## Envision Math 5th Grade Textbook Answer Key Topic 2.7 Problem Solving

Problem Solving

Draw a Picture and Write an Equation

Three friends have music collections. How many more CDs does Susan have than Larry? Another Example

Rori had some balloons and then gave 35 of them away. She now has 21 left. How many balloons did Rori have to begin with? One Way
Think The total is unknown.
35 were given away and 21 are left.
Write an Equation
x – 35 = 21
21 + 35 = 56, so 56 is the total.
x = 56

Another Way
Think 35 were given away. Rori has 21 left.
The total is unknown.
Write an Equation
35 + 21 = x
35 + 21 = 56, so 56 is the total.
x = 56
Rori had 56 balloons to begin with.

Explain It

Question 1.
Why do both ways use addition to solve for x?

Question 2.
How can you check if 56 is a reasonable answer?

What do I know?
Susan has 42 CDs and Larry has 26 CDs.
What am I asked to find?
The difference between the number of CDs from these two collections

Plan and Solve

Draw a Picture Write an Equation
Let n = the number of
additional CDs Susan has.
42 – 26 = n Susan has 16 more CDs in her collection than Larry

Guided Practice*

Do you know HOW?

Draw a picture and write an equation. Solve.

Question 1.
Alec prints digital photos at a camera store. The first order was for 24 prints. The second order was for 85 prints, and the third for 60 prints. How many fewer prints were in the first order than the third order?

Question 2.
What phrase from the above example gives you a clue that you will use subtraction in your drawing to solve the problem?

Question 3.
Write a Problem Write a real-world problem that uses subtraction and can be solved by drawing a picture and writing an equation.

Independent Practice

In 4, copy and complete the picture. Then write an equation and solve.

Question 4.
Rose needs 22 tacos for a party. She has made 12 tacos so far. How many more tacos does Rose need to make? In 5, draw a picture, write an equation in two different ways, then solve.

Question 5.
Aryanna is planning to spend a certain number of days on a trip to Florida. If she plans to spend 5 of the days in Orlando, she’ll have 16 more days for the rest of her vacation. How many days does Aryanna plan to spend in Florida?

In 6, use the bar graph at the right.

Question 6.
Foster Middle School raised money to help care for some endangered animals. The bar graph shows the number of animals they will help with the money raised.
a. How many sea turtles and snow leopards can they help?
b. What is the difference between the greatest number of animals to be helped and the least number to be helped?
c. Show how you can use mental math to find the total number of animals helped. Question 7.
Writing to Explain Don is adding 407 and 512. How do you know his sum will be less than 1,000?

Question 8.
Writing to Explain Is 1,200 a good estimate for the difference of 4,725 – 2,689? Explain.

Question 9.
A planetarium is 39 miles from Marco’s school. The class leaves for the field trip at 8:00 A.M. After driving for 17 minutes and traveling 15 miles, the driver of the bus got caught in traffic. How many more miles are left to travel to the planetarium? Write an equation to solve. Question 10.
Marlee is taking a class to improve her reading. She began reading a book on Monday and completed 3 pages. Tuesday she read 6 pages, Wednesday, 12 pages. If this pattern continues, how many pages will Marlee read on Friday?

Think About the Process

Question 11.
Three fifth-grade classes took a survey and found that 35 students take the bus to school, 25 come by car, 15 walk, and 5 ride their bikes. Which shows how to find how many more students take the bus than walk?
A. Subtract 35 from 5
B. Subtract 15 from 35
C. Add 15 and 35
D. Add 35 and 5

Question 12.
Darcy brought home 43 seashells from his vacation. Rich brought home x shells. Together they brought home 116 seashells. Which equation can you solve to find the number of shells Rich brought home?
A. 43 + x = 116
B. 116 + x = 43
C. 116 + 43 = x
D. x – 43 = 116

Stop and Practice

Find each difference. Estimate to check if the answer is reasonable.

Question 1. Question 2. Question 3. Question 4. Question 5. Question 6. Question 7. Question 8. Find each difference. Estimate to check if the answer is reasonable

Question 9. Question 10. Question 11. Question 12. Question 13. Question 14.
1.17 – 0.362

Question 15.
4.9 – 1.003

Question 16.
6.73 – 4.816

Error Search Find each sum or difference that is not correct.
Write it correctly and explain the error.

Question 17. Question 18. Question 19. Question 20. Question 21. Number Sense

Estimating and Reasoning Write whether each statement is true or false. Explain your reasoning.

Question 22.
The sum of 56,141 and 3,052 is less than 59,000.

Question 23.
The sum of 50.73 and 40.22 is greater than 90 but less than 92.

Question 24.
The difference of 63,432 and 21,089 is greater than 41,000 and less than 43,000.