Algebra I Lesson

Crack the Code: Factoring Trinomials When a ≠ 1

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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 trinomials of the form $a x^{2} + b x + c$ where $a \neq = 1$ using the AC method (factor by grouping), including cases requiring a GCF first.

Lesson Overview

Students progress from factoring out a GCF through the AC method for trinomials with leading coefficients other than 1, building one step at a time on vertical surfaces. The lesson uses a 'spy code' theme where each factored form unlocks the next clue.

Materials

Vertical whiteboards or large chart paper
Dry-erase markers (multiple colors per group)
Erasers or paper towels
Random grouping cards
AC Method reference strip (one per group — see cardSets)
Scratch paper for factor-pair searches

Scaffolded Task Progression

1Task 1

Factor:

x^{2} + 7 x + 12

Spy warm-up — find two numbers that multiply to

12

and add to

7

. Write the factored form.

2Task 2

Factor:

2 x^{2} + 7 x + 3

Step 1: Find

a \cdot c

. Step 2: Find two numbers that multiply to

a c

and add to

b

. Step 3: Rewrite and group.

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