Category: Envision Math

Envision Math 1st Grade Textbook Answer Key Topic 2 Reteaching

Reteaching

Set A

You can stack cubes to find which group has more.

Write each number. Circle is less than or is greater than.
Question 1.

Answer:

Question 2.

Answer:

Set B

You can use cube towers to put numbers in order.

Use cubes. Write the numbers in order from least to greatest.

Question 3.

Answer:

Question 4.

Answer:

Set C

You can use a number line to find missing numbers.

Write the missing number.

Use the number line. Write the missing numbers.
Question 5.
7 _____ 9
Answer:

Question 6.
4 ______ 6
Answer:

Set D

You can use cubes to act out a story.
Ed is 7. Ann is 4. Reza is 8.

Who is oldest?
8 is the greatest number.
So Reza is oldest.

Use cubes to act out the story. Write the numbers in order from least to greatest.
Question 7.
Mary made 5 cards.
Jim made 9 cards.
Saul made 6 cards.

Who made the most cards? ________
Answer:

Envision Math 2nd Grade Textbook Answer Key Topic 2 Test

Test

Question 1.
2 + 6 = ______

Answer:

Question 2.
1 + 8 = _____

Answer:

Question 3.
9 + 9 = _____

Answer:

Question 4.
6 + 7 = ______

Answer:

Question 5.

Answer:

Question 6.
4 + 3 = 7

Answer:

Question 7.
5 + 8 = 13

Answer:

Oral Directions Say:
Mark the correct answer. 1–5. Add. 6–7. Mark the answer that changes the order of the addends.

Question 8.

Answer:

Question 9.

Answer:

Question 10.

Answer:

Question 11.

Answer:

Oral Directions Say:
Mark the correct answer. 8–10. Add. 11. Choose the number sentence that answers the question. Jake
has 8 fish in one tank. He has 4 fish in another tank. How many fish does Jake have altogether?

Envision Math 2nd Grade Textbook Answer Key Topic 1 Test Prep

Test

Question 1.

Answer:

Question 2.

Answer:

Question 3.

Answer:

Question 4.

Answer:

Oral Directions
Say: Mark the correct answer.
1. Mark the number sentence that matches the model.
2. Beth feeds 5 goats. Keith feeds 8 ducks. How many animals do they feed in all?
3. Mark the number sentence that matches the model.
4. Tim has 10 balloons. He gives 8 away. How many balloons does Tim have now?

Question 5.

Answer:

Question 6.

Answer:

Question 7.

Answer:

Oral Directions
Say: Mark the correct answer.
5. Rico has 12 fish. Carla has 5 fish. How many more fish does Rico have than Carla?
6. Which other subtraction sentence matches the model?
7. Which number sentence matches this story and the model? Tina has 5 blue flowers and 7 pink flowers. How many flowers does she have in all?

Go through the enVision Math Common Core Grade 4 Answer Key Topic 14 Algebra: Generate and Analyze Patterns regularly and improve your accuracy in solving questions.

enVision Math Common Core 4th Grade Answers Key Topic 14 Algebra Generate and Analyze Patterns

Essential Questions:
How can you use a rule to continue a pattern? How can you use a table to extend a pattern? How can you use a repeating pattern to predict a shape?

enVision STEM Project: Patterns and Waves
Journal: Write a Report Include what you found. Also in your report:
Do Research Use the Internet or other sources to learn about 2 industries where oscilloscopes can be used. Name the industry and what can be observed using the oscilloscope.

Oscilloscopes are used to observe patterns in waves. Suppose a scientist created a pattern with three levels of sounds: quiet, loud, medium. If the scientist repeats the pattern of sounds, what would be the 41st sound in the pattern? Explain.

Review What You Know

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

• even number
• odd number
• inverse operations
• variable

Question 1.
A(n) ________ can be divided into groups of 2 without a remainder.
Answer:
Even number
Explanation:
Even numbers are those numbers that can be divided into two equal groups or pairs and are exactly divisible by 2.

Question 2.
A symbol or letter that stands for a number is called a(n) ___________.
Answer: Variable
Explanation:
A variable is a letter or symbol used as a placeholder for an unknown value

Question 3.
Operations that undo each other are called _________
Answer: Inverse Operation.
Explanation:
Inverse operations are operations that are opposite or “undo” each other.
For example, addition undoes subtraction and division undoes multiplication.
Inverse operations are useful when solving equations

Addition and Subtraction Patterns

Add or subtract to find the missing number in each pattern.
Question 4.
3, 6, 9, 12, ____,18
Answer: 15
Explanation:
Pattern : Add 3

Question 5.
4,8, 12, ____, 20, 24
Answer: 16
Explanation:
Pattern : Add 4

Question 6.
8, 7, 6, ____,4, 3
Answer: 5
Explanation:
Pattern : Add 1 then less 1

Question 7.
30, 25, 20, 15, ____,5
Answer: 10
Explanation:
Pattern : Subtract 5

Question 8.
1, 5, 9, ____, 17, 21
Answer: 13
Explanation:
Pattern : Add 4

Question 9.
12, 10, 8, 6, ___, 2
Answer: 4
Explanation:
Pattern : Subtract 2

Multiplication and Division Patterns

Multiply or divide to find the missing number in each pattern.
Question 10.
1, 3, 9, 27, ___, 243
Answer: 81
Explanation:
Pattern : Multiply 3

Question 11.
64, 32, 16, ____, 4, 2
Answer:  8
Explanation:
Pattern : Divide by 2

Question 12.
1,5, 25, ____, 625
Answer: 125
Explanation:
Pattern : Multiply 5

Question 13.
1, 2, 4, 8, ____, 32
Answer:
Explanation:
Pattern : Multiply by 2

Question 14.
1, 4, 16, ____, 256
Answer: 64
Explanation:
Pattern : Multiply by 4

Question 15.
729, 243, 81,27, 9, ____
Answer: 3
Explanation:
Pattern : Divided by 3

Problem Solving

Question 16.
Look for Relationships James places 1 counter in the first box. He places 2 counters in the second box, 4 counters in the third box, 8 counters in the fourth box, and continues the pattern until he gets to the tenth box. How many counters did James place in the tenth box?

Answer: 512
Explanation:
Pattern is multiply by 2

Pick a Project

PROJECT 14A
How have roller coasters changed through the years?
Project: Make a Model Roller-Coaster Car

PROJECT 14B
How can you use currency from different countries?
Project: Make Your Own Currency

PROJECT 14C
How can patterns be used in sidewalks?
Project: Design Your Own Sidewalk

PROJECT 14D
How many stadiums in the United States have retractable roofs?
Project: Make a Seating Diagram

Lesson 14.1 Number Sequences

Solve & Share
Look at the rules and starting numbers below. What are the next 6 numbers in each pattern? Tell how you decided. Describe features of the patterns. Solve these problems any way you choose.
I can … use a rule to create and extend a number pattern and identify features of the number pattern not described by the rule.

Look Back! Look for Relationships Create two patterns that use the same rule but start with different numbers. Identify a feature of each pattern. For example, identify whether the numbers are all even, all odd, or alternate between even and odd.

Essential Question
How Can You Use a Rule to Continue a Pattern?

Visual Learning Bridge
The house numbers on a street follow the rule “Add 4.” If the pattern continues, what are the next three house numbers? Describe a feature of the pattern.

You can use a number line to help make sense of the problem and find the next three house numbers.

Use a number line to continue the pattern.
A rule is a mathematical phrase that tells how numbers or shapes in a pattern are related. The rule for the house numbers is “Add 4.”

The next three house numbers are 20, 24, and 28.

Describe features of the pattern.
Some patterns have features that are not given in the rule.
16, 20, 24, 28
One of the features of this pattern is all of the house numbers are even numbers.
Another feature is all of the house numbers are multiples of 4.

Convince Me! Generalize Can you use the rule “Add 4” to create a different pattern with all odd numbers? Explain.
Explanation:
No, we cannot apply this rule on odd numbers
when u add 4 to a odd number the answers all will be in odd numbers
but not the multiples.

Another Example!
On another street, the house numbers follow the rule “Subtract 5.” What are the next three house numbers after 825? Describe a feature of the pattern.

The next three house numbers are 820, 815, and 810. All of the house numbers are multiples of 5.

Guided Practice

Do You Understand?
Question 1.
Rudy’s rule is “Add 2.” He started with 4 and wrote the numbers below. Which number does NOT belong to Rudy’s pattern? Explain. 4,6, 8, 9, 10, 12
Answer: 9
Explanation:
9 number does NOT belong to Rudy’s pattern
Because it is not the multiple of 2

Do You Know How?
Continue the pattern. Describe a feature of the pattern.
Question 2.
Subtract 6
48, 42, 36, 30, 24, _____, _____, ______
Answer: 18,12,6.
Explanation:
Pattern = multiples of 6

Independent Practice

For 3-6, continue each pattern. Describe a feature of each pattern.
Question 3.
Subtract 3: 63, 60, 57, _____, _____
Answer: 54,51,48
Explanation:
Pattern is multiples of 3

Question 4.
Add 7: 444, 451, 458, _____, _____
Answer: 465,472.
Explanation:
pattern = Multiples of 7

Question 5.
Add 25: 85, 110, 135, _____, _____
Answer: 160,185
Explanation:
The sequence is completed by adding 25

Question 6.
Subtract 4: 75, 71, 67, _____, _____
Answer: 63,59
Explanation:
The sequence is completed by  subtracting 4

For 7-12, use the rule to generate each pattern.
Question 7.
Rule: Subtract 10
90, _____, _____
Answer: 80,70
Explanation:
The sequence is completed by subtracting 10

Question 8.
Rule: Add 51
16, _____, _____
Answer: 67,83
Explanation:
The sequence is completed by adding 51

Question 9.
Rule: Add 5
96, _____, _____
Answer: 101, 106
Explanation:
The sequence is completed by adding 5

Question 10.
Rule: Add 107
43, _____, _____
Answer:  150, 257
Explanation:
The sequence is completed by adding 107

Question 11.
Rule: Subtract 15
120, _____, _____
Answer: 105, 90
Explanation:
The sequence is completed by Subtracting 15

Question 12.
Rule: Subtract 19
99, _____, _____
Answer: 80, 61
Explanation:
The sequence is completed by Subtracting 19

Problem Solving

Question 13.
Reasoning Orlando delivers mail. He sees one mailbox that does not have a number. If the numbers are in a pattern, what is the missing number?

Answer: 31
Explanation:
Pattern : Add 2
The missing number is 31

Question 14.
A bus tour runs 9 times a day, 6 days a week. The bus can carry 30 passengers. Find the greatest number of passengers who can ride the tour bus each week.
Answer: 1620
Explanation:
6 x 9 = 54 trips
54 x 30 = 1620
The greatest number of passengers who can ride the tour bus each week is 1620 passengers.

Question 15.
The year 2017 was the year of the Rooster on the Chinese calendar. The next year of the Rooster will be 2029. The rule is “Add 12.” What are the next five years of the Rooster?

Answer: 2041, 2053, 2065, 2077, 2089
Explanation:
The next five years of the Rooster are 2041, 2053, 2065, 2077, 2089

Question 16.
Describe a feature of the year of the Rooster pattern.
Answer: Multiples of 12
Explanation:
Feature of the year of the Rooster pattern is multiples of 12

Question 17.
Vocabulary Define rule. Create a number pattern using the rule “Subtract 7.”
Answer: Rule = multiples of 7
Explanation:
70, 63, 56, 49
Is the pattern of Subtract 7

Question 18.
Higher Order Thinking Some patterns use both addition and subtraction in their rules. The rule is “Add 3, Subtract 2.” Find the next three numbers in the pattern.
1, 4, 2, 5, 3, 6, 4, 7, _____, _____, _____
Answer: 5, 8 , 6
Explanation:
The next three numbers in the pattern is 5, 8 , 6

Assessment Practice

Question 19.
Rima used “Subtract 3” as the rule to make a pattern. She started with 60, and wrote the next six numbers in her pattern. Which number does NOT belong in Rima’s pattern?

A. 57
B. 54
C. 45
D. 26
Answer: D
Explanation:
26 number does NOT belong in Rima’s pattern

Question 20.
Ivan counted all the beans in a jar. If he counted the beans in groups of 7, which list shows the numbers Ivan could have named?
A. 77, 84, 91, 99
B. 301, 308, 324, 331
C. 574, 581, 588, 595
D. 14, 24, 34, 44
Answer: B
Explanation:
301, 308, 324, 331 list shows the numbers Ivan could have named

Lesson 14.2 Patterns: Number Rules

Solve & Share
There are 6 juice boxes in 1 pack, 12 in 2 packs, and 18 in 3 packs. How many juice boxes are in 4 packs? in 5 packs? in 6 packs? Use the rule to complete the table. Describe features of the pattern. Then find how many juice boxes are in 10 packs and 100 packs.
I can … use a rule to extend a number pattern, identify features of the number pattern, and use the number pattern to solve a problem.

Look Back! Reasoning Create a table showing the relationship between the number of bicycles and the number of bicycle wheels. Start with 1 bicycle. Complete 5 rows of the table using the rule “Multiply by 2.” Describe features of the pattern.
gf

Essential Question
What is the Pattern?

Visual Learning Bridge
There are 3 leaflets on 1 cloverleaf. There are 6 leaflets on 2 cloverleaves. There are 9 leaflets on 3 cloverleaves. How many leaflets are on 4 cloverleaves? How many cloverleaves will have 12 leaflets?

You can use a table to create, extend, and identify features of a pattern.

How many leaflets are on 4 cloverleaves?

There are 12 leaflets on 4 cloverleaves. The number of leaflets is a multiple of the number of cloverleaves.

How many cloverleaves for 12 leaflets?

There are 4 cloverleaves for 12 leaflets. The number of cloverleaves is a factor of the number of leaflets.

Convince Me! Model with Math If you know the number of leaflets, l, what expression can you use to find the number of cloverleaves, c? If you know the number of cloverleaves, what expression can you use to find the number of leaflets?

Guided Practice

Do You Understand?
Question 1.
The rule for this table is “Multiply by 4.” What number does not belong?

Answer: 15
Explanation:
4 x  4 = 16
15 does not belong to the  group

Do You Know How?
Complete the table. Describe a feature of the pattern.
Question 2.
Rule: Divide by 4

Answer: 5

Explanation:
5 x 4 = 20
Multiply by 4 is the pattern

Independent Practice

For 3-6, use the rule to complete each table. Describe a feature of each pattern.
You can multiply or divide to find the patterns in these tables.
Question 3.
Rule: Multiply by 8

Answer:

Explanation:
2 x 8 = 16
5 x 8 = 40
The sequence is completed by the multiplies of 8

Question 4.
Rule: Divide by 5

Answer:

Explanation:
The sequence is completed by Divide by 5

Question 5.
Rule: Multiply by 16

Answer:

Explanation:
The sequence is completed by the multiples of 16

Question 6.
Rule: Divide by 2

Answer:

Explanation:
The sequence is completed by dividing with 2
500 divided by 2 is 250
730 divided by 2 is 365

Problem Solving

Question 7.
The table shows how much money Joe makes painting. How much money will Joe make when he paints for 6 hours?
Rule: Multiply by 45

Answer: 270

Explanation:
$270 money will Joe make when he paints for 6 hours

Question 8.
The table shows the total number of pounds of potatoes for different numbers of bags. How many bags does it take to hold 96 pounds of potatoes?
Rule: Divide by 8

Answer: 12

Explanation:
12 bags it take to hold 96 pounds of potatoes

Question 9.
Number Sense What is the greatest number you can make using each of the digits 1,7,0, and 6 once?
Answer: 7106
Explanation:
7106  is the greatest number you can make using each of the digits 1,7,0, and 6 once

Question 10.
Algebra A penguin can swim 11 miles per hour. At this speed, how far can it swim in 13 hours? Use s as a variable. Write and solve an equation.
Answer: 143 miles
Explanation:
s = 11 x 13
s = 143 miles

For 11-12, the rule is “Multiply by 3.”

Question 11.
Reasoning Using the rule, how many batteries do 8 flashlights need?
Answer: 24
Explanation:
8 x 3 = 24
24 batteries has 8 flashlights needed.

Question 12.
Higher Order Thinking How many more batteries do 20 flashlights need than 15 flashlights? Explain.
Answer:
15 x 3 = 45
20 x 3 = 60
60 – 45 = 15
Explanation:
15 more batteries do 20 flashlights need than 15 flashlights

Assessment Practice

Question 13.
There are 6 rolls in each package. Use the rule “Divide by 6” to show the relationship between the number of rolls and the number of packages. Use each digit from the box once to complete the table.

Answer:

Explanation:
Used each digit from the box once to complete the table.

Lesson 14.3 Patterns: Repeating Shapes

Solve & Share
The rule for the repeating pattern below is “Square, Triangle.” What will be the 37th shape in the pattern? Explain. Solve this problem any way you choose.
I can … use a rule to predict a number or shape in a pattern.

Look Back! When the pattern has 37 shapes, how many are triangles?
Answer:
37 divided by 2 is 18 times triangles
37 is the triangle

Essential Question
How Can You Use a Repeating Pattern to Predict a Shape?

Visual Learning Bridge
Rashad is making a repeating pattern for the rule “Triangle, Square, Trapezoid.” What will be the 49th shape in the pattern?
A repeating pattern is made up of shapes or numbers that form a part that repeats.

Explanation:
49th shape is triangle
48 divided by 3 is 16
so, the next is triangle

Look for Features of the Repeating Pattern

The trapezoid is the 3^rd, 6^th, and 9^th shape in the pattern. The positions of the trapezoids are multiples of 3.

The triangle is the 15^th, 4^th, and 7^th shape in the pattern. The positions of the triangles are 1 more than a multiple of 3.

The square is the 2^nd, 5^th, and 8^th shape in the pattern. The positions of the squares are 1 less than a multiple

Use the Repeating Pattern to Solve
When you divide 49 by 3, the quotient is 16 R1. The pattern repeats 16 times. The 1st shape in the repeating pattern, a triangle, then appears.

49 is one more than a multiple of 3.
The 49th shape is a triangle.

Convince Me! Be Precise Suppose the rule is “Square, Triangle, Square, Trapezoid” in a repeating pattern. What is the 26th shape in the pattern? Describe features of the repeating pattern. Be precise in your description.

