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Mathematics · Grade 7

Expressions and Structural Reasoning

Learners combine like terms and subtract expressions with rational coefficients, expand products such as −3(2x − 5) and (1/2)(4x + 6), and factor expressions by taking out a common factor, including negative and fractional factors. They then rewrite expressions to reveal what they mean in context, for example seeing that a + 0.05a = 1.05a describes a 5% increase.

  • 4 lessons
  • About 90 minutes
  • Expressions and structure check: 10 questions
  • Ways to answer: fill in the blanks, choose an answer, type a fraction, match pairs, type a number and sort into groups
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What learners will discover

  • Add and subtract linear expressions with rational coefficients by combining like terms, including subtracting an expression in parentheses.
  • Expand linear expressions with rational coefficients, including negative factors, using the distributive property.
  • Factor linear expressions by taking out a common factor, including the greatest common factor, a negative factor or a fractional factor.
  • Rewrite an expression in an equivalent form to show how the quantities in a problem are related, such as a + 0.05a = 1.05a.

Lessons

  1. Like terms and subtracting expressions 8 steps5 practiceabout 22 min
  2. Expanding with the distributive property 8 steps5 practiceabout 22 min
  3. Factoring: the distributive property backward 9 steps5 practiceabout 23 min
  4. Rewriting to reveal meaning 9 steps5 practiceabout 23 min
  5. Expressions and structure check 10 questions at the end

Keep exploring

Games to practice with

  • Number-Line HopHelp the frog hop to the right number — from counting to negative fractions.
  • Ratio KitchenScale recipes, fill ratio tables and find the better buy.
  • Coordinate CourierDrive the parcel van to the right address on the coordinate grid.

More 7th grade math

Guide for grown-ups