Curriculum / Math / 7th Grade / Unit 3: Numerical and Algebraic Expressions / Lesson 5
Math
Unit 3
7th Grade
Lesson 5 of 11
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Add and simplify expressions by combining like terms.
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.
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Use the expression below to answer the questions that follow.
$${\frac{1}{3}x-2y-5x+8}$$
a. How many terms are there in the expression?
b. Which terms are “like terms”?
c. Are there any constants? If so, what are they?
d. What are the variables in the expression?
e. What are the coefficients in the expression?
Rewrite the expression $${5x+3x}$$ and the expression $${5x-3x}$$ by combining like terms.
a. Do this by expanding each term using addition.
b. Do this by factoring out a common factor and using the distributive property.
c. Can you rewrite the expression $${5x+3y}$$ or the expression $${5x-3y}$$ by combining terms? Why or why not? Use reasoning from parts a and b to support your answer.
Grade 7 Mathematics > Module 3 > Topic A > Lesson 1 of the New York State Common Core Mathematics Curriculum from EngageNY and Great Minds. © 2015 Great Minds. Licensed by EngageNY of the New York State Education Department under the CC BY-NC-SA 3.0 US license. Accessed Dec. 2, 2016, 5:15 p.m..
Find the sum of $${\left ( 0.75x-12y \right )}$$ and $$(-5+6y-0.5x)$$. Show each step in your work and explain why each step is equivalent to the expression in the step before.
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Students in Mr. Jackson’s class are simplifying an expression written on the board:
$${{-12p-5n+8n+20p}}$$
Amal simplified the expression to be $${8p+3n}$$, and Andre simplified the expression to be $${-32p-13n}$$.
Mr. Jackson saw a few different answers around the classroom, so he gave the students a hint on the board, writing:
$${-12p+20p-5n+8n}$$
$${(-12+20)p+(-5+8)n}$$
a. What did Mr. Jackson do in each step he wrote on the board?
b. Is either Amal or Andre correct? Explain why.
Lesson 4
Lesson 6
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.
Subtract and simplify expressions.
Simplify expressions by combining like terms and using the distributive property and properties of operations (Part 1).
Simplify expressions by combining like terms and using the distributive property and properties of operations (Part 2).
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.