Another Example!
Write the next three numbers in the repeating pattern. Then name the 100th number in the pattern.

Rule: 1, 3, 5, 7 1, 3, 5, 7, 1, 3, 5, 7, 1, 3, 5, 7, 1, 3, 5 …
There are 4 items in the repeating pattern. To find the 100^th number, divide by 4. The pattern repeats 25 times. The 100^th number is 7.

Guided Practice

Do You Understand?
Question 1.
In the “Triangle, Square, Trapezoid” example on the previous page, what will be the 48^th shape? the 50^th shape? Explain.
Answer: 48th is trapezoid, 50th is square
Explanation:
When you divide 49 by 3, the quotient is 16 R1. The pattern repeats 16 times. The 1st shape in the repeating pattern, a triangle, then appears.

Do You Know How?
Question 2.
What is the 20^th shape? The rule is “Triangle, Circle, Circle.”

Answer: circle
Explanation:
When you divide 20 by 3, the quotient is 6 R2. The pattern repeats 6 times. The 1st shape in the repeating pattern, a circle, then appears.

Question 3.
Write the next three numbers. The rule is “9, 2, 7, 6.”
9, 2, 7, 6, 9, 2, 7, 6, ____, _____, ______
Answer: 9,2,7
Explanation:
The next three numbers 9, 2, 7

Independent Practice

For 4-7, draw or write the next three items to continue each repeating pattern.
Question 4.
The rule is “Square, Triangle, Square.”

Answer:

Explanation:
The pattern is completed with the help of rule

Question 5.
The rule is “Up, Down, Left, Right.”

Answer:

Explanation:
The pattern is completed with the help of rule

Question 6.
The rule is “1, 1, 2.”
1, 1, 2, 1, 1, 2, ____ , ____, ____ ……
Answer: 1,1,2
Explanation:
The pattern is completed with the help of rule

Question 7.
The rule is “5, 7, 4, 8.”
5, 7, 4, 8, 5, 7, 4, 8, 5, 7, ____, ____, ____ ……
Answer: 4, 8, 5
Explanation:
The pattern is completed with the help of rule

For 8-9, determine the given shape or number in each repeating pattern.
Question 8.
The rule is “Tree, Apple, Apple.” What is the 19^th shape?

Answer:
Explanation:
When you divide 19 by 3, the quotient is 6 R1. The pattern repeats 6 times. The 1st shape in the repeating pattern, a tree, then appears.

Question 9.
The rule is “1, 2.” What is the 42^nd number?
1, 2, 1, 2, 1, 2, …
Answer:
Explanation:
When you divide 42 by 2, the quotient is 21 R0. The pattern repeats 21 times.
The pattern is closed so the pattern end with 2.

Problem Solving

Question 10.
Create a repeating pattern using the rule “Triangle, Square, Square.”
Answer:

Explanation:
Created a repeating pattern using the rule “Triangle, Square, Square.”
Ends with the triangle.

Question 11.
enVision® STEM Margot measured the distance for 6 wavelengths of visible light as 2,400 nanometers. What is the distance for 1 wavelength?
Answer:
2400 divided by 6 = 400
Explanation:
400 is the distance for 1 wavelength

Question 12.
Look for Relationships Hilda is making a repeating pattern with the shapes below. The rule is “Heart, Square, Triangle.” If Hilda continues the pattern, what will be the 11th shape?

Answer:
Explanation:
When you divide 11 by 3, the quotient is 3 R2. The pattern repeats 3 times.
The 2nd shape in the repeating pattern, a square, then appears.

Question 13.
Look for Relationships Josie puts beads on a string in a repeating pattern. The rule is “Blue, Green, Yellow, Orange.” There are 88 beads on her string. How many times did Josie repeat her pattern?
Answer: 22 times
Explanation:
When you divide 88 by 4, the quotient is 22 R0. The pattern repeats 22 times.
The pattern is closed so the pattern end with yellow

Question 14.
How many more years passed between the first steam locomotive and the gasoline-powered automobile than between the gasoline-powered automobile and the first diesel locomotive?

Answer: 81 , 27
Explanation:
steam locomotive and the gasoline-powered automobile
1885 – 1804 = 81
81 years
gasoline-powered automobile and the first diesel locomotive
1912 – 1885= 27

Question 15.
Louisa used the rule “Blue, Green, Green, Green” to make a bracelet with a repeating pattern. She used 18 green beads. How many beads did Louisa use to make the bracelet? How many beads were NOT green?
Answer:
18 divided by 3 is 6
so, pattern repeated 6 times
6 x 4 = 24
24 – 18 = 6
Explanation:
6 beads were NOT green

Question 16.
Higher Order Thinking Marcus is using shapes to make a repeating pattern. He has twice as many circles as squares. Make a repeating pattern that follows this rule.
Answer: The rule is circle , square , square

Explanation:
The pattern is made according to the rule.

Assessment Practice

Question 17.
Which rules give a repeating pattern that has a square as the 15th shape? Select all that apply.
☐ Square, Circle
☐Circle, Square, Triangle
☐ Square, Circle, Triangle
☐ Circle, Triangle, Square
☐ Trapezoid, Circle, Square
Answer:

Explanation:
Selected all that apply
where the 15th shape is a square.

Question 18.
Which rules give a repeating pattern that has a 7 as the 15^th number? Select all that apply.
☐ 1, 7
☐ 1, 7, 9
☐ 1, 9, 7
☐ 1, 7, 7
☐ 7, 1, 9
Answer:

Explanation:
selected pattern rules give a repeating pattern that has a 7 as the 15^th number

Lesson 14.4 Problem Solving

Look For and Use Structure
Solve & Share
Evan’s baby brother is stacking blocks. Using the rule “Add 1 block to the number of blocks in the previous stack,” how many blocks will be in the 6th stack? Explain. Justify your answer.
I can … use patterns to help solve problems.

Thinking Habits
• What patterns can I see and describe?
• How can I use the patterns to solve the problem?
· Can I see expressions and objects in different ways?

Look Back! Look For Relationships How many blocks are in the 10th stack? Explain.

Essential Question
How Can I Look For and Make Use of Structure?

Visual Learning Bridge
Alisa made three walls with cubes. She recorded her pattern. If she continues the pattern, how many cubes will be in a 10-layer wall? a 100-layer wall?

What do you need to do to find the number of cubes in a 10-layer and 100-layer wall?
I need to continue the pattern using the rule and analyze the pattern to find features not stated in the rule itself.

How can I make use of structure to solve this problem?
I can

• look for and describe patterns in three dimensional shapes.
• use the rule that describes how objects or values in a pattern are related.
• use features of the pattern not stated in the rule to generate or extend the pattern.

Here’s my thinking.
Make a table and look for patterns.

There are 4 cubes in each layer. Multiply the number of layers by 4 to calculate the number of cubes.
A 10-layer wall contains 10 × 4 = 40 cubes.
A 100-layer wall contains 100 × 4 = 400 cubes.

Convince Me! Look for Relationships How could you use multiples to describe Alisa’s pattern?

Guided Practice

Use Structure
Leah arranged triangular tiles in a pattern like 1 row the one shown. She used the rule “Multiply the number of rows by itself to get the number of small triangles.” How many small triangles would be in the pattern if there were 10 rows?

Question 1.
Complete the table to help describe the pattern.

Answer:

Explanation:
Multiplied the number by itself

Question 2.
Describe the pattern another way.
Answer:
4 x 4 = 12
5 x 5 = 25
Explanation:
used the rule “Multiply the number of rows by itself to get the number of small triangles

Question 3.
How many triangles would be in 10 rows?
Answer: 100
Explanation:
10 x 10= 100
used the rule “Multiply the number of rows by itself to get the number of small triangles

Independent Practice

Look for Relationships
Alan built the towers shown using the rule “Each story has 2 blocks.” How many blocks will a 10-story tower have? Use Exercises 4-6 to answer the question.

Question 4.
Complete the table to help describe the pattern.

Answer: 10 x 2 = 20

Explanation:
Pattern is add by 2

Question 5.
What is another way to describe the pattern that is not described by the rule?
Answer:
Explanation:
Pattern is add by 2

Question 6.
How many blocks are in a 10-story tower? Explain.
Answer: 10 x 2 = 20
Explanation:
used the rule “Multiply the number with 2″

Problem Solving

Performance Task

Glass Stairs
An art gallery staircase is built using glass cubes. The diagram below shows 4 steps are 4 cubes high and 4 cubes across. Five steps are 5 cubes high and 5 cubes across. How many glass cubes are used to make 7 steps? Use Exercises 7-10 to answer the question.

Question 7.
Make Sense and Persevere What do you know, and what do you need to find?
Answer:
4 steps are 4 cubes high and 4 cubes across. Five steps are 5 cubes high and 5 cubes across
is what we know
7 steps is to find
seven steps are 7 cubes high and 7 cubes across

Question 8.
Reasoning Complete the table.

Answer:

Explanation:
Pattern = multiply by 3

Question 9.
Look For Relationships What pattern can you determine from the table?

Answer: Pattern = multiply by 3
Explanation:
multiply by 3 pattern can you determine from the table

Question 10.
Reasoning How many cubes are needed for 7 steps? Write and solve an equation.
Answer: 49 cubes
Explanation:
7 x 7 = 49
seven steps are 7 cubes high and 7 cubes across
49 cubes are needed for 7 steps

Topic 14 Fluency Practice Activity

Point & Tally
Find a partner. Get paper and a pencil. Each partner chooses a different color: light blue or dark blue. Partner 1 and Partner 2 each point to a black number at the same time. Each partner adds the two numbers. If the answer is on your color, you get a tally mark. Work until one partner has twelve tally marks.
I can … add multi-digit whole numbers.

Topic 14 Vocabulary Review

Understand Vocabulary
Word List

• equation
• even number
• factor
• multiple
• odd number
• repeating pattern
• rule
• unknown

Question 1.
Circle the term that best describes 28.
even
odd
equation
unknown
Answer: Even
Explanation:
Even is the word which is divisible by 2

Question 2.
Circle the term that best completes this sentence: 4 is a _________ of 16.
even
odd
factor
multiple
Answer: factor
Explanation:
2, 4 , 8 are the factors of 16

Question 3.
Circle the term that best describes 17.
even
odd
equation
unknown
Answer: Odd
Explanation:
Odd numbers are the numbers that cannot be divided by 2 evenly.

Question 4.
Circle the term that best completes this sentence: 9 is a _________ of 3.
even
odd
factor
multiple
Answer: Multiple of 3
Explanation:
3 x 3 = 9
9 is the multiple of 3

Question 5.
Draw a line from each term to its example.

Answer:

Explanation:
The preview  words are matched with the correct answers.

Use Vocabulary in Writing
Question 6.
Use at least 3 terms from the Word List to describe the pattern.
50, 48, 46, 44, 42 …
Answer:
Even numbers
Multiple
Rule
Explanation:
The above all numbers are even numbers
They are multiples of 2
Rule= less 2

Topic 14 Reteaching

Set A pages 521-524

You can use the rule “Subtract 3” to continue the pattern.

The next three numbers in the pattern are 9,6, and 3
A feature of the pattern is all the numbers are multiples of 3.
Another feature is all the numbers in the pattern alternate even, odd.

Remember to check that the numbers in your pattern follow the rule.

Use the rule to continue each pattern. Describe a feature of the pattern.
Question 1.
Rule: Add 20
771, 791, 811, _____, _____, _____
Answer: 831, 851
Explanation:
A feature of the pattern is all the numbers are odd numbers

Question 2.
Rule: Subtract 12
122, 110, 98, _____, _____, ______
Answer: 86, 74, 62
Explanation:
A feature of the pattern is all the numbers are even numbers

Set B pages 525-528

The regular price is twice the sale price. You can use the rule “Divide by 2” to continue the pattern.

Remember to look for features of the pattern not described by the rule.

Use the rule to continue each pattern. Describe a feature of the pattern.
Question 1.
Rule: Multiply by 18

Answer:

Explanation:
A feature of the pattern is all the numbers are even numbers

Question 2.
Rule: Divide by 9

Answer:  $100

Explanation:
A feature of the pattern is all the numbers are even and odd numbers

Question 3.
Rule: Multiply by 24

Answer:

Explanation:
A feature of the pattern is all the numbers are even

Set C pages 529-532

You can use the rule “Circle, Triangle, Square” to continue the repeating pattern.

You can use the rule to find the 25^th shape in the pattern.
25 ÷ 3 = 8 R1.
The pattern will repeat 8 times, then the 1^st shape will appear.
The circle is the 25^th shape in the pattern.

Remember to use the rule to continue the pattern.

Question 1.
a. Draw the next three shapes in the repeating pattern. The rule is “Right, Up, Up.”

Answer:

Explanation:
Up, Up, Right is the next three shapes in the repeating pattern

b. Draw the 50^th shape in the pattern.
Answer:
Explanation:
You can use the rule to find the 50^th shape in the pattern.
50 ÷ 3 = 16 R2.
The pattern will repeat 16 times, then the 1^st shape will appear.
The up is the 50^th shape in the pattern.

Question 2.
a. Write the next three numbers in the repeating pattern. The rule is “3, 5, 7, 9.”
3, 5, 7, 9, 3, 5, 7, ____, _____, ______
Answer: 9, 3, 5, 7
Explanation:
9, 3, 5, 7 the next three numbers in the repeating pattern

b. What will be the 100^th number in the pattern?
Answer:
Explanation:
You can use the rule to find the 100^th number in the pattern.
100 ÷ 4 = 25 R0.
The pattern will repeat 25 times,
There the pattern ends so, the 100th  number is 7

Set D pages 533-536

Think about these questions to help you Look For and Use Structure.
Thinking Habits

• What patterns can I see and describe?
• How can I use the patterns to solve the problem?
• Can I see expressions and objects in different ways?
  

Remember to use the rule that describes how objects or values in a pattern are related.

Sam creates a pattern using the rule “Each story has 3 blocks.”

Question 1.
Draw the next shape in Sam’s pattern.
Answer:

Explanation:
4 x 4 is the Sam’s next shape

Question 2.
Use the rule to continue Sam’s pattern.

Answer:

Explanation:
pattern = multiple of 3

Question 3.
How many blocks are in the 10th shape in Sam’s pattern?
Answer:
10 x 10 = 100
Explanation:
100 blocks are in the 10th shape in Sam’s pattern.

Topic 14 Assessment Practice

Question 1.
Football players come out of the tunnel, and their jerseys have the number pattern shown below. They follow the rule “Add 4.”

A. What number belongs on the front of the blank jersey? Explain.
Answer: 24
Explanation:
Number 24 belongs on the front of the blank jersey

B. Describe two features of the pattern.
Answer:
Explanation:
A feature of the pattern is all the numbers are even
A feature of the pattern is all the numbers are multiples of  4

Question 2.
One dozen eggs is 12 eggs. Two dozen eggs is 24 eggs. Match the number of dozens to the number of eggs. The rule is “Multiply by 12.”

Answer:

Explanation:
Matched the eggs with the dozen

Question 3.
Use the rule “Multiply by 6” to continue the pattern. Then describe a feature of the pattern.

Answer:

Explanation:
A feature of the pattern is all the numbers are even

Question 4.
Use the rule “Divide by 3” to continue the pattern. Then write 4 terms of a different pattern that follows the same rule.
729, 243, 81, ____, _____
Answer: 27, 9 , 3, 1
Explanation:
4 terms of a different pattern that follows the same rule is 27, 9 , 3, 1

Question 5.
Nicole arranges her shopping purchases by price. Each item costs $6 more than the last. The first item costs $13. The last costs $61. Her brother John says that the price of each item is an odd number. Is John correct? Find the cost of each item to explain.
Answer: 19 , 25 , 31, 37 , 43, 49, 55, 61.
Explanation:
John says that the price of each item is an odd number. yes, John correct

Question 6.
The rule for the repeating pattern is “5, 7, 2, 8.” Write the next three numbers in the pattern. Then tell what will be the 25th number in the pattern. Explain.
5, 7, 2, 8, 5, 7, 2, 8, 5, _____, _____, _____
Answer:
5, 7, 2, 8, 5, 7, 2, 8, 5, 7, 2, 8
Explanation:
You can use the rule to find the 25^th number in the pattern.
25 ÷ 4 = 6 R1.
The pattern will repeat 6 times,
then the 1^st number will appear.
The 5 is the 25^th number in the pattern

Question 7.
Jackson wrote different patterns for the rule “Subtract 5.” Select all of the patterns that he could have written. Then write 4 terms of a different pattern that follows the same rule.
☐ 27, 22, 17, 12,7
☐ 5, 10, 15, 20, 25
☐ 55, 50, 35, 30, 25
☐ 100, 95, 90, 85, 80
☐ 75, 65, 55, 45, 35
Answer:

Explanation:
different patterns for the rule “Subtract 5.”
Selected all of the patterns that he could have written

Question 8.
The rule is “Subtract 7.” What are the next 3 numbers in the pattern? Describe two features of the pattern.
70,63, 56, 49, 42,35
Answer: 28, 21, 14, 7
Explanation:
28, 21, 14, 7 the next 3 numbers in the pattern

Question 9.
The table shows the different number of teams formed by different numbers of players. The rule is “Divide by 8.”

A. How many teams can be formed with 40 players?
_______ teams
Answer: 5
Explanation:
5 teams can be formed with 40 players

B. How many players are there on 13 teams? How do you know?
Answer: 104
Explanation:
104 players are there on 13 teams

Question 10.
A. Select all the true statements for the repeating pattern. The rule is “Circle, Heart, Triangle.”

☐ The next shape is the circle.
☐ The circle only repeats twice.
☐ The 10^th shape is the heart.
☐ The 12^th shape is the triangle.
☐ The circle is the 1^st, 4^th, 7^th, etc. shape.
Answer:

Explanation:
Selected all the true statements for the repeating pattern.

B. How many triangles are there among the first 22 shapes?
Answer: 7
Explanation:
7 triangles are there among the first 22 shapes

Topic 14 Performance Task

Wall Hangings Michael uses knots to make wall hangings to sell.

