Curriculum / Math / 7th Grade / Unit 3: Numerical and Algebraic Expressions / Lesson 7
Math
Unit 3
7th Grade
Lesson 7 of 11
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Lesson Notes
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Simplify expressions by combining like terms and using the distributive property and properties of operations (Part 1).
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
Lessons 7 and 8 pull together the concepts from the previous four lessons and engage students in simplifying complex expressions. In Lesson 7, students look at and discuss common misconceptions, and the problems become progressively more complex and challenging by the end of Lesson 8. Students will need to draw on their skills of computing with rational numbers from Unit 2.
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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
In math class, students are attempting to simplify the expression written on the board:
$${7-2(3-8x)}$$
Three students make an attempt at a first step:
Len writes: $${5(3-8x)}$$
Monty writes: $${7-2(-5x)}$$
Nailany writes: $${7-6-16x}$$
a. Do you agree with any of the students? Explain your reasoning for each one.
b. Oscar is a little stuck, so he rewrites the problem in a different way to help him determine what to do. He writes $${ 7+(-2)(3-8x)}$$. How might this new expression help Oscar simplify the expression?
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Draft 6–8 Progression on Expressions and Equations, by the Common Core Standards Writing Team is made available by Institute for Mathematics and Education, University of Arizona. © 2007 The Arizona Board of Regents. All contents copyrighted. All rights reserved. Accessed Oct. 9, 2017, 10:34 a.m.. For updates and more information about the Progressions, see http://ime.math.arizona.edu/progressions.
Which expressions below are equivalent to $${4-3(6x-3)}$$? Select all that apply.
Determine which expression is equivalent to $${\frac{3}{4}-x\left ( \frac{1}{2}-\frac{5}{8} \right )+\left ( -\frac{3}{8}x \right )}$$.
Math Spring Operational 2015 Grade 7 End of Year 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, 10:41 a.m..
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
Simplify the expressions.
a. $${-2x+15-4(3x-1)}$$
b. $${-(a+b)-\frac{3}{2}(a-b)}$$
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
Simplify expressions by combining like terms and using the distributive property and properties of operations (Part 2).
Topic A: Evaluating Numerical and Algebraic Expressions
Evaluate numerical expressions with rational numbers using the order of operations.
Standards
7.EE.A.17.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.
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.37.NS.A.3
Model real-world problems involving rational numbers using reasoned estimates.
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