Elon

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.

Envision Math 5th Grade Textbook Answer Key Topic 2 Test Prep

Test prep

Question 1.
The Chen family’s home has 1,515 square feet downstairs and 625 square feet upstairs. Which of the following is the best estimate of the total square footage in the home? (2-3)
A. 2,100
B. 2,200
C. 2,300
D. 2,500
Answer:

Question 2.
What is 2.934 rounded to the nearest hundredth? (2-2)
A. 2.90
B. 2.93
C. 2.94
D. 3.00
Answer:

Question 3.
Eduardo is training for a marathon. He ran his first mile in 12.567 minutes and his second mile in 12.977 minutes. What is his combined time for the first two miles? (2-5)
A. 24.434 minutes
B. 24.544 minutes
C. 25.444 minutes
D. 25.544 minutes
Answer:

Question 4.
To add 18 + 25 using mental math, Braxton did the following. What is the missing number that makes the statement true?

A. 43
B. 25
C. 20
D. 2
Answer:

Question 5.
Which two trails combined are less than 4 miles? Use estimation to decide. (2-3)

A. Red and Yellow
B. Blue and Green
C. Red and Green
D. Blue and Yellow
Answer:

Question 6.
The Thomas Jefferson Memorial is on 18.36 acres of land and the Franklin Delano Roosevelt Memorial is on 7.5 acres of land. How many more acres of land is the Jefferson Memorial on than the Roosevelt memorial? (2-6)
A. 9.86
B. 10.86
C. 11.31
D. 17.61
Answer:

Question 7.
The table shows the areas of two islands. How many more square miles is the area of Greenland than the area of New Guinea? (2-4)

A. 1,156,614
B. 1,145,504
C. 587,716
D. 523,384
Answer:

Question 8.
In 2005, there were 2,100,990 farms in the United States. Which of the following is 2,100,990 rounded to the nearest thousand? (2-2)
A. 2,101,100
B. 2,101,000
C. 2,100,900
D. 2,100,000
Answer:

Question 9.
Which picture represents the problem? Parson’s Sporting Goods ordered 56 T-shirts in sizes small, medium and large. If 23 T-shirts are medium and 12 T-shirts are large, how many are small? (2-7)

Answer:

Question 10.
A lecture hall has 479 desk chairs and 216 folding chairs. How many seats are there in all? Use mental math to solve. (2-1)
A. 615
B. 685
C. 695
D. 785
Answer:

Question 11.
Parker had a batting average of 0.287 and Keenan had an average of 0.301. How much higher was Keenan’s batting average than Parker’s? (2-6)
A. 0.256
B. 0.14
C. 0.023
D. 0.014
Answer:

Question 12.
April logged the miles she rode on her bicycle in the table shown. Which is the best estimate of the total miles April rode during the first two weeks? (2-3)

A. 19
B. 20
C. 26
D. 38
Answer:

Question 13.
What is 87.25 + 7.69? (2-5)
A. 79.56
B. 94.2569
C. 94.94
D. 95.94
Answer:

Question 14.
In the 2004 Presidential Election, 62,040,610 people voted for George W. Bush and 59,028,439 people voted for John F. Kerry. What was the total number of votes for the two men? (2-4)
A. 121,069,049
B. 121,068,049
C. 111,069,049
D. 121,169,049
Answer:

Envision Math 6th Grade Textbook Answer Key Topic 2.7 Using Expressions to Describe Patterns

Using Expressions to Describe Patterns

How can you write expressions to describe patterns?
Answer:
Delvin saves a part of everything he earns. The table at the right shows Delvin’s savings pattern.
The INPUT column shows the money he has earned.
The OUTPUT column shows the money he has saved.

Question.
Write an expression to describe the pattern.

Answer:

Guided Practice

Do you know HOW?
Use the input/output table for 1 and 2.

Question 1.
If the input number is 8, what is the output number?
Answer:
11
Explanation:

Question 2.
Write an algebraic expression that describes the output pattern.
Answer:
x + 3
Explanation:

Do you UNDERSTAND?
Question 3.
Suppose that Delvin earned $36 mowing lawns. What input and output entries would you add to his table?
Answer:
IN: $36; OUT: $18
Explanation:

Question 4.
Reasonableness Is it reasonable for an output to be greater than the input in the table above? Explain.
Answer:
See margin.
Explanation:

Question 5.
What is the algebraic expression that describes the output pattern for the table above if the input is x?
Answer:
\(\frac{1}{2}\)x.
Explanation:

Independent Practice

Use this table for 6 and 7.

Question 6.
What is the cost of 4 lb, 5 lb, and 10 lb of apples?
Answer:

Question 7.
Write an algebraic expression that describes the output pattern if the input is a variable a.
Answer:
2a
Explanation:

Use this table for 8 and 9.

Question 8.
Copy and complete the table.
Answer:

Question 9.
Write an algebraic expression that describes the relationship between the input and output values.
Answer:
x ÷ 3
Explanation:

An input/output table is a table of related values. Identify the pattern.
What is the relationship between the values?
\(\frac{1}{2}\) (84) = 42 → 42 is half of 84
\(\frac{1}{2}\) (66) = 33 → 33 is half of 66
\(\frac{1}{2}\) (50) = 25 → 25 is half of 50.

The pattern is: \(\frac{1}{2}\) (INPUT) = OUTPUT
Let x= INPUT.
So, the pattern is \(\frac{1}{2}\) x.
Use the pattern to find the missing values.

\(\frac{1}{2}\) (22) = 11
\(\frac{1}{2}\) (30) = 15

Problem Solving

Use the input/output table at right for 10 and 11.

Question 10.
Hazem keeps \(\frac{1}{3}\) of the tips he earns. Also, he gets $1 each night to reimburse his parking fee. This information is shown in the input/output table. Write an algebraic expression that describes the output pattern if the input is the variable k.
Answer:
(k ÷ 3) + 1 or \(\frac{1}{3}\) k + 1
Explanation:

Question 11.
How much money would Hazem keep in a night if he takes in $36 in tips?
Answer:
$13
Explanation:

Use the input/output table at right for 12 and 13.

Question 12.
Ms. Windsor’s classroom has a tile floor. The students are making stars to put in the center of 4-tile groups. This input/ output chart shows the pattern. Write an algebraic expression that describes the output pattern if the input is the variable t.
Answer:
t ÷ 4
Explanation:

Question 13.
Writing to Explain There are 30 rows with 24 tiles in each row on a floor. Explain how to find the number of stars needed to complete the pattern for the floor.
Answer:
See margin.
Explanation:

Use the table at right for 14.

Question 14.
Think About the Process Which algebraic expression shows the cost of a chosen number of books b?
A. b + $2.50
B. $2.50b
C. $b – $2.50
D. b + $2.50
Answer:
B. $2.50b

Envision Math 6th Grade Textbook Answer Key Topic 1.4 Decimal Place Value

Decimal Place Value

How can you read very small decimal numbers? One gallon equals 3.7854 liters. How do you read this number?
Answer:
A decimal is a number that uses a decimal point and has one or more digits to the right of the decimal point.

Another Example
What are different ways to write decimals?
Answer:
The atomic mass of the chemical chromium is 51.9961.
Use a place-value chart to write the decimal in different forms.

Standard form: 51.9961
Short-word form: 51 and 9,961 ten thousandths
Word form: fifty-one and nine thousand nine hundred sixty-one ten thousandths
Expanded form: (5 × 10) + (1 × 1) + (9 × 0.1) + (9 × 0.01) + (6 × 0.001) + (1 × 0.0001) = 50 + 1 + 0.9 + 0.09 + 0.006 + 0.0001

Explain It

Question 1.
What is the purpose of the decimal point in a decimal number?
Answer:
It separates the whole number portion of the number from the decimal portion of the number.
Explanation:

Question 2.
If the first digit to the right of the decimal were removed from the number above, how would you write it in different forms?
Answer:
51.0961; 51 and 961 ten thousandths; fifty-one and nine hundred sixty-one ten thousandths; (5 × 10) + (1 × 1) + (9 × 0.01) + (6 × 0.001) + (1 × 0.0001) = 50 + 1 + 0.09 + 0.006 + 0.0001
Explanation:

Use a place-value chart to help you read a decimal.

Short-word form: 3 and 7,854 ten thousandths
Standard form: 3.7854

Guided Practice

Do you know HOW?
In 1 through 4, write the place and value of the underlined digit.
Answer:
See margin.
Explanation:

Question 1.
17.001
Answer:

Question 2.
987.6542
Answer:

Question 3.
14.9284
Answer:

Question 4.
7.2916
Answer:

In 5 through 7, write the number in the form indicated.
Answer:
See margin.
Explanation:

Question 5.
1.5629 in word form
Answer:

Question 6.
568.0101 in short-word form
Answer:

Question 7.
27.6003 in expanded form
Answer:

Do you UNDERSTAND?
Question 8.
How do you use a decimal point to read and write very small numbers?
Answer:
See margin.
Explanation:

Question 9.
In the example at the top of the page, how do you know that 0.005 is the value of the digit 5?
Answer:
See margin.
Explanation:

Question 10.
What is the decimal portion of 63.029? What is the whole number portion?
Answer:
See margin.
Explanation:

Independent Practice

Tips: All digits to the left of the decimal point are whole numbers, and all digits to the right of the decimal point are decimals.