Question 1.
The Michael’s Basic Wall Hanging figure shows a simple wall hanging Michael makes by repeating the shapes shown. What is the 16th shape in the repeating pattern? The rule is “Circle, Triangle, Square.” Explain.
Answer:
Explanation:
You can use the rule to find the 25^th number in the pattern.
16 ÷ 3 =  R1.
The pattern will repeat 5 times,
then the 1^st shape will appear.
The circle is the 16^th shape in the pattern

Question 2.
The Snowflake Design figure shows a knot Michael likes to use.

Part A
List the number of knots that Michael uses to form 1 to 6 snowflake designs. The rule is “Add 11.”
Answer: 11 , 22, 33, 44, 55, 66
Explanation:
The number of knots that Michael uses to form 1 to 6 snowflake designs 11 , 22, 33, 44, 55, 66

Part B
Describe a feature of the pattern you listed in Part A that is not part of the rule. Explain why it works.
Answer:
Explanation:
A feature of the pattern is all the numbers are even and odd

Question 3.
The Michael’s Wall Hanging figure shows the design of a wall hanging Michael makes using the Snowflake Design. Answer the following to find how many knots Michael ties to make a wall hanging with 28 snowflakes.

Part A
Each column of 4 snowflakes has 4 connectors. There are also 4 connectors between columns. Complete the Connectors table using the rule “Add 8 connectors for each column.” Describe a feature of the pattern.

Answer:

Explanation:
Completed the table by following the rule

Part B
Complete the Total Knots table using the following rules.
Snowflake Knots rule: Multiply the number of snowflakes by 11.
Connector Knots rule: Multiply the number of connectors from the Connectors table by 3.
Total Knots rule: Add the number of snowflake knots and the number of connector knots.

Answer:

Explanation:
Snowflake Knots rule: Multiply the number of snowflakes by 11.
Connector Knots rule: Multiply the number of connectors from the Connectors table by 3.
Total Knots rule: Add the number of snowflake knots and the number of connector knots.

Envision Math 6th Grade Textbook Answer Key Topic 2.3 Order of Operations

Order of Operations

How do you know which operation to perform first?
Evaluate 14 + 8 × 6.
Answer:

Other Examples
Evaluate 20 + (30 – 10) ÷ 5.
Using order of operations:
20 + (30 – 10) ÷ 5 ← Compute inside the parentheses first.
20 + 20 ÷ 5 ← Next, divide.
20 + 4 ← Finally, add.
24

Using a scientific calculator:
Press:

Use the order of operations to evaluate.

Evaluate 4² – (4 + 6) ÷ 2.
Using order of operations:
42 – (4 + 6) ÷ 2 ← Compute inside theparentheses first.
42 – 10 ÷ 2 ← Evaluate exponents.
16 – 10 ÷ 2 ← Then divide.
16 – 5 ← Finally, subtract.
11

Using a scientific calculator:
Press:

Explain It
Question 1.
To evaluate 3 × (7 + 5), what should you do first and why?
Answer:
First, add 7 + 5 since that operation is inside the parentheses.
Explanation:

Question 2.
In the second example using the scientific calculator, what is the purpose of the key?
Answer:
It is the key that is used to evaluate a base number raised to the power of an exponent.
Explanation:

Mathematicians use a set of rules known as order of operations , the order in which to perform operations in calculations.
1. Compute inside parentheses.
2. Evaluate terms with exponents.
3. Multiply and divide from left to right.
4. Add and subtract from left to right.

Using the correct order of operations, 14 + 8 × 6 = 62.
A scientific calculator uses order of operations.

Guided Practice

Do you know HOW?
Evaluate each expression.
Question 1.
36 ÷ 6 + 6
Answer:
12
Explanation:

Question 2.
36 ÷ (6 + 6)
Answer:
3
Explanation:

Question 3.
24 ÷ (4 + 8) + 2
Answer:
4
Explanation:

Question 4.
48 ÷ (4 + 8) + 2²
Answer:
8
Explanation:

Question 5.
24 ÷ 4 + 8 + 2
Answer:
16
Explanation:

Question 6.
48 ÷ 4 + 8 + 2²
Answer:
24
Explanation:

Do you UNDERSTAND?
Question 7.
Where could you insert parentheses to make this number sentence true? 80 ÷ 8 × 5 + 4= 90
Answer:
See margin.
Explanation:

Question 8.
Donavan entered 12 + 4 × 36 into Lidia’s scientific calculator.The display showed 18. In what order did the calculator complete the operations?
Answer:
See margin.
Explanation:

Independent Practice

Evaluate each expression.
Question 9.
3³ – 8 × 3
Answer:
3
Explanation:

Question 10.
(5² + 7) ÷ 4
Answer:
8
Explanation:

Question 11.
6 × 4 – 4 + 2
Answer:
8
Explanation:

Question 12.
18 – 3 × 5 + 2
Answer:
5
Explanation:

Question 13.
49 – 4 × (49 ÷ 7)
Answer:
21
Explanation:

Question 14.
(64 ÷ 8) × 3 + 6
Answer:
30
Explanation:

Question 15.
72 ÷ (4 + 4) × 5
Answer:
45
Explanation:

Question 16.
(3 × 3) × (2 × 2) ÷ 36
Answer:
1
Explanation:

Use parentheses to make each number sentence true.
Answer:
See margin.
Explanation:

Question 17.
5 + 4 × 3 × 3 = 41
Answer:

Question 18.
9 × 0 + 4 = 36
Answer:

Question 19.
5² – 6 × 0 = 25
Answer:

Question 20.
8 × 9 – 2 – 3 = 32
Answer:

 

Question 21 .
5 + 4 × 3 × 3 = 81
Answer:

Question 22.
9 × 0 + 4 = 4
Answer:

Question 23.
5² – 6 × 0 = 0
Answer:

Question 24.
8 × 9 – 2 – 3 = 53
Answer:

Question 25.
1 + 2 × 3 + 4 = 21
Answer:

Question 26.
2² + 4 × 6 = 48
Answer:

Question 27.
5 × 6 × 8 – 7 = 30
Answer:

Question 28.
6² + 7 + 9 × 10 = 133
Answer:

Question 29.
Number Sense Use the symbols +, -, ×, and ÷ to make the number sentence true.
Answer:

Explanation:

Question 30.
Meredith bought 3 T-shirts for $12.00 each. Her grandmother paid for half the total cost. To find how much Meredith paid, evaluate the expression: (3 × 12) ÷ 2.
Answer:
(3 × 12) ÷ 2 = $18. Meredith paid $18.
Explanation:

Question 31.
Luke needs a new fence around his garden, but the gate across the narrow end of the garden will not be replaced. To find how many feet of fencing Luke needs, evaluate the expression: 12 + (2 × 14).

Answer:
40 feet
Explanation:

Question 32.
Writing to Explain If p is greater than zero, tell which of these expressions will result in the higher number: (2 × p) + 5 or 2 × (p + 5). Explain how you know.
Answer:
See margin.
Explanation:

Question 33.
Jaron walked 15 blocks north and then 3 blocks west to school. Marisol walked 3 blocks east and then 15 blocks south to school. Write an expression to show that each traveled the same distance.
Answer:
3 + 15 = 15 + 3
Explanation:

Question 34.
On Saturday, every seat in Mazen Theater was full. The balcony has 10 rows with 22 seats in each. The main floor has 25 rows with 30 seats each. To find the number of people at the theater, evaluate the following expression: (10 × 22) + (25 × 30).
A. 16
B. 87
C. 970
D. 14,100
Answer:
C. 970
Explanation:

Question 35.
On her math test, Bianca scored 5 points on each of 5 questions, 2 points on each of 2 questions, and 3 points on each of 4 questions. To find the number of points she scored, evaluate the expression: 5² + 2² + (3 × 4).
A. 26
B. 40
C. 41
D. 84
Answer:
C. 41
Explanation:

Question 36.
The world’s largest flag measures 505 ft by 225 ft. The flag hangs by a cable through grommets on one of the shorter sides. There is a grommet every 30 in. If there is a grommet at each end, evaluate the expression 1 + (225 × 12) ÷ 30 to find out how many grommets are used to hang the flag.

Answer:
91 grommets
Explanation:

Going Digital

Exponents and Order of Operations

Evaluate 5⁶ on a calculator Ono ways.

Evaluate 9³ + (27 ÷ 3 + 47) on a calculator two ways
Step 1: Use the calculator’s order of operations.

Step 2: Follow order of operations to verify that the calculator used the correct order of operation.

Practice

Evaluate each expression two ways.
Question 1.
8⁵
Answer:
32, 768
Explanation:

Question 2.
7⁴
Answer:
2,401
Explanation:

Question 3.
8 × 19 – 36 + 12⁵
Answer:
248,948
Explanation:

Question 4.
(72 ÷ 9) + 6 × 3⁵
Answer:
1,466
Explanation:

Question 5.
3⁷
Answer:
2,187
Explanation:

Question 6.
1204 ÷ 14 – 2⁵ + 178
Answer:
232
Explanation:

Envision Math 1st Grade Textbook Answer Key Topic 1 Test

Test

Oral Directions Say: Mark the correct answer. 1. Rover likes bones. How many bones does he have? 2. Bonnie drew 5 flowers. Then she drew 3 more. How many flowers did Bonnie draw in all? 3–4. Which number does the picture show?

Question 1.

Answer:

Question 2.

Answer:

Question 3.

Answer:

Question 4.

Answer:

Oral Directions Say: Mark the correct answer. 5–6. Which number does the picture show? 7. Chuck made 4 paper airplanes. Then he made 4 more. Which model shows how many airplanes Chuck made altogether? 8. Mel’s cat had 5 kittens. Which model shows the number of kittens

Question 5.

Answer:

Question 6.

Answer:

Question 7.

Answer:

Question 8.

Answer:

Envision Math 1st Grade Textbook Answer Key Topic 1.1 0 to 5

Review What You Know

Question 1.
Circle the number that tells how many.

Answer:

Question 2.
Circle the group that has more

Answer:

Question 3.
Circle the group that has 4

Answer:

Home-School Connection

Dear Family,
Today my class started Topic 1, Numbers to 12. I will learn ways to count and model numbers using real objects. Here are some things we can do to help me with my math.
Love, ___________

Book to Read

Reading math stories reinforces concepts. Look for this title in your local library:
Numbers by Henry Pluckrose (Children’s Press, 1995)

Home Activity
Have your child make a number collage. Ask him or her to write a number between 1 and 12 on a piece of paper. Then ask him or her to glue or tape that number of items to the paper. Use common items such as buttons, toothpicks, or paper clips.

Counting Safari

0 to 5

Home Connection Your child showed the numbers 0 through 5 with counters.
Home Activity Have your child use pennies or other small items to show the numbers 0 through 5
Question 1.

Answer:

Question 2.

Answer:

Question 3.

Answer:

Question 4.

Answer:

Guided Practice

Draw the counters to show the number.
Question 1.

Answer:

Question 2.

Answer:

Question 3.

Answer:

Question 4.

Answer:

Question 5.

Answer:

Question 6.

Answer:

Do you understand?
How is 3 the same as ?
Answer:

Independent Practice

Write the number that tells how many.
Question 7.

Answer:

Question 8.

Answer:

Question 9.

Answer:

Question 10.

Answer:

Question 11.

Answer:

Question 12.

Answer:

Number Sense
Question 13.
Use counters. Show a number from 1 to 5. Draw the counters. Write the number.

Answer:

Problem Solving

Solve the problems below.
Question 14.
Ann has 3 dogs. Each dog has a toy. Draw their toys.

Answer:

Question 15.
Bob likes acorns. How many does he have?

Answer:

Question 16.
Journal Draw a picture of some friends. How many did you draw?
Write the number and the number word.

Answer:

Go through the enVision Math Common Core Grade 4 Answer Key Topic 13 Measurement: Find Equivalence in Units of Measure regularly and improve your accuracy in solving questions.

enVision Math Common Core 4th Grade Answers Key Topic 13 Measurement: Find Equivalence in Units of Measure

Essential Questions:
How can you convert from one unit to another? How can you be precise when solving math problems?

enVision STEM Project: Erosion and Measurement
Do Research The Colorado River has played a large part in shaping North America. Use the Internet and other resources to research the states through which the river travels.
Journal: Write a Report Include what you found. Also in your report:

• Look up geology and geometry in the dictionary. Write the definitions and explain how these words are related. What does the prefix “geo” mean in both words?
• A.J. takes a 4-mile tour of the Grand Canyon. Explain how to convert the length of A.J.’s tour from miles to feet.

Review What You Know

Vocabulary

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

• capacity
• gram
• liter
• mass

Question 1.
The amount of liquid a container can hold is called its ________.
Answer:
The amount of liquid a container can hold is called its __capacity______.

 

Question 2.
________ is the amount of matter that something contains.
Answer:
___Mass_____ is the amount of matter that something contains.

 

Question 3.
One metric unit of capacity is a ________.
Answer:
One metric unit of capacity is a __Liter______.

 

Perimeter
Find the perimeter of each shape.
Question 4.

Answer:
Perimeter of the given rectangle shape = 134 centimeters.

Explanation:
Length of the given rectangle shape = 42 centimeters.
Width of the given rectangle shape = 25 centimeters.
Perimeter of the given rectangle shape = 2 × (Length of the given rectangle shape × Width of the given rectangle shape)
= 2 × (42 + 25)
= 2 × 67
= 134 centimeters.

 

Question 5.

Answer:
Perimeter of the given square shape = 28 feet.

Explanation:
Length of the given square shape = 7 feet.
Perimeter of the given square shape = 4 × Length of the given square shape
= 4 × 7
= 28 feet.

 

 

Question 6.

Answer:
Perimeter of the given Triangular shape = 9 yards.

Explanation:
Length of the given Triangular shape = 3 yards.
Perimeter of the given Triangular shape =  Length of the given Triangular shape + Length of the given Triangular shape + Length of the given Triangular shape
= 3 + 3 + 3
= 9 yards.

 

 

 

Question 7.

Answer:
Perimeter of the given Quadrilateral shape = 62 inches.

Explanation:
Length of the given Quadrilateral shape:
Side 1 length = 17 inches.
Side 2 length = 12 inches.
Side 3 length = 21 inches.
Side 4 length = 12 inches.
Perimeter of the given Quadrilateral shape = Side 1 length + Side 2 length + Side 3 length + Side 4 length
= 17 + 12 + 21 + 12
= 29 + 21 + 12
= 50 + 12
= 62 inches.

Question 8.

Answer:
Perimeter of the given hexagon shape = 90 centimeters.

Explanation:
Length of the given hexagon shape = 15 centimeters.
Perimeter of the given hexagon shape = 6 × Length of the given hexagon shape
= 6 × 15
= 90 centimeters.

 

 

Question 9.

Answer:
Perimeter of the given rectangle shape = 40.67 feet.

Explanation:
Length of the given rectangle shape = 19 (11/12) feet.
Width of the given rectangle shape =  7 (5/12) feet.
Perimeter of the given rectangle shape = 2 × (Length of the given rectangle shape × Width of the given rectangle shape)
= 2 × (19 11/12 + 7 5/12)
= 2 × (209/12 + 35/12)
= 2 × 244/12
= 488/12
= 40.67 feet.

 

 

Area
Find the area of each shape.
Question 10.

Answer:
Area of the given rectangle shape = 10 square yards.

Explanation:
Length of the given rectangle shape = 5 yards.
Width of the given rectangle shape =  2 yards.
Area of the given rectangle shape = Length of the given rectangle shape × Width of the given rectangle shape
= 5 × 2
= 10 square yards.

 

Question 11.

Answer:
Area of the given rectangle shape = 1/2 or 0.5 inches.

Explanation:
Length of the given rectangle shape = 2 inches.
Width of the given rectangle shape =  1/4 inches.
Area of the given rectangle shape = Length of the given rectangle shape × Width of the given rectangle shape
= 2 × 1/4
= 1/2 or 0.5 inches.

Question 12.

Answer:
Area of the given rectangle shape = 21 square centimeters.

Explanation:
Length of the given rectangle shape = 7 centimeters.
Width of the given rectangle shape = 3 centimeters.
Area of the given rectangle shape = Length of the given rectangle shape × Width of the given rectangle shape
= 7 × 3
= 21 square centimeters.

Problem Solving
Question 13.
Make Sense and Persevere A league is a nautical measurement equal to about 3 miles. If a ship travels 2,000 leagues, about how many miles does the ship travel?
Answer:
Number of miles the ship travelled = 6000 miles.

Explanation:
1 league = 3 miles.
Number of leagues the ship travelled = 2000.
Number of miles the ship travelled = 3 × Number of leagues the ship travelled
=> 3 × 2000
=> 6000 miles.

 

Pick a Project
PROJECT 13A
What makes the St. Johns River special?
Project: Make a Travel Brochure About Rivers in Your Home State

Answer:

PROJECT 13B
How are tin cans useful?
Project: Cooking on a Budget

Answer:
Ways to Cook on a Budget

 

 

PROJECT 13C
Who invented the jigsaw puzzle?
Project: Make Your Own Jigsaw Puzzle

Answer:

3-ACT MATH PREVIEW

Math Modeling
A Pint’s a Pound

I can … model with math to solve a problem that involves estimating and computing with units of weight and capacity.

Lesson 13.1 Equivalence with Customary Units of Length

Solve & Share
Jeremy jogged 75 yards from his house to school. How many feet did Jeremy jog? Solve this problem any way you choose.
I can … convert customary units of length from one unit to another and recognize the relative size of different units.

Look Back! Look for Relationships What do you notice about the relationship between the number of yards and the number of feet Jeremy jogged?
Answer:
The relationship between the number of yards and the number of feet Jeremy jogged is 3 times more than the number of yards Jeremy jogged.

Explanation:
Number of yards Jeremy jogged = 75.
Number of feet Jeremy jog = 3 × Number of yards Jeremy jogged
= 3 × 75
= 225 feet.

 

Essential Question
How Can You Convert from One Unit of Length to Another?
Answer:
We can Convert from One Unit of Length to Another, by following steps:
1. Write the conversion as a fraction (that equals one)
2. Multiply it out (leaving all units in the answer)
3. Cancel any units that are both top and bottom.

 

Visual Learning Bridge
Maggie has a tree swing. How many inches long is each rope from the bottom of the branch to the swing?

