw a rectangle; 8 draw a triangle; 9 draw a square. 10 Higher Order Thinking Have students choose yarn, string, pipe cleaners, or straws to build a circle. Have them attach it to this page, and then explain why some materials are better than others for building circles.
Question 7.

Question 8.

Question 9.

Question 10.

Explanation:
Circle has no vertices or corners, for circle shape objects must have flexible material like pipe cleaners

### Lesson 13.7 Build 3-D Shapes

Solve & Share
Directions Say: Jackson wants to build this building with solid figures. Which solid figures con he use? Tell how you know.
I can … use materials to build 3-D shapes.

Visual Learning Bridge

Guided Practice

Directions 1 and 2 have students use straws, clay, craft sticks, paper, or other materials to build the solid figure shown.
Question 1.

Question 2.

Directions Have students: 3 and 4 use tools to build the shape, and then draw a circle around the solid figures that build the shape; 5 and 6 use tools to find the shape the solid figures can build, and then draw a circle around the shape.
Question 3.

Question 4.

Question 5.

Question 6.

Independent Practice

Directions Have students: 7 use tools to find the shape the solid figures can build, and then draw a circle around the shapes; 8 use tools to build the shape, and then draw a circle around the solid figures that build the shape. 9 Higher Order Thinking Have students use straws, yarn, pipe cleaners, or other materials to build a solid figure that is NOT a cone. Say: Draw a sketch of the solid figure you made. 10 Higher Order Thinking Have students use straws, clay, craft sticks, paper, or other materials to build the shape shown.
Question 7.

Question 8.

Question 9.

Question 10.

### Topic 13 Fluency Practice Activity

Find a Match
Directions 1 and 2 Have students find a partner. Have them point to a clue in the top row, and then solve the addition or subtraction problem in the clue. Then have them look at the clues in the bottom row to find o match, and then write the clue letter above the match. Have students find a match for every clue.
I can … add and subtract fluently within 5.

### Topic 13 Vocabulary Review

Directions Understand Vocabulary Have students: 1 draw a circle around the solid figures that roll; 2 draw a circle around the solid figures that stack; 3 draw a circle around the solid figures that slide.
Question 1.

Question 2.

Question 3.

### Topic 13 Reteaching

Directions Have students: 1 listen to the clues, mark an X on the shapes that do NOT fit the clues, draw a circle around the shape that the clues describe, and then tell how the shapes they marked with an X are similar to the shape they drew a circle around. I am NOT round. I have 4 sides. They are NOT all the same length; 2 draw a circle around the solid figure that does NOT stack and slide.

Set A

Question 1.

Set B

Question 2.

Directions Have students: 3 mark an X on the shapes that do NOT fit the clues, and then draw a circle around the shape the clues describe: I have no sides. I do NOT roll. Which shape am I? 4 draw or use yarn, pipe cleaners, or straws to make a triangle and a shape that is NOT a triangle, and then attach their shapes to this page.

Set C

Question 3.

Set D

Question 4.

### Topic 13 Assessment Practice

Directions Have students mark the best answer. 1 Look at the shape on the left. Mark the two solid figures that have a flat surface with that same shape. 2 Which shape that was built using different materials or drawn matches the shape on the left? 3 Which shape can be built using the solid figures on the left?
Question 1.

Question 2.

Question 3.

Directions Have students: 4 look at the object on the left that slides, and then draw a circle around all of the other objects that slide; 5 listen to the clues, and then draw the shape that the clues describe. I have more than 1 flat surface. I can stack on top of another shape. I can roll. What solid figure am I?; 6 write the number that tells how many triangle pattern blocks can cover the shape; 7 listen to the clues, mark an X on the shapes that do NOT fit the clues, and then draw a circle around the shape that the clues describe. I am a flat shape. I have 4 straight sides. Two of my sides are shorter than the other 2 sides. What shape am I?
Question 4.

Question 5.

Question 6.

Question 7.

Rectangle

Directions Bria’s Bash Say: Bria has a party for her friends. These are some objects that are at her party. Have students: 1 draw a circle around the objects that can slide. Have them tell how the shapes of those objects are different from the shapes of the other objects. Then have students mark an X on the objects that are cylinders. 2 draw what one flat surface of a cylinder looks like, and then name that shape. 3 Say: Bria puts her party hat on top of a present. Have students draw a circle around the solid figures that could be used to build the same shape. If needed, have students use tools to help them.
Question 1.

