Curriculum / Math / 6th Grade / Unit 6: Equations and Inequalities / Lesson 10
Math
Unit 6
6th Grade
Lesson 10 of 14
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Lesson Notes
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Write and graph inequalities for real-world conditions. (Part 2)
The core standards covered in this lesson
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.
The foundational standards covered in this lesson
6.NS.C.7 — Understand ordering and absolute value of rational numbers.
The essential concepts students need to demonstrate or understand to achieve the lesson objective
Suggestions for teachers to help them teach this lesson
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.
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Problems designed to teach key points of the lesson and guiding questions to help draw out student understanding
25-30 minutes
The variable $$w$$ represents the number of words in Erica’s English essay.
a. What does $$w<500$$ mean in context of the situation?
b. What does $$w≥ 275$$ mean in context of the situation?
c. What does $$w=389$$ mean in context of the situation?
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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.
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.
A set of suggested resources or problem types that teachers can turn into a problem set
15-20 minutes
Give your students more opportunities to practice the skills in this lesson with a downloadable problem set aligned to the daily objective.
A task that represents the peak thinking of the lesson - mastery will indicate whether or not objective was achieved
5-10 minutes
The variable $$s$$ represents Phil’s driving speed in miles per hour on a highway.
a. What does $$s≤65$$ mean in context of the situation?
b. What does $$s>40$$ mean in context of the situation?
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?
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.
Next
Solve one-step inequalities.
Topic A: Reasoning About and Solving Equations
Represent equations in the form $${ x+p=q }$$ and $${px=q}$$ using tape diagrams and balances.
Standards
6.EE.B.66.EE.B.7
Define and identify solutions to equations.
6.EE.B.5
Write equations for real-world situations.
Solve one-step equations with addition and subtraction.
Solve one-step equations with multiplication and division.
Solve percent problems using equations.
6.EE.B.76.RP.A.3.C
Solve multi-part equations leading to the form $${x+p=q }$$ and $${px=q}$$.
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Topic B: Reasoning About and Solving Inequalities
Define and identify solutions to inequalities.
6.EE.B.56.EE.B.8
Write and graph inequalities for real-world conditions. (Part 1)
6.EE.B.8
6.EE.B.66.EE.B.8
Topic C: Representing and Analyzing Quantitative Relationships
Write equations for and graph ratio situations. Define independent and dependent variables.
6.EE.C.96.RP.A.3.A
Represent the relationship between two quantities in graphs, equations, and tables. (Part 1)
Represent the relationship between two quantities in graphs, equations, and tables. (Part 2)
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