Step 1
Find the length of the rope in feet. r = 10 – 2\(\frac{1}{4}\)

Each rope is 7\(\frac{3}{4}\) feet long.

Step 2
Convert the length of the rope to inches.

Each rope is 93 inches long.

Convince Me! Generalize How do you know the answer is reasonable when converting a larger unit to a smaller unit?
Answer:
When converting a larger unit to a smaller one, you multiply; when you convert a smaller unit to a larger one, you divide. Hence, the answer is reasonable when converting a larger unit to a smaller unit.

 

Another Example!
Mark moved forward yard when doing a back flip. Daisy moved forward 3\(\frac{1}{6}\) feet. How much more did Daisy move forward than Mark? One yard is 3 times as long as a foot.

Guided Practice
Do You Understand?
Question 1.
Does it take more inches or feet to equal a given length? Explain.
Answer:
Converting Between Units of Length:
There are many more inches for a measurement than there are feet for the same measurement, as feet is a longer unit of measurement. You could use the conversion factor.

 

Question 2.
Which is a greater distance, 9 yards or 9 miles?
Answer:
9 miles is a greater distance between 9 yards or 9 miles.

Explanation:
1 miles = 1760 yards.
9 miles = ??? yards.
=> 9 × 1760
=> 15840 yards.

 

Do You Know How?
For 3-4, convert each unit.
Question 3.
2 miles = _________ yards
Answer:
2 miles = __3520 _______ yards.

Explanation:
1 miles = 1760 yards.
2 miles = 2 × 1760
=> 3520 yards.

Question 4.
\(\frac{2}{3}\) yard = _____feet
Answer:
\(\frac{2}{3}\) yard = __2___feet.

Explanation:
1 yard = 3 feet.
\(\frac{2}{3}\) yard = \(\frac{2}{3}\) × 3
=> 2 feet.

 

Independent Practice
In 5-7, write > or < in each to compare the measures.
Question 5.
6 inches 6 feet
Answer:
6 inches <  6 feet.

Explanation:
1 feet = 12 inches.
6 feet = 6 × 12
=> 72 inches.

 

Question 6.
2 yards 7 feet
Answer:
2 yards < 7 feet.

Explanation:
1 yard = 3 feet.
2 yards = 2 × 3
=> 6 feet.

 

Question 7.
4 yards 100 inches
Answer:
4 yards > 100 inches.

Explanation:
1 yard = 36 inches.
4 yards = 4 × 36
=> 144 inches.

 

 

For 8-11, convert each unit.
Question 8.
8 yards = _______ inches
Answer:
8 yards = __288_____ inches.

Explanation:
1 yard = 36 inches.
8 yards = 8 × 36
=> 288 inches.

 

Question 9.
28 yards = ______ feet
Answer:
28 yards = __84____ feet.

Explanation:
1 yard = 3 feet.
28 yards = 3 × 28
=> 84 feet.

 

Question 10.
18 feet = ________ inches
Answer:
18 feet = ___216_____ inches.

Explanation:
1 feet = 12 inches.
18 feet = 12 × 18
=> 216 inches.

 

Question 11.
7 miles = ______ yards
Answer:
7 miles = __12320____ yards.

Explanation:
1 mile = 1760 yards.
7 miles = 1760 × 7
=> 12320 yards.

 

Problem Solving
Question 12.
Be Precise Lou cuts 3 yards from a 9-yard roll of fabric. Then he cuts 4 feet from the roll. How many feet of fabric are left on the roll?
Answer:
Remaining feet of fabric are left on the roll = 14.

Explanation:
Length of fabric Lou cuts = 3 yards.
Length of roll of fabric = 9 yards.
Remaining length of roll of fabric = Length of roll of fabric – Length of fabric Lou cuts
= 9 – 3
= 6 yards.
Conversion: 1 yard = 3 feet.
= 6 yards = ??? feet
=> 6 × 3 feet
= 18 feet.
Length of fabric later cut = 4 feet.
Remaining feet of fabric are left on the roll = Remaining length of roll of fabric – Length of fabric later cut
= 18 – 4
= 14 .

 

Question 13.
What customary units would you use to measure the length of a praying mantis? Explain.
Answer:
The customary system of measurement is inches used to measure the length of a praying mantis.

Explanation:
The customary system of measurement is defined as a set of weights and measures used for measuring length, weight, capacity, and temperature. Most praying mantis are no more than 5 inches in length. The smaller species measure around 2 to 3 inches while the bigger specimens reach the overall length of 6 to 7 inches.

 

Question 14.
Algebra On the field trip, Toni collected 4 times as many bugs as Kaylie. Kaylie collected 14 bugs. Draw a bar diagram, and write and solve an equation to find b, how many bugs Toni collected.
Answer:
Number of bugs Toni collected = 56.

Explanation:
Number of bugs Kaylie collected = 14.
Toni collected 4 times as many bugs as Kaylie.
Number of bugs Toni collected = 4 × Number of bugs Kaylie collected
= 4 × 14
=> 56.

 

Question 15.
Which is greater, 3 miles or 5,000 yards? How much greater? Explain.
Answer:
3 miles is greater by 280 yards than 5,000 yards.

Explanation:
3 miles,5000 yards.
Conversion: 1 mile = 1760 yards.
3 miles = ??? yards
=> 3 × 1760
=> 5280 yards.
Difference:
5280 yards – 5000 yards
=> 280 yards.

 

Question 16.
Higher Order Thinking Jenna uses \(\frac{1}{2}\) yard of ribbon for each box she wraps. How many inches of ribbon does she need to wrap 4 boxes? Use the linear model to help solve.

Answer:
Number of inches of ribbon she needs to wrap 4 boxes = 72 inches.

Explanation:
Length of ribbon Jenna uses for each box she wraps = \(\frac{1}{2}\) yard.
Total Length of ribbon she needs to wrap 4 boxes = 4 × Length of ribbon Jenna uses for each box she wraps
= 4 × \(\frac{1}{2}\) yard
= 2 yards.
Conversion: 1 yard = 36 inches.
Number of inches of ribbon she needs to wrap 4 boxes = Total Length of ribbon she needs to wrap 4 boxes × 36 inches
= 2  × 36
=> 72 inches.

 

 

Assessment Practice
Question 17.
Connor has 3\(\frac{3}{4}\) feet of brown fabric and \(\frac{3}{4}\) yard of green to make a costume for the school play. How many more feet of brown than green fabric does Connor have? Show both measures with points on the number line.

Answer:
1 \(\frac{2}{4}\) feet more feet of brown than green fabric Connor have.

Explanation:
Length of brown fabric Connor has = 3\(\frac{3}{4}\) feet.
Length of green fabric Connor has = \(\frac{3}{4}\) yard
Conversion: 1 yard = 3 feet.
\(\frac{3}{4}\) yard = ?? feet
=> 3 × \(\frac{3}{4}\)
=> 2 \(\frac{1}{4}\)  feet.
Difference:
Length of brown fabric Connor has  – Length of green fabric Connor has
= 3\(\frac{3}{4}\) feet – 2 \(\frac{1}{4}\) feet
= 1 \(\frac{2}{4}\) feet.

 

Question 18.
Charlotte made \(\frac{11}{2}\) yard of a paper chain for the school dance. Josh made 4\(\frac{1}{12}\) feet, and Mika made 3\(\frac{4}{12}\) feet. How many feet of chain did they make in all?
A. 8\(\frac{4}{12}\) feet
B. 9\(\frac{4}{12}\) feet
C. 10\(\frac{2}{12}\) feet
D. 10\(\frac{4}{12}\) feet
Answer:
Total length of feet of chain they make in all = 9\(\frac{4}{12}\) feet.
B. 9\(\frac{4}{12}\) feet.

Explanation:
Length of a paper chain Charlotte made = \(\frac{11}{2}\) yard.
Conversion:
1 yard = 3 feet.
\(\frac{11}{2}\) yard = \(\frac{11}{2}\) × 3
= 16 \(\frac{1}{2}\) feet.
Length of a paper chain Josh made = 4\(\frac{1}{12}\) feet.
Length of a paper chain Mika made = 3\(\frac{4}{12}\) feet.
Total length of feet of chain they make in all = Length of a paper chain Charlotte made + Length of a paper chain Josh made + Length of a paper chain Mika made
= 16 \(\frac{1}{2}\) feet + 4\(\frac{1}{12}\) feet + 3\(\frac{4}{12}\) feet
= 9\(\frac{4}{12}\) feet.

 

Lesson 13.2 Equivalence with Customary Units of Capacity

Solve & Share
Casey has \(\frac{1}{2}\) gallon of juice. How many 1-pint containers can he fill? Solve this problem any way you choose.
I can … convert customary units of capacity from one unit to another and recognize the relative size of different units.

Look Back! Generalize How did you convert from a larger unit of capacity to a smaller unit of capacity? Did you use the same process you used to convert from a larger unit of length to a smaller unit of length? Explain.

Answer:
When converting a larger unit of capacity to a smaller one of capacity, you multiply; when you convert a smaller unit of capacity to a larger one of capacity, you divide.
Yes, I used the same process you used to convert from a larger unit of length to a smaller unit of length.

 

 

Essential Question
How Can You Convert from One Unit of Capacity to Another?
Answer:
We can convert from One Unit of Capacity to Another by converting a larger unit of capacity to a smaller one of capacity, you multiply; when you convert a smaller unit of capacity to a larger one of capacity, you divide.

 

 

Visual Learning Bridge
Ms. Nealy’s class needs 5 gallons of punch for family math night. How much of each ingredient is needed to make enough punch with the recipe shown?

Units of capacity include gallons, quarts, pints, cups, and fluid Ounces.
Capacity is how much liquid a container can hold. This diagram shows the relative sizes of customary units of capacity. 1 gallon is 4 times as much as 1 quart

Step 1
Convert 5 gallons to pints.

5 gallons = 40 pints

Step 2
Add the number of pints in the recipe to find how many batches the class needs to make.
5 + 4 +1 = 10
10 × n = 40
n = 4
The class needs to make 4 batches of the recipe.

Step 3
Find how much of each ingredient is in 4 batches.
4 × 5 = 20 pints
4 × 4 = 16 pints
4 × 1 = 4 pints
20 pints of apple juice, 16 pints of lemon/lime soda, and 4 pints of frozen orange juice are needed.

Convince Me! Reasoning Complete the sentence below.
One gallon equals _______ quarts, _______ pints, or _______ cups.
Answer:
One gallon equals ___4____ quarts, ____8___ pints, or ___16____ cups.

Explanation:
1 gallon = 8 pints.
1 gallon = 4 quarts.
1 gallon = 16 cups.

 

Guided Practice
Do You Understand?
Question 1.
How many cups of punch does 5 gallons of the punch from the previous page make?
Answer:
Number of cups of punch 5 gallons of the punch from the previous page makes = 80 cups.

Explanation:

Number of cups of punch 5 gallons of the punch from the previous page makes =
5 gallons = ??? cups
Conversion:
1 gallon = 16 cups.
5 gallons = 5 × 16
= 80 cups.

 

Question 2.
Which size container holds more, 3 pints or 3 quarts?
Answer:
3 quarts size container holds more.

Explanation:
3 pints and 3 quarts.
1 quarts = 2 pints.
3 quarts = 3 × 2
= 6 pints.

 

Do You Know How?
For 3-5, convert each unit.
Question 3.
2 cups = _______ fluid ounces
Answer:
2 cups = ___16____ fluid ounces.

Explanation:
Conversion: 1 cup = 8 fluid ounces.
2 cups = 8 × 2
= 16 fluid ounces.

 

 

Question 4.
\(\frac{1}{2}\) gallon = _______ pints
Answer:
\(\frac{1}{2}\) gallon = ___4____ pints.

Explanation:
Conversion: 1 gallon = 8 pints.
\(\frac{1}{2}\) gallon = 8 × \(\frac{1}{2}\)
= 4 pints.

 

Question 5.
5 pints = ______ cups
Answer:
5 pints = __10____ cups.

Explanation:
Conversion: 1 pint = 2 cups.
5 pints = 2 × 5
= 10 cups.

 

Independent Practice
In 6-8, write > or < in each to compare the measures.
Question 16.
2 pints 2 gallons
Answer:
2 pints < 2 gallons.

Explanation:
2 pints and 2 gallons.
Conversion: 1 gallon = 8 pints.
2 gallons = 8 × 2
= 16 pints.

 

Question 7.
5 quarts 8 pints
Answer:
5 quarts  >  8 pints.

Explanation:
5 quarts and 8 pints.
Conversion: 1 quart = 2 pints.
5 quarts = 2 × 5
= 10 pints.

 

Question 8.
10 cups 2 quarts
Answer:
10 cups > 2 quarts.

Explanation:
10 cups and 2 quarts.
Conversion: 1 quart = 4 cups.
2 quarts = 4 × 2
= 8 cups.

 

 

For 9-12, convert each unit.
Question 9.
7 quarts = ________ cups
Answer:
7 quarts = ____28____ cups.

Explanation:
Conversion:  1 quart = 4 cups.
7 quarts = 4 × 7
= 28 cups.

 

 

Question 10.
12 gallons = ______ quarts
Answer:
12 gallons = ___48___ quarts.

Explanation:
Conversion: 1 gallon = 4 quarts.
12 gallons = 4 × 12
= 48 quarts.

 

 

Question 11.
7 pints = _______ fluid ounces
Answer:
7 pints = __112_____ fluid ounces.

Explanation:
Conversion: 1 pint = 16 fluid ounces.
7 pints = 16 × 7
= 112 fluid ounces.

 

Question 12.
\(\frac{3}{4}\) gallon = ______ pints
Answer:
\(\frac{3}{4}\) gallon = ___6___ pints.

Explanation:
Conversion: 1 gallon = 8 pints.
\(\frac{3}{4}\) gallon = 8 × \(\frac{3}{4}\)
= 6 pints.

 

 

For 13-14, convert each unit.
Question 13.

Answer:

Explanation:
Conversion: 1 pint = 16 fluid ounces.
\(\frac{2}{4}\) = 16 × \(\frac{2}{4}\)
= 8 fluid ounces.
1 pint = 16 fluid ounces.
2 pints = 16 × 2
= 32 fluid ounces.
4 pints = 16 × 4
= 64 fluid ounces.

 

Question 14.

Answer:

Explanation:
Conversion: 1 gallon = 16 cups.
2 gallon = 16 × 2 = 32 cups.
3 gallon = 16 × 3 = 48 cups.
4 gallon = 16 × 4 = 64 cups.

 

Problem Solving
Question 15.
en Vision® STEM Scientists measure how much water and debris flow past a river station at different times of the year. The water and debris are called discharge. The table shows the average discharge at the Camp Verde station on the Verde River in two months. How many more quarts of discharge per second are there in December than November?

Answer:
2664 more quarts of discharge per second are there in December than November .

Explanation:
Average discharge at the Camp Verde station on the Verde River for November month = 1619 gallons per second.
Average discharge at the Camp Verde station on the Verde River for December month = 2285 gallons per second.
Conversion: 1 gallon = 4 quarts.
Number of quarts of discharge per second  in November = Average discharge at the Camp Verde station on the Verde River for November month × 4
= 1619 × 4
= 6476 quarts.
Number of quarts of discharge per second  in December = Average discharge at the Camp Verde station on the Verde River for December month × 4
= 2285 × 4
= 9140 quarts.
Difference:
Number of quarts of discharge per second  in December – Number of quarts of discharge per second  in November
= 9140 – 6476
= 2664 .

 

Question 16.
How many quarts of discharge per second were recorded in November and December?
Answer:
Number of quarts of discharge per second  in November = 6476 quarts.
Number of quarts of discharge per second  in December = 9140 quarts.

Explanation:
Conversion: 1 gallon = 4 quarts.
Number of quarts of discharge per second  in November = Average discharge at the Camp Verde station on the Verde River for November month × 4
= 1619 × 4
= 6476 quarts.
Number of quarts of discharge per second  in December = Average discharge at the Camp Verde station on the Verde River for December month × 4
= 2285 × 4
= 9140 quarts.

 

 

Question 17.
Make Sense and Persevere Annabelle had the following containers of paint left over: \(\frac{1}{2}\) gallon, \(\frac{3}{4}\) quart, and \(\frac{1}{4}\) gallon. How many quarts of paint does Annabelle have left over? Explain.
Answer:
Total quarts of paint does Annabelle have left over = 3 \(\frac{3}{4}\) quarts.

Explanation:
Quantity of containers of paint left over:
First container = \(\frac{1}{2}\) gallon.
Second container = \(\frac{3}{4}\) quart.
Third container = \(\frac{1}{4}\) gallon.

Conversion: 1 gallon = 4 quarts.
First container = \(\frac{1}{2}\) gallon.
= \(\frac{1}{2}\)  × 4
= 2 quarts.
Third container = \(\frac{1}{4}\) gallon.
= \(\frac{1}{4}\)  × 4
= 1 quarts.
Total quarts of paint does Annabelle have left over = First container + Second container + Third container
= 2 quarts + \(\frac{3}{4}\)  + 1 quarts
= 3 \(\frac{3}{4}\) quarts.

 

 

Question 18.
Higher Order Thinking A caterer combines 3 quarts of orange juice, 5 pints of milk, and 5 cups of pineapple juice to make smoothies. How many cups can be filled with smoothies? Explain.
Answer:
Number of cups can be filled with smoothies = 27 cups.

Explanation:
Quantity of orange juice = 3 quarts.
Quantity of pints of milk = 5 pints.
Quantity of cups of pineapple juice = 5 cups.
Conversion: 1 pint = 2 cups.
Quantity of pints of milk = 5 pints.
=> 5 pints = 2 × 5 = 10 cups.

Conversion: 1 quarts = 4 cups.
Quantity of orange juice = 3 quarts.
=> 3 quarts = 4 × 3
= 12 cups.
Number of cups can be filled with smoothies = Quantity of orange juice + Quantity of pints of milk + Quantity of cups of pineapple juice
= 12 cups + 10 cups + 5 cups
= 27 cups.

