We included **HMH Into Math Grade 3 Answer Key**** PDF** **Module 8 Lesson 4 Solve Two-Step Problems** to make students experts in learning maths.

## HMH Into Math Grade 3 Module 8 Lesson 4 Answer Key Solve Two-Step Problems

I Can write equations using the four operations with an unknown to solve two-step problems.

**Step It Out**

1. Mr. Cole paints airplanes. He has 6 gallons of paint in a sprayer. He also has 7 equal¬sized buckets of paint. The total amount of paint he has is 41 gallons. How much paint is in each bucket?

Answer:

The paint in each bucket is 5 gallons.

Explanation:

Let the paint in each bucket be P. As he has 6 gallons of paint in a sprayer and also has 7 equal¬sized buckets of paint. So the equation will be

6+7P = 41,

7P = 41-6,

7P = 35,

P = 35÷7

P = 5.

So the paint in each bucket is 5 gallons.

Look at the information in the problem and plan steps to solve.

A. Circle the numbers you know.

B. Complete the bar model to show how many gallons of paint Mr. Cole has. Use p for the unknown number.

Answer:

P = 35 gallons.

Explanation:

The equation is 6+P = 41 where P is

P = 41-6

= 35 gallons.

C. Step 1: How can you use an equation to find the amount of paint in all the buckets?

Answer:

The amount of paint in all the buckets is 35 gallons.

Explanation:

The equation to find the amount of paint in all the buckets

6+P = 41,

P = 41-6,

= 35 gallons.

Use a ___ equation to find the amount of paint in all the buckets. Solve for p.

Answer:

P = 35 gallons.

Explanation:

Here, we have used subtraction to find the amount of paint in all the buckets. The equation is 41-6 = P, where P is 35 gallons.

**Turn and Talk** How can you use p to find the amount of paint that is in each bucket?

Answer:

We can use p to find the amount of paint that is in each bucket by using subtraction.

**Step It Out**

D. What numbers do you know? What do the numbers represent? ___________

Answer:

As 7 equal-sized buckets have 35 gallons total in the buckets.

E. Complete the bar model to show how many gallons of paint Mr. Cole has in each bucket. Use g for the unknown number.

Answer:

P = 35 gallons.

Explanation:

Here, we have used g for the unknown numbers. So Mr. Cole has 7×5 which is 35 gallons.

You can use your solution from Step 1 in order to find how much paint is in each bucket for Step 2.

F. **Step 2:** How can you use an equation to find the amount of paint in each bucket?

Now use a ___ equation to find the amount of paint in each bucket. Solve for g.

Answer:

The amount of paint in each bucket is 7 buckets.

Explanation:

The equation to find the amount of paint in each bucket is 35÷7 which is 5 buckets.

G. What operations can you use to check the reasonableness of your answers? ________________

Answer:

The operations that we have used are division, subtraction.

**Turn and Talk** What is another strategy you could use to solve the problem?

2. Brie is painting a fence. The fence has 7 sections that are eaçh 9 feet long and one 17-foot-long section. Use steps and equations to find the total length of the fence.

A. Think about the information you know.

Answer:

The total length of the fence is 80 feet.

Explanation:

Given that Brie is painting a fence and the fence has 7 sections that are eaçh 9 feet long which is 7×9 = 63 feet long and one 17-foot-long section. So the total length of the fence is 63+17 which is 80 feet.

**Step 1:** Draw a bar model and write a multiplication equation to find the total length of the 7 same-length sections of fence. Use s for the unknown number. Then solve.

Answer:

7×9 = 63.

Explanation:

The multiplication equation is 7×9 = s, where s is 7×9 =63.

Think: What do I need to find? What information do I need to use’ What steps and equations can I use to find the answer?

Answer:

The equation is 7×9 =63.

Explanation:

Here, we have found the total length of the fence and the equation is 7×9 =63.

Step 2: Draw a bar model and write an addition equation to find the total length of the fence. Use f for the unknown number. Then solve.

Answer:

f is 80.

Explanation:

As length of 7 sections is 63 and length of extra section is 17. So f is 80.

**Turn and Talk** How can you use division and subtraction to check your answer?

Answer:

Here, when we add the difference to the smaller number and if the sum equals to the larger number then our answer is correct.

**Check Understanding Math Board**

Question 1.

Mike buys 7 packs of erasers. Each pack has 4 erasers. He also has 5 loose erasers. How many erasers does he have now? Write two equations with letters for the unknowns. Solve.

Answer:

The two equations are 7×4 = e where e is 28 erasers and 28-5 = l where l is 23 erasers.

Explanation:

Given that Mike bought 7 packs of erasers and each pack has 4 erasers which is 7×4 = e where e is 28 erasers. As he looses 5 erasers, he have 28-5 = l where l is 23 erasers.

**On Your Own**

**Model with Mathematics Write two equations with letters for the unknowns. Solve. You can use a visual model to help.**

Question 2.

Lanni checks out 6 sets of books from the library. Each set has the same number of books. She reads 7 of the books, and she has 11 books left to read. How many books are in each set?

Answer:

There will be 3 books in each set.

Explanation:

Given that Lanni checks out 6 sets of books from the library and each set has the same number of books. As she reads 7 of the books, and she has 11 books left to read. So the equation will be 11+7 = b where b is 18 books. As there is a set of 6 books, so the equation will be 18÷6 = s where s is 3 books. So there will be 3 books in each set.