Write the place and value of the underlined digit.
Question 11.
1,957.01
Answer:
hundredths; 0.01
Explanation:

Question 12.
647.476
Answer:
thousandths; 0.006
Explanation:

Question 13.
84.48
Answer:
tenths; 0.4
Explanation:

Question 14.
327.0094
Answer:
hundredths; 0
Explanation:

Question 15.
0.0521
Answer:
thousandths; 0.002
Explanation

Question 16.
78.667
Answer:
tenths; 0.6
Explanation

Question 17.
3.016
Answer:
ones; 3
Explanation:

Question 18.
8.5914
Answer:
ten thousandths; 0.0004
Explanation:

Independent Practice

Use the place-value chart to answer 19 through 23.

Question 19.
What is the place value of the last digit?
Answer:
Ten thousandths
Explanation:

Question 20.
From left to right, what is the value Ten thousandths of the second 8 in the number?
Answer:
0.0008
Explanation:

Question 21.
How would you write the number in short-word form?
Answer:
22 and 9,808 ten thousandths
Explanation:

Question 22.
How would you write the number in word form?
Answer:
See margin.
Explanation:

Question 23.
How would you write the number in expanded form?
Answer:
(2 × 10) + (2 × 1) + (9 × 0.1) + (8 × 0.01) + (8 × 0.0001)

Problem Solving

Question 24.
Number Sense Write a decimal that has the digit 9 in the tenths place and happen if you removed the decimal the ten-thousandths place.
Answer:
Sample answer: 1.9009
Explanation:

Question 25.
Writing to Explain What would point from a number?
Answer:
The number would become a whole number, and its value would be greater.
Explanation:

Use this data table to answer items 26 through 29.

Question 26.
Number Sense Which place do you use to tell that the new record is faster?
A. tens
B. tenths
C. hundreds
D. thousandths
Answer:
B. tenths
Explanation:

Question 27.
Which is the word form of the new record?
A. one hundred fifty-four and one hundred sixty-five thousandths
B. one hundred fifty-four and twenty-five thousandths
C. one hundred fifty-four and twenty-five hundredths
D. one hundred fifty-four
Answer:
C. one hundred fifty-four and twenty-five hundredths
Explanation:

Question 28.
Think About the Process Which expression tells how to find how much faster the new record was?
A. 154.165 + 154.25
B. 154.25 – 154.165
C. 154.165 × 154.25
D. 154.25 ÷ 154.165
Answer:
B. 154.25 – 154.165
Explanation:

Question 29.
Writing to Explain Explain why writing the new record as 154.250 mph does not change its value.
Answer:
Sample answer: The 0 in the thousandths place has a value of 0.
Explanation:

Mixed Problem Solving

Use the table above to answer 1 through 3.
Question 1.
Write the height of an adult grizzly bear in short-word form.
Answer:
2 and 1 tenth
Explanation:

Question 2.
Write the length of an adult grizzly bear’s claw length in expanded form.
Answer:
(1 × 10) + (1 × 0.1) + (6 × 0.01)
Explanation:

Question 3.
If newborn grizzlies weigh about 0.45 kg, how many kilograms do grizzly bears gain from the time they are newborn until they are adults?
Answer:
681.37 kg
Explanation:

Question 4.
Answer:
If a bear ran at a speed of 54.078 km/h, then increased its speed two-hundredths of a kilometer per hour, how fast would it be running?
Answer:
54.098 km/h
Explanation:

Question 5.
The grizzly bear disappeared from the state of California in 1922. How many years before 2009 did the grizzly disappear?
Answer:
87 years
Explanation:

Question 6.
The female grizzly has one to four cubs every other year. If a female has four cubs every other year for 12 years, how many cubs would she have given birth to?
Answer:
24 cubs
Explanation:

Question 7.
If one cub weighed 0.45 kg and another cub weighed 1.23 kg, how much more would the heavier cub weigh than the lighter one?
Answer:
0.78 kg
Explanation:

Envision Math 6th Grade Textbook Answer Key Topic 1.1 Place Value

Review What You Know

Vocabulary
Choose the best term from the box,

Question 1.
A period placed in a number to separate whole number values from values less than one is called a ? .
Answer:
decimal point
Explanation:

Question 2.
The value of the position of any digit in a number is called its ? .
Answer:
place
Explanation:

Question 3.
The symbols used to write numbers 0, 1,2 3, 4, 5, 6, 7, 8, and 9 are ? .
Answer:
digits
Explanation:

Writing Numbers
Write each word form in standard form.
Question 4.
nineteen
Answer:
19
Explanation:

Question 5.
thirty-seven
Answer:
37
Explanation:

Question 7.
two thousand twelve
Answer:
2,012
Explanation:

Question 8.
forty thousand
Answer:
40,000
Explanation:

Question 9.
one hundred thousand
Answer:
100, 000
Explanation:

Write the word form of each number.
Answer:
See margin
Explanation:

Question 10.
49
Answer:

Question 11.
112
Answer:

Question 12.
10,465
Answer:

Decimals
Writing to Explain Write an answer for the question.

Question 13.
How would you locate 3.33 on the number line? Explain.
Answer:
See margin.
Explanation:

Place Value

How can you read very large numbers?
Answer:
In astronomy, a light-year is the distance that light can travel in one year. One light-year is equal to about 9,500,000,000,000 kilometers. Use a place-value chart to help you find the value of the digit 9 and read the number.

Another Example
What are different ways to write very large numbers?
Answer:
A place-value chart can help you write a very large number, such as 44,600,000,000, in different forms.

Standard form: 44,600,000,000
Word form: forty-four billion, six hundred million
Short word form: 44 billion, 600 million
Expanded form: 40,000,000,000 + 4,000,000,000 + 600,000,000 or
(4 × 10,000,000,000) + (4 × 1,000,000,000) + (6 × 100,000,000)

Explain It
Question 1.
What is the relationship between the commas in a number and the periods in a place-value chart?
Answer:
See margin.
Explanation:

Question 2.
In the example above, how do you know what the addends are for a number written in expanded form?
Answer:
See margin.
Explanation:

You can use the word form to read the number.
Word form: nine trillion, five hundred billion

Guided Practice

Do you know HOW?
In 1 through 4, write the place and value of the underlined digit.
Question 1.
1,234,567
Answer:
See margin.
Explanation:

Question 2.
9,870,563,142,000
Answer:

Question 3.
36,192,748
Answer:
See margin
Explanation:

Question 4.
82,765,432,109,497
Answer:

In 5 and 6, write each number in the form indicated.
Question 5.
57,000,000,009 in expanded form
Answer:
See margin.
Explanation:

Question 6.
321 trillion, 705 thousand in standard form
Answer:
See margin.
Explanation:

Do you UNDERSTAND?
Question 7.
How do you use periods to read and write very large numbers?
Answer:
See margin.
Explanation:

Question 8.
In the example at the top, how would you write the number in expanded form?
Answer:
See margin.
Explanation:

Question 9.
When writing 136,000,000 in expanded form, why would you skip the hundred thousands, ten thousands, thousands, hundreds, tens, and ones?
Answer:
Those places are occupied by zeros.
Explanation:

Independent Practice

In 10 through 12, write the place and value of the digit 3 in each number?
Answer:
See margin.
Explanation:
Question 10.
3,476
Answer:

Question 11.
384,400
Answer:

Question 12.
5,437,200,184,400
Answer:

In 13 through 15, write each number in short-word form.
Answer:
See margin.
Explantion:

Question 13.
18,429,000,050,000
Answer:

Question 14.
10,007,000,000,000
Answer:

Question 15.
8,507,004,041
Answer:

For 16 through 19, use the number 1,435,600,000,000.
Question 16.
What is the place and value of the digit 5? billions,
Answer:
5,000,000,000
Explanation:

Question 17.
What is the value of the digit 3?
Answer:
30,000,000,000
Explanation:

Question 18.
Write the number in word form.
Answer:
One trillion, four hundred thirty-five billion, six hundred million

Question 19.
Using both multiplication and addition, how would you write this number in expanded form?
Answer:
See margin.
Explanation:

Problem Solving

Question 20.
How do you write the number of stars in the Milky Way galaxy in standard form?
Answer:
200,000,000,000
Explanation:

Question 21.
Writing to Explain Describe how you would use the standard form of a number to write the short-word form.
Answer:
See margin.
Explanation:

In a recent year, the world used an estimated 15,850,000,000 kilowatt hours of electricity. Use this information to answer 22 through 24.