Question 2.

Question 3.

Directions 4 Say: Bria makes a puzzle for her friends. She uses pattern blocks to make this spaceship. Show how Bria makes her puzzle. Have students use pattern blocks to cover, and then draw lines on the spaceship. Have them write the number that tells how many of each pattern block they used. 5 Say: Bria plays a game at her party. She gives her friends clues and has them tell her what object she is thinking about. Bria gives these clues: The object is NOT a solid shape. The object is NOT round. The object has 3 sides. Have students mark an X on each object that does NOT fit the clues, draw a circle around the object that Bria describes, and then name the shape of that object.
Question 4.

Question 5.

Triangle

## Envision Math Common Core Grade K Answers Key Topic 12 Identify and Describe Shapes

Essential Question:
How can two- and three-dimensional shapes be identified and described?
A two-dimensional (2D) shape has only two measurements, such as length and height.
A square, triangle, and circle are all examples of a 2D shape.
However, a three-dimensional (3D) shape has three measurements, such as length, width, and height.
A cube, prism and cylinder are example of 3D shapes.

enVision STEM project: Pushing and Pulling Objects
Directions Read the character speech bubbles to students. Find Out! Have students investigate different kinds of wheels. Say: Not all wheels look alike, but they are all the same shape. Talk to your friends and relatives about the shape of a wheel and ask them how it can help when you need to push and pull objects. Journal: Make a Poster Have students make a poster that shows various objects with wheels. Have them draw up to 5 different kinds of objects that have wheels.
Yes, students can investigate different kinds of wheels by recollecting means of transport like bus, car, bike and so on., while travelling.
Not all wheels look alike, but they are all the same shape.
With this we can bring the concept of circle shape to the students
Wheels are everywhere in our world today, in very obvious places like car, bus trucks etc., but also hidden inside everything from computer hard drives, dishwashers. Six thousand years ago, there weren’t any wheels at all. The rise of the wheel, from a basic turntable that helped people mold clay pots to a key component in hundreds of important invention owes everything to the simple and effective way it helps us capture and harness energy and transform forces. So we need wheels to push and pull the objects.
Poster:

Review What You Know

Question 1.

Question 2.

Question 3.

Question 4.

Question 5.

Question 6.

Directions Have students: 1 draw a circle around the set of numbers that shows a pattern of counting by tens; 2 draw a circle around the hundred chart; 3 draw a circle around the numbers fifty-five and ninety-nine; 4 count the objects, write the numbers, and then draw a circle around the number that is greater than the other number; 5 count the objects, and then write the number; 6 draw a circle around the number that tells how many counters.

Pick a Project

A

Project A:
Bone is specific to vertebrates, and originated as mineralization around the basal membrane of the throat or skin, giving rise to tooth-like structures and protective shields in animals with a soft cartilage-like endoskeleton. The bones gives the shape and posture to the body.
Steps to be followed for Dinosaur puzzles:
The primary material that you need for this project is corrugated cardboard or double layered cardboard.
The first thing that you need to do is find a template or draw the picture of Dinosaur.
Now that you have a template, you need to print it out in the size that you want.
Then attach the templates to the cardboard, you can use tape or a removable glue.
Then you need to mark the outline of each piece on the cardboard. You can do this by tracing each piece with a dark pen. You could also use a sharp object such as a knife or a needle to pierce through the template and into the cardboard.
Cut out the puzzle pieces and now comes the fun part i.e., putting the puzzle together.

B

PROJECT: B

Directions Say: You will choose one of these projects. Look at picture A. Think about this question: Where did all those bones come from? If you choose Project A, you will create dinosaur puzzles. Look at picture B. Think about this question: Would you rather design buildings or build them? If you choose Project B, you will design and build a structure.

C

Project C
Depending on its size, it could be a pyramid, a clown’s hat, a slice of pie, a bird’s beak.
Depending on how they’re placed, they might suggest a mountain range or a tent encampment, a pine tree farm, or a schooner’s etc.,

D

Project D

1. Cookies are baked or cooked items that are small, flat and sweet. It is prepared using flour, sugar and some type of oil or fat.
2. Maida : 2½ cups.
3. Butter : 1 cup.
4. Sugar : 1 cup.
5. Egg : 1.
6. Milk : 2 table spoons.
7. Vanilla essence : 1 teaspoon.
8. Salt : a pinch.

