We included **HMH Into Math Grade 5 Answer Key PDF** **Module 15 Lesson 3 Assess Reasonableness of Products **to make students experts in learning maths.

## HMH Into Math Grade 5 Module 15 Lesson 3 Answer Key Assess Reasonableness of Products

I Can assess the reasonableness of the product of a decimal less than one and a whole number.

**Spark Your Learning
**Rosalind’s school is holding a Math Fun Fair. One of the games is a sorting game with the numerical expressions shown.

8 × 0.45

8 × 0.6

6 × 0.81

8 × 0.52

8 × 0.8

4 × 0.99

8 × 0.49

4 × 0.9

Sort the numerical expression.

Answer:

Explanation:

8 × 0.45 = 3.6.

8 × 0.6 = 4.8.

6 × 0.81 = 4.86.

8 × 0.52 = 4.16.

8 × 0.8 = 6.4.

4 × 0.99 = 3.96.

8 × 0.49 = 3.92.

4 × 0.9 = 3.6.

**Turn and Talk** How does the value of the expression 8 × 0.45 compare to the value of the expression 4 × 0.99? Explain how you know.

Answer:

The value of the expression 8 × 0.45 is comparably less to the value of the expression 4 × 0.99.

Explanation:

8 × 0.45 = 3.6.

4 × 0.99 = 3.96.

=> 8 × 0.45 < 4 × 0.99.

**Build Understanding
**Question 1.

One of the prizes at the Math Fun Fair is erasers. The value of each eraser is $0.77. There are 8 erasers on the prize table. Joni says the value of the 8 erasers is greater than $6.00. How is she able to make this claim? Is her claim reasonable?

A. Did Joni give an exact value or an estimate for the 8 erasers?

Answer:

Yes, Joni claim is reasonable.

Explanation:

Cost of each eraser = $0.77.

Number of erasers on the prize table = 8.

Total cost of 8 erasers = Cost of each eraser × Number of erasers on the prize table

= $0.77 × 8

= $6.16.

Joni says the value of the 8 erasers is greater than $6.00.

B. Decimals and fractions both name fractional parts of a whole. It is often easier to calculate using fractions rather than decimals. Complete the number line to show the decimal equivalents of some common fractions.

Answer:

Explanation:

\(\frac { 1 }{ 4 } \) = 0.25.

\(\frac { 1 }{ 2 } \) = 0.50.

\(\frac { 3 }{ 4 } \) = 0.75.

C. To which decimal number is $0.77 closest?

Answer:

Decimal number is $0.77 closest to \(\frac { 3 }{ 4 } \) = 0.75

Explanation:

\(\frac { 1 }{ 4 } \) = 0.25.

\(\frac { 1 }{ 2 } \) = 0.50.

\(\frac { 3 }{ 4 } \) = 0.75.

D. What fraction is equivalent to 0.75?

Answer:

\(\frac { 3 }{ 4 } \) fraction is equivalent to 0.75.

Explanation:

\(\frac { 1 }{ 4 } \) = 0.25.

\(\frac { 1 }{ 2 } \) = 0.50.

\(\frac { 3 }{ 4 } \) = 0.75.

E. Use the fraction to find the value of the 8 erasers. Show your work.

Answer:

Total cost of 8 erasers = $6.16.

Explanation:

Cost of each eraser = $0.77.

Number of erasers on the prize table = 8.

Total cost of 8 erasers = Cost of each eraser × Number of erasers on the prize table

= $0.77 × 8

= $6.16.

F. How does 0.77 compare to 0.75?

Answer:

0.77 > 0.75.

Explanation:

0.77 compare to 0.75.

=> 0.77 > 0.75

G. Is Joni’s claim reasonable? Explain.

Answer:

Yes, Joni claim is reasonable.

Explanation:

Cost of each eraser = $0.77.

Number of erasers on the prize table = 8.

Total cost of 8 erasers = Cost of each eraser × Number of erasers on the prize table

= $0.77 × 8

= $6.16.

