Equations and Inequalities

Lesson 12

Objective

Model with inequalities.

Common Core Standards

Core Standards

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  • 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.B — Solve word problems leading to inequalities of the form px + q > r or px + q < r, where p, q, and r are specific rational numbers. Graph the solution set of the inequality and interpret it in the context of the problem. For example: As a salesperson, you are paid $50 per week plus $3 per sale. This week you want your pay to be at least $100. Write an inequality for the number of sales you need to make, and describe the solutions.

Foundational Standards

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  • 6.EE.B.5

  • 6.EE.B.8

Criteria for Success

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  1. Analyze real-world situations and identify important information needed to solve a problem.
  2. Create inequalities to model real-world applications and use them to test out solutions (MP.4).

Tips for Teachers

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This lesson includes a three-act task for Anchor Problem #1, aligned to the objective. The Problem Set Guidance includes and recommends spiraled review of skills and concepts from the unit. 

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Anchor Problems

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Use Andrew Stadel's 3-Act Math Task Sweet Snacks for this problem.

Show Act 1 video (46 seconds)
Ask: 

  • What do you notice? 
  • What do you wonder?

Show Act 2 video (26 seconds)
Ask:

  • What new information do you have?
  • What different combinations of Teddy Grahams and Circus Animals can he buy with $20? 
  • How many combinations can you find? 

Show Act 3 – The solution (53 seconds)
Ask: 

  • How many of the combinations shown did you find? 
  • Which combinations did you find that are not shown in the solution video?
  • Are there other combinations that work?

Guiding Questions

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References

Andrew Stadel's 3-Act Math Tasks Sweet Snacks

Sweet Snacks from Andrew Stadel's 3-Act Math Tasks is made available by Andrew Stadel. Accessed Nov. 9, 2017, 5:52 p.m..

Modified by The Match Foundation, Inc.

Problem Set

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With Fishtank Plus, you can download a complete problem set and answer key for this lesson. Download Sample

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

  • Include other review problems from earlier in unit on equations and inequalities.

Target Task

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Isaiah is filling 12 small plastic bags with candy for a party. He puts 2.5 pounds of candy into each bag, but then he reads on the package that there is a recommended weight limit so the bags do not break. Isaiah then takes out the same amount of weight from each bag.

  1. Which inequality best represents the situation? 

a.  $$12x-2.5≤21$$

b.  $$12(2.5-x)≤21$$

c.  $$12(x-2.5)≤21$$

d.  $$21-12x≤2.5$$

  1. Explain how the inequality you chose matches the situation. In your explanation, describe what the number 21 represents and what the variable represents. 

Mastery Response

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