 

 

Assessment Practice
Question 19.
Which equals 3 quarts?
A. 6 cups
B. 12 cups
C. 12 pints
D. 3 gallons
Answer:
3 quarts = 12 cups.
B. 12 cups

Explanation:
1 quarts = 4 cups.
3 quarts = 4 × 3 = 12 cups.
1 quart = 2 pint.
3 quarts = 2 × 3 = 6 pints.
1 quart = 0.25 gallon.
3 quarts = 3 × 0.25 = 0.75 gallon.

 

 

Question 20.
Select all the comparisons that are true.
☐ 4 cups < 4 pints
☐ 7 pints > 7 fluid ounces
☐ 2 gallons > 9 quarts
☐ 3 quarts < 14 cups
☐ 3 gallons < 18 pints
Answer:
All the comparisons that are true:
4 cups < 4 pints (TRUE)
7 pints > 7 fluid ounces (TRUE)
3 quarts < 14 cups (TRUE)
3 gallons < 18 pints (TRUE)

Explanation:
All the comparisons that are true:
☐ 4 cups < 4 pints (TRUE)
☐ 7 pints > 7 fluid ounces (TRUE)
☐ 2 gallons > 9 quarts (FALSE)
☐ 3 quarts < 14 cups (TRUE)
☐ 3 gallons < 18 pints (TRUE)

☐ 4 cups < 4 pints
1 pint = 2 cups.
4 cups < 4 pints
=> 4 × 2 = 8 cups < 4 pints.

☐ 7 pints > 7 fluid ounces
1 pint = 16 fluid ounces
=> 7 × 16 = 112 > 7 fluid ounces.

1 gallon = 4 quarts.
☐ 2 gallons > 9 quarts
=> 2 × 4 = 8 quarts > 9 quarts.

1 quarts = 4 cups.
☐ 3 quarts < 14 cups
=> 3 × 4 = 12 < 14 cups.

1 gallon = 8 pints.
3 gallons < 18 pints
=> 3 × 8 = 24 < 18 pints.

 

Lesson 13.3 Equivalence with Customary Units of Weight

Solve & Share
When Lori’s puppy, Bay, was born she weighed \(\frac{3}{8}\) pound. What was Bay’s weight in ounces? Solve this problem any way you choose.
I can … convert customary units of weight from one unit to another and recognize the relative size of different units.

Look Back! Be Precise How did you know you needed to convert units to solve the problem above?
Answer:
Well, we need to know the units given in the problem to convert. Next we should find the units value into which, the value should be converted into and later convert into the required units to solve the problem asked above.

 

 

Essential Question
How Can You Convert from One Unit of Weight to Another?
Answer:
We have also learnt conversion of one unit to another. We can convert from One Unit of Weight to Another by knowing the value of the conversion unit and multiplying it.

For example:
We can convert kilogram into grams by multiplying the number of kilograms by 1000. To convert grams into kilograms, we divide the number of grams by 1000.

 

 

Visual Learning Bridge
Mark made dinner for his family using the ingredients shown. How many 6-ounce servings did Mark make?
Weight is how heavy an object is. Units of weight include ounces, pounds, and tons.
This table shows the relative sizes of customary units of weight. 1 pound is 16 times as heavy as 1 ounce.

To convert the weight of the pasta and the meatballs to ounces, multiply each weight by 16.
Pasta:
2 × 16 = 32
= 6\(\frac{2}{5}\) ounces
Meatballs:
\(\frac{3}{5}\) × 16 = \(\frac{48}{5}\)
= 9\(\frac{3}{5}\) ounces

Add the weights of all the ingredients to find the total ounces.

The weight of all the ingredients is 24 ounces.

Divide to find s, the number of servings.

24 = 6 = s
s = 4
Mark made four 6-ounce servings.

Convince Me! Generalize How do you convert a larger unit of weight to a smaller unit of weight?
Answer:
We can convert a larger unit of weight to a smaller unit of weight by multiplying. To convert from a smaller unit to a larger one, divide.

 

 

Guided Practice
Do You Understand?
Question 1.
Would it make sense to describe the total weight of Mark’s dinner in tons? Why or why not?
Answer:
No, it does not makes sense to describe the total weight of Mark’s dinner in tons because it is not asked in the problem to find.

 

 

 

Do You Know How?
For 2-4, convert each unit.
Question 2.
9 tons = ________ pounds
Answer:
9 tons = ________ pounds.

Explanation:
Conversion: 1 ton = 2000 pounds.
9 tons = 2000 × 9
= 18000 pounds

 

 

Question 3.
\(\frac{3}{4}\) pound = _______ ounces
Answer:
\(\frac{3}{4}\) pound = ___12____ ounces

Explanation:
Conversion: 1 pound = 16 ounces.
\(\frac{3}{4}\) pound = 16 × \(\frac{3}{4}\)
= 12 ounces.

 

 

Question 4.
17 pounds = _________ ounces
Answer:
17 pounds = ___272______ ounces.

Explanation:
Conversion: 1 pound = 16 ounces.
17 pounds = 16 × 17
= 272 ounces.

 

 

Independent Practice
In 5-7, write > or < in each to compare the measures.
Question 5.
6 ounces 6 pounds
Answer:
6 ounces < 6 pounds.

Explanation:
6 ounces and 6 pounds.
Conversion: 1 pound = 16 ounces.
6 pounds = 16 × 6
= 96 ounces.

 

Question 6.
3 pounds 40 ounces
Answer:
3 pounds > 40 ounces.

Explanation:
3 pounds  and 40 ounces.
Conversion: 1 pound = 16 ounces.
3 pounds = 16 × 3
= 48 ounces.

 

Question 7.
5,000 pounds 2 tons
Answer:
5,000 pounds > 2 tons.

Explanation:
5,000 pounds and 2 tons.
Conversion: 1 ton = 2000 pounds.
2 tons = 2000 × 2
= 4000 pounds.

 

 

For 8-13, convert each unit.
Question 8.
15 pounds = ________ ounces
Answer:
15 pounds = ___240_____ ounces.

Explanation:
Conversion: 1 pound = 16 ounces.
15 pounds = 16 × 15
= 240 ounces.

 

Question 9.
7 tons = _______ pounds
Answer:
7 tons = _14000______ pounds.

Explanation:
Conversion: 1 ton = 2000 pounds.
7 tons = 2000 × 7
= 14000 pounds.

 

Question 10.
46 pounds = ________ounces
Answer:
46 pounds = __736______ounces.

Explanation:
Conversion: 1 pound = 16 ounces.
46 pounds = 16 × 46
= 736 ounces.

 

Question 11.
\(\frac{1}{8}\) pound = ________ ounces
Answer:
\(\frac{1}{8}\) pound = ____2____ ounces.

Explanation:
Conversion: 1 pound = 16 ounces.
\(\frac{1}{8}\) pound = 16 × \(\frac{1}{8}\)
= 2 ounces.

 

Question 12.
6 tons = _______ pounds
Answer:
6 tons = ___12000______ pounds.

Explanation:
Conversion: 1 ton = 2000 pounds.
6 tons = 2000 × 6
= 12000 pounds.

 

 

Question 13.
3 pounds = _______ ounces
Answer:
3 pounds = __48_____ ounces.

Explanation:
Conversion: 1 pound = 16 ounces.
3 pounds = 16 × 3
= 48 ounces.

 

For 14-15, complete each table.
Question 14.

Answer:

Explanation:
Conversion: 1 ton = 2000 pounds.
2 tons = 2000 × 2 = 4000 pounds.
3 tons = 2000 × 3 = 6000 pounds.

 

 

Question 15.

Answer:

Explanation:
Conversion: 1 pound = 16 ounces.
\(\frac{2}{4}\) pound = 16 × \(\frac{2}{4}\)
= 8 ounces.
1 pound = 16 ounces.
2 pounds = 16 × 2 = 32 ounces.

 

Problem Solving
For 16-19, use the line plot at the right.

Question 16.
Be Precise What is the total weight in ounces of the three kittens that weight the least?
Answer:
Total weight in ounces of the three kittens that weight the least = 40 ounces.

Explanation:
Weight of Three kittens that weight the least = \(\frac{3}{4}\) pound + \(\frac{3}{4}\) pound + 1 pound.
= 2\(\frac{2}{4}\) pound.
Conversion: 1 pound = 16 ounces.
Total weight in ounces of the three kittens that weight the least = 2\(\frac{2}{4}\) pound = 16 × 2\(\frac{2}{4}\)
= 40 ounces.

 

 

Question 17.
Higher Order Thinking Two kittens had a total weight of 3\(\frac{1}{4}\) pounds. What could their individual weights have been?
Answer:
Their individual weights could be = 1\(\frac{2}{4}\) pounds + 1\(\frac{3}{4}\) pounds.

Explanation:
Weight of two kitten had a total weight of 3\(\frac{1}{4}\) pounds:
Their individual weights could be = 1\(\frac{2}{4}\) pounds + 1\(\frac{3}{4}\) pounds.
= 3\(\frac{1}{4}\) pounds.

 

Question 18.
Algebra How many more pounds did the heaviest kitten weigh than the lightest kitten?
Answer:
1\(\frac{2}{4}\) more pounds the heaviest kitten weights than the lightest kitten,

Explanation:
Weight of the heaviest kitten = 2\(\frac{1}{4}\) pounds.
Weight of the lightest kitten = \(\frac{3}{4}\) pounds.
Difference:
Weight of the heaviest kitten – Weight of the lightest kitten
= 2\(\frac{1}{4}\) pounds – \(\frac{3}{4}\) pounds
= 1\(\frac{2}{4}\) pounds.

 

 

Question 19.
Each of the greatest number of kittens weighed how many pounds?
Answer:
1\(\frac{1}{4}\) pounds is the greatest number of kittens weighed of 3\(\frac{3}{4}\) pounds.

Explanation:
Greatest number of kittens weighed = 3 × 1\(\frac{1}{4}\) pounds
= 3\(\frac{3}{4}\) pounds.

 

 

Question 20.
About how many pounds does this African elephant weigh? Complete the table to solve.

Answer:
This African elephant weights = 10000 pounds.

Explanation:
This African elephant weights = 5 tons.
Conversion: 1 ton = 2000 pounds.
=> 5 tons = 2000 × 5
= 10000 pounds.
Table :
\(\frac{2}{4}\) ton = 2000 × \(\frac{2}{4}\) = 1000 pounds.
1 ton = 2000 pounds.
2 ton = 2000 × 2 = 4000 pounds.
3 ton = 2000 × 3 = 6000 pounds.
4 ton = 2000 × 4 = 8000 pounds.
5 ton = 2000 × 5 = 10000 pounds.

 

 

Assessment Practice
Question 21.
Which is most likely to weigh 3 ounces?
A. A shoe
B. A large spider
C. A box of cerea!
D. A loaded pick-up truck
Answer:
A shoe is most likely to weigh 3 ounces.
A. A shoe

Explanation:
A. A shoe    – 9.5 ounces.
B. A large spider    – 5300 ounces.
C. A box of cereal    – 12 ounces to 18 ounces.
D. A loaded pick-up truck   – 64000 ounces.

 

 

Question 22.
Which comparison is true?
A. 7,000 pounds < 3 tons
B. 5 pounds > 85 ounces
C. 50 ounces > 3 pounds
D. 4 pounds < 60 ounces
Answer:
The following below comparison is true:
C. 50 ounces > 3 pounds.

Explanation:
A. 7,000 pounds < 3 tons (False)
Conversion: 1 ton = 2000 pounds.
=> 3 tons = 2000 × 3 = 6000 pounds.
B. 5 pounds > 85 ounces (False)
Conversion: 1 pound = 16 ounces.
=> 5 pounds = 16 × 5 = 80 ounces.
C. 50 ounces > 3 pounds (True)
=> 3 pounds = 16 × 3 = 48 ounces.
D. 4 pounds < 60 ounces (False)
=> 4 pounds = 16 × 4 = 64 ounces.

 

 

Lesson 13.4 Equivalence with Metric Units of Length

Solve & Share
Find the length of the marker shown in both centimeters and millimeters. Describe the relationship between the two units.
I can …convert metric units of length from one unit to another and recognize the relative size of different units.

Look Back! The length of Toby’s giant pencil is 25 centimeters. How could you find the length of his pencil in millimeters?
Answer:
We can find the length of his pencil in millimeter by using conversion of units into another required unit.
Length of his pencil in millimeters = 250 millimeters.

Explanation:
Length of Toby’s giant pencil = 25 centimeters.
Conversion: 1 centimeter =  10 millimeters.
Length of his pencil in millimeters = 25 centimeters = 10 × 25
= 250 millimeters.

 

Essential Question
How Can You Convert from One Metric Unit of Length to Another?
Answer:
To convert from one unit to another within the metric system usually means moving a decimal point. If you can remember what the prefixes mean, you can convert within the metric system relatively easily by simply multiplying or dividing the number by the value of the prefix

 

 

Visual Learning Bridge
For the standing long jump, Corey jumped 2 meters and Gary jumped 175 centimeters. Who jumped farther?

Step 1
Convert 2 meters to centimeters.
1 meter = 100 centimeters

Corey jumped 200 centimeters.

Step 2
Compare the lengths jumped.
200 centimeters is greater than 175 centimeters.
Corey jumped farther than Gary

Convince Me! Critique Reasoning Shayla says 5 kilometers are equal to 500 meters. Do you agree? Explain.
Answer:
Yes, I agree with Shayla saying ” 5 kilometers are equal to 500 meters.”

Explanation:
Conversion: 1 kilometer = 1000 meters.
5 kilometers = 1000 × 5 = 5000 meters.

 

 

Another Example!
Kendra and Lili measured the length of several rosebuds. The longest one Kendra measured was 2.4 centimeters long. The longest one Lili measured was 1.8 centimeters. Who measured the longest rosebud? Use a linear model to help explain.

Since 2.4 cm > 1.8 cm, Kendra measured the longest rosebud.

Guided Practice
Do You Understand?
Question 1.
What metric unit would you use to measure the length of a field?
Answer:
The most common units that we use to measure length of a field in the metric system are the millimeter, centimeter, meter, and kilometer.

 

 

Do You Know How?
For 2-3, convert each unit.
Question 2.
5 kilometers = _______ meters
Answer:
5 kilometers = __5000_____ meters.

Explanation:
Conversion: 1 kilometer = 1000 meters.
5 kilometers = 1000 × 5
= 5000 meters.

 

Question 3.
75 centimeters = ________ millimeters
Answer:
75 centimeters = _____750_______ millimeters.

Explanation:
Conversion: 1 centimeters  = 10 millimeters.
75 centimeters = 10 × 75
= 750 millimeters.

 

 

Independent Practice
In 4-6, tell what metric unit you would use to measure each.
Question 4.
The length of your math book
Answer:
Metric unit used to measure the length of your math book centimeter (cm).

 

 

Question 5.
The distance between cities
Answer:
Metric unit used to measure the distance between cities is  Kilometers per hour.

 

 

 

Question 6.
The length of a fly
Answer:
Metric unit used to measure the length of a fly is meter.

 

 

For 7-8, complete each table.
Question 7.

Answer:

Explanation:
Conversion: 1 meter = 1000 millimeter.
2 meter = 2 × 1000 = 2000 millimeter.
3 meter = 3 × 1000 = 3000 millimeter.

 

 

Question 8.

Answer:

Explanation:
Conversion: 1 centimeter = 10 millimeter.
2 centimeter  = 10 × 2 = 20 millimeter.
3 centimeter  = 10 × 3 = 30 millimeter.

 

 

Problem Solving
For 9-10, use the table at the right.

Question 9.
Be Precise The table shows the amount of rainfall students measured for a week. What was the total rainfall for the week, in millimeters?
Answer:
Total rainfall for the week, in millimeters = 110 millimeters.

Explanation:
Amount of rainfall on Monday = 3 cm.
Amount of rainfall on Tuesday = 0 cm.
Amount of rainfall on Wednesday = 1 cm.
Amount of rainfall on Thursday = 5 cm.
Amount of rainfall on Friday = 2 cm.
Total rainfall for the week = Amount of rainfall on Monday  + Amount of rainfall on Tuesday + Amount of rainfall on Wednesday + Amount of rainfall on Thursday + Amount of rainfall on Friday
= 3 cm + 0 cm + 1 cm  + 5 cm + 2 cm
= 11 cm.
Conversion: 1 cm = 10 mm.
Total rainfall for the week, in millimeters = Total rainfall for the week × 10
=> 11 × 10 = 110 millimeters.

 

Question 10.
How many more millimeters of rain fell on Thursday than on Monday and Wednesday combined?
Answer:
10 more millimeters of rain fell on Thursday than on Monday and Wednesday combined.

Explanation:
Amount of rainfall on Monday = 3 cm.
Amount of rainfall on Wednesday = 1 cm.
Amount of rainfall on Thursday = 5 cm.
Combine Rain fell on Monday and Wednesday = Amount of rainfall on Monday + Amount of rainfall on Wednesday
= 3 cm + 1 cm
= 4 cm.
Difference:
Amount of rainfall on Thursday – Combine Rain fell on Monday and Wednesday
= 5 cm – 4 cm
= 1 cm.
Conversion: 1 centimeter = 10 millimeter.
Difference in  millimeter of rain fell on Thursday than on Monday and Wednesday combined = 1 centimeter = 10 millimeter.

 

Question 11.
Which is greater, 2,670 meters or 2 kilometers? Explain.
Answer:
2,670 meters is greater.

Explanation:
2,670 meters or 2 kilometers.
Conversion: 1 kilometer = 1000 meters.
2 kilometers = 1000 × 2 = 2000 meters.

 

Question 12.
Critique Reasoning Milo thinks 8 hours is greater than 520 minutes. Is Milo correct? Remember 1 hour is equal to 60 minutes.
Answer:
No, Milo  is incorrect because 8 hours = 480 minutes less than 520 minutes.

Explanation:
Conversion: 1 Hour = 60 minutes.
8 hours = 60 × 8 = 480 minutes.

 

 

Question 13.
Algebra Leah ran around the track 8 times. She ran a total of 2,000 meters. How many meters equal 1 lap? Use the bar diagram to write an equation which can be used to find m, the meters in one lap.

Answer:
1 Lap = 400 meters.