Directions
1. Preheat oven to 375 degrees F (190 degrees C). In a small bowl, stir together flour, baking soda, and baking powder.
2. In a large bowl, cream together the butter and sugar until smooth. Beat in egg and vanilla.
3. Bake 8 to 10 minutes in the preheated oven, or until golden.
ACT
Its a pleasant evening Leena is siting outside and watching the surroundings, suddenly she started to smell the baking fragrance of cookies. Then she also wanted to prepare cookies and give a surprise party to her family members as it was discussed above she prepared cookies accordingly and plated decorative cookies in front of the family members. All ate delicious cookies and praised Leena for her cookies.

Directions Say: You will choose one of these projects. Look at picture C. Think about this question: What can you draw using only triangles? If you choose Project C, you will make a shape picture. Look at picture D. Think about this question: How are all those cookies made? If you choose Project D, you will act out a party.

### Lesson 12.1 Two-Dimensional(2-D) and Three-Dimensional (3-D) Shapes

Solid figures are identified according to the features that are unique to each type of solid. Specifically, one can observe the numbers of faces, edges, and vertices, as well as the shape of the base.
A plane horizontal surface with no depths is called the flat surface.
The following groups are different based upon their shape and structure.
Classified into 2 dimensional and 3 dimensional shapes.
Flat and Solid shapes.

Directions Say: Pick 6 shapes from a bag. Put the shapes into two groups. Tell how the groups are different. Then draw a picture of the shapes you put on each table.

Visual Learning Bridge

Guided Practice

Question 1.

Directions 1 Have students draw a circle around the objects that are flat, and mark an X on the objects that are solid.

Question 2.

Question 3.

Question 4.

4 marked on X on the objects that are NOT flat

Question 5.

5 marked on X on the objects that are NOT Solid.

Directions Have students 2 and 3 draw a circle around the objects that are flat, and mark an X on the objects that are solid. 4 mark on X on the objects that are NOT flat; 5 mark on X on the objects that are NOT Solid.

Independent Practice

Question 6.

X marked on the objects that are solid. circled around the objects that are flat

Question 7.

Marked an X on the objects that are NOT solid

Question 8.
Yes, students can draw the Picture of an objects that are solid based upon previous concept of 2 dimensional and 3 dimensional shapes.

Directions Have students: 6 mark an X on the objects that are solid. Then have them draw a circle around the objects that are flat; 7 mark an X on the objects that are NOT solid 8 Higher Order Thinking Have students draw a picture of an object that is solid.

### Lesson 12.2 Circles and Triangles

Directions Say: Go on a shape hunt. Find shapes and objects in the classroom or outside that look like the shapes shown on the page. Draw the shapes. Use your own words to tell where you found them. Then say: Tell how the shapes are different.
Answer may vary according to the visualization of students.
The shapes and objects that are found in the classroom or outside are:
Football, cricket ball, basket ball, flying disc, pyramid etc., are found outside the classroom.
Clock, birthday caps etc., are found in classroom.
Both circle and triangle are different from each other as circle is round in shape and triangle has 3 sides.

Visual Learning Bridge

Guided Practice

Question 1.

Question 2.

Directions 1 and 2 Have students color the circle in each raw, and then mark an X on each triangle.

Question 3.

Question 4.

Question 5.

Directions 3 Have students color the circle and mark an X on the triangle. 4 Number Sense Have students mark an X on the shape that has 3 sides. 5 Have students mark an X on the objects that look like a triangle, and then draw a box around the objects that look like a circle.

Independent Practice

Question 6.

Question 7.

Question 8.

Question 9.

Question 10.
Yes, by understanding the concept of shapes students can able to draw a picture of an object that is shaped like a triangle.
Picture of an object may vary from student to student.

Directions 6-9 Have students color the circles and mark an X on the triangles in each row. 10 Higher Order Thinking Have students draw a picture of an object that is shaped like a triangle.

### Lesson 12.3 Squares and Other Rectangles

Solve & Share

Directions Say: Emily has a large quilt on her bed. The shape outlined with black lines is a rectangle. The rectangular quilt is made up of square rectangles of different colors. How many other rectangles can you find in the picture? How many of the rectangles are squares? Count the shapes and tell where you see them.
only 1 rectangle
6 squares are rectangle
6 square shapes on the quilt

Visual Learning Bridge

Guided Practice

Question 1.

Question 2.

Directions 1 and 2 Have students color the rectangles in each row, and then mark an X on each rectangle that is also a square.

Question 3.