Curriculum / Math / 7th Grade / Unit 3: Numerical and Algebraic Expressions / Lesson 6
Math
Unit 3
7th Grade
Lesson 6 of 11
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Subtract and simplify expressions.
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
This lesson includes problems such as $${3x - (6 + 8x) }$$ but does not include problems such as $${3x - 2(6 + 8x)}$$, where a multiple of an expression is being subtracted. This will be covered in Lesson 7 and Lesson 8. The concept of distributing a negative through a parentheses group can be challenging for students, so this lesson focuses on students understanding that when an expression is subtracted, every term in the expression is subtracted, not just the first term.
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Problems designed to teach key points of the lesson and guiding questions to help draw out student understanding
Consider the numerical expression: $${12-(3+4)}$$
The expression is rewritten so it does not include parentheses. Which expression will give the same value as the original expression? Explain your reasoning for each one.
$${12-3+4}$$ $${12-3-4}$$
Subtract: $${(4x+9y-4)-(7x+10)}$$
Match each subtraction problem on the left with the equivalent simplified expression on the right.
A. $$5x-(3x+1)$$
1. $$-8x-1$$
B. $$5x-(-3x-1)$$
2. $$-2x+1$$
C. $$-5x-(3x+1)$$
3. $$2x-1$$
D. $$-5x-(-3x-1)$$
4. $$8x+1$$
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
Two expressions are given below.
Expression A: $${5q-r}$$
Expression B: $${ -2q+3r-4}$$
a. Write a simplified expression that represents A + B.
b. Write a simplified expression that represents 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.
Lesson 5
Lesson 7
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.
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.
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