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# Special Factoring Situations

Lesson 8 of 15

## Objective: Students will be able to factor differences of squares, and sums and differences of cubes.

#### Warm up and Homework Review

*10 min*

I include **Warm ups** with a **Rubric** as part of my daily routine. My goal is to allow students to work on **Math Practice 3** each day. Grouping students into homogenous pairs provides an opportunity for appropriately differentiated math conversations. The Video Narrative specifically explains this lesson’s Warm Up- Special Factoring Situations which asks students to describe how they factor a trinomial.

I also use this time to correct and record any past Homework.

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This lesson is a foundational lesson to ensure student success in the Common Core Algebra 2 standards.** **

I give the students the expression m^{2} – 9 to factor without any introduction. Once they have struggled with it a bit, I may give them the hint that this is really a trinomial. A further hint is that we need to add the m term but there is no m term. They should get the point where they rewrite this m^{2} +0m – 9 and then factor it. I give them the next two.

At this point, I ask them to talk to their partner and determine the pattern (**Math Practice 7**) . We then make a list as a class. The goal is that the students recognize.

- Both terms are perfect squares.
- There are only two terms.
- They form a difference.
- The factored form is the sum and difference of their square roots.

The next portion of this lesson involves a set of differences of squares, a few of which are prime. This is my favorite part of this lesson. I tease the students that I am going to try to trick them. For a lesson like this, this is a relatively brisk guided practice. We run through the problems and whenever we get to a problem that is prime, we discuss the issue after they have tried it. With a bit of tease, I have found that the students are motivated to really try and not get tricked.

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Sums and differences of cubes are a challenge to teach. I have found that focusing on the pattern is the best method. We begin by looking at the volume model of a^{3} – b^{3 }(**Math Practice 4**). We look at this model and then I ask the students to find the volume of each of the three prisms. It may help more concrete learners to have a model build out of unit blocks or legos to model taking the b^{3} out of the a^{3}. We then re-factor those to become (a – b) (a^{2} + ab + b^{2}).

We now look at the pattern formulas for both sums and differences of cubes. I ask the students to do a think-pair-share on the similarities and differences between these two patterns. The remainder of the lesson uses Guided Practice for factoring cubes. This is one of those places where students need to practice several times to really get the pattern.

#### Resources

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#### Exit Ticket

*2 min*

I use an exit ticket each day as a quick formative assessment to judge the success of the lesson.

Today's Exit Ticket asks students to factor a perfect cube.

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The goal of this homework is to solidify the patterns for factoring squares and cubes. The cubes in particular need repetition for students to become confident using it as a tool.

This assignment was created using Kuta Software, a product I would highly recommend to any mathematics teacher.

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- UNIT 1: Modeling with Expressions and Equations
- UNIT 2: Modeling with Functions
- UNIT 3: Polynomials
- UNIT 4: Complex Numbers and Quadratic Equations
- UNIT 5: Radical Functions and Equations
- UNIT 6: Polynomial Functions
- UNIT 7: Rational Functions
- UNIT 8: Exponential and Logarithmic Functions
- UNIT 9: Trigonometric Functions
- UNIT 10: Modeling Data with Statistics and Probability
- UNIT 11: Semester 1 Review
- UNIT 12: Semester 2 Review

- LESSON 1: Laws of Exponents
- LESSON 2: Sorting Polynomial Equations and Identities
- LESSON 3: Operations with Polynomials Day 1 of 2
- LESSON 4: Operations with Polynomials Day 2 of 2
- LESSON 5: Products of Polynomial Functions
- LESSON 6: Factoring GCF and Grouping
- LESSON 7: Factoring Trinomials
- LESSON 8: Special Factoring Situations
- LESSON 9: Polynomial Quiz and Factoring Puzzle
- LESSON 10: Factoring Completely
- LESSON 11: Modeling Equations and Functions with Factoring
- LESSON 12: Polynomial Inequalities
- LESSON 13: Polynomial Review Day 1
- LESSON 14: Polynomial Review Day 2
- LESSON 15: Polynomial Test