Lesson 10 Introduction MGSE4.OA.3 ... - fultonschools.org

Introduction

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Use What You Know

Lesson 10 Solve Multi-Step Problems

Lesson 10Solve Multi-Step Problems

In Lesson 9, you learned how to write equations for multi-step problems. In this lesson, you will solve those equations. Take a look at this problem.

a. Write an expression that represents Lola’s score on the first 3 questions.

b. Write an expression that represents Lola’s score on the other 2 questions.

c. What operation can be used to combine her scores on the first 3 questions with

her scores on the other 2 questions?

d. Choose a letter to represent Lola’s total score and write an equation that could be

used to solve the problem.

e. What was Lola’s total score on the first 3 questions?

f. What was Lola’s total score on the last 2 questions?

g. What was Lola’s total score on all 5 questions?

On a test, Lola scored 6 points on each of the first 3 questions and 4 points on each of the other 2 questions. Write an equation to find Lola’s total score.

Question Score1 6 points

2 6 points

3 6 points

4 4 points

5 4 points

MGSE4.OA.3

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Find Out More


There is often more than one way to find the answer to a problem.

• One Way The bar model below shows one way to think about the problem about Lola’s scores.

6

First 3 questions Last 2 questions

6 6 4 4

P

• Another Way You can also represent the problem with an equation. Sometimes you can write more than one equation to represent a problem. Both of the equations below show a correct way to solve a problem.

(3 3 6) 1 (2 3 4) 5 P (6 3 3) 1 4 1 4 5 P 18 1 8 5 P 18 1 4 1 4 5 P 26 5 P 26 5 P

Lola’s total score was 26 points.

How can you tell if the answer is reasonable? Lola scored 6 points on some questions and 4 points on others. You could think of it as scoring 5 points for each question. 5 3 5 5 25, so the answer of 26 makes sense.

Reflect1 How would the bar model change if Lola scored 5 points on each of the last

2 questions? How would the first equation change?

Modeled and Guided Instruction

Learn About


Lesson 10


Solving Multi-Step Problems

Read the problem below. Then explore different ways to understand it.

Ms. Dennison is packing up the books in her classroom for the summer. Each box holds 9 books. She has 24 math books and 27 science books to pack. How many boxes will she need?

Model It You can use a number line to help understand the problem and write an equation.

0 3 6

24 27

9 12 15 18 21 24 27 30 33 36 39 42 45 48 51 54

The total number of books is shown above the number line (24 1 27). The number line shows jumps of 9 because each box holds 9 books.

Let X equal the number of boxes needed. Remember to use parentheses to show what to do first.

X 5 (24 1 27) 4 9

Solve It You can solve the equation that represents the problem.

X 5 (24 1 27) 4 9 X 5 51 4 9

When a number doesn’t divide evenly, you have some left over. The amount left over is called a remainder, shown with an R.

51 4 9 5 R6

©Curriculum Associates, LLC Copying is not permitted. 95Lesson 10 Solve Multi-Step Problems

Connect It Now you will explore the problem from the previous page further.

2 What does the 5 in the solution 5 R6 mean?

What does the R6 mean?

3 How many books are left over that do not make a full box?

Is another box needed to hold the 6 left over books?

4 How many boxes will Ms. Dennison need?

5 Check the solution to the equation:

boxes 3 books per box 1 books 5 51 total books

6 How could you estimate to make sure your answer is reasonable?

7 Explain why the solution to an equation is not always the answer to a problem

when there is a remainder.

Try It Use what you just learned to solve these problems. Show your work on a separate sheet of paper.

8 Cadence ordered a $4 sandwich, a $2 drink, and a $3 smoothie for lunch. She has $10. Write and solve an equation to find out if she has enough money for lunch.

9 In the problem above, will Cadence get any change back from her $10? Explain

how you know.

Guided Practice

Practice


Lesson 10



Pair/ShareDiscuss the reasonableness of the answer.

Pair/ShareDo you get the same answer if you write the equation a different way?

How many cats does the store have?

The student could estimate the answer to check whether it is reasonable!

Example

10 A pet store has 17 rabbits. They have 5 fewer cats than rabbits. Write and solve an equation to find how many rabbits and cats the store has altogether.

Show your work.

Solution

Myron and Suzanne are making banana bread. Each batch uses 3 bananas. Myron has 5 bananas and Suzanne has 8 bananas. Write and solve an equation to find out how many batches of banana bread they can make. Will they have bananas left over?

Look at how you could show your work using a model.

0 1 2

5 8

3 4 5 6 7 8 9 10 11 12 13

Let B 5 number of batches

(5 1 8) 4 3 5 B 13 4 3 4 R1

Solution

Study the example below. Then solve problems 10–12.

They can make 4 batches with 1 banana left over.


Pair/ShareCompare the strategies you both used to solve the problem.

Pair/ShareWhat would happen if Taylor didn’t think about the remainder?

What does the remainder tell you?

11 Taylor earns $5 each time she walks her neighbor’s dog. She has already earned $25. Write and solve an equation to find out how many more times Taylor needs to walk the dog to earn enough to buy a bike that costs $83.

Show your work.

Solution

12 Lindsay sold 47 boxes of oranges for a fundraiser. Tim sold 12 fewer boxes than Lindsay. How many more boxes of oranges does Tim need to sell to have sold 60 boxes? Circle the letter of the correct answer.

A 1

B 25

C 35

D 48

Shonda chose A as the correct answer. How did she get that answer?

A picture can help make sense of all the numbers!

Independent Practice

Practice


Lesson 10



Solve the problems.

1 Franklin uses 3 eggs to make a large omelet and 2 eggs to make a small omelet. How many eggs would he need to make 5 large omelets and 4 small omelets?

A 14 eggs

B 22 eggs

C 23 eggs

D 26 eggs

2 The student council needs drinks for the Grade

Total Number of People

4th Graders 28

5th Graders 23

6th Graders 24

annual Fun Run. They can buy water, juice, or sports drinks. The table shows how many people will be participating.

Which combinations will provide enough drinks so that each participant can have at least one drink? Circle the letter for all that apply.

A 3 packs of water

B 2 packs of water, 2 packs of juice, 2 packs of sports drink

C 2 packs of water, 5 packs of sports drink

D 1 pack of water, 8 packs of juice

E 1 pack of water, 6 packs of sports drink

Self Check


Go back and see what you can check off on the Self Check on page 45.

3 Petra walked 9 miles the first week of this month, twice that far the second week, and

6 miles the third week. How many miles did Petra walk altogether?

4 Ms. Ruiz planted 14 flowers in 3 pots. She planted 4 flowers in the 1 blue pot and split the rest equally between the 2 red pots.

Write and solve an equation to find the number of flowers Ms. Ruiz planted in each of the 2 red pots.

Show your work.

5 Gabriel owns 27 fiction books and 23 non-fiction books. If 8 books fit on each shelf, how many shelves does he need for all of his books?

Solve the problem and explain how the remainder affected your answer.

Show your work.

Lesson 10 Introduction MGSE4.OA.3 ... - fultonschools.org

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