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6-8 Grade 7 Unit 6 Lesson 11

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Lesson 1 Lesson 2 Lesson 3 Lesson 4 Lesson 5 Lesson 6 Lesson 7 Lesson 8 Lesson 9 Lesson 10 •Lesson 11 Lesson 12 Lesson 13 Lesson 14 Lesson 15 Lesson 16 Lesson 17 Lesson 18 Lesson 19 Lesson 20 Lesson 21 Lesson 22

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IM K-5 Math
IM 6-8 Math
IM 9-12 Math

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Lesson 11

11.1 Warm-up 11.2 Activity 11.3 Activity Student Lesson Summary

Unit 6, Lesson 11

Using Equations to Solve Problems

Grade 7

11.1

Warm-up

Remember Tape Diagrams

Tape diagram, 6 parts, a, 2, a, 2, a, 2, total 24. Across the top, brackets above an a and 2 indicate a + 2.

Write a story that could be represented by this tape diagram.
Write an equation that could be represented by this tape diagram.

Are You Ready for More?

11.2

Activity

At the Community Festival

Tyler makes invitations to the community festival. He has already made some of the invitations, and he wants to finish the rest of them within a week. He plans to make the same number of invitations each day. Tyler draws a diagram to represent the situation.
1. Explain how each part of the situation is represented in Tyler’s diagram:
  How many total invitations Tyler is trying to make
  
  How many invitations he has made already
  
  How many days he has to finish the invitations
2. How many invitations should Tyler make each day to finish his goal within a week? Explain or show your reasoning.
3. Write an equation that represents the situation. Explain how each part of the situation is represented in your equation.
4. Show how to solve your equation.
Noah and his sister make prize bags for a game at the festival. Noah puts 7 pencil erasers in each bag. His sister puts an equal number of stickers in each bag. After filling 3 of the bags, they have used a total of 57 items.
1. Explain how the diagram represents the situation.
2. Noah writes the equation to represent the situation. Do you agree with him? Explain your reasoning.
3. How many stickers does Noah's sister put in each prize bag? Explain or show your reasoning.
A family of 6 goes to the festival. They have a coupon for $1.50 off each ticket. If they pay $46.50 for all their tickets, how much does each ticket cost without the coupon? Explain or show your reasoning. If you get stuck, consider drawing a diagram or writing an equation.

Are You Ready for More?

11.3

Activity

Running Around

Priya, Han, and Elena, are members of the running club at school.

Priya was busy studying this week and ran 7 fewer miles than last week. She ran 9 times as far as Elena ran this week. Elena only had time to run 4 miles this week.
1. How many miles did Priya run last week?
2. Elena wrote the equation to represent the situation. She solved the equation by multiplying each side by 9 and then adding 7 to each side. How does her solution compare to the way you found Priya's miles?
One day last week, 6 teachers joined of the members of the running club in an after-school run. Priya counted a total of 31 people running that day. How many members does the running club have?
Priya and Han plan a fundraiser for the running club. They begin with a balance of -80 dollars because of expenses. In the first hour of the fundraiser, they collect equal donations from 9 people, which brings their balance to -44. How much did each person give?
The running club uses the money they raised to pay for a trip to a canyon. At one point during a run in the canyon, the students are at an elevation of 128 feet. After descending at an average rate of 50 feet per minute, they reach an elevation of -472 feet. How long did the descent take?

Are You Ready for More?

Student Lesson Summary

Many problems can be solved by writing and solving an equation. Here is an example:

Clare ran 4 miles on Monday. Then for the next 6 days, she ran the same distance each day. Clare ran a total of 22 miles during the week. How many miles did she run on each of the 6 days?

One way to solve the problem is to represent the situation with an equation, , where represents the distance, in miles, Clare ran on each of the 6 days. Solving the equation gives the solution to this problem.

Clare ran 3 miles each day.

Glossary

None