Question 22.
What is the value of each non-zero digit in the number
Answer:
10,000,000,000; 5,000,000,000; 800,000,000; 50,000,000
Explanation:

Question 23.
Number Sense From left to right, what is the place of the second 5 in this number?
A. trillions
B. hundred millions
C. ten millions
D. hundred thousands
Answer:
C. ten millions
Explanation:

Question 24.
Algebra At this rate, how many kilowatt hours of electricity might the world use over a 10-year period?
A. 160 million
B. 160 billion
C. 16 trillion
D. 160 trillion
Answer:
B. 160 billion
Explanation:

Question 25.
Which of these numbers represents seventy-six trillion, two hundred seven thousand?
A. 76,000,000,207,000
B. 76,000,000,007,200
C. 76,000,207,000,000
D. 76,000,207,000
Answer:
A. 76,000,000,207,000
Explanation:

Question 26.
Which of these numbers is ten million more than three billion, four hundred twenty-nine million?
A. 3,419,000,000,000
B. 3,439,000,000,000
C. 3,419,000,000
D. 3,439,000,000
Answer:
D. 3,439,000,000
Explanation:

Mixed Problem Solving

Ancient Civilizations in Today’s World

Use the estimated populations shown on the map above to answer 1 through 10.
Question 1.
Which countries have a population in the billions?
Answer:
India and China
Explanation:

Question 2.
Which value does the digit 1 have in Greece’s population?
Answer:
10 million
Explanation:

Question 3.
Which places does the digit 3 occupy in China’s population?
Answer:
Hundred millions, millions, thousands, and ones
Explanation:

Question 4.
Which country has a population close to 80 million?
Answer:
Egypt
Explanation:

Question 5.
Which countries have a population between ten million and one hundred million?
Answer:
Greece, Egypt, and Italy
Explanation:

Question 6.
Draw a place-value chart to show the place and value of each of the digits in I ndia’s population.
Answer:
Place-value chart should show 1,095,351,995.
Explanation:

Question 7.
Which country has the least population? 8. How much less is its population than the greatest population shown?
Answer:
Greece; 1,303,285,655
Explanation:

Question 8.
How many people would India need to gain for its population to equal that of China?
Answer:
218,621,718
Explanation:

Question 9.
In a recent year, the population of Italy’s 10. capital, Rome, was about 2,553,873. About how many times larger was Italy’s population than the population of Rome?
Answer:
About 20 times larger
Explanation:

Question 10.
It is projected that China’s population will increase approximately 20% by 2025. Approximately how many more people will China have?
A. 130,000,000
B. 89,000,000
C. 260,000,000
D. 3,190,000,000
Answer:
C. 260,000,000
Explanation:

Go through the enVision Math Common Core Grade 4 Answer Key Topic 11 Represent and Interpret Data on Line Plots regularly and improve your accuracy in solving questions.

enVision Math Common Core 4th Grade Answers Key Topic 11 Represent and Interpret Data on Line Plots

Essential Questions:
How can you solve problems using data on a line plot? How can you make a line plot?

enVision STEM Project: Safety and Data
Do Research Use the Internet or other sources to find what causes an earthquake and how the power of an earthquake is measured. Tell how people can stay safe during earthquakes.
Journal: Write a Report Include what you found. Also in your report:

• The size, or magnitude, of an earthquake is measured with the Richter scale. Explain how the scale is used.
• Research the magnitudes of at least 6 earthquakes that have occurred in your lifetime. Make a table showing when they occurred and their magnitudes, and then show their magnitudes on a line plot.

Review What You Know
Vocabulary
Choose the best term from the box. Write it on the blank.

• compare
• data
• line plot
• scale

Question 1.
A _________ is a way to organize data on a number line.
Answer:
A __line plot_______ is a way to organize data on a number line.

Question 2.
Numbers that show the units used on a graph are called a __________
Answer:
Numbers that show the units used on a graph are called a __scale________.

 

Question 3.
_________ are pieces of information.
Answer:
___Data______ are pieces of information.

 

Comparing Fractions
Write >, <, or = in the .
Question 4.
\(\frac{7}{8}\) \(\frac{3}{4}\)
Answer:
\(\frac{7}{8}\) > \(\frac{3}{4}\).

Explanation:
\(\frac{7}{8}\) \(\frac{3}{4}\)
=> 0.875  __>__  0.75.

 

Question 5.
\(\frac{1}{2}\) \(\frac{5}{8}\)
Answer:
\(\frac{1}{2}\) < \(\frac{5}{8}\).

Explanation:
\(\frac{1}{2}\) \(\frac{5}{8}\)
=> 0.5   __<___  0.625.

 

Question 6.
\(\frac{1}{4}\) \(\frac{2}{8}\)
Answer:
\(\frac{1}{4}\) = \(\frac{2}{8}\)

Explanation:
\(\frac{1}{4}\) \(\frac{2}{8}\)
=> 0.25  __=___  0.25.

 

 

Fraction Subtraction

Find the difference.
Question 7.
10\(\frac{3}{8}\) – 4\(\frac{1}{8}\) = _______
Answer:
10\(\frac{3}{8}\) – 4\(\frac{1}{8}\) = 6\(\frac{1}{4}\).

Explanation:
10\(\frac{3}{8}\) – 4\(\frac{1}{8}\) = ???
=> 6\(\frac{1}{4}\) .

 

Question 8.
5\(\frac{1}{4}\) – 3\(\frac{3}{4}\) = _______
Answer:
5\(\frac{1}{4}\) – 3\(\frac{3}{4}\) = 1\(\frac{1}{2}\).

Explanation:
5\(\frac{1}{4}\) – 3\(\frac{3}{4}\) = ???
=> 1\(\frac{1}{2}\).

 

 

Question 9.
7\(\frac{4}{8}\) – 2\(\frac{4}{8}\) = __________
Answer:
7\(\frac{4}{8}\) – 2\(\frac{4}{8}\) = 5.

Explanation:
7\(\frac{4}{8}\) – 2\(\frac{4}{8}\) = ???
=> 5.

 

Interpreting Data
Use the data in the chart to answer each exercise.

Question 10.
What is the greatest snake length? What is the least snake length?
Answer:
The greatest snake length is 24 inches.
The least snake length is 12 \(\frac{1}{2}\) inches.

 

Question 11.
Which of the snake lengths are recorded more than once? Which length was recorded the most?
Answer:
The snake lengths are recorded more than once are 12 \(\frac{1}{2}\) inches, 16 inches and 17 inches.
Length that was recorded the most is 16 inches.

 

Question 12.
What is the difference between the greatest length and the shortest length recorded?
Answer:
The difference between the greatest length and the shortest length recorded is 11 \(\frac{1}{2}\) inches.

Explanation:
The difference between the greatest length and the shortest length recorded is:
The greatest snake length – The least snake length
= 24 inches – 12 \(\frac{1}{2}\) inches.
= 11 \(\frac{1}{2}\) inches.

 

 

Pick a Project
PROJECT 11A
What are fun ways to get up off the couch and move?
Project: Design a Park

Answer:

 

PROJECT 11B
What are the most commonly chosen state insects?
Project: Write a Poem and Make a Graph about a State Insect

Answer:

 

PROJECT 11C
Have you ever baked a pie?
Project: Make a Pamphlet of Pie Recipes

Answer:

 

3-ACT MATH PREVIEW
Math Modeling
It’s a Fine Line

I can… model with math to solve a problem that involves analyzing and interpreting data on line plots.

Lesson 11.1 Read Line Plots

Solve & Share
Emily went fishing. She plotted the lengths of 12 fish caught on the line plot shown below. What was the length of the longest fish caught? What was the length of the shortest fish caught?
I can … interpret data using line plots.

Look Back! What other observations can you make from the line plot about the lengths of fish caught?
Answer:
Other observations can be made from the line plot about the lengths of fish caught is that every quarterly he caught new fish added one more than it.

 

Essential Question
How Can You Read Data in a Line Plot?
Answer:
It is read easily because the line plot is clear stating its refers to lengths of different fishes caught and represented on the line its catching points of intervals, by this way I can read given Data in a Line Plot.

 

 

Visual Learning Bridge
A line plot shows data along a number line. Each dot above a point on the line represents one number in the data set.
The table below shows the distance Eli walked his dog each day for seven days.

Here is how the data look on a line plot.

The numbers along the bottom of the line plot are the scale of the graph.

Interpret the data on the line plot.
The most dots are above 1 on the line plot.
The most common distance walked is 1 mile.
The longest distance walked is 3 miles.
The shortest distance walked is \(\frac{1}{2}\) mile.

What is the difference between the longest distance and the shortest distance Eli walked his dog?
3 – \(\frac{1}{2}\) = \(\frac{6}{2}\) – \(\frac{1}{2}\)
= \(\frac{5}{2}\) or 2\(\frac{1}{2}\) miles

Convince Me! Model with Math Write and solve an equation to find how many miles m, Eli walked his dog in all for the 7 days.
Answer:
Total distance walked by Eli his dog in all for the 7 days = 9 \(\frac{1}{2}\) miles.

Explanation:
Distance walked by Eli on Monday = \(\frac{1}{2}\) mile.
Distance walked by Eli on Tuesday = 1 \(\frac{1}{2}\) miles.
Distance walked by Eli on Wednesday = 1 mile.
Distance walked by Eli on Thursday = 1 \(\frac{1}{2}\) miles.
Distance walked by Eli on Friday = 3 miles.
Distance walked by Eli on Saturday = 1mile.
Distance walked by Eli on Sunday = 1mile.
Total distance walked by Eli his dog in all for the 7 days = Distance walked by Eli on Monday + Distance walked by Eli on Tuesday + Distance walked by Eli on Wednesday + Distance walked by Eli on Thursday  + Distance walked by Eli on Friday  + Distance walked by Eli on Saturday + Distance walked by Eli on Sunday
= 1 + \(\frac{1}{2}\) + 1 \(\frac{1}{2}\) + 1 + 1 \(\frac{1}{2}\) + 3 + 1
= 1 \(\frac{1}{2}\)+ 1 \(\frac{1}{2}\) + 1 + 1 \(\frac{1}{2}\) + 3 + 1
= 3 + 1 + 1 \(\frac{1}{2}\) + 3 + 1
= 4 + 1 \(\frac{1}{2}\) + 3 + 1
= 5 \(\frac{1}{2}\) + 3 + 1
= 8 \(\frac{1}{2}\) + 1
= 9 \(\frac{1}{2}\) miles.