Explanation:
Number of meters She ran = 2000m.
Number of times Algebra Leah ran around the track = 8.
Number of meters equal 1 lap = Number of meters She ran ÷ Number of times Algebra Leah ran around the track
= 2000 ÷ 8
= 400 meters.
1 Lap = 400 meters

 

 

Question 14.
Higher Order Thinking Signs are placed at the beginning and at the end of a 3-kilometer hiking trail. Signs are also placed every 500 meters along the trail. How many signs are along the trail? Explain.
Answer:
Total signs along the trail = 7.

Explanation:
Distance of Signs are placed at the beginning and at the end of a hiking trail = 3 kilometer.
Signs  placed along the trail = 500 meters.
Conversion: 1 km = 1000 meters.
3 km = 1000 × 3 = 3000 meters.
Total signs along the trail = Distance of Signs are placed at the beginning and at the end of a hiking trail ÷ Signs  placed along the trail + 1
= 3000 ÷ 500 + 1
= 6 + 1
= 7.

 

 

Assessment Practice
Question 15.
Select all the true statements.
☐ 14 meters = 1,400 centimeters
☐ 10 centimeters = 1,000 millimeters
☐ 55 kilometers = 5,500 meters
☐ 3 meters = 3,000 millimeters
☐ 5 meters = 500 centimeters
Answer:
All the true statements:
14 meters = 1,400 centimeters
55 kilometers = 5,500 meters
3 meters = 3,000 millimeters
5 meters = 500 centimeters

Explanation:
☐ 14 meters = 1,400 centimeters. (True)
Conversion: 1 meters = 100 centimeters.
14 meters = 10 × 14 = 1400 centimeters.

☐ 10 centimeters = 1,000 millimeters. (False)
Conversion: 1 centimeters = 10 millimeters.
10 centimeters = 10 × 10 = 100 millimeters.

☐ 55 kilometers = 5,500 meters. (True)
Conversion: 1 kilometers  =  1000 meters.
55 kilometers  = 1000 × 55 = 5500 meters.

☐ 3 meters = 3,000 millimeters. (True)
Conversion: 1 meter = 1000 millimeters.
3 meters = 1000 × 3 = 3000 millimeters.

☐ 5 meters = 500 centimeters. (True)
Conversion: 1 meter = 100 centimeters.
5 meters = 100 × 5 = 500 centimeters.

 

 

Question 16.
Select all the true statements.
☐ 3 meters > 3,000 centimeters
☐ 2 kilometers < 2,500 meters
☐ 4 centimeters > 38 millimeters
☐ 3.5 meters < 3.2 meters
☐ 5 kilometers < 5,200 meters
Answer:
All the true statements:
2 kilometers < 2,500 meters.
4 centimeters > 38 millimeters.
5 kilometers < 5,200 meters.

Explanation:
☐ 3 meters > 3,000 centimeters. (False)
Conversion: 1 meter = 100 centimeters.
3 meters = 100 × 3 = 300 centimeters.

☐ 2 kilometers < 2,500 meters . (True)
Conversion: 1 kilometers  =  1000 meters.
2 kilometers = 1000 × 2 = 2000 meters.

☐ 4 centimeters > 38 millimeters. (True)
Conversion: 1 centimeters = 10 millimeters.
4 centimeters = 10 × 4 = 40 millimeters.

☐ 3.5 meters < 3.2 meters. ( False)

☐ 5 kilometers < 5,200 meters. (True)
Conversion: 1 kilometers  =  1000 meters.
5 kilometers  = 1000 × 5 = 5000 meters.

 

 

Lesson 13.5 Equivalence with Metric Units of Capacity and Mass

Solve & Share
Jenny has 3 liters of water. How many milliliters of water does she have, and what is the mass of the water in grams? Solve this problem any way you choose.
I can… convert metric units of capacity and mass from one unit to another and recognize the relative size of different units.

Look Back! Why did you need to convert units to solve the problem above?
Answer:
Well, it is the conversion between an amount in one unit to the corresponding amount in a desired unit using various conversion factors. This is valuable because certain measurements are more accurate or easier to find than others.

 

 

Essential Question
How Can You Convert from One Metric Unit of Capacity or Mass to Another?
Answer:
We convert from One Metric Unit of Capacity or Mass to Another, larger unit multiply, smaller unit divide.

 

 

 

Visual Learning Bridge
Louis needs 8 liters of apple juice. He has 5,000 milliliters of juice. Does Louis have enough apple juice?

Step 1
Find how many milliliters of apple juice Louis needs.
1 liter = 1,000 milliliters

Louis needs 8,000 milliliters of juice.

Step 2
Compare to find if Louis has enough apple juice.
8,000 milliliters > 5,000 milliliters
Louis does not have enough apple juice. How much more does he need?
8,000 – 5,000 = 3,000
Louis needs 3,000 milliliters more.

Convince Me! Be Precise Why did you need to convert liters to milliliters?
Answer:
We need to convert liters to milliliters because Louis needs milliliters of juice not liters.

 

 

Another Example!
How many grams of apples are needed to make 1 liter of apple juice?

1 kilogram = 1,000 grams
2 kilograms = 2 × 1,000 grams
= 2,000 grams
2,000 grams of apples make 1 liter of apple juice.

Guided Practice
Do You Understand?
Question 1.
What metric unit would you use to measure your mass? the amount of blood in your body? Explain.
Answer:
The gram and kilogram are two units used to measure mass in the metric system. the amount of blood in your body is measured in units of millimeters of mercury (mmHg).

 

Do You Know How?
For 2-3, convert each unit.
Question 2.
6 grams = _______ milligrams
Answer:
6 grams = ___6000____ milligrams.

Explanation:
Conversion: 1 gram = 1000 milligrams.
6 grams = 1000 × 6
= 6000 milligrams.

 

Question 3.
9 liters = _________ milliliters
Answer:
9 liters = ___9000______ milliliters.

Explanation:
Conversion: 1 gram = 1000 milligrams.
9 liters = 1000 × 9
= 9000 milliliters.

 

 

Independent Practice
In 4-6, tell what metric unit you would use to measure each.
Question 4.
Medicine in a pill
Answer:
Orally administered liquid medications should be dosed exclusively by using metric-based dosing with milliliters (ie, mL) to avoid confusion and dosing errors associated with common kitchen spoons

 

 

Question 5.
Ink in a pen
Answer:
Metric unit used to measure Ink in a pen is grams.

 

 

Question 6.
The mass of a pencil
Answer:
Metric unit used to measure the mass of a pencil is grams.

 

 

For 7-10, convert each unit.
Question 7.
5 kilograms = ________ grams
Answer:
5 kilograms = ___5000_____ grams.

Explanation:
Conversion: 1 kilograms = 1000 grams.
5 kilograms = 1000 × 5
= 5000 grams.

 

Question 8.
2 liters = _______ milliliters
Answer:
2 liters = ___2000______ milliliters.

Explanation:
Conversion: 1 liter = 1000 milliliters.
2 liters = 1000 × 2
= 2000 milliliters.

 

Question 9.
4 grams = _______ milligrams
Answer:
4 grams = _____4000______ milligrams.

Explanation:
Conversion: 1 gram =  1000  milligrams.
4 grams = 1000 × 4
= 4000 milligrams.

 

Question 10.
9 kilograms = ________ grams
Answer:
9 kilograms = _____9000______ grams.

Explanation:
Conversion: 1 kilogram = 1000 grams.
9 kilograms = 1000 × 9
= 9000 grams.

 

 

Problem Solving
Question 11.
Reasoning A cardboard box has a mass of 800 grams. When 4 books of equal mass are put into the box, the filled box has a mass of 8 kilograms. What is the mass of each book in grams? Explain.

Answer:
The mass of each book in grams = 1800 grams.

Explanation:
Mass of a cardboard box has = 800 grams.
4 books of equal mass are put into the box, Mass of the filled box has = 8 kilograms.
Conversion: 1 kilogram = 1000 grams.
=> 8 kilograms = 1000 × 8 = 8000 grams.
The mass of each book in grams = Mass of the filled box has – Mass of a cardboard box has ÷ 4
= 8000 grams – 800 grams ÷ 4
= 7200 grams ÷ 4
= 1800 grams.

 

Question 12.
en Vision® STEM The Cape Hatteras Lighthouse was a kilometer from the shore in 1870. How far was the lighthouse from the shore in 1970? Explain.

Answer:
Distance of  the lighthouse away from the shore in 1970 = 920 meters.

Explanation:
Distance of the Cape Hatteras Lighthouse from the shore in 1870 = 1 kilometer.
Conversion: 1 kilometer = 1000 meters.
Distance of the beach near the Cape Hatteras Lighthouse eroded = 8 meters each year.
Distance of  the lighthouse away from the shore in 1970 = 1 kilometer –  (Distance of the beach near the Cape Hatteras Lighthouse eroded × number of years from 1870 – 1970)
=1000 – (8 × 10)
= 1000 – 80
= 920 meters.

 

Question 13.
The mass of 4 large zucchini is about 2 kilograms. About how many grams will 1 large zucchini have?
Answer:
Number of grams will 1 large zucchini = 500 grams.

Explanation:
Mass of 4 large zucchini = 2 kilograms.
Conversion: 1 kilogram = 1000 grams.
=> 2 kilograms = 1000 × 2 = 2000 grams.
Number of zucchini = 4.
Number of grams will 1 large zucchini = Mass of 4 large zucchini ÷ Number of zucchini
= 2000 ÷ 4
= 500 grams.

 

 

Question 14.
Higher Order Thinking A small sofa has a mass of 30 kilograms. A pillow on the sofa has a mass of 300 grams. How many pillows would it take to equal the mass of the sofa?
Answer:
Number of pillows it take to equal the mass of the sofa = 100.

Explanation:
Mass of small sofa = 30 kilograms.
Conversion: 1 kilograms = 1000 grams.
=> 30 kilograms = 1000 × 30 = 30000 grams.
Mass of a pillow on the sofa = 300 grams.
Number of pillows it take to equal the mass of the sofa = Mass of small sofa ÷ Mass of a pillow on the sofa
= 30000 ÷ 300
= 100 .

 

 

Assessment Practice
Question 15.
Which shows a correct comparison?
A. 5 milliliters > 50 liters
B. 2 liters < 200 milliliters
C. 100 liters < 1,000 milliliters
D. 3,200 milliliters > 3 liters
Answer:
A correct comparison:
D. 3,200 milliliters > 3 liters

Explanation:
A. 5 milliliters > 50 liters. (False)
Conversion: 1 liter = 1000 milliliters.
=> 50 liters = 1000 × 50 = 50000 liters.

B. 2 liters < 200 milliliters. (False)
Conversion: 1 liter = 1000 milliliters.
=> 20 liters = 1000 × 2 = 2000 milliliters.

C. 100 liters < 1,000 milliliters. (False)
Conversion: 1 liter = 1000 milliliters.
=> 100 liters = 1000 × 100 = 100000 milliliters.

D. 3,200 milliliters > 3 liters. (True)
Conversion: 1 liter = 1000 milliliters.
=> 3 liters = 1000 × 3 = 3000 milliliters.

 

Question 16.
Write the missing numbers in the table.

Answer:
Conversion: 1 kilograms = 1000 grams.
2 kilograms = 1000 × 2 = 2000 grams.
3 kilograms = 1000 × ?? = 3000 grams.
=> 3000 ÷ 1000 = 3.
4 kilograms = 1000 × 4 = 4000 grams.

 

Lesson 13.6 Solve Perimeter and Area Problems

Solve & Share
A can of paint is used to cover all 168 square feet of a wall. The wall is 8 feet high. Tape is placed along the top, bottom, and sides of the wall. What is the width of the wall? How much tape is needed? Solve this problem any way you choose.
I can … find the unknown length or width of a rectangle using a known area or perimeter.

Look Back! Describe the steps you would use to solve the problem.
Answer:
The steps used to solve the problem:
1. Collect the given complete information of the problem.
2. Find the width of the wall.
3. Find out the perimeter of the wall to find the how much tape to be needed.
.

 

Essential Question
How Can You Use Perimeter and Area to Solve Problems?
Answer:
The perimeter is the distance around the outside of an object. The perimeter is found by adding the lengths of all of the sides of the object together. Area is the size of the surface of the object or the total amount of space that the object covers.

 

 

Visual Learning Bridge
The state park shown has a perimeter of 36 miles. What is the area of the state park?

Step 1
Find the length of the state park.
Use the perimeter, 36 miles, and the width, 7 miles, to find the length.
Opposite sides of a rectangle are the same length, so multiply the width by 2. 7 × 2 = 14
Subtract 14 from the perimeter. 36 – 14 = 22
22 miles is the length of two sides of the park. Divide 22 by 2 to find the length of one side. 22 =2= 11
The length of the park is 11 miles.

Step 2
Find the area of the state park.

w = 7 miles
l = 11 miles
A = l × w
= 11 × 7
= 77
The area of the state park is 77 square miles,

Convince Me! Make Sense and Persevere If the area of another state park is 216 square miles, and the park has a width of 8 miles, what is the park’s length? What is the perimeter of this state park?
Answer:
Length of another state park = 27 miles.
Perimeter of this state park = 70 miles.

Explanation:
Area of the another state park = 216 square miles.
Width of another state park = 8 miles.
Length of another state park = L miles.
Area of the another state park = L × W = 216 square miles.
=> L × 8 = 216
=> L = 216 ÷ 8
=> L = 27 miles.
Perimeter of this state park = 2(L + W)
=> 2(27 + 8)
=> 2 × 35
= 70 miles.

 

Guided Practice
Do You Understand?
Question 1.
A sandbox is shaped like a rectangle. The area is 16 square feet. The side lengths are whole numbers. What are the possible dimensions of the sandbox? Do all possible dimensions make sense?
Answer:
The possible dimensions of the sandbox = (8miles and 2 miles) or (4miles and 4 miles).

Explanation:
Area of sandbox = 16 square feet.
The side lengths are whole numbers.
Let the Length of sandbox be L.
Width of sandbox be W.
Area of sandbox = L × W
=> 16 = L × W
=> 16 ÷ L = W.
or 16 ÷ W = L.
Length of sandbox  and Width of sandbox dimensions can be 8 miles and 2 miles or 4 miles or 4 miles.

 

 

Question 2.
Write and solve an equation to find the width of a room if the length of the floor is 8 feet and the area of the room is 96 square feet.
Answer:
Width of the room = 12 feet.

Explanation:
Area of the room = 96 square feet.
Length of the floor = 8 feet.
Let Width of the room = W feet.
Area of the room = L × W = 96 square feet.
=> 8 × W = 96
=> W = 96 ÷ 8
=> W = 12 feet.

 

Do You Know How?
For 3-5, complete each calculation.
Question 3.
Find n. Perimeter = 46 in.

Answer:
Width of the rectangle = 15 inches.

Explanation:
Perimeter of the rectangle = 46 inches.
Length of the rectangle = 8 inches.
Width of the rectangle = n inches.
Perimeter of the rectangle = 2(L + W) = 46 inches.
=>2(8 + n) = 46
=> 16 + 2n = 46
=> 2n = 46 – 16
=> n = 30 ÷ 2
=> n = 15 inches.

 

 

Question 4.
Find n and A. Perimeter = 26 cm

Answer:
Width of the rectangle = 4 cm.
Area of the rectangle = 36 sq cm.

Explanation:
Perimeter of the rectangle = 26 cm.
Length of the rectangle = 9 cm.
Width of the rectangle = n cm.
Perimeter of the rectangle = 2(L + W) = 26 cm.
=> 2(9 + n) = 26
=> 18 + 2n = 26
=> 2n = 26 – 18
=> n = 8 ÷ 2
=> n = 4 cm.
Area of the rectangle = L × w
= 9 × 4
= 36 square cm.

 

Question 5.
Find the perimeter.

Answer:
Perimeter of the square = 22 yards.

Explanation:
Side of the square = 5\(\frac{2}{4}\) yards.
Perimeter of the square = 4 × Side of square
= 4 × 5\(\frac{2}{4}\)
= 22 yards.

 

 

Independent Practice
For 6-9, find the missing dimension.
Question 6.
Find n.

Answer:
Width of the rectangle = 10 ft.

Explanation:
Area of the rectangle = 60 sq ft.
Length of the rectangle = 6 ft.
Width of the rectangle = n ft.
Area of the rectangle = L × W = 60 sq ft
=> 6 × n = 60
=> n = 60 ÷ 6
=> n = 10 ft.

 

 

Question 7.
Find n. Perimeter = 65 in.

Answer:
Width of the rectangle = 21 inches.

Explanation:
Perimeter of the rectangle = 65 inches.
Length of the rectangle = 11\(\frac{2}{4}\) inches.
Width of the rectangle = n inches.
Perimeter of the rectangle = 2(L + W) = 65 inches.
=> 2 (11\(\frac{2}{4}\) + n) = 65
=> 23 + 2n = 65
=> 2n = 65 – 23
=> n = 42 ÷ 2
=> n = 21 inches.

 

Question 8.
Find n. Perimeter = 84 yd

Answer:
Width of the rectangle = 20 yd.

Explanation:
Perimeter of the rectangle = 84 yd.
Length of the rectangle = 22 yd.
Width of the rectangle = n yd.
Perimeter of the rectangle = 2(L + W) = 84 yd.
=> 2 (22 + n) = 84
=> 44 + 2n = 84
=> 2n = 84- 44
=> n = 40 ÷ 2
=> n = 20 yd.

 

Question 9.
A rectangle has a length of 9 millimeters and an area of 270 square millimeters. What is the width? What is the perimeter?

Answer:
Width of the rectangle = 30 millimeters.
Perimeter of the rectangle = 78 millimeters.

Explanation:
Length of the rectangle = 9 millimeters.
Area of the rectangle = 270 square millimeters.
Width of the rectangle = w millimeters.
Area of the rectangle = L × W = 270 square millimeters.
=> 9 × w = 270
=> w = 270 ÷ 9
=> w = 30 millimeters.
Perimeter of the rectangle = 2(L+ W)
= 2(9 + 30)
= 2 × 39
= 78 millimeters.

 

Problem Solving

Question 10.
Greg built the picture frame shown to the right. It has a perimeter of 50\(\frac{2}{4}\) inches. How wide is the picture frame?
Answer:
Width of the picture frame = 10 inches.

