Algebra 1 Lesson

Special Factoring Patterns: Difference of Squares & Perfect Square Trinomials

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8th or 9th GradeThin-SlicingCCSS.MATH.CONTENT.HSA.SSE.A.2,CCSS.MATH.CONTENT.HSA.SSE.B.360 min

Learning Objective

Students will identify and apply the Difference of Squares pattern ( $a^{2} - b^{2} = (a - b) (a + b)$ ) and Perfect Square Trinomial patterns ( $a^{2} \pm 2 ab + b^{2} = (a \pm b)^{2}$ ) to factor polynomial expressions completely, including multi-step cases requiring a GCF first.

Lesson Overview

Students discover the Difference of Squares and Perfect Square Trinomial patterns through geometric box models at vertical whiteboards, progressing from visual grid exploration to symbolic generalization and multi-step factoring.

Materials

Vertical whiteboards (VNPS) or large chart paper
Dry-erase markers (one per group)
Erasers or paper towels
Random grouping cards or app
Anchor chart paper for consolidation
Exit slip half-sheets

Scaffolded Task Progression

1Task 1

[Anchored Teacher Problem — Low-Floor Launch]

Draw a

2 \times 2

grid on your board. Place

x^{2}

in the top-left box and

- 25

in the bottom-right box.

I want you to fill in the missing diagonal boxes so that when you combine all four cells, the middle

x

-term is completely gone (

0 x

).

What must the two diagonal terms be? What are the outside factors

(x + ?) (x - ?)

2Task 2

[Anchored Teacher Problem — Low-Floor Launch]

Draw a

2 \times 2

grid on your board. Place

x^{2}

in the top-left box and

- 25

in the bottom-right box.

I want you to fill in the missing diagonal boxes so that when you combine all four cells, the middle

x

-term is completely gone (

0 x

).

What must the two diagonal terms be? What are the outside factors

(x + ?) (x - ?)

?

Word bank:
- factor: a number or expression that is multiplied by another number or expression.
- grid: a box or table used to organize the parts of a math problem.
- diagonal: boxes that are across from each other in the grid.
- middle term: the term with

x

in the middle of a trinomial.
- difference of squares: a pattern like

a^{2} - b^{2}

that factors into

(a + b) (a - b)

3Task 3

[Thin Slice 1 — Difference of Squares Progression]

Now factor

4 x^{2} - 49

without drawing a full box if you don't need it.

- What is the square root of the first term?
- What is the square root of the second term?
- How do the signs inside the binomials behave?

Write your final factored form.

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