Guided Practice
Do You Understand?
Question 1.
How can you tell the longest distance Eli walked his dog from the line plot?
Answer:
It can be said the longest distance Eli walked his dog from the line plot by checking and comparing the numerical values given in the given data and finding out the highest among them in all.

 

Question 2.
If a line plot represented 10 pieces of data, how many dots would it have? Explain.
Answer:
If a line plot represented 10 pieces of data, dots would be of 10 because the data is of 10 pieces.

 

 

Do You Know How?
For 3-5, use the line plot below.

Question 3.
How many giraffes are 14 feet tall?
Answer:
Two or 2 giraffes are 14 feet tall.

 

Question 4.
What is the most common height?
Answer:
The most common height is 15 feet.

 

Question 5.
How tall is the tallest giraffe?
Answer:
16 feet is the tallest giraffe.

 

Independent Practice
For 6-10, use the line plot at the right.

Question 6.
How many people ran the 100-meter sprint?
Answer:
20 people ran the 100-meter sprint.

 

Question 7.
Which time was the most common?
Answer:
11 hours is the most common time.

 

Question 8.
What is the difference between the fastest sprint and the slowest sprint?
Answer:
The difference between the fastest sprint and the slowest sprint is 3 \(\frac{3}{4}\) seconds.

Explanation:
The fastest sprint = 10 \(\frac{1}{4}\).
The slowest sprint = 12 \(\frac{2}{4}\).
The difference between the fastest sprint and the slowest sprint:
= 12 \(\frac{2}{4}\) – 10 \(\frac{1}{4}\)
= 6 – 2 \(\frac{1}{4}\)
= 3 \(\frac{3}{4}\) seconds.

 

Question 9.
How many more people ran 100 meters in 11\(\frac{2}{4}\) seconds than in 10\(\frac{1}{4}\) seconds?
Answer:
2 more people ran 100 meters in 11\(\frac{2}{4}\) seconds than in 10\(\frac{1}{4}\) seconds.

Explanation:
More people ran 100 meters in 11 \(\frac{2}{4}\) seconds than in 10 \(\frac{1}{4}\) seconds
= 2.

 

Question 10.
Curtis said more than half the people ran 100 meters in less than 11 seconds. Do you agree? Explain.
Answer:
Yes, I agree with what Curtis said because its 17 people who ran 100 meters in less than 11 seconds.

 

 

Problem Solving
For 11-12, use the line plot at the right.

Question 11.
Reasoning Mr. Dixon recorded the times it took students in his class to complete a project. Which time was most often needed to complete the project?
Answer:
3 Hours was most often needed to complete the project.

 

Question 12.
How much longer was the greatest amount of time spent completing the project than the least amount of time?
Answer:
1 hour longer was the greatest amount of time spent completing the project than the least amount of time.

Explanation:
The greatest amount of time spent completing the project = 3 \(\frac{2}{4}\) hours.
The least amount of time spent completing the project = 2 \(\frac{2}{4}\) hours.
Difference:
The greatest amount of time spent completing the project – The least amount of time spent completing the project
= 3 \(\frac{2}{4}\) – 2 \(\frac{2}{4}\)
= 1 hour.

 

 

Question 13.
Number Sense Jorge collects sports cards. He displays his cards in an album. There are 72 pages in the album. Each page holds 9 cards. Explain how to decide whether or not the album holds more than 600 cards.
Answer:
Yes, the album holds more than 600 cards because by the calculation of total number of cards and result is 648.

Explanation:
Number of pages in the album = 72.
Number of cards in each page = 9.
Total number of cards the album holds = Number of pages in the album × Number of cards in each page
= 72 × 9
= 648.

 

 

Question 14.
Higher Order Thinking Bob and 2 friends each were able to juggle with bean bags for \(\frac{3}{4}\) minute. How long did they juggle altogether?
Answer:
Total time taken by them = \(\frac{9}{4}\) minutes.

Explanation:
Number of people were juggling with bean bags = 3.
Time taken for each to juggle with bean bags = \(\frac{3}{4}\) minute = 3/4 minute.
Total time taken by them = Number of people were juggling with bean bags × Time taken for each to juggle with bean bags
= 3 × \(\frac{3}{4}\) minute
= \(\frac{9}{4}\) minutes.

 

Assessment Practice
For 15-16, use the line plot at the right.

Question 15.
How much longer is the longest nail than the shortest nail?
A. 1\(\frac{1}{4}\) inches
B. 1\(\frac{2}{4}\) inches
C. 1\(\frac{3}{4}\) inches
D. 2\(\frac{1}{4}\) inches
Answer:
1\(\frac{2}{4}\) inches is the longest nail than the shortest nail.
B. 1\(\frac{2}{4}\)

Explanation:
The longest nail = 2 \(\frac{1}{4}\) inches.
The shortest nail = \(\frac{3}{4}\)  inches.
Difference:
The longest nail – The shortest nail
= 2 \(\frac{1}{4}\) – \(\frac{3}{4}\)
= 1\(\frac{2}{4}\) inches.

 

Question 16.
Ed measured the nails that were 2\(\frac{1}{4}\) inches long incorrectly. They were each actually \(\frac{3}{4}\) inch longer. What was the length of the nails?
A. \(\frac{3}{4}\) inch
B. 1\(\frac{2}{4}\) inches
C. 3 inches
D. 3\(\frac{1}{4}\) inches
Answer:
1\(\frac{2}{4}\) inches is the the length of the nails.
B. 1\(\frac{2}{4}\)

Explanation:
Wrong measurement of nails = 2\(\frac{1}{4}\) inches.
Correct measurement of nails = \(\frac{3}{4}\) inch.
the length of the nails = Wrong measurement of nails  – Correct measurement of nails
= 2\(\frac{1}{4}\) – \(\frac{3}{4}\)
= 1\(\frac{2}{4}\) inches.

 

 

 

Lesson 11.2 Make Line Plots

Solve & Share
The manager of a shoe store kept track of the lengths of the shoes sold in a day. Complete the line plot using the data from the shoe store. What length shoe was sold the most?
I can … make a line plot to represent data.

Look Back! Generalize How can you use a line plot to find the data that occur most often?
Answer:
We can use a line plot to find the data that occur most often by counting the number of times which occurred more in the given data.

Explanation:

Essential Question
How Can You Make Line Plots?
Answer:
We can make line plots by using the data given representing it on line. To create a line plot, ​first create a number line that includes all the values in the data set.

 

 

Visual Learning Bridge
Serena measured the lengths of her colored pencils. How can Serena make a line plot to show these lengths?

Making a Line Plot

Step 1
Draw a number line and choose a scale based on the lengths of Serena’s pencils. Mark halves, fourths, and eighths. The scale should show data values from the least to the greatest.

Step 2
Write a title for the line plot. Label the line plot to tell what the numbers represent.

Step 3
Draw a dot for each pencil length.

Convince Me! Model with Math Write and solve an equation to find the difference , in length between Serena’s two shortest colored pencils.
Answer:
Difference , in length between Serena’s two shortest colored pencils = \(\frac{1}{4}\) inches.

Explanation:
Length of First shortest colored pencil = 4 \(\frac{1}{2}\) inches.
Length of Second shortest colored pencil = 4 \(\frac{3}{4}\) inches.
Difference:
Length of Second shortest colored pencil – Length of First shortest colored pencil
= 4 \(\frac{3}{4}\) – 4 \(\frac{1}{2}\)
= \(\frac{1}{4}\) inches.

 

 

 

Guided Practice
Do You Understand?
Question 1.
The scale of the line plot, Lengths of Serena’s Pencils, goes from 4 to 5 by eighths. Why is this a good scale to use?
Answer:
This is a good scale to use because its easy to plot the measurements on the line and easy to understand the values.

Explanation:
The scale of the line plot, Lengths of Serena’s Pencils, goes from 4 to 5 by eighths. This is a good scale to use because its easy to plot and to understand too.

 

 

Question 2.
Use the table shown at the right to compare the lengths of Sandy’s pencils with the lengths of Serena’s pencils shown on the previous page. Who has more pencils that are the same length, Serena or Sandy? Which set of data was easier to compare? Why?
Answer:
Serena has more more pencils that are the same length of 4 \(\frac{3}{4}\) inches. Both set of data are easier to compare because the values are clear to understand.

Explanation:

 

 

 

Do You Know How?
Question 3.
Complete the line plot.

Answer:

Explanation:
Line plotting for the following data:

 

 

Independent Practice
Leveled Practice For 4-5, use the table at the right.

Question 4.
Use the data in the table to make a line plot.
Answer:

Explanation:
Line plotting of data:

 

 

Question 5.
What is the length of the longest bracelet? What is the shortest length? What is the difference?
Answer:
Difference = 2 inches.

Explanation:
Length of the longest bracelet =  8 \(\frac{1}{2}\) inches.
Length of the shortest bracelet = 6 \(\frac{1}{2}\) inches.
Difference:
Length of the longest bracelet – Length of the shortest bracelet
= 8 \(\frac{1}{2}\) – 6 \(\frac{1}{2}\)
= 2 inches.