Explanation:
Length of the picture frame = 15\(\frac{1}{4}\) inches.
Perimeter of the picture frame = 50\(\frac{2}{4}\) inches.
Let Width of the picture frame be w inches.
Perimeter of the picture frame = 2(L + W) = 50\(\frac{2}{4}\) inches.
=> 2(15\(\frac{1}{4}\) + w) = 50\(\frac{2}{4}\)
=> 30\(\frac{2}{4}\) + 2w = 50\(\frac{2}{4}\)
=> 2w = 50\(\frac{2}{4}\) – 30\(\frac{2}{4}\)
=> w = 20 ÷ 2
=> w = 10 inches.

 

 

Question 11.
Greg covered the back of the picture with a piece of felt. The picture is 17 inches shorter than the frame and 1\(\frac{1}{4}\) inch less in width. What is the area of the felt?
Answer:
Area of the felt = 70 inches.

Explanation:
Length of the picture frame = 15\(\frac{1}{4}\) inches.
Width of the picture frame = 10 inches.
Perimeter of the picture frame = 50\(\frac{2}{4}\) inches.
The picture is 17 inches shorter than the frame and 1\(\frac{1}{4}\) inch less in width.
=> Width of the felt = Width of the picture frame – 1\(\frac{1}{4}\) inch
=> 10 – 1\(\frac{1}{4}\)
=> 8\(\frac{3}{4}\) inches.
=> Perimeter of the picture frame – 17 inches = Perimeter of the felt.
=> 50\(\frac{2}{4}\) – 17 = Perimeter of the picture.
=> 33\(\frac{2}{4}\) inches = Perimeter of the picture.
Length of the felt = L inches.
Perimeter of the felt = 2(L + W)
33\(\frac{2}{4}\) = 2(L + 8\(\frac{3}{4}\) )
33\(\frac{2}{4}\) = 2L + 17\(\frac{2}{4}\)
33\(\frac{2}{4}\) – 17\(\frac{2}{4}\) = 2L
16 ÷ 2 = L
8 inches = L.
Area of the felt = L × W
= 8 × 8\(\frac{3}{4}\)
= 70 inches.

 

Question 12.
Al has a goal to read 2,000 pages over summer break. He has read 1,248 pages. How many more pages does Al need to read to reach his goal?
Answer:
Number of more pages Al needs to read to reach his goal = 752.

Explanation:
Number of pages Al has a goal to read = 2000.
Number of pages he has read = 1248.
Number of more pages Al needs to read to reach his goal = Number of pages Al has a goal to read  – Number of pages he has read
= 2000 – 1248
= 752.

 

 

Question 13.
The area of a tabletop is 18 square feet. The perimeter of the same table is 18 feet. What are the dimensions of the tabletop?
Answer:
Dimensions of the tabletop (L and W) are:
(9 feet and 2 feet) or (6 feet and 3 feet) or (2 feet and 9 feet)  or (3 feet and 6 feet)

Explanation:
Area of a tabletop = 18 square feet.
Perimeter of a tabletop = 18 feet.
Area of a tabletop = L × W = 18 sq feet.
=> L = 18 ÷ W
or W = 18 ÷ L.
Dimensions of the tabletop are:
(9 feet and 2 feet) or (6 feet and 3 feet) or (2 feet and 9 feet)  or (3 feet and 6 feet)

 

 

Question 14.
Construct Arguments Amy and Zach each have 24 feet of fencing for their rectangular gardens. Amy makes her fence 6 feet long. Zach makes his fence 8 feet long. Whose garden has the greater area? How much greater? Explain.
Answer:
Amy garden has the greater area than Zach garden by 4 sq ft.

Explanation:
Perimeter of the rectangular garden fencing Amy and Zach each have = 24 feet.
Length of rectangular garden fence Zach makes = 8 feet.
Length of rectangular garden fence Amy makes = 6 feet.
Width of rectangular garden fence Amy makes = W feet.
Perimeter of the rectangular garden Amy makes = 2(L + W) = 24 feet.
=> 2(6 + W) = 24
=> 12 + 2W = 24
=> 2W = 24 – 12
=> W = 12 ÷ 2
=> W = 6 feet.
Area of the rectangular garden Amy makes = Length of rectangular garden fence Amy makes × Width of rectangular garden fence Amy makes
= 6 × 6
= 36 sq ft.
Length of rectangular garden fence Zach makes = 8 feet.
Width of rectangular garden fence Zach makes = w feet.
Perimeter of the rectangular garden Zach makes = 2(L + W) = 24 feet.
=> 2(8 + w) = 24
=> 16 + 2w = 24
=> 2w = 24 – 16
=> w = 8 ÷ 2
=> w = 4 feet.
Area of the rectangular garden Zach makes = Length of rectangular garden fence Zach makes × Width of rectangular garden fence Zach makes
= 8 × 4
= 32 sq ft.
Difference in areas of Zach and Amy rectangular gardens :
Area of the rectangular garden Amy makes – Area of the rectangular garden Zach makes
= 36 sq ft – 32 sq ft
= 4 sq ft.

 

 

Question 15.
Higher Order Thinking Nancy made a table runner that has an area of 80 square inches. The length and width of the table runner are whole numbers. The length is 5 times greater than the width. What are the dimensions of the table runner?
Answer:
The dimensions of the table runner:
Length of the table = 40 inches.
Width of the table = 8 inches.

Explanation:
Area of the table runner which Nancy made = 80 square inches.
The length is 5 times greater than the width.
Let the Length of the table be L inches.
=>L =  5W
Width of the table be W inches.
Area of the table runner = Length of the table × Width of the table = 80 square inches.
=> 5W × W = 80
=> 2W = 80 ÷ 5
=> 2W = 16
=> W = 16 ÷ 2
=> W = 8 inches.
Length of the table = 5W = 5 × 8 = 40 inches.

 

 

 

 

Assessment Practice
Question 16.
The rectangle has an area of 144 square centimeters. Which is its perimeter?

A. 26 cm
B. 48 cm
C. 52 cm
D. 72 cm
Answer:
Perimeter of the rectangle = 52 cm.
C. 52 cm

Explanation:
Area of the rectangle = 144 square centimeters.
Length of the rectangle = 8 cm.
Width of the rectangle = W cm
Area of the rectangle = L × W = 144 square centimeters.
=> 8 × W = 144
=> W = 144 ÷ 8
=> W = 18 cm.
Perimeter of the rectangle = 2(L + W )
= 2 (8 + 18)
= 2 × 26
= 52 cm.

 

Lesson 13.7 Problem Solving

Precision
Solve & Share
Mr. Beasley’s science class wants to decorate one wall in the classroom like an underwater scene. They use sheets of blue poster board that are 2 feet long and 2 feet wide. How many sheets of blue poster board are used to cover the entire area of the wall? Use math words and symbols to explain how you solve.
I can … be precise when solving math problems.

Thinking Habits
Be a good thinker! These questions can help you.

• Am I using numbers, units, and symbols appropriately?
• Am I using the correct definitions?
• Am I calculating accurately?
• Is my answer clear?

Look Back! Be Precise How can calculating the area of the whole wall and the area of one sheet of poster board help you determine the total number of sheets of poster board needed to cover the entire area of the wall?
Answer:
The wall is to be covered by the sheets so, it is required for calculating the area of the whole wall and the area of one sheet of poster board help you determine the total number of sheets of poster board needed to cover the entire area of the wall.

 

 

Essential Question
How Can You Be Precise When Solving Math Problems?
Answer:
We can Precise When Solving Math Problems by the following the below steps:

1. Teach with Intention.
2. Use Practice Sheets Appropriately.
3. Use Best Practice Math Strategies and Instruction.
4. Use Problems with Multiple Solutions.
5. Differentiation is Critical.

 

 

Visual Learning Bridge
Piper has a fish tank and wants to cover all four sides \(\frac{6}{10}\) of the way to the top with clear plastic for insulation. She measures and finds the dimensions shown. How much plastic does Piper need? Use math words and symbols to explain how to solve.

What do you need to know so you can solve the problem?
I need to find how much plastic is needed for the fish tank. I need to be precise in my calculations and explanation.

How can I be precise in solving this problem?
I can

• correctly use the information given.
• calculate accurately.
• decide if my answer is clear and appropriate.
• use the correct units.

Here’s my thinking.
The height of the plastic is \(\frac{6}{10}\) times 15 inches.
\(\frac{6}{10}\) × 15 = \(\frac{90}{10}\) or 9
The plastic is 9 inches high.
Front and back: A = 9 × 24
A = 216 square inches
Each side: A = 9 × 12
A = 108 square inches
Add: 216 + 216 + 108 + 108 = 648 square inches
Piper needs 648 square inches of plastic.

Convince Me! Be Precise How did you use math words and numbers to make your explanation clear?
Answer:
To justify a solution, we need to be able to use appropriate mathematical language to give reasons for the particular approach used to solve a problem. Any time we produce a ‘solution’ in an attempt to solve a problem, that ‘solution’ needs to be justified.

 

 

Guided Practice
Be Precise
Jeremy uses \(\frac{2}{3}\) yard of tape for each box he packs for shipping. How many inches of tape does Jeremy need to pack 3 boxes?

Question 1.
How can you use the information given to solve the problem?
Answer:
We can use the information given to solve the problem for :

• Defining the problem.
• Generating alternatives.
• Evaluating and selecting alternatives.
• Implementing solutions.

 

 

Question 2.
How many inches of tape does Jeremy need to pack 3 boxes? Explain.
Answer:
Number of inches of tape Jeremy needs to pack 3 boxes = 72 inches.

Explanation:
Jeremy uses \(\frac{2}{3}\) yard of tape for each box he packs for shipping. How many inches of tape does Jeremy need to pack 3 boxes?
Length of the tape Jeremy uses to tape each box he packs for shipping = \(\frac{2}{3}\) yard.
Number of tapes Jeremy needs to pack 3 boxes = Length of the tape Jeremy uses to tape each box he packs for shipping  × 3
= \(\frac{2}{3}\) × 3
= 2 yards.
Conversion: 1 yard = 36 inches.
Number of inches of tape Jeremy needs to pack 3 boxes = Number of tapes Jeremy needs to pack 3 boxes  × 36 inches
= 2 × 36
= 72 inches.

 

 

Question 3.
Explain why you used the units you did in your answer.
Answer:
Units are important because without proper measurement and units to express them, we can never express physical laws precisely just from qualitative reasoning.

 

 

Independent Practice
Be Precise
Mrs. Reed collects shells. Each shell in her collection weighs about 4 ounces. Her collection weighs about 12 pounds in all. About how many shells are in Mrs. Reed’s collection? Use Exercises 4-6 to solve.

Question 4.
How can you use the information given to solve the problem?
Answer:
We can use the information given to solve the problem for :

• Defining the problem.
• Generating alternatives.
• Evaluating and selecting alternatives.
• Implementing solutions.

 

 

Question 5.
What is the total weight of Mrs. Reed’s shell collection, in ounces?
Answer:
Total weight of her collection in ounces = 192 ounces.

Explanation:
Weight of each shell in Mrs. Reed’s collection = 4 ounces.
Total weight of her collection = 12 pounds.
Conversion : 1 pound = 16 ounces.
Total weight of her collection in ounces = 12 pounds
= 16 × 12 = 192 ounces.

 

 

Question 6.
How many shells are in Mrs. Reed’s shell collection?
Answer:
48 shells are in Mrs. Reed’s shell collection.

Explanation:
Weight of each shell in Mrs. Reed’s collection = 4 ounces.
Total weight of her collection = 12 pounds.
Conversion : 1 pound = 16 ounces.
Total weight of her collection in ounces = 12 pounds
= 16 × 12 = 192 ounces.
Number of shells are in Mrs. Reed’s collection = Total weight of her collection ÷ Weight of each shell in Mrs. Reed’s collection
= 192 ÷ 4
= 48.

 

Problem Solving
Performance Task
Making Thank You Cards Tanesha is making cards by gluing 1 ounce of glitter on the front of the card and then making a border out of ribbon. She makes each card the dimensions shown. How much ribbon does Tanesha need?

Question 7.
Reasoning What quantities are given in the problem and what do the numbers mean?
Answer:
Quantities are given in the problem:
Quantity of glitter used for making Thank You Cards by Tanesha = 1 ounce.
Length of the card = 9 cm.
Width of the card = 85 mm.
Number mean the amount of quantity measured and measurements of the cards.

 

Question 8.
Reasoning What do you need to find?
Answer:
We need to find how much quantity of ribbon Tanesha needs.

 

 

Question 9.
Model with Math What are the hidden questions that must be answered to solve the problem? Write equations to show how to solve the hidden questions.
Answer:
The hidden questions that must be answered to solve the problem is that we need the length of the ribbon required for which we should  find out the perimeter of the card and convert the units.
Quantity of glitter used for making Thank You Cards by Tanesha = 1 ounce.
Length of the card = 9 cm.
Conversion: 1 cm = 10 mm.
Width of the card = 85 mm.
Perimeter of the card = 2(Length of the card + Width of the card)

 

 

Question 10.
Be Precise How much ribbon does Tanesha need? Use math language and symbols to explain how you solved the problem and computed accurately.

Answer:
Length of the ribbon required = 350 mm.

Explanation:
Quantity of glitter used for making Thank You Cards by Tanesha = 1 ounce.
Length of the card = 9 cm.
Conversion: 1 cm = 10 mm.
=> 9 cm = 10 × 9 = 90 mm.
Width of the card = 85 mm.
Perimeter of the card = 2(Length of the card + Width of the card)
= 2(90 + 85)
= 2 × 175
= 350 mm.

 

 

Question 11.
Reasoning What information was not needed in the problem?
Answer:
Quantity of glitter used for making Thank You Cards by Tanesha = 1 ounce. This information was not needed in the problem.

 

 

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
A. The sum is between 2,000 and 2,500.
B. The difference is exactly 10,000.
C. The sum is exactly 6,000.
D. The difference is exactly 4,500.
E. The sum is exactly 16,477.
F. The sum is between 5,500 and 5,600.
G. The difference is between 1,000 and 2,000.
H. The difference is between 8,000 and 9,000.

Answer:

Explanation:
10005+6472 = 16477.
1050+1200=2250.
7513-5676=1837.
3778+2222 = 6000.
35000-25000=10000.
10650-2150=8500.
1234+4321=5555.
9000-4500=4500.

 

 

Topic 13 Vocabulary Review

Understand Vocabulary
Word List

• area
• capacity
• centimeter (cm)
• cup (c).
• formula
• gallon (gal)
• gram (g)
• kilogram (kg)
• kilometer (km)
• liter (L)
• mass
• meter (m)
• milligram (mg)
• milliliter (mL)
• millimeter (mm)
• ounce (oz)
• perimeter
• pint (pt)
• pound (lb)
• quart (qt)
• ton (T)
• weight
• fluid ounce (fl oz)

Question 1.
Cross out the units that are NOT used to measure length.
centimeter (cm)
pint (pt)
pound (lb)
kilogram (kg)
Answer:
The units that are NOT used to measure length:
centimeter (cm)
pint (pt)
pound (lb)
kilogram (kg)    X

 

Question 2.
Cross out the units that are NOT used to measure capacity.
millimeter (mm)
ounce (oz)
gallon (gal)
milliliter (mL)
Answer:
The units that are NOT used to measure capacity:
millimeter (mm)       X
ounce (oz)
gallon (gal)
milliliter (mL)

 

Question 3.
Cross out the units that are NOT used to measure weight.
cup (c)
liter (L)
meter (m)
ton (T)
Answer:
The units that are NOT used to measure weight:
cup (c)
liter (L)
meter (m)       X
ton (T)

 

 

 

Question 4.
Cross out the units that are NOT used to measure mass.
liter (L)
kilometer (km)
milligram (mg)
quart (qt)
Answer:
The units that are NOT used to measure mass:
liter (L)
kilometer (km)     X
milligram (mg)
quart (qt)

 

 

Label each example with a term from the Word List.
Question 5.
2 × 4 = 8 square units _________
Answer:
2 × 4 = 8 square units __Area_______.

 

 

Question 6.
3 + 7 + 3 + 7 = 20 units __________
Answer:
3 + 7 + 3 + 7 = 20 units ___perimeter_______.

 

 

Question 7.
Area = l × w _________
Answer:
Area = l × w __Formula_______.

 

Use Vocabulary in Writing
Question 8.
Mike uses 24 meters of fence to enclose a rectangular garden. The length of the garden is 10 meters. What is the width? Use at least 3 terms from the Word List to explain.
Answer:
Width of the garden = 2 meters.

Explanation:
Length of fence to enclose a rectangular garden Mike uses = 24 meters.
Perimeter of the rectangular garden Mike uses = 24 meters.
Length of the garden =10 meters.
Width of the garden = W meters.
Formula:
Perimeter of the rectangular garden = 2(L + W) = 24 meters.
=> 2(10 + W) = 24
=> 20 + 2W = 24
=> 2W = 24- 20
=>W = 4 ÷ 2
=> W = 2 meters.

 

 

Topic 13 Reteaching

Set A pages 481-492

Customary units can be used when measuring length, capacity, and weight.

Remember when converting from a larger unit to a smaller unit, multiply. Use the conversion charts to help solve.
Question 1.
9 yards = _________ inches
Answer:
9 yards = ____324_____ inches.

Explanation:
1 yard = 36 inches.
9 yards = 36 × 9
= 324 inches.

 

 

Question 2.
5 miles = _________ yards
Answer:
5 miles = ____8800_______ yards.

Explanation:
1 mile = 1760 yards.
5 miles = 1760 × 5
= 8800 yards.

 

Question 3.
215 yards = _________ feet
Answer:
215 yards = ____645_____ feet.

Explanation:
1 yard = 3 feet.
215 yards = 3 × 215
= 645 feet.

 

Question 4.
9 pints = _________ fluid ounces
Answer:
9 pints = ___144______ fluid ounces.

Explanation:
1 pint = 16 fluid ounces.
9 pints = 16 × 9
= 144 fluid ounces.

 

 

Question 5.
372 quarts = _________ cups
Answer:
372 quarts = ___1488______ cups.

Explanation:
1 quart =  4 cups.
372 quarts = 4 × 372
= 1488 cups.

