Curriculum / Math / 8th Grade / Unit 2: Solving One-Variable Equations / Lesson 1
Math
Unit 2
8th Grade
Lesson 1 of 12
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Write equivalent expressions using properties of operations and verify equivalence using substitution.
The core standards covered in this lesson
8.EE.C.7 — Solve linear equations in one variable.
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.EE.A.3 — Apply the properties of operations to generate equivalent expressions. For example, apply the distributive property to the expression 3 (2 + x) to produce the equivalent expression 6 + 3x; apply the distributive property to the expression 24x + 18y to produce the equivalent expression 6 (4x + 3y); apply properties of operations to y + y + y to produce the equivalent expression 3y.
7.EE.A.1 — Apply properties of operations as strategies to add, subtract, factor, and expand linear expressions with rational coefficients.
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Problems designed to teach key points of the lesson and guiding questions to help draw out student understanding
a. Find the sum of the two expressions.
Expression A: $${12a-5b-8}$$
Expression B: $${ -b+3a-4}$$
b. Write the expression below as a sum of two terms.
$${\frac{1}{2}(6x+18)}$$
c. Write the expression below as a product of two factors.
$${24m-6}$$
For each expression, write an equivalent simplified expression. Then verify that the expressions are equivalent by substituting a value in for $${ x}$$ and evaluating.
Write an expression for the sequence of operations. Then simplify each expression.
a. Add 3 to $$x$$, subtract the result from 1, then double what you have.
b. Add 3 to $$x$$, double what you have, then subtract 1 from the result.
Writing Expressions, accessed on Aug. 30, 2017, 4:17 p.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.
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A task that represents the peak thinking of the lesson - mastery will indicate whether or not objective was achieved
Simplify each expression.
a. $${\frac{5}{3}x-4\left ( x-\frac{1}{3} \right )}$$
b. $${-\frac{1}{2}\left ( -8x+6x+10 \right )-2x}$$
Are the two expressions equivalent? Justify your answer using substitution.
$${-5x+15}$$ and $${5(-x+3)}$$
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Lesson 2
Topic A: Simplifying Expressions and Verifying Solutions
8.EE.C.7
Define a solution to an equation. Solve and check solutions to 1 and 2 step equations.
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Topic B: Analyzing and Solving Equations in One Variable
Justify each step in solving a multi-step equation with variables on one side of the equation.
8.EE.C.7.A 8.EE.C.7.B
Write and solve multi-step equations to represent situations, with variables on one side of the equation.
8.EE.C.7.B
Model with equations using a three-act task.
Solve equations with variables on both sides of the equal sign.
Write and solve multi-step equations to represent situations, including variables on both sides of the equation.
Understand that equations can have no solutions, infinite solutions, or a unique solution; classify equations by their solution.
8.EE.C.7.A
Solve and reason with equations with three types of solutions.
Use equations to model a business plan and determine the break-even point.
Topic C: Analyzing and Solving Inequalities in One Variable
Solve and graph inequalities with variables on one side of the inequality (optional).
A.REI.B.3
Solve and graph inequalities with variables on both sides of the inequality (optional).
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