 

 

Problem Solving
Question 6.
Nora weighed each of the 7 beefsteak tomatoes she picked from her garden. The total weight of the 7 tomatoes was 10\(\frac{3}{4}\) pounds. Her line plot shows only 6 dots. What was the weight of the missing tomato?

Answer:
Weight of the missing tomato = 1\(\frac{3}{4}\) pounds.

Explanation:
Total weight of the 7 tomatoes =10 \(\frac{3}{4}\) pounds.
Number of dots shown on line plot = 6.
Total weight of the 7 tomatoes = dots value plotted on line + Weight of the missing tomato
10 \(\frac{3}{4}\)  =  1 + 1 + 1\(\frac{1}{4}\) + 1\(\frac{2}{4}\) + 2 + 2\(\frac{1}{4}\) + Weight of the missing tomato
=> 10 \(\frac{3}{4}\)  = 9 + Weight of the missing tomato
=> 10 \(\frac{3}{4}\) – 9 =  Weight of the missing tomato
=> 1\(\frac{3}{4}\) pounds = Weight of the missing tomato.

 

 

Question 7.
Make Sense and Persevere Alyssa made a pink-and-white-striped blanket for her bed. There are 7 pink stripes and 6 white stripes. Each stripe is 8 inches wide. How wide is Alyssa’s blanket? Explain.
Answer:
Total length of Alyssa’s blanket = 104 inches.

Explanation:
Number of blanket with pink stripes = 7.
Number of blanket with pink stripes = 6.
Length of each stripe = 8 inches.
Total length of Alyssa’s blanket = (Number of blanket with pink stripes + Number of blanket with pink stripes) × Length of each stripe
= (7 + 6) × 8
= 13 × 8
= 104 inches.

 

 

For 8-9, use the table at the right.

Question 8.
Trisha measured how far her snail moved each day for 5 days. Make a line plot of Trisha’s data.
Answer:

Explanation:

 

 

Question 9.
Higher Order Thinking Write a question that would require addition or subtraction to solve using Trisha’s data. What is the answer?
Answer:
Total distance Trisha’s snail moved in 5 days = 7 \(\frac{2}{8}\) inches.

Explanation:

Distance Trisha’s snail moved on Monday = 1\(\frac{4}{8}\)
Distance Trisha’s snail moved on Tuesday =1\(\frac{3}{8}\)
Distance Trisha’s snail moved on Wednesday =1\(\frac{1}{8}\)
Distance Trisha’s snail moved on Thursday = 2\(\frac{1}{8}\)
Distance Trisha’s snail moved on Friday = 1\(\frac{1}{8}\)
Total distance Trisha’s snail moved in 5 days = Distance Trisha’s snail moved on Monday +
Distance Trisha’s snail moved on Tuesday + Distance Trisha’s snail moved on Wednesday  + Distance Trisha’s snail moved on Thursday + Distance Trisha’s snail moved on Friday
= 1\(\frac{4}{8}\) + 1\(\frac{3}{8}\) + 1\(\frac{1}{8}\) + 2\(\frac{1}{8}\) + 1\(\frac{1}{8}\)
= 2 \(\frac{7}{8}\) + 1\(\frac{1}{8}\) + 2\(\frac{1}{8}\) + 1\(\frac{1}{8}\)
= 4 + 2\(\frac{1}{8}\) + 1\(\frac{1}{8}\)
= 6 \(\frac{1}{8}\) + 1\(\frac{1}{8}\)
= 7 \(\frac{2}{8}\) inches.

 

 

Assessment Practice
Question 10.
Brianna is making bracelets for her friends and family members. The bracelets have the following lengths in inches:
6, 6\(\frac{3}{4}\), 6\(\frac{1}{4}\), 5\(\frac{3}{4}\), 5, 6, 6\(\frac{2}{4}\), 6\(\frac{1}{4}\), 6, 5\(\frac{3}{4}\)
Use the data set to complete the line plot.

Answer:

Explanation:
The bracelets lengths in inches:
6, 6\(\frac{3}{4}\), 6\(\frac{1}{4}\), 5\(\frac{3}{4}\), 5, 6, 6\(\frac{2}{4}\), 6\(\frac{1}{4}\), 6, 5\(\frac{3}{4}\)

 

 

 

Lesson 11.3 Use Line Plots to Solve Problems

Solve & Share
Ms. Earl’s class measured the lengths of 10 caterpillars in the school garden. The caterpillars had the following lengths in inches:
\(\frac{3}{4}\), 1\(\frac{1}{4}\), 1\(\frac{3}{4}\), 1\(\frac{1}{2}\), 1, 1, \(\frac{3}{4}\), 1\(\frac{1}{4}\), 1\(\frac{3}{4}\), 1\(\frac{1}{2}\)
Plot the lengths on the line plot. Write and solve an equation to find the difference in length between the longest and shortest caterpillars.
I can … use line plots to solve problems involving fractions.

Look Back! How can a line plot be used to find the difference between the greatest and least values?
Answer:
A line plot can be used to find the difference between the greatest and least values by doing the subtraction function between the two numbers.

 

Essential Question
How Can You Use Line Plots to Solve Problems involving Fractions?
Answer:
We can use line plots to Solve Problems involving Fractions by dividing the fractions by fractions to find the required solution to the problem.

 

 

Visual Learning Bridge
Alma and Ben are filling water balloons. The line plots show the weights of their water balloons. Who filled more water balloons? How many more? How much heavier was Alma’s heaviest water balloon than Ben’s heaviest water balloon?

Who filled more water balloons? How many more?
Each dot in the line plots represents 1 water balloon.
Alma filled 20 water balloons.
Ben filled 15 water balloons.
20 – 15 = 5
Alma filled 5 more water balloons than Ben.

How much heavier was Alma’s heaviest water balloon than Ben’s heaviest water balloon?

The dot farthest to the right in each line plot represents the heaviest water balloon.
Alma’s heaviest water balloon was 2\(\frac{2}{8}\) pounds.
Ben’s heaviest water balloon was 2\(\frac{1}{8}\) pounds.
Subtract.
2\(\frac{2}{8}\) – 2\(\frac{1}{8}\) = \(\frac{1}{8}\)
Alma’s heaviest water balloon was pound heavier than Ben’s heaviest water balloon.

Convince Me! Make Sense and Persevere How much heavier was Alma’s heaviest water balloon than her lightest water balloon? How much heavier was Ben’s heaviest water balloon than his lightest water balloon? Write and solve equations.
Answer:
1\(\frac{1}{8}\) pounds heavier was Alma’s heaviest water balloon than her lightest water balloon.
\(\frac{6}{8}\) pounds heavier was Ben’s heaviest water balloon than her lightest water balloon.

Explanation:
Weight of Alma’s heaviest water balloon = 2\(\frac{2}{8}\) pounds
Weight of Alma’s lightest water balloon = 1\(\frac{1}{8}\) pounds
Difference:
Weight of Alma’s heaviest water balloon – Weight of Alma’s lightest water balloon
= 2\(\frac{2}{8}\) – 1\(\frac{1}{8}\)
= 1\(\frac{1}{8}\) pounds.

Weight of Ben’s heaviest water balloon = 2\(\frac{1}{8}\)pounds
Weight of Ben’s lightest water balloon = 1\(\frac{4}{8}\) pounds
Difference:
Weight of Ben’s heaviest water balloon – Weight of Ben’s lightest water balloon
= 2\(\frac{1}{8}\) – 1\(\frac{4}{8}\)
= \(\frac{6}{8}\) pounds.

Another Example!
Rowan’s class measured the snowfall for 5 days. The line plot shows the heights of snowfall they recorded. How many inches of snow were recorded? What amount of snowfall occurred most often?

Find the total number of inches of snowfall recorded.
\(\frac{1}{4}\) + \(\frac{2}{4}\) + \(\frac{2}{4}\) + \(\frac{2}{4}\) + \(\frac{3}{4}\) = 2\(\frac{2}{4}\) inches
The amount of snowfall that occurred most often was \(\frac{2}{4}\) inch.

Guided Practice
Do You Understand?
Question 1.
Use Structure How could you use the Commutative and Associative Properties of Addition to make the addition in the Another Example easier?
Answer:
We can use the Commutative and Associative Properties of Addition to make the addition in the Another Example easier by rewriting the values and doing addition because the result is same.

 

 

Do You Know How?
For 2-3, use the example on the previous page.
Question 2.
Who filled more water balloons over 2 pounds?
Answer:
Ben filled more water balloons over 2 pounds.

Explanation:
Ben’s heaviest water balloon was 2\(\frac{1}{8}\) pounds.

 

Question 3.
How much heavier were Alma’s two heaviest water balloons than Ben’s two heaviest?
Answer:
\(\frac{1}{8}\) pounds heavier were Alma’s two heaviest water balloons than Ben’s two heaviest.

Explanation:
Weight of Alma’s two heaviest water balloons = 2 × 2\(\frac{2}{8}\)
Weight of Ben’s two heaviest water balloon = 2 × 2\(\frac{1}{8}\) pounds.
Difference:
Weight of Alma’s two heaviest water balloons – Weight of Ben’s two heaviest water balloon
= 2 × 2\(\frac{2}{8}\) – 2 × 2\(\frac{1}{8}\)
= 4 \(\frac{2}{8}\)  – 4 \(\frac{1}{8}\)
= \(\frac{1}{8}\) pounds.