 

 

Question 6.
1,620 gallons = _________ pints
Answer:
1,620 gallons = _____12960_______ pints.

Explanation:
1 gallon = 8 pints.
1,620 gallons = 8 × 1620
= 12960 pints.

 

Question 7.
9 pounds = _________ ounces
Answer:
9 pounds = ___144______ ounces.

Explanation:
1 pound = 16 ounces.
9 pounds = 16 × 9
= 144 ounces.

 

Question 8.
5 tons = _________ pounds
Answer:
5 tons = ____10000_____ pounds.

Explanation:
1 ton = 2000 pounds.
5 tons = 2000 × 5
= 10000 pounds.

 

 

Question 9.
12 feet = _________ inches
Answer:
12 feet = ___144______ inches.

Explanation:
1 feet =  12 inches.
12 feet = 12 × 12
= 144 inches.

 

Set B pages 493-500

Metric units can be used to measure length, capacity, and mass.

Remember metric units can be converted using multiples of 10. Use the conversion charts to help.
Question 1.
9 kilometers = _________ meters
Answer:
9 kilometers = ___9000______ meters.

Explanation:
1 kilometer = 1000 meters.
9 kilometers = 1000 × 9
= 9000 meters.

 

Question 2.
55 centimeters = _________ millimeters
Answer:
55 centimeters = ____550_____ millimeters.

Explanation:
1 centimeter = 10 millimeters.
55 centimeters = 10 × 55
= 550 millimeters

 

Question 3.
2 meters = _________ centimeters
Answer:
2 meters = ___200______ centimeters.

Explanation:
1 meter = 100 centimeters.
2 meters = 100 × 2
= 200 centimeters.

 

Question 4.
9 liters = _________ milliliters
Answer:
9 liters = ___9000______ milliliters.

Explanation:
1 liter = 1000 milliliters.
9 liters = 1000 × 9
= 9000 milliliters.

 

Question 5.
4 grams = _________ milligrams
Answer:
4 grams = ___4000______ milligrams.

Explanation:
1 gram = 1000 milligrams.
4 grams = 1000 × 4
= 4000 milligrams.

 

Question 6.
5 kilograms = _________ grams
Answer:
5 kilograms = ___5000______ grams.

Explanation:
1 kilogram = 1000 grams.
5 kilograms = 1000 × 5
= 5000 grams.

 

Question 7.
8 kilograms = _________ grams
Answer:
8 kilograms = _____8000______ grams.

Explanation:
1 kilograms = 1000 grams.
8 kilograms = 1000 × 8
= 8000 grams.

 

Question 8.
5 grams = _________ milligrams
Answer:
5 grams = ___5000______ milligrams.

Explanation:
1 gram = 1000 milligrams.
5 grams = 1000 × 5
= 5000 milligrams.

 

 

Set C pages 501-504

The perimeter of Ted’s pool is 16 yards. The pool is 3 yards wide. He has 150-square feet of plastic. Does Ted have enough plastic to cover the pool?
Use the formula for perimeter to find the length. Substitute the numbers you know.
Perimeter = (2 × l) + (2 × w)
16 = (2 × l) + (2 × 3)
l = 5
The length of the pool is 5 yards.
3 yards wide × 3 = 9 feet wide
5 yards long × 3 = 15 feet long
Find the area of the pool.
A = 15 × 9
A = 135
The area of the pool is 135 square feet. 135 < 150, so Ted has enough plastic to cover the pool.

Remember to label your answer with the appropriate unit.
Question 1.
Find n.
P = 108 inches

Answer:
Width of rectangle = 36 inches.

Explanation:
Perimeter of rectangle = 108 inches.
Length of rectangle = 18 inches.
Width of rectangle = n inches.
Perimeter of rectangle = 2(L + W) = 108 inches.
=> 2 (18 + n) = 108
=> 36 + 2n = 108
=> 2n = 108 -36
=>n = 72 ÷ 2
=> n = 36 inches.

 

Question 2.
Find the area.
P = 26 m

Answer:
Area of rectangle = 36 sq m.

Explanation:
Perimeter of rectangle = 26 m.
Length of rectangle = 4m.
Width of rectangle = Wm.
Perimeter of rectangle = 2(L + W) =26m.
=>2(4 + W) = 26
=> 8 + 2W = 26
=> 2W = 26 – 8
=>W = 18 ÷ 2
=> W = 9m.
Area of rectangle = L × W
= 4 × 9
= 36 sq m.

 

 

Question 3.
Find the perimeter of the square.

Answer:
Perimeter of square = 10 yards.

Explanation:
Side of square = 2\(\frac{2}{4}\) yards.
Perimeter of square = 4 × Side
= 4 × 2\(\frac{2}{4}\)
= 10 yards.

 

 

Set D pages 505-508

Think about these questions to help you be precise.
Thinking Habits

• Am I using numbers, units, and symbols appropriately?
• Am I using the correct definitions?
• Am I calculating accurately?
• Is my answer clear?
  

Remember to give an explanation that is clear and appropriate.

A puppy pen is 4 feet wide and 5 feet long.
Question 1.
Is 21 square feet of fabric large enough to make a mat for the pen? Explain.
Answer:
Yes, it is enough to make a mat for the pen because it requires 20 sq feet for the mat and its 1 sq feet more than required.

Explanation:
Width of the puppy pen = 4 feet.
Length of the puppy pen = 5 feet.
Area of the puppy pen = L × W
= 5 × 4
= 20 sq feet.

 

 

Question 2.
Puppy fencing comes in sizes that are 12 feet, 24 feet, and 30 feet in length. Which length would be the best for the pen? How much, if any, will have to be left over? Explain.
Answer:
24 feet length would be the best for the pen and it leaves with 6 feet of more.

Explanation:
Puppy fencing comes in sizes that are 12 feet, 24 feet, and 30 feet in length.
Width of the puppy pen = 4 feet.
Length of the puppy pen = 5 feet.
=> Perimeter of fencing required for puppy pen = 2(L + W)
=> 2(5 + 4)
=> 2 × 9
=> 18 feet.
Difference:
18 feet – 12 feet = 6 feet.
24 feet – 18 feet = 6 feet.
30 feet – 18 feet = 12 feet.

 

 

Topic 13 Assessment Practice

Question 1.
A window is 5 feet long. What is the length of the window in inches?
Answer:
Length of the window = 60 inches.

Explanation:
Length of the window = 5 feet.
Conversion: 1 feet = 12 inches.
5 feet = 12 × 5
= 60 inches.

 

 

Question 2.
Mrs. Warren bought 6 liters of lemonade for a party. How many milliliters of lemonade did she buy?
A. 9,000 milliliters
B. 6,000 milliliters
C. 3,000 milliliters
D. 1,200 milliliters
Answer:
6000 milliliters of lemonade did she buy.
B. 6,000 milliliters.

Explanation:
Quantity of lemonade Mrs. Warren bought for a party = 6 liters.
Conversion: 1 liter = 1000 milliliters.
= 1000 × 6
= 6000 milliliters.

 

 

Question 3.
Select the equivalent measurement for each measurement on the left.

Answer:

Explanation:
Conversion:
1 feet = 12 inches.
9 feet = 12 × 9 = 108 inches.

1 cup = 8 fluid ounces.
9 cups = 8 × 9 = 72 fluid ounces.

1 ton = 2000 lb.
4 tons = 2000 × 4 = 8000 lb.

1 yard = 36 inches.
4 yards = 36 × 4 = 144 inches.

 

 

Question 4.
A picnic table is 9 feet long and 3 feet wide. Write and solve an equation to find the area of the rectangular surface of the table.
Answer:
Area of the rectangular surface of the table = 27 square feet.

Explanation:
Length of a picnic table = 9 feet.
Width of a picnic table = 3 feet.
Area of the rectangular surface of the table = L × W
= 9 × 3
= 27 square feet.

 

 

Question 5.
The Girl’s Club is making muffins. Mindy’s recipe calls for 3 cups of buttermilk. Josie’s recipe calls for 20 fluid Ounces of buttermilk. Georgia’s recipe calls for 1 pint of buttermilk. Whose recipe calls for the most buttermilk? Explain.
Answer:
Georgia’s recipe calls for the most buttermilk because its most between 0.05 cup and 3 cups.

Explanation:
Quantity of buttermilk Mindy’s recipe calls for = 3 cups.
Quantity of buttermilk Josie’s recipe calls for = 20 fluid Ounces.
Quantity of buttermilk Georgia’s recipe calls for = 1 pint .
Conversion:
1 cup = 8 fluid ounces.
=> 20 fluid Ounces = 1 ÷ 20 = 0.05 cups.
1 pint = 2 cups.

 

 

Question 6.
Andrea ran 4 kilometers over the weekend. How many meters did Andrea run?
Answer:
Number of meters Andrea run =4000 meters.

Explanation:
Distance Andrea ran over the weekend = 4 kilometers.
Conversion: 1 kilometer = 1000 meters.
Number of meters Andrea run = 1000 × 4
= 4000 meters.

 

 

Question 7.
Choose numbers from the box to complete the table. Some numbers will not be used.

Answer:

Explanation:
Conversion:
1 pound = 16 ounces.
1\(\frac{2}{4}\) pounds = 16 × 1\(\frac{2}{4}\)
= 24 ounces.
2 pounds = 16 × 2
= 32 ounces.
2\(\frac{2}{4}\) pounds = 16 × 2\(\frac{2}{4}\)
= 40 ounces.
3 pounds = 16 × 3
= 48 ounces.
3\(\frac{2}{4}\)  pounds = 16 × 3\(\frac{2}{4}\) pounds
= 56 ounces.

 

 

Question 8.
Select each correct equation.
☐ 1l = 100 mL
☐ 1 kg = 1,000 g
☐ 4 yd = 14 ft
☐ 15 cm = 150 mm
☐ 1 gal = 13 cups
Answer:
Correct equation:
1 kg = 1,000 g.

Explanation:
☐ 1l = 100mL (False)
☐ 1 kg = 1,000 g (True)
☐ 4 yd = 14 ft (False)
☐ 15 cm = 150 mm (False)
☐ 1 gal = 13 cups (False)
Conversion:
1 l = 100 mL. (False)
1 kg = 1000 g.

1 yd = 3 ft
=> 4 yd = 3 × 4 = 12 ft.

1 cm = 100 mm.
=> 15 cm = 100 × 15 = 1500 mm.

1 gal = 16 cups.

 

 

Question 9.
Morgan rode her bike 2 kilometers from her house to her friend’s house. From her friend’s house, she rode 600 meters in all going to and from the library. Then she rode back home. How many meters did Morgan bike in all?
Answer:
Distance in meters she rode in all = 2600 meters.

Explanation:
Distance Morgan rode her bike from her house to her friend’s house = 2 kilometers.
Distance From her friend’s house, she rode in all going to and from the library = 600 meters.
Distance in meters she rode in all = Distance Morgan rode her bike from her house to her friend’s house + Distance From her friend’s house, she rode in all going to and from the library
= 2 kilometers + 600 meters
Conversion: 1 km = 1000 m.
=> 2 kilometers = 1000 × 2 = 2000 meters.
=> 2000 + 600 = 2600 meters.

 

 

Question 10.
Which statement is true about the bedrooms in the drawings below?

A. Erin’s room has a greater area than Steve’s room.
B. Steve’s room has a greater perimeter than Erin’s room.
C. They both have the same perimeter.
D. None of the above
Answer:
Statement is true about the bedrooms in the drawings below:
C. They both have the same perimeter.

Explanation:
Length of Steve’s room = 9 ft.
Width of Steve’s room = 8 ft.
Area of Steve’s room = L × W
= 9 × 8
= 72 square feet.
Perimeter of Steve’s room = 2(L + W)
= 2(9 + 8)
= 2 × 17
= 34 feet.

Length of Erin’s room = 10 ft.
Width of Erin’s room = 7 ft.
Area of Erin’s room = L × W
= 10 × 7
= 70 square feet.
Perimeter of Erin’s room = 2(L + W)
= 2(10 + 7)
= 2 × 17
= 34 feet.

A. Erin’s room has a greater area than Steve’s room. (False)
B. Steve’s room has a greater perimeter than Erin’s room. (False)
C. They both have the same perimeter. (True)
D. None of the above. (False)

 

Question 11.
Tim has 3 meters of yarn. How many centimeters of yarn does Tim have?
Answer:
33.34 centimeters of yarn Tim has.

Explanation:
Length of yarn Tim has = 3 meters.
Conversion: 1 m = 100 cm.
3 meters = 100 ÷  3
= 33.34 centimeters.

 

 

Question 12.
Mrs. Li’s classroom is 34 feet wide and 42 feet long.

A. What is the area of the classroom?
Answer:
Area of Mrs. Li’s classroom = 1428 square feet.

Explanation:
Length of Mrs. Li’s classroom = 34 feet.
Width of Mrs. Li’s classroom = 42 feet.
Area of Mrs. Li’s classroom = L × W
= 34 × 42
= 1428 square feet.

 

 

B. How much area is taken up by the objects in the classroom? How much area is left for the students’ desks? Write and solve equations to find the area.
Answer:
Area left for the students’ desks = 1194 square feet.

Explanation:

Area of Mrs.Li’s desk = 8 square feet.
Area of Fish tank = 6 square feet.
Area of Math center = 100 square feet.
Area of Reading center = 120 square feet.
Area taken up by the objects in the classroom = Area of Mrs.Li’s desk + Area of Fish tank + Area of Math center + Area of Reading center
= 8 + 6 + 100 + 120
= 234 square feet.
Area left for the students’ desks = Area of Mrs. Li’s classroom – Area taken up by the objects in the classroom
= 1428 square feet – 234 square feet
= 1194 square feet.

 

Question 13.
Select the equivalent measurement for each measurement on the left.

Answer:

Explanation:
Conversion:
1g = 1000 mg.
=> 3 g = 1000 × 3 = 3000 mg.

1kg = 1000 g.
=> 3 kg = 1000 × 3 = 3000 g.

1L = 1000 mL.
=> 3 L = 1000 × 3 = 3000 mL.

1m = 1000 mm.
=> 3 m = 1000 × 3 = 3000 mm.

 

 

Topic 13 Performance Task

Watermelons Kasia grows watermelons.

Question 1.
Kasia plants her watermelons in rows. Kasia’s watermelon field has a perimeter of 71\(\frac{1}{3}\) yards and is 14\(\frac{2}{3}\) yards wide. Each row is yard wide and the rows will be planted 2 yards apart.

Part A
What is the length of Kasia’s field? Explain.
Answer:
The length of Kasia’s field = 14\(\frac{2}{3}\) yards because its given in the problem.

Explanation:
The length of Kasia’s field = 14\(\frac{2}{3}\) yards.

 

 

Part B
What is the area of Kasia’s field? Complete the table to convert the length to feet. Be sure to use the correct units on your answer. Explain.
Answer:
Area of Kasia’s field = 308 square yards.

Explanation:
Length of Kasia’s field = 14\(\frac{2}{3}\) yards.
Width of Kasia’s field = W yards.
Perimeter of Kasia’s field = 71\(\frac{1}{3}\) yards.
Perimeter of Kasia’s field = 2(L + W) = 71\(\frac{1}{3}\) yards.
=> 2 (14\(\frac{2}{3}\) + W) = 71\(\frac{1}{3}\)
=> 28\(\frac{1}{3}\) + 2W = 71\(\frac{1}{3}\)
=> 2W = 71\(\frac{1}{3}\) – 29\(\frac{1}{3}\)
=> W = 42 ÷ 2
=> W = 21 yards.
Area of Kasia’s field = L × W
= 14\(\frac{2}{3}\)  × 21
= 308 square yards.

Conversion: 1 yard = 3  feet.
10 yards = 3 × 10 = 30 feet.
20 yards = 3 × 20 = 60 feet.
21 yards = 3 × 21 = 63 feet.

 

 

Part C
How many rows can Kasia plant? Explain.
Answer:
Number of rows Kasia plant = 154.

Explanation:
Number of rows Kasia plant = 2.
Length of each row = 1 yard.
Width of the rows will be planted = 2 yards.
Area of Kasia’s field = 308 square yards.
Number of rows Kasia plant = Area of Kasia’s field  ÷ Width of the rows will be planted
= 308 ÷ 2
= 154.

 

 

Question 2.
Use the information in the Watermelon table.

Part A
If there are twenty-eight 8-ounce servings in a 20-pound watermelon, how many pounds does the rind weigh? Explain.
Answer:
Quantity of rind in pounds = 2 pounds.

Explanation:
Quantity of watermelon = 20 pounds.
Quantity of watermelon servings = 288 ounces.
Conversion: 1 pound = 16 ounces.
=> 20 pounds = 16 × 20 = 320 ounces.
Quantity of rind = Quantity of watermelon – Quantity of watermelon servings
= 320 – 288
= 32 ounces.
Conversion: 1 pound = 16 ounces.
=> 32 ounces = 1 × 32 ÷ 16
= 32 ÷ 16 = 2 pounds.

 

 

Part B
How many cups of fruit does Kasia get from a 20-pound watermelon? Explain. Show your computations. Do not include the weight of the rind.
Answer:
Number of cups of fruit does Kasia get from a 20-pound watermelon = 40\(\frac{2}{4}\) cups.

Explanation:
Quantity of watermelon = 20 pounds.
Quantity of rind in pounds = 2 pounds.
Quantity of watermelon Kasia gets in pounds = Quantity of watermelon – Quantity of rind in pounds
= 20 – 2
= 18 pounds.
Conversion: 1 pound = 2\(\frac{1}{4}\) cups
Number of cups of fruit does Kasia get from a 20-pound watermelon =
=> 18 pounds = 2\(\frac{1}{4}\) × 18
=> 40\(\frac{2}{4}\) cups.

Question 3.
Use the information from the Watermelon and Nutrition picture to answer the question.

How many more milligrams of fiber than potassium are in a serving of watermelon? Explain.
Answer:
730 mg more milligrams of fiber than potassium are in a serving of watermelon.

Explanation:
Quantity of serving of fiber = 1 gram.
Conversion:
1g = 1000 mg
Quantity of serving of potassium = 270 milligram.
Difference:
Quantity of serving of fiber – Quantity of serving of potassium
= 1000 – 270
= 730 mg.