Maryland Math 7.AT.B.5
The Standard
subtract, factor, and expand linear expressions with rational coefficients.
Maryland College and Career Ready Standards for Mathematics (2025) · LOOK FOR AND MAKE USE OF STRUCTURE TO REWRITE EXPRESSIONS IN EQUIVALENT FORMS AND REASON ABOUT THEIR PROPERTIES.
Teacher's field guide
What This Standard Means
What Students Need to Do
- Students expand expressions with fractions, decimals, and negative numbers. They subtract expressions, combine like terms, and factor out a shared number to write an equivalent expression.
What Mastery Looks Like
- A student can turn 3/4(8x - 4) - (2x + 1) into 4x - 4, then 4(x - 1). They can check that the forms give the same result for a chosen value of x.
Common Misconceptions
- Students may change the sign of only one term when subtracting parentheses. They may multiply the x term but not the constant when expanding. Some factor 4x - 4 as 4(x - 4).
How to Assess It
- Exit ticket: Simplify 3/4(8x - 4) - (2x + 1), then factor your result.
Lesson moves
Ways to Teach It
Cut paper strips labeled x, x/2, 1, and 1/2; use them to build 1/2(4x + 6) and rearrange it as 2x + 3.
Ask: Why is 3x - (1/2x - 2) equal to 5/2x + 2, not 5/2x - 2? Show each step.
Give partners cards showing 0.75(4x - 8), 3x - 6, and other expressions; have them match equivalent pairs and explain one match.
Compare taxi fares of $2.50x + $4 and $1.75x + $7 for x miles; write and factor the difference.
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Printable 7.AT.B.5 Worksheet
A ready-to-print activity worksheet aligned to 7.AT.B.5, with an answer key for the teacher on its own page. No account needed.
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Related Standards
- 7.NOS.A.2
Multiply and divide rational numbers using multiple strategies and representations.
- 7.NOS.A.3.a
Apply properties of operations to efficiently compute with rational numbers and convert between forms when appropriate to support problem solving.
- 7.NOS.A.1
Add and subtract rational numbers using multiple strategies and representations.
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