Numerical and Algebraic Expressions

Lesson 9

Math

Unit 3

7th Grade

Lesson 9 of 11

Objective


Write and interpret expressions in different ways to shed new meaning on a context.

Common Core Standards


Core Standards

  • 7.EE.A.2 — Understand that rewriting an expression in different forms in a problem context can shed light on the problem and how the quantities in it are related. For example, a + 0.05a = 1.05a means that "increase by 5%" is the same as "multiply by 1.05."

Foundational Standards

  • 6.EE.A.3

Criteria for Success


  1. Write multiple equivalent expressions to represent a situation.
  2. Interpret each expression as it relates to the situation. 
  3. Understand how different expressions are interpreted differently in a situation.

Tips for Teachers


This lesson touches upon standard 7.EE.2; this standard will be revisited in Unit 5 with percentages and other related contexts.

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Anchor Problems


Problem 1

Malia is at an amusement park. She bought 14 tickets, and each ride requires 2 tickets.

a.   Write an expression that gives the number of tickets Malia has left in terms of $$x$$, the number of rides she has already gone on. Find at least one other expression that is equivalent to it.

b.   The expression $${14}{-2}x $$ represents the number of tickets Malia has left after she has gone on $$x$$ rides. How can each of the following numbers and expressions be interpreted in terms of tickets and rides?

i.   $$14$$

ii.   $$-2$$

iii.   $$2x$$

c.   The expression $$2(7-x)$$ also represents the number of tickets Malia has left after she has gone on $$x$$ rides. How can each of the following numbers and expressions be interpreted in terms of tickets and rides?

i.   $$7$$

ii.   $$(7-x)$$

iii.   $$2$$

Guiding Questions

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References

Illustrative Mathematics Ticket to Ride

Ticket to Ride, accessed on Oct. 9, 2017, 11:15 a.m., is licensed by Illustrative Mathematics under either the CC BY 4.0 or CC BY-NC-SA 4.0. For further information, contact Illustrative Mathematics.

Problem 2

A square fountain area with side length $$s$$ feet is bordered by a single row of square tiles as shown. 

What are three different ways to represent the number of tiles needed for the border? Show each representation using the diagram.

Guiding Questions

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References

EngageNY Mathematics Grade 7 Mathematics > Module 3 > Topic A > Lesson 3Example 6

Grade 7 Mathematics > Module 3 > Topic A > Lesson 3 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


A picture with dimensions $$x$$ by $$y$$ inches, is framed by a rectangular border. The border is 1 inch wide, as shown in the figure below.  Write 2 different expressions to represent the area of the border around the picture.

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.

  • Include any review from previous lessons.
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Lesson 8

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Lesson 10

Lesson Map

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

Topic A: Evaluating Numerical and Algebraic Expressions

Topic B: Generating Equivalent Expressions

Topic C: Solving Multi-Step Problems using Expressions

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