Joni says the value of the 8 erasers is greater than $6.00.

**Turn and Talk** What would the value of one eraser need to be so that the value of 8 erasers would be greater than or equal to $2.00 and less than or equal to $4.00?

Answer:

The value of one eraser need to be $0.25 so that the value of 8 erasers would be greater than or equal to $2.00 and $0.50 less than or equal to $4.00

Explanation:

The value of 8 erasers would be greater than or equal to $2.00.

=> $2.00 ÷ 8

= $0.25.

The value of 8 erasers would be less than or equal to $4.00

=> $4.00 ÷ 8

=> $0.50.

**Step It Out
**Question 2.

At another Math Fun Fair booth, a player chooses a digit from 1 to 9, spins the wheel, and multiplies the two numbers. If the product is greater than or equal to the digit, the player wins a prize.

A. Taylor chooses the digit 4 and spins the number 0.7. Does she win a prize? How do you know?

Answer:

No, Taylor wont win the prize because product (4 × 0.7 = 2.8.) is less than 4.

Explanation:

Taylor chooses the digit 4 and spins the number 0.7.

=> Product = 4 × 0.7 = 2.8.

If the product is greater than or equal to the digit, the player wins a prize.

B. Is there any digit Taylor could have chosen for which a spin of 0.7 results in her winning a prize? Why?

Answer:

Yes, Taylor could chosen for a spin of 0.7 results in her winning a prize are 0.7 × 1 = 0.7 as number is equal to the product.

Explanation:

Digit Taylor could have chosen for which a spin of 0.7 results in her winning a prize:

0.7 × 0.5 = 0.35.

0.7 × 0.6 = 0.42.

0.7 × 0.7 = 0.49.

0.7 × 0.8 = 0.56.

0.7 × 0.9 =0.63.

0.7 × 1 = 0.7

0.7 × 1.1 = 0.77.

0.7 × 1.2 = 0.84.

0.7 × 1.3 = 0.91.

0.7 × 1.4 = 0.98.

C. For what other numbers on the wheel will Taylor not win a prize?

Answer:

Other numbers on the wheel will Taylor not win a prize are:

0.7 × 0.5 = 0.35.

0.7 × 0.6 = 0.42.

0.7 × 0.7 = 0.49.

0.7 × 0.8 = 0.56.

0.7 × 0.9 =0.63.

0.7 × 1.1 = 0.77.

0.7 × 1.2 = 0.84.

0.7 × 1.3 = 0.91.

0.7 × 1.4 = 0.98.

Explanation:

Other numbers on the wheel will Taylor not win a prize are:

0.7 × 0.5 = 0.35.

0.7 × 0.6 = 0.42.

0.7 × 0.7 = 0.49.

0.7 × 0.8 = 0.56.

0.7 × 0.9 =0.63.

0.7 × 1.1 = 0.77.

0.7 × 1.2 = 0.84.

0.7 × 1.3 = 0.91.

0.7 × 1.4 = 0.98.

D. Which numbers on the wheel will result in Taylor winning a prize?

Answer:

0.7 × 1.1 = 0.77 and 0.7 × 1 = 0.7 numbers on the wheel will result in Taylor winning a prize.

Explanation:

0.7 × 1.1 = 0.77 and 0.7 × 1 = 0.7 numbers on the wheel will result in Taylor winning a prize.

**Turn and Talk** Suppose the numbers on the wheel change. How can you tell whether a player will win a prize or not win a prize?

Answer:

If the numbers on the wheel change, the product of the numbers will be changed and she can win if it is more than the number and vise verse.

Explanation:

If the numbers on the wheel change, the product of the numbers will be changed and she can win if it is more than the number and vise verse.

**Check Understanding
**Question 1.

There are also 4 sticker packs on the prize table. The value of each is $0.46. Javier claims that the total value is less than $2.00. Is his claim reasonable? Explain.