 

Independent Practice
For 4-5, use the line plot at the right.

Question 4.
What is the difference in height between the tallest and shortest patients?
Answer:
1 \(\frac{3}{4}\) feet is the difference in height between the tallest and shortest patients.

Explanation:
Height of the tallest patient = 6 feet.
Height of the shortest patient = 4\(\frac{1}{4}\) feet.
Difference:
Height of the tallest patient – Height of the shortest patient
= 6 – 4\(\frac{1}{4}\)
= 6 – 4.25
= 1 \(\frac{3}{4}\) feet.

 

Question 5.
Oscar says 5 feet is the most common height Dr. Chen measured. Do you agree? Explain.
Answer:
No, 5 feet is not the most common height Dr. Chen measured as Oscar says because 5 \(\frac{2}{4}\) feet is most common height Dr. Chen measured.

Explanation:
Most common height Dr. Chen measured = 5\(\frac{2}{4}\) feet in the given data.

 

Problem Solving
Question 6.
Make Sense and Persevere Marcia measured her dolls and showed the heights using a line plot. How much taller are Marcia’s two tallest dolls combined than her two shortest dolls? Explain.

Answer:
2\(\frac{3}{4}\) inches taller are Marcia’s two tallest dolls combined than her two shortest dolls.

Explanation:
Marcia’s two tallest dolls heights = 7 inches and 6\(\frac{3}{4}\) inches.
Marcia’s two tallest dolls combined = 7 inches + 6\(\frac{3}{4}\) inches.
= 13 \(\frac{3}{4}\)  inches.
Marcia’s two shortest dolls heights = 5\(\frac{1}{4}\) inches and 5 \(\frac{3}{4}\) inches.
Marcia’s two shortest dolls combined = 5\(\frac{1}{4}\) inches + 5 \(\frac{3}{4}\) inches.
= 5.25 + 5.75
= 11 inches.
Difference:
Marcia’s two tallest dolls combined – Marcia’s two tallest dolls combined
= 13 \(\frac{3}{4}\) inches – 11 inches
= 2\(\frac{3}{4}\) inches.

 

 

Question 7.
Higher Order Thinking Marlee is knitting a scarf. The line plot shows the length she knits each day. How many more inches does Marlee need to knit so the scarf is 30 inches long?

Answer:
2 inches more inches Marlee needs to knit so the scarf is 30 inches long.

Explanation:
The length she knits each day = 2, 2\(\frac{2}{8}\) inches, 2\(\frac{2}{8}\) inches, 2\(\frac{4}{8}\) inches, 2\(\frac{4}{8}\) inches, 2\(\frac{4}{8}\) inches, 2\(\frac{5}{8}\) inches, 2\(\frac{6}{8}\) inches, 2\(\frac{6}{8}\) inches,  2\(\frac{7}{8}\) inches, 3 inches.

Total of the lengths she knits all days = 2 + 2\(\frac{2}{8}\) + 2\(\frac{2}{8}\)  + 2\(\frac{4}{8}\) + 2\(\frac{4}{8}\) + 2\(\frac{4}{8}\) + 2\(\frac{5}{8}\) + 2\(\frac{6}{8}\) + 2\(\frac{6}{8}\)  + 2\(\frac{7}{8}\) + 3 inches
= 28 inches.

More inches Marlee needs to knit so the scarf is 30 inches long = 30 – Total of the lengths she knits all days
= 30 – 28 inches
= 2 inches.

 

Assessment Practice
For 8-9, use the line plot.

Question 8.
Which of the following statements are true? Select all that apply.
☐ Most of the players are 6 feet or taller.
☐ Five players are 6 feet tall.
☐ The combined height of two of the shortest players is 1\(\frac{1}{2}\) feet.
☐ The difference between the tallest and the shortest players is \(\frac{3}{4}\) foot.
☐ All of the players are taller than 5\(\frac{3}{4}\) feet.
Answer:
Statements which are true:
Most of the players are 6 feet or taller.
All of the players are taller than 5\(\frac{3}{4}\) feet.

Explanation:
Statements which are true:
☐ Most of the players are 6 feet or taller.
☐ Five players are 6 feet tall.
☐ The combined height of two of the shortest players is 1\(\frac{1}{2}\) feet.
Combined height of two of the shortest players =
5\(\frac{3}{4}\) + 5\(\frac{3}{4}\)
= 11\(\frac{2}{4}\).

☐ The difference between the tallest and the shortest players is \(\frac{3}{4}\) foot.
Tallest player height = 6\(\frac{3}{4}\) feet.
Shortest player height = 5\(\frac{3}{4}\) feet.
Difference:
Tallest player height – Shortest player height
= 6\(\frac{3}{4}\) – 5\(\frac{3}{4}\)
= 1 feet.

☐ All of the players are taller than 5\(\frac{3}{4}\) feet.

 

 

Question 9.
If one of the shortest players grew \(\frac{3}{4}\) foot before the next season started, how tall would the player be?
A. \(\frac{6}{4}\) feet
B. 5\(\frac{3}{4}\) feet
C. 6 feet
D. 6\(\frac{2}{4}\) feet

Answer:
6\(\frac{2}{4}\) feet taller the player would be.

Explanation:
Shortest player height = 5\(\frac{3}{4}\) feet.
If one of the shortest players grew \(\frac{3}{4}\) foot.
=> 5\(\frac{3}{4}\) + \(\frac{3}{4}\)
=> 6\(\frac{2}{4}\) feet.

 

 

Lesson 11.4 Problem Solving

Critique Reasoning
Solve & Share
A class made a line plot showing the amount of snowfall for 10 days. Nathan analyzed the line plot and said, “The difference between the greatest amount of snowfall recorded and the least amount of snowfall recorded is 3 because the first measurement has one dot and the last measurement has 4 dots.” How do you respond to Nathan’s reasoning?
I can … use what I know about line plots to critique the reasoning of others.

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

• What questions can ask to understand other people’s thinking?
• Are there mistakes in other people’s thinking?
• Can I improve other people’s thinking?

Look Back! Critique Reasoning Millie said that the total amount of snowfall for the 5 days above was 10 inches. Is Millie correct?
Answer:
No, Millie is incorrect because Total amount of snowfall for the 5 days is 5 \(\frac{2}{4}\) inches. not 10 inches.

Explanation:
Amount of snowfall for the 5 days = \(\frac{3}{4}\), 1, 1, 1\(\frac{1}{4}\), 1\(\frac{2}{4}\)
Total amount of snowfall for the 5 days = \(\frac{3}{4}\) + 1 + 1 + 1\(\frac{1}{4}\) + 1\(\frac{2}{4}\)
= 5 \(\frac{2}{4}\) inches.

 

 

Essential Question
How Can You Critique the Reasoning of Others?
Answer:
We can Critique the Reasoning of Others by checking the process how the problem is solved and finally tallying their solution.

 

 

Visual Learning Bridge
The line plots show the amount of rainfall for two months.

Val said, “The total rainfall for February was greater than the total rainfall for January because \(\frac{7}{8}\) + \(\frac{7}{8}\) equals \(\frac{14}{8}\), and the highest rainfall in January was \(\frac{5}{8}\)“.

What is Val’s reasoning?
Val compared the two highest amounts of rainfall for each month.

How can I critique the reasoning of others?
I can

• ask questions for clarification.
• decide if the strategy used makes sense.
• look for flaws in estimates or calculations.

Here’s my thinking.
Val’s reasoning is not correct.
She compared the days with the greatest amount of rainfall for the two months. The days with the greatest amounts of rainfall are not the total for the months.

Val should have added the amounts for each month. Then she could compare the amounts.
January \(\frac{1}{8}+\frac{1}{8}+\frac{1}{8}+\frac{3}{8}+\frac{3}{8}+\frac{3}{8}+\frac{5}{8}=\frac{17}{8}\) inches
February: \(\frac{1}{8}+\frac{1}{8}+\frac{5}{8}+\frac{7}{8}+\frac{7}{8}=\frac{21}{8}\) inches
During February, there was \(\frac{21}{8}-\frac{17}{8}=\frac{4}{8}\) inch more rain than January

Convince Me! Critique Reasoning Bev thought January had more rainfall because it rained on 7 days and February only had rain on 5 days. How do you respond to Bev’s reasoning?
Answer:
Well, Bev’s reasoning is not correct because to find the more rainfall in between January and February months, you should calculate the rainfall not the number of days.

 

Guided Practice
Critique Reasoning At a dog show, a judge wrote down the heights of 12 dogs. Cole made a line plot of the heights, shown to the right. He concluded, “The height with the most dots is 1\(\frac{1}{4}\) feet, so that is the greatest height of the dogs at the dog show.”

Question 1.
What is Cole’s conclusion? How did he reach this conclusion?
Answer:
Cole concluded, “The height with the most dots is 1\(\frac{1}{4}\) feet, so that is the greatest height of the dogs at the dog show.” He reached this conclusion by marking most dots on 1\(\frac{1}{4}\) feet in the line plot chart.

 

 

Question 2.
Is Cole’s conclusion correct? Explain.
Answer:
No, Cole’s conclusion incorrect because what he marked as the highest height of dog is the most common height of dogs and highest height of dog is 3 feet not 1\(\frac{1}{4}\) feet.

