Algebra I Lesson

Factor by Grouping: Cracking the Code

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8th or 9th GradeThin-SlicingCCSS.MATH.CONTENT.HSA.SSE.A.2, CCSS.MATH.CONTENT.HSA.SSE.B.350 min

Learning Objective

Students will factor four-term polynomials by grouping, identifying and extracting the GCF from each pair of terms and then recognizing the resulting common binomial factor.

Lesson Overview

Students discover the grouping strategy by noticing structure in four-term polynomials, progressing from identifying common factors in pairs to fully factoring expressions with leading coefficients not equal to 1.

Materials

Vertical whiteboards or large chart paper
Dry-erase markers (multiple colors)
Markers/erasers for each group
Random grouping cards or name sticks
Printed Mild/Medium/Spicy practice sets

Scaffolded Task Progression

1Task 1

Factor out the GCF from each expression. Write your answer in factored form.
a)

6 x + 15

4 x^{2} + 10 x

2Task 2

Look at your answers from Task 1:

6 x + 15 = 3 (2 x + 5)

4 x^{2} + 10 x = 2 x (2 x + 5)

Now write these two results as a SUM, then factor out the shared binomial:

3 (2 x + 5) + 2 x (2 x + 5) = ?

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