Montana Math MT.7.EE.1

Math7th GradeExpressions and Equations

The Standard

Use properties of operations to add, subtract, factor, and expand linear expressions with rational coefficients and generate equivalent expressions.

2026 Montana Mathematics Content Standards

Teacher's field guide

What Students Need to Do: Students rewrite expressions with fractions, decimals, and negative numbers. They distribute, combine like terms, and factor without changing an expression's value.
What Mastery Looks Like: A student rewrites 1/2(4x - 6) + x as 3x - 3, then factors it as 3(x - 1). They can explain why the forms have the same value for any x.
Common Misconceptions: Students often subtract the first term in parentheses but forget to subtract the second. They may combine unlike terms, such as x and 2, or multiply only one term when distributing.
How to Assess It: Exit ticket: Simplify 1/2(6x - 4) - (x + 2), factor your result, and check both forms at x = 3.

Lesson moves

Give pairs paper cards marked x/2 and -1/2; build three copies of (x/2 - 1/2), then collect like cards.
Ask: Are 1/2(4x - 6) and 2x - 3 equivalent? Explain by distributing and testing x = -2.
Play expression match with cards 2(x - 3/2), 2x - 3, x + x - 3, and 2x + 3; reject the extra.
Show a receipt for two notebooks at x dollars each with a $1.50 coupon; compare 2x - 1.50 with 2(x - 0.75).

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