Answer:

Yes, total cost of sticker packs = $1.84 his claim is reasonable as its less than $2.00.

Explanation:

Number of sticker packs on the prize table = 4.

Cost of each = $0.46.

Total cost of sticker packs = Number of sticker packs on the prize table × Cost of each

= 4 × $0.46

= $1.84.

Javier claims that the total value is less than $2.00.

**Determine whether the statement is true or false.
**Question 2.

6 × o.52 < 3

Answer:

Its false 6 × o.52 < 3.

Explanation:

6 × o.52 = 3.12.

Question 3.

4 × 0.61 > 2

Answer:

Its true 4 × 0.61 > 2.

Explanation:

4 × 0.61 = 2.44.

Question 4.

7 × 0.87 > 7

Answer:

Its false 7 × 0.87 > 7.

Explanation:

7 × 0.87 = 6.09.

**On Your Own
**Question 5.

**STEM**Human hair grows about 0.43 millimeter each day. Is it reasonable to expect that hair grows more than 3.5 millimeters in one week? Explain.

Answer:

No, it is not reasonable to expect that hair grows more than 3.5 millimeters in one week because number of millimeters hair grows in a week = 3.01.

Explanation:

Number of millimeter each day Human hair grows = 0.43.

Number of days in a week = 7.

Number of millimeters hair grows in a week = Number of millimeter each day Human hair grows × Number of days in a week

= 0.43 × 7

= 3.01.

**Determine whether the statement is true or false.
**Question 6.

2 × 0.51 > 1

Answer:

Its false 2 × 0.51 > 1

Explanation:

2 × 0.51 = 1.02.

Question 7.

4 × 0.49 > 2

Answer:

Its true 4 × 0.49 > 2.

Explanation:

4 × 0.49 = 1.96

Question 8.

5 × 0.97 > 5

Answer:

Its false 5 × 0.97 > 5.

Explanation:

5 × 0.97 = 4.85.

Question 9.

Jan goes to the grocery store to buy apples and oranges.

Jan buys 5 apples. Is it reasonable that the apples weigh less than 5 pounds? Explain how you know.

Answer:

Yes, its reasonable that the apples weigh less than 5 pounds because Weight of 5 apples = 3.71 lb.

Explanation:

Number of apples Jan buys = 5.

Weight of each apple = 0.74 lb.

Weight of 5 apples = Number of apples Jan buys × Weight of each apple

= 5 × 0.74 lb

= 3.70 lb.

Jan buys 6 oranges. Is it reasonable that the oranges weigh less than 3 pounds? Explain how you know.

Answer:

Explanation:

Number of oranges Jan buys = 6.

Weight of each orange = 0.55 lb.

Weight of 5 oranges = Number of oranges Jan buys × Weight of each orange

= 5 × 0.55 lb

= 2.75 lb.

Question 10.

**Reason** Suppose you multiply 4 and 0.____7. What are the possible values of the unknown digit if the product is less than 1? Explain.

Answer:

The possible values of the unknown digit if the product is less than 1 are 4 × 0.07 = 0.28 and

4 × 0.17 = 0.68.

Explanation:

Let the missing number be from 0 to 9:

4 × 0.07 = 0.28.

4 × 0.17 = 0.68.

4 × 0.27 = 1.08.

4 × 0.37 = 1.48.

4 × 0.47 = 1.88.

4 × 0.57 = 2.28.

4 × 0.67 = 2.68.

4 × 0.77 = 3.08.

4 × 0.87 = 3.48.

4 × 0.97 = 3.88.

**I’m in a Learning Mindset!
**What strategies do I use to stay on task?

Answer:

Strategies I use to stay on task:

Plan and Visualize a Few Critical Tasks Each Day.

Find Your Peak Hours.

Avoid Multitasking.

Treat Your Mind Like a Muscle.

Build Willpower and Discipline.

Acknowledge Your Need to Avoid Pain and to Gain Pleasure.

Avoid Distractions.

Leverage the Power of Habits.