Equations and Inequalities

Lesson 3

Math

Unit 4

7th Grade

Lesson 3 of 12

Objective


Solve equations in the forms $${px+q=r}$$  and $${p(x+q)=r}$$  using tape diagrams.

Common Core Standards


Core Standards

  • 7.EE.B.3 — Solve multi-step real-life and mathematical problems posed with positive and negative rational numbers in any form (whole numbers, fractions, and decimals), using tools strategically. Apply properties of operations to calculate with numbers in any form; convert between forms as appropriate; and assess the reasonableness of answers using mental computation and estimation strategies. For example: If a woman making $25 an hour gets a 10% raise, she will make an additional 1/10 of her salary an hour, or $2.50, for a new salary of $27.50. If you want to place a towel bar 9 3/4 inches long in the center of a door that is 27 1/2 inches wide, you will need to place the bar about 9 inches from each edge; this estimate can be used as a check on the exact computation.
  • 7.EE.B.4.A — Solve word problems leading to equations of the form px + q = r and p(x + q) = r, where p, q, and r are specific rational numbers. Solve equations of these forms fluently. Compare an algebraic solution to an arithmetic solution, identifying the sequence of the operations used in each approach. For example, the perimeter of a rectangle is 54 cm. Its length is 6 cm. What is its width?

Foundational Standards

  • 6.EE.B.7

Criteria for Success


  1. Model situations with tape diagrams and equations.
  2. Understand operations needed to solve for a variable using tape diagrams.
  3. Compare the solution strategy for equations in the form $${px+q=r}$$  to those in the form $${p(x+q)=r}$$.
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Anchor Problems


Problem 1

During one rainy day in the summer, the Martinez family decides to watch a matinee movie in the morning and a drive-in movie in the evening. The price for a matinee movie in the morning is $6 per person, which is different than the cost of a drive-in movie in the evening. The family of 5 spends a total of $75 on movies for the day. How much does each person spend that day on movie tickets if the ticket costs for each family member are the same? What is the cost for a ticket for the drive-in movie in the evening? 

Guiding Questions

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Problem 2

The Chacon family is planning a trip to Guatemala to visit extended family. The parents have up-to-date passports, but the three kids need to apply for their passports. It costs $456 to get the kids' passports, including $51 for the photos and a processing fee for each application. How much is the processing fee for a kid's passport?

Guiding Questions

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Problem 3

The cost of a babysitting service is $10 for the first hour and $12 for each additional hour. If the total cost of babysitting baby Aaron was $58, how many hours was Aaron with the babysitter?
Draw a tape diagram and write an equation to represent the situation. Then find the solution. 

Guiding Questions

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References

EngageNY Mathematics Grade 7 Mathematics > Module 2 > Topic C > Lesson 17Exercise

Grade 7 Mathematics > Module 2 > Topic C > Lesson 17 of the New York State Common Core Mathematics Curriculum from EngageNY and Great Minds. © 2015 Great Minds. Licensed by EngageNY of the New York State Education Department under the CC BY-NC-SA 3.0 US license. Accessed Dec. 2, 2016, 5:15 p.m..

Problem Set

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Target Task


Riley takes two walks every day, one in the morning and one in the evening, and walks for a total of $$5\frac{1}{4}$$hours in a 7 day week.  If he walks for 15 minutes each morning, how many minutes does he walk for each evening?

Draw a tape diagram and write an equation to represent the situation. Use either model to solve.

Student Response

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Additional Practice


The following resources include problems and activities aligned to the objective of the lesson that can be used for additional practice or to create your own problem set.

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Lesson 2

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Lesson 4

Lesson Map

A7CB09C2-D12F-4F55-80DB-37298FF0A765

Topic A: Solving and Modeling with Equations

Topic B: Solving and Modeling with Inequalities

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