Equations and Inequalities

Lesson 10

Objective

Write and graph inequalities for real-world conditions. (Part 2)

Common Core Standards

Core Standards

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  • 6.EE.B.8 — Write an inequality of the form x > c or x < c to represent a constraint or condition in a real-world or mathematical problem. Recognize that inequalities of the form x > c or x < c have infinitely many solutions; represent solutions of such inequalities on number line diagrams.

Foundational Standards

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  • 6.NS.C.7

Criteria for Success

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  1. Interpret an inequality in context of a real-world situation (MP.2).
  2. Given a list of values, determine an inequality that represents the values.
  3. Distinguish between a graph with discrete values, such as number of people, and a graph with continuous values, such as weight. 

Tips for Teachers

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Lessons 9 and 10 engage students in using inequalities to represent constraints in real-world situations. In Lesson 10, students interpret inequalities for different situations and distinguish between a continuous solution and a discrete solution.

Remote Learning Guidance

If you need to adapt or shorten this lesson for remote learning, we suggest prioritizing Anchor Problem 2 (benefits from worked example). Find more guidance on adapting our math curriculum for remote learning here.

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Anchor Problems

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Problem 1

The variable $$w$$ represents the number of words in Erica’s English essay. 

  1. What does $$w<500$$ mean in context of the situation?
  2. What does $$w≥ 275$$ mean in context of the situation?
  3. What does $$w=389$$ mean in context of the situation?

Guiding Questions

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Problem 2

Erica’s teacher assigned another essay for homework. She gave the students a minimum number of words and a maximum number of words to include in their essays. The number of words in ten students’ essays are shown below. All students stayed within the boundaries given by their teacher. 

133    115    196    210    154    102    246    250    218    179

Frank wrote the inequality $$x>100$$ to represent the number of words to include in the essay.

Hayat wrote the inequality $$x\leq250$$ to represent the number of words to include in the essay. 

Do you agree with the inequalities written by Frank and Hayat? Explain why or why not.

Guiding Questions

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Problem 3

Two similar situations are described below.

Situation A: A backpack can hold at most 8 books.
Situation B: A backpack can hold at most 8 pounds.

Draw a graph for each situation to represent the solution set. Compare and contrast the two graphs.

Guiding Questions

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Problem Set

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

Target Task

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Problem 1

The variable $$s$$ represents Phil’s driving speed in miles per hour on a highway. 

  1. What does $$s≤65$$ mean in context of the situation?
  2. What does $$s>40$$ mean in context of the situation?

Problem 2

On a different road, Phil noticed the speed limit and checked his speed several times to make sure he was driving within the limit. These were his speeds when he checked:

48      45      47      44

If Phil was driving within the speed limit, which inequality could represent the speed limit of the road that Phil was driving on? 

  1.     $${s<44}$$
  2.   $${s>45}$$
  3.   $${s<48}$$
  4.   $${s<50}$$

Mastery Response

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