Curriculum / Math / 7th Grade / Unit 3: Numerical and Algebraic Expressions / Lesson 8
Math
Unit 3
7th Grade
Lesson 8 of 11
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Simplify expressions by combining like terms and using the distributive property and properties of operations (Part 2).
The core standards covered in this lesson
7.EE.A.1 — Apply properties of operations as strategies to add, subtract, factor, and expand linear expressions with rational coefficients.
The foundational standards covered in this lesson
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.
6.EE.A.4 — Identify when two expressions are equivalent (i.e., when the two expressions name the same number regardless of which value is substituted into them). For example, the expressions y + y + y and 3y are equivalent because they name the same number regardless of which number y stands for.
7.NS.A.1 — Apply and extend previous understandings of addition and subtraction to add and subtract rational numbers; represent addition and subtraction on a horizontal or vertical number line diagram.
7.NS.A.2 — Apply and extend previous understandings of multiplication and division and of fractions to multiply and divide 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
The numbers used in the problems in this lesson require skills working with positive and negative rational numbers. This is a good opportunity to spiral in skills from the previous unit aligned to 7.NS.1 and 7.NS.2. Resources in the Problem Set Guidance include a range of problems from simpler, with just integers, to more complex, with fractions and decimals. Students should get exposure to a wide range of difficulty levels.
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Problems designed to teach key points of the lesson and guiding questions to help draw out student understanding
A student simplified the expression below as part of their homework. Review their work and check for any mistakes. For each line in their work, explain what they did to get their next step.
Homework Problem:
$${-\frac{1}{3}(5x-2y)-2\left ( \frac{1}{2}x+\frac{1}{3}y \right )}$$
Student’s Work:
Step 1: $${-\frac{5}{3}x+\frac{2}{3}y-x-\frac{2}{3}y}$$
Step 2: $${-\frac{5}{3}x-x+\frac{2}{3}y-\frac{2}{3}y}$$
Step 3: $${\left ( -\frac{5}{3}-1 \right )x+0}$$
Step 4: $${-\frac{8}{3}x}$$
Find the perimeter of the parallelogram.
An expression is given.
$${-2y+\frac{3}{2}x+\frac{7}{4}}$$
Which are equivalent to the given expression? Select each correct answer.
Math Spring Operational 2016 Grade 7 Released Items is made available by The Partnership for Assessment of Readiness for College and Careers (PARCC). Copyright © 2017 All Rights Reserved. Accessed Oct. 9, 2017, 10:59 a.m..
A set of suggested resources or problem types that teachers can turn into a problem set
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
Which expressions are equivalent to the expression $$n+\frac{5}{6}(m-n)-\frac{1}{3}m$$? Select all that apply.
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.
Lesson 7
Lesson 9
Topic A: Evaluating Numerical and Algebraic Expressions
Evaluate numerical expressions with rational numbers using the order of operations.
7.EE.A.1 7.NS.A.3
Write and evaluate expressions for mathematical and contextual situations.
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Topic B: Generating Equivalent Expressions
Expand and factor expressions using the distributive property and the greatest common factor.
7.EE.A.1
Expand and factor expressions with negative rational numbers.
Add and simplify expressions by combining like terms.
Subtract and simplify expressions.
Simplify expressions by combining like terms and using the distributive property and properties of operations (Part 1).
Write and interpret expressions in different ways to shed new meaning on a context.
7.EE.A.2
Topic C: Solving Multi-Step Problems using Expressions
Solve multi-step real-world problems with rational numbers.
7.EE.B.3 7.NS.A.3
Model real-world problems involving rational numbers using reasoned estimates.
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