 

 

Independent Practice
Critique Reasoning
Natasha keeps a log of the total amount of time her students practiced on their violins outside of their weekly lesson. She creates the line plot shown. Each dot represents one student who practices a specific amount of time in one week. Natasha says that 5 of her students’ practice times combined is 1\(\frac{1}{4}\) hours because there are 5 dots above 1\(\frac{1}{4}\).

Question 3.
What is Natasha’s argument? How does she support it?
Answer:
Natasha’s argument is that 5 of her students’ practice times combined is 1\(\frac{1}{4}\) hours. She supports it because there are 5 dots above 1\(\frac{1}{4}\).

 

Question 4.
Critique Natasha’s reasoning.
Answer:
Natasha’s reasoning says that 5 of her students’ practice times combined is 1\(\frac{1}{4}\) hours because there are 5 dots above 1\(\frac{1}{4}\). She thinks its correct but she is saying about more common hours the students who practiced a specific amount of time in one week.

 

 

Problem Solving
Performance Task

Taking Inventory
Mr. Pally is building a desk using screws of different lengths. The instructions show how many screws of each length he will need to use. Mr. Pally concludes he will use more of the shortest screws than the longest screws.
Question 5.
Model with Math Draw a line plot to show the screw lengths Mr. Pally will use to build the desk.

Answer:

Explanation:

 

 

Question 6.
Reasoning How can you use the line plot to find which length of screw Mr. Pally will need the most?
Answer:
We use the line plot to find which length of screw Mr. Pally will needs the most by counting the dots potted on the line, which occurred many times.

 

 

Question 7.
Critique Reasoning is Mr. Pally’s conclusion correct? How did you decide? If not, what can you do to improve his reasoning?

Answer:
Yes, Mr. Pally conclusion he will use more of the shortest screws than the longest screws is correct because in the line plotted shows many dots on shorter screws than the longest screws.

Explanation:
Mr. Pally concludes he will use more of the shortest screws than the longest screws.

 

 

Topic 11 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.
I can …add and subtract multi-digit whole numbers.

Clues
A. The sum is between 3,510 and 3,520.
B. The difference is exactly 3,515.
C. The sum is between 3,560 and 3,570.
D. The difference is between 3,530 and 3,540.
E. The sum is exactly 3,584.
F. The difference is between 3,590 and 3,600.
G. The sum is exactly 3,987.
H. The difference is between 1,000 and 2,000.

Answer:

Explanation:
Clues
A. The sum is between 3,510 and 3,520.
B. The difference is exactly 3,515.
C. The sum is between 3,560 and 3,570.
D. The difference is between 3,530 and 3,540.
E. The sum is exactly 3,584.
F. The difference is between 3,590 and 3,600.
G. The sum is exactly 3,987.
H. The difference is between 1,000 and 2,000.

 

 

 

 

Topic 11 Vocabulary Review

Understand Vocabulary
Word List

• data set
• graph
• line plot
• number line
• scale
• table

Write T for true and F for false.
Question 1.
________ Graphs are used to display and represent data.
Answer:
__True______ Graphs are used to display and represent data.

 

Question 2.
_________ A data set is a collection of pieces of information.
Answer:
____True_____ A data set is a collection of pieces of information.

 

Question 3.
__________ A table is never used to display data.
Answer:
___False_______ A table is never used to display data.

 

Question 4.
__________ A line plot shows data along a number line.
Answer:
___True_______ A line plot shows data along a number line.

 

Question 5.
_________ A line plot may have more points than there are numbers in the data set.
Answer:
___False______ A line plot may have more points than there are numbers in the data set.

 

Write always, sometimes, or never.
Question 6.
A line plot _________ displays data.
Answer:
A line plot ___always______ displays data.

 

Question 7.
The scale on a line plot is ________ numbered using fractions.
Answer:
The scale on a line plot is ___sometimes_____ numbered using fractions.

 

Question 8.
A number line is __________ numbered out of order.
Answer:
A number line is ___never_______ numbered out of order.

 

 

Use Vocabulary in Writing
Question 9.
Use at least 3 terms from the Word List to describe another way Patrick can display his data.

Answer:
Graph, Line plot and Number line are the 3 terms from the Word List to describe another way Patrick can display his data.

Explanation:
Word List given:

• data set
• graph
• line plot
• number line
• scale
• table

 

 

Topic 11 Reteaching

Set A pages 417-420

The line plot shows the number of hours Mrs. Mack was at the gym each day, during a two week period.

Remember each dot above the line plot represents one value in the data set.

Question 1.
How many days did Mrs. Mack go to the gym?
Answer:
Mrs. Mack went to the gym for 11 days.

Question 2.
What is the least amount of time Mrs. Mack spent at the gym?
Answer:
1\(\frac{1}{4}\) hours is the least amount of time Mrs. Mack spent at the gym.

Question 3.
How many hours was Mrs. Mack at the the gym during the two weeks?
Answer:
25\(\frac{3}{4}\) hours Mrs. Mack was at the the gym during the two weeks.

Explanation:

Number of hours Mrs. Mack was at the the gym during the two weeks:
1, 1\(\frac{1}{4}\) , 1\(\frac{2}{4}\) ,2 , 2 , 2\(\frac{1}{4}\) , 2 \(\frac{1}{4}\) , 2\(\frac{1}{4}\) ,2 \(\frac{2}{4}\) , 2\(\frac{3}{4}\) ,3 , 3.
Total number of hours Mrs. Mack was at the the gym during the two weeks = 1 + 1\(\frac{1}{4}\) + 1\(\frac{2}{4}\) + 2 + 2 + 2\(\frac{1}{4}\) + 2 \(\frac{1}{4}\) + 2\(\frac{1}{4}\) + 2 \(\frac{2}{4}\) + 2\(\frac{3}{4}\) + 3 + 3
= 25\(\frac{3}{4}\) hours.

Set B pages 421-424

Lilly measured the lengths of the ribbons in her craft kit and drew a line plot.

The number line shows the lengths from least to greatest. The labels show what the dots represent.

Remember to choose a reasonable scale for your number line.

A zoo in Australia studied platypuses. Their masses are recorded below.

Question 1.
Draw a line plot for the data set.
Answer:

Explanation:

 

 

 

Question 2.
What is the difference in mass of the platypus with the greatest mass and the platypus with the least mass?
Answer:
1\(\frac{1}{8}\) kg is the difference in mass of the platypus with the greatest mass and the platypus with the least mass.

Explanation:
The greatest mass of the platypus = 2\(\frac{6}{8}\) kg.
The least mass of the platypus = 1\(\frac{5}{8}\) kg.
Difference:
The greatest mass of the platypus – The least mass of the platypus
= 2\(\frac{6}{8}\)  – 1\(\frac{5}{8}\)
= 1\(\frac{1}{8}\) kg.

 

Set C pages 425-428

Carly and Freddie pick up trash. The line plots show how much they picked up each day for 14 days. What is the difference between the greatest and least amounts Carly picked up?

The greatest amount of trash Carly picked up was 3 pounds. The least amount was \(\frac{1}{2}\) pound.
Subtract. 3 – \(\frac{1}{2}\) = 2\(\frac{1}{2}\) pounds

Remember you can use equations to help solve problems with data from line plots.

For 1-3, use the line plots at the left.
Question 1.
Explain how to find the total weight of the trash Freddie picked up.
Answer:
We can find the total weight of the trash Freddie picked up in 14 days by adding the every day trash he collected.

Explanation:

Question 2.
Write and solve an equation to find , the difference between the greatest amount Freddie collected and the least amount he collected.
Answer:
2 pounds is the difference between the greatest amount Freddie collected and the least amount he collected.

Explanation:
The greatest amount Freddie collected = 2\(\frac{1}{2}\) pounds.
The least amount he collected = \(\frac{1}{2}\) pounds.
Difference:
The greatest amount Freddie collected – The least amount he collected
= 2\(\frac{1}{2}\) pounds – \(\frac{1}{2}\) pounds
= 2 pounds.

Question 3.
What is the sum of Carly’s most frequent weight and Freddie’s most frequent weight? Explain.
Answer:
5 pounds is the sum of Carly’s most frequent weight and Freddie’s most frequent weight.

Explanation:
Carly’s most frequent weight = 2\(\frac{1}{2}\) pounds.
Freddie’s most frequent weight = 1\(\frac{1}{2}\) pounds.
Sum:
Carly’s most frequent weight + Freddie’s most frequent weight
= 2\(\frac{1}{2}\) pounds + 1\(\frac{1}{2}\) pounds
= 5 pounds.

 

 

Set D pages 429-432

Think about these questions to help you critique the reasoning of others.
Thinking Habits!

• What questions can ask to understand other people’s thinking?
• Are there mistakes in other people’s thinking?
• Can I improve other people’s thinking?
  

Remember you can use math to identify mistakes in people’s thinking.

Question 1.
Spencer says 2\(\frac{3}{8}\) miles is the most common delivery distance. Do you agree? Explain.
Answer:
No, I disagree with what Spencer says 2\(\frac{3}{8}\) miles is the most common delivery distance because the most common delivery distance is \(\frac{6}{8}[/Latex] miles.

 

 

 

Topic 11 Assessment Practice

Question 1.
What is the difference between the heaviest and lightest weights?

Answer:
1 pounds is the difference between the heaviest and lightest weights.

