Curriculum / Math / 6th Grade / Unit 6: Equations and Inequalities / Lesson 8
Math
Unit 6
6th Grade
Lesson 8 of 14
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Lesson Notes
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Define and identify solutions to inequalities.
The core standards covered in this lesson
6.EE.B.5 — Understand solving an equation or inequality as a process of answering a question: which values from a specified set, if any, make the equation or inequality true? Use substitution to determine whether a given number in a specified set makes an equation or inequality true.
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.EE.A.1 — Write and evaluate numerical expressions involving whole-number exponents.
6.EE.A.2 — Write, read, and evaluate expressions in which letters stand for numbers.
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 8–11 address one-variable inequalities. Students have prior experience reading and interpreting inequality comparisons from Unit 4 when they compared rational numbers.
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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
An inequality and an equation are shown below.
$${8x=32}$$ $${8x>32}$$
a. Which value in the set of numbers {$$4$$, $$4\frac{1}{2}$$, $$5$$} is a solution to the equation?
b. Which values in the set of numbers {$$4$$, $$4\frac{1}{2}$$, $$5$$} are a solution to the inequality?
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Which set of numbers includes values that are all solutions to the inequality $${ 1.3x-2<7}$$?
Isabel is moving her office to a new location. She has a box that can hold up to $$40$$ pounds, and she has already put $$18\frac{1}{2}$$pounds in the box. Isabel has several books that each weigh $$3$$ pounds that she also wants to put in the box.
The inequality $${3x+18{1\over2}≤40}$$, where $$x$$ represents the number of books, can be used to determine how many books Isabel can put in the box without it breaking.
Which of the following number of books can Isabel put in the box without it breaking? Select all that apply.
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
Which of the following values are solutions to the inequality $${ 5x-8≥42}$$ ? Select all that apply.
How is the inequality $${5x-8≥42}$$ different from the equation $${5x-8=42}$$?
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
Write and graph inequalities for real-world conditions. (Part 1)
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
6.EE.B.56.EE.B.8
6.EE.B.8
Write and graph inequalities for real-world conditions. (Part 2)
Solve one-step inequalities.
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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