We included **HMH Into Math Grade 4 Answer Key**** PDF** **Module 3 Lesson 4 Use Comparisons to Solve Problem Situations** to make students experts in learning maths.

## HMH Into Math Grade 4 Module 3 Lesson 4 Answer Key Use Comparisons to Solve Problem Situations

I Can write equations with letters for the unknown values to model and solve multiplicative and additive comparison problems.

**Step It Out**

1. Anton is making chili for lunch at a soup kitchen. He uses 8 cups of navy beans. The recipe calls for 3 times as many black beans as navy beans. How many cups of black beans does Anton use?

A. Draw a box around what you want to know. Then underline the facts you will use.

B. Identify the type of comparison. ____

Explanation:

Multiplication type of comparison

C. Identify the unknown in the comparison. Circle the answer.

Smaller quantity how many times as many

larger quantity how many more/fewer

Explanation:

The black beans are larger in quantity

D. Write an equation to model the problem. Use n for the unknown.

smaller quantity + how many more/fewer = larger quantity

how many times as many × smaller quantity = larger quantity

___________________________

Explanation:

smaller quantity + how many more/fewer = larger quantity

8 + 8 + 8 = n

24 = n

n = 3 x 8

n = 24

E. Solve the problem. Find the value for n that makes the equation true. ___________

Explanation:

n = 3 x 8

n = 24

F. Anton uses ____ cups of black beans.

Explanation:

F. Anton uses 24 cups of black beans.

He uses 8 cups of navy beans.

The recipe calls for 3 times as many black beans as navy beans.

let n be the cups of black beans

n = 3 x 8

n = 24

**Turn and Talk** How could you use a bar model or other visual model to represent the problem?

Explanation:

**Step It Out**

2. Some students are helping out at a soup kitchen. They bring in 42 cases of water and 7 cases of juice. How many more cases of water than juice do the students bring in?

A. Identify the type of comparison. ____

Explanation:

subtraction type of comparison

B. Identify the unknown. ____

Unknown is number of water cans

Explanation:

C. Write an equation to model the comparison and solve the problem. Use n for the unknown.

_____ ___ = ____

n = ____

Explanation:

42 – 7 = 35

n = 35

D. The students bring in ____ more cases of water.

Explanation:

The students bring in 35 more cases of water.

**Turn and Talk** Would you solve the problem differently if it asked how many times as many cases of water as juice? Explain.

Explanation:

7 x n = 42

n = 42 ÷ 7

n = 6

6 times as many cases of water as juice

**Check Understanding Math Board**

**Write an equation to model and solve the problem. Use n for the unknown.**

Question 1.

Tina donates 3 fewer cans of corn than green beans. She donates 15 cans of green beans. How many cans of corn does Tina donate?

Tina donates _____ cans of corn.

Answer:

Explanation:

Question 2.

There are 42 students and 6 adults volunteering at the soup kitchen. How many times as many students as adults are volunteering?

There are ____ times as many students as adults.

Answer:

let n be the many students as adults are volunteering

6 x n = 42

n = 42 ÷ 6

n = 7

Explanation:

There are 7 times as many students as adults.

**On Your Own**

**Model with Mathematics** Write an equation to model and solve the problem. Use n for the unknown.

Question 3.

Mr. Torres makes 12 cups of rice and 8 cups of couscous for the soup kitchen. How many more cups of rice than couscous does Mr. Torres make?

Answer:

4 more cups of rice than couscous

Explanation:

Mr. Torres makes 12 cups of rice and 8 cups of couscous for the soup kitchen.

n be the unknown

n = 12 – 8

n = 4

Question 4.

Carrie spends 45 minutes making chicken noodle soup. That is 5 times as many minutes as she spends making a salad. How many minutes does Carrie spend making the salad?

Answer:

9 minutes that Carrie spend making the salad

Explanation:

Carrie spends 45 minutes making chicken noodle soup.

That is 5 times as many minutes as she spends making a salad.

n x 5 = 45

n = 45 ÷ 5

n = 9

Question 5.

Reason Draw a line to match each comparison problem to the equation that models it.

Answer:

Explanation:

Matched with the appropriate equation.

**On Your Own**

Question 6.

**Use Structure** Ms. Novak volunteers 15 hours at the soup kitchen this week. That is 5 times as many hours as Gina volunteers. How many hours does Gina volunteer at the soup kitchen?

Use inverse operations to write two different equations to model the problem. Let h = the number of hours Gina volunteers.

Answer:

Explanation:

Let h = the number of hours Gina volunteers.

h x 5 = 15

h = 3

Inverse operation:

15 ÷ 5 = 3

h = 3

**Model with Mathematics** Write an equation to model and solve the problem. Use n for the unknown.

Question 7.

Joshua makes these centerpieces. He makes 2 fewer centerpieces than Betty. How many centerpieces does Betty make?

Answer:

let m be the unknown

m = 4 – 2 = 2

m = 2

Explanation:

Joshua makes these centerpieces.

He makes 2 fewer centerpieces than Betty.

2 centerpieces that Betty make

Question 8.

Five students sign up to be cooks at the soup kitchen.

- Four more students sign up to be servers than cooks. How many students sign up to be servers?

___________________________ - Four times as many students sign up to be cleaners as cooks. How many students sign up to be cleaners?

___________________________

Answer:

20 students as servers

20 students as cleaners

Explanation:

Four more students sign up to be servers than cooks.

Five students as cooks

5 x 4 = 20

20 students sign up to be servers

Four times as many students sign up to be cleaners as cooks.

Five students as cooks

5 x 4 = 20

20 students sign up to be cleaners