Explanation:
The heaviest weight = 3[latex]\frac{2}{4}\) pounds.
The lightest weight = 2\(\frac{2}{4}\) pounds.
Difference:
The heaviest weight – The lightest weight
= 3\(\frac{2}{4}\)  – 2\(\frac{2}{4}\)
= 1 pounds.

Question 2.
How many dots would be placed above 1\(\frac{3}{4}\) in a line plot of these data?

A. 3 dots
B. 2 dots
C. 1 dot
D. 0 dots
Answer:
3 dots dots would be placed above 1\(\frac{3}{4}\) in a line plot of these data.
A. 3 dots.

Explanation:

Dots would be placed above 1\(\frac{3}{4}\) in a line plot of these data:
3 dots.

 

 

Question 3.
Which is the most common length of snail Fred has in his backyard?

Answer:
3 inches is the most common length of snail Fred has in his backyard.

Explanation:

3 inches is the most common length of snail Fred has in his backyard.

 

Question 4.
During a sleep study, the number of hours 15 people slept was recorded in the table below.

A. Use the data in the table to draw a line plot.
Answer:

Explanation:

B. How many more hours did the person who slept the greatest number of hours sleep than the person who slept the least number of hours? Explain.
Answer:
3\(\frac{1}{2}\) more hours the person who slept the greatest number of hours sleep than the person who slept the least number of hours.

Explanation:
The person who slept the greatest number of hours = 9 .
The person who slept the least number of hours = 5\(\frac{1}{2}\).
Difference:
The person who slept the greatest number of hours – The person who slept the least number of hours
= 9 – 5\(\frac{1}{2}\)
= 3\(\frac{1}{2}\).

Question 5.
Use the line plot below. Select all the true statements.

☐ The greatest height is 2\(\frac{1}{2}\) inches.
☐ More plants have a height of 2 inches than 1\(\frac{1}{2}\) inches.
☐ There are 3 plants with a height of 1 inch.
☐ There are 3 plants with a height of 2 inches and 3 plants with a height of 2\(\frac{1}{2}\) inches.
☐ The tallest plant is 1\(\frac{1}{2}\) inches taller than the shortest plant.
Answer:
All the true statements:
The greatest height is 2\(\frac{1}{2}\) inches.
There are 3 plants with a height of 2 inches and 3 plants with a height of 2\(\frac{1}{2}\) inches.
The tallest plant is 1\(\frac{1}{2}\) inches taller than the shortest plant.

Explanation:
Select all the true statements:
☐ The greatest height is 2\(\frac{1}{2}\) inches. (True)
☐ More plants have a height of 2 inches than 1\(\frac{1}{2}\) inches. (False)
☐ There are 3 plants with a height of 1 inch. (False)
No, There are 2 plants with a height of 1 inch.
☐ There are 3 plants with a height of 2 inches and 3 plants with a height of 2\(\frac{1}{2}\) inches. (True)
☐ The tallest plant is 1\(\frac{1}{2}\) inches taller than the shortest plant. (True)
=> Tallest plant height = 2\(\frac{1}{2}\) inches.
Shortest plant height = 1inches.
Difference:
Tallest plant height – Shortest plant height
= 2\(\frac{1}{2}\) – 1
= 1\(\frac{1}{2}\).

 

Question 6.
Mr. Tricorn’s class measured the lengths of crayons. How many crayons did they measure? Use the line plot.

Answer:
Total number of crayons they measured = 10.

Explanation:
Number of crayons of length 1\(\frac{1}{2}\) inches = 1.
Number of crayons of length 2\(\frac{1}{2}\) inches = 4.
Number of crayons of length 3\(\frac{1}{2}\) inches = 2.
Number of crayons of length 4\(\frac{1}{2}\) inches = 3.
Total number of crayons measured = Number of crayons of length 1\(\frac{1}{2}\) inches + Number of crayons of length 2\(\frac{1}{2}\) inches + Number of crayons of length 3\(\frac{1}{2}\) inches + Number of crayons of length 4\(\frac{1}{2}\) inches
= 1 + 4 + 2 + 3
= 10.

 

 

Question 7.
Use the line plot from Exercise 6. How many crayons were greater than 3 inches long?
A. 9
B. 5
C. 6
D. 3
Answer:
Number of crayons greater than 3 inches long = 5.
B. 5.

Explanation:
Number of crayons of length 1\(\frac{1}{2}\) inches = 1.
Number of crayons of length 2\(\frac{1}{2}\) inches = 4.
Number of crayons of length 3\(\frac{1}{2}\) inches = 2.
Number of crayons of length 4\(\frac{1}{2}\) inches = 3.
Number of crayons greater than 3 inches long = Number of crayons of length 3\(\frac{1}{2}\) inches + Number of crayons of length 4\(\frac{1}{2}\) inches
= 2 + 3
= 5.

 

Question 8.
Ms. Garcia measured the heights of her students.

A. Use the data in the table to draw a line plot.
Answer:

Explanation:

 

 

B. Use the data in Exercise 8. Select all of the statements that are true.
☐ The tallest student is 4 feet tall.
☐ The tallest student is 4\(\frac{2}{4}\) feet tall.
☐ The shortest student is 3\(\frac{3}{4}\) feet tall.
☐ The tallest student is 1 foot taller than the shortest student.
☐ The most common height of the students was 4 feet tall.
Answer:
All of the statements that are true:
The tallest student is 4\(\frac{2}{4}\) feet tall.
The tallest student is 1 foot taller than the shortest student.
The most common height of the students was 4 feet tall.

Explanation:
Select all of the statements that are true.
☐ The tallest student is 4 feet tall. (False)
☐ The tallest student is 4\(\frac{2}{4}\) feet tall. (True)
☐ The shortest student is 3\(\frac{3}{4}\) feet tall. (False)
☐ The tallest student is 1 foot taller than the shortest student. (True)
=> Tallest student = 4\(\frac{2}{4}\) feet.
Shortest student = 3\(\frac{2}{4}\) feet.
Difference:
Tallest student – Shortest student
= 4\(\frac{2}{4}\) feet  – 3\(\frac{2}{4}\) feet
= 1 feet.
☐ The most common height of the students was 4 feet tall. (True)

 

 

Topic 11 Performance Task

Measuring Pumpkins Mr. Chan’s class picked small pumpkins from the pumpkin patch and then weighed their pumpkins.
Question 1.
The class made the Pumpkin Weights line plot of the data.

Part A
What is the most common weight of the pumpkins?
Answer:
The most common weight of the pumpkins = 4\(\frac{1}{4}\) pounds.

Part B
Write and solve an equation to find, how much more the heaviest pumpkin weighs than the lightest pumpkin.
Answer:
1\(\frac{3}{4}\) pounds more the heaviest pumpkin weighs than the lightest pumpkin.

Explanation:
The heaviest pumpkin weight = 5pounds.
The lightest pumpkin weight = 3\(\frac{1}{4}\) pounds.
Difference:
The heaviest pumpkin weight – The lightest pumpkin weight
= 5 – 3\(\frac{1}{4}\)
= 1\(\frac{3}{4}\) pounds.

Part C
Ayana said 3 pumpkins weigh 4\(\frac{2}{4}\) pounds. Critique Ayana’s reasoning. Is she correct?
Answer:
Yes, she is correct because there are three pumpkins weigh 4\(\frac{2}{4}\) pounds.

 

Question 2.
The class also measures the distance around their pumpkins to the nearest half-inch. They recorded their data in the Pumpkin Size list. Pumpkin Size: 19\(\frac{1}{2}\), 20\(\frac{1}{2}\), 19\(\frac{1}{2}\), 20, 20\(\frac{1}{2}\), 21\(\frac{1}{2}\), 20, 21, 22, 19\(\frac{1}{2}\), 20\(\frac{1}{2}\), 21\(\frac{1}{2}\), 21, 21, 21\(\frac{1}{2}\), 20\(\frac{1}{2}\)

Part A
Draw a line plot of Pumpkin Size data.
Answer:

Explanation:
Pumpkin Size:
19\(\frac{1}{2}\), 20\(\frac{1}{2}\), 19\(\frac{1}{2}\), 20, 20\(\frac{1}{2}\), 21\(\frac{1}{2}\), 20, 21, 22, 19\(\frac{1}{2}\), 20\(\frac{1}{2}\), 21\(\frac{1}{2}\), 21, 21, 21\(\frac{1}{2}\), 20\(\frac{1}{2}\)

 

 

Part B
Drew says 1 more pumpkin was 20\(\frac{1}{2}\) inches around than was 19\(\frac{1}{2}\) inches because 20\(\frac{1}{2}\) – 19\(\frac{1}{2}\) = 1. Critique Drew’s reasoning.
Answer:
No, he is incorrect because pumpkin size of 20\(\frac{1}{2}\) – pumpkin size of 19\(\frac{1}{2}\) = 1 is the difference between two different sized pumpkins but not 1 more pumpkins added to the count.

Explanation:
20\(\frac{1}{2}\) – 19\(\frac{1}{2}\) = 1. Difference between different pumpkins.

 

Part C
What is  the difference between the longest distance and the shortest distance ? Write and solve an equation.
Answer:
3 inches is the difference between the longest distance and the shortest distance

Explanation:
The longest pumpkin sized = 22 inches.
The shortest pumpkin sized = 19 inches.
Difference:
The longest pumpkin sized – The shortest pumpkin sized
= 22 – 19
= 3 inches.