Question 3.

Sal cuts a piece of yarn for a project into 3 equal-length pieces. Then he cuts 5 inches off one of the pieces, leaving 4 inches of yarn. What was the length of the original piece of yarn?

Answer:

The length of the original piece of yarn is 27 inches.

Explanation:

Given that Sal cuts a piece of yarn for a project into 3 equal-length pieces and then he cuts 5 inches off one of the pieces, leaving 4 inches of yarn. So the equation will be 4+5 = p where p is 9 in. The length of the original piece of yarn is 3×9 which is 27 inches.

Question 4.

At the lake, Jansen can rent a canoe for $5 each hour plus a one time fee of $7. He rents a canoe for 3 hours. How much does it cost Jansen to rent the canoe?

Answer:

The equation will be 3×5 = r where r is $15.

The equation will be 15+7= c where c is $22.

Explanation:

Given that Jansen can rent a canoe for $5 each hour plus a one time fee of $7 and he rents a canoe for 3 hours. So the equation will be 3×5 = r where r is $15. And the cost of Jansen to rent the canoe, so the equation will be 15+7= c where c is $22.

**Model with Mathematics Write two equations with letters for the unknowns. Solve. You can use a visual model to help.**

Question 5.

Jason has $30 to buy books. His aunt gives him $10 more. If each book that he wants costs $8, how many books can Jason buy?

Answer:

Jason bought 5 books.

Explanation:

Given that Jason has $30 to buy books and his aunt gives him $10 more, so now Jason will have $30+$10 = t where t is $40. As each book that he wants costs $8, so the number of books can Jason bought is $40÷$8 = b where b is 5 books.

Question 6.

Beth pays a total of $20 to rent skates and go ice skating for 2 hours. If the cost for the skate rental is $6, what is the cost for each hour of ice skating?

Answer:

The cost for each hour of ice skating is $7.

Explanation:

Given that Beth pays a total of $20 to rent skates and go ice skating for 2 hours and if the cost for the skate rental is $6, so the equation will be $20-$6 = s where s is $14. As Beth goes ice skating for 2 hours, so the equation will be 14÷2 = r where r is 7. So the cost for each hour of ice skating is $7.

Question 7.

Sean scores 21 points during a basketball game. One of his baskets is a three-point shot. He scores the rest of his points with two-point baskets. How many two-point baskets does Sean score during the game?

Answer:

The number of two-point baskets does Sean score during the game is 9.

Explanation:

Given that Sean scores 21 points during a basketball game and one of his baskets is a three-point shot, so the equation will be 21-3 = p where p is 18. As he scores the rest of his points with two-point baskets, so the two -point baskets does Sean score during the game is 18÷2 = b where b is 9.

Question 8.

**Open Ended** Write a two-step word problem that can be solved using two equations with different operations. Then write the two equations and solve the problem.

Answer:

**On Your Own**

**Model with Mathematics** Write two equations with letters for the unknowns. Solve. You can use a visual model to help.

Question 9.

Mr. Ed’s school bus route has 8 stops. The same number of students is waiting at each stop. So far, he has picked up 20 students. There are 12 students waiting to be picked up. How many students are at each bus stop?

Answer:

There are 4 students at each bus stop.

Explanation:

Given that Mr. Ed’s school bus route has 8 stops and the same number of students is waiting at each stop. So far, he has picked up 20 students and there are 12 students waiting to be picked up. So the equation will be 20+12 = b where b is 32. As there are 8 stops, so the equation will be 32÷8 = 4. So there are 4 students at each bus stop.

Question 10.

Xavier watches an old TV show by streaming it on a computer. The show had 5 seasons. Xavier has watched 7 episodes. He has 43 more episodes to watch. If each season has the same number of episodes, how many episodes does each season have?

Answer:

The number of episodes does each season had is 5 episodes.

Explaantion:

As there are 5 seasons and Xavier has watched 7 episodes and he 43 more episodes to watch. So the equation is 43+7 = t where t is 50 episodes. As the show had 5 seasons, so the equation will be 50÷5 = e where e is 5. So the number of episodes does each season had is 5 episodes.

Question 11.

Jamie’s plant grows 3 inches each week for three weeks. During the fourth week, it grows 5 inches. How many inches does Jamie’s plant grow over the four weeks?

Answer:

The number of inches does Jamie’s plant grow over the four weeks is 14 inches.

Explanation:

Given that Jamie’s plant grows 3 inches each week for three weeks and during the fourth week, it grows 5 inches. So the number of inches does Jamie’s plant grow over the four weeks is, the equation is 3×3 = p where p is 9. As it grows 5 inches, so the equation will be 9+5 = g where g is 14 inches.

Question 12.

Natasha buys 2 bunches of tulips. Each bunch has the same number of tulips. She puts the tulips in a vase with 5 roses. There are now 17 flowers in the vase. How many tulips are in each bunch?

Answer:

The number of tulips are in each bunch is 6 tulips.

Explanation:

Given that Natasha bought 2 bunches of tulips and each bunch has the same number of tulips. As she puts the tulips in a vase with 5 roses there are now 17 flowers in the vase, so the equation is 17-5 = t where t is 12. As Natasha bought 2 bunches of tulips, so the equation will be 12÷2 = b where b is 6 tulips.