##
* *Reflection: Intervention and Extension
Polynomials and Factor by Grouping - Section 3: Exit Slip

You can see from the first student example of the Exit Slip that the student does provide the correct factors for problems **a** through **e**. However, it does look like that the student continued solving for x in problem **c**. Students continually get confused between the instructions to** Factor **or **Solve. **Repeating and modeling the difference between these two verbs is important for student success in this Unit and the next Unit which is Quadratic Functions.

Another Important reflection about this lesson, is that students need to understand that factoring and multiplying are inverses of each other. The student that turned in the second example of the Exit Slip made several mistakes which may have been prevented if the student would have checked that the product of the factors was the original problem. Encouraging students to continually check factors by multiplying them back together is another way to ensure students success with this such important skill of **Factoring**.

*Continually Assessing*

*Intervention and Extension: Continually Assessing*

# Polynomials and Factor by Grouping

Lesson 8 of 9

## Objective: SWBAT factor four terms of a Polynomial using the Factor by Grouping method and apply it to finding the dimensions of a garden.

## Big Idea: To observe that Factoring by Grouping can be used for Difference of Squares, and Factoring Trinomials, but must be the method used to factor four terms.

*50 minutes*

#### Warm Up

*15 min*

The purpose of this lesson is to present to all of the students that Factor by Grouping is the only method to apply to factor four terms in a Polynomial. However, after teaching several methods previously in this unit including Factor by Grouping to factor Quadratic Trinomials, some students are still struggling with factoring.

So I use the Warm Up of this lesson to demonstrate that Factor by Grouping can be used to factor any of the methods including Difference of Squares. My reasoning is to provide lower level students with one method to factor all of the Polynomials. I demonstrate the Warm Up in the video below.

#### Resources

*expand content*

#### Partner Activity

*15 min*

**For the Partner Activity, I use this Card Game from the website listed below.**

**http://mathconceptualized.com/DEMO/Concepts/15_SolveQuadEqnsByFactor/Activities/FactorPolyCardGame.pdf**

In this game as the instructions state, the Polynomial cards are placed face down in a stack in the middle of the table. The factors are handed out to four students evenly. The students turn a Polynomial Card over from the stack in the middle of the table, and each student tries to factor the Polynomial on their worksheet. Once the students factor the Polynomial, the student(s) with the correct factors discards those factors from their hand. The student who discards all of their factors first, wins the game.

I did not use the Factor and Polynomial labels for the back of the cards. I made copies of the Polynomials and the Factors on regular Copy Paper so the students could write on the cards if they desired. However, Card Stock would probably provide a more permanent set of cards to use later.

*expand content*

#### Exit Slip

*20 min*

I provide students with about 20 minutes to complete the Exit Slip for this lesson. I use the Exit Slip for a formative assessment on the students ability to Factor Polynomials. Students may use any method to factor the binomials and the trinomials. Students must apply Factor by Grouping to the Polynomial with four terms.

In this Exit Slip, I provide students with an application problem. The application problem provides the area of given crops of a farm as Polynomials. Students have to factor the Polynomials to find the dimensions of each crop. I have students submit their responses for this Exit Slip online, but it can be handed in as well. There are two student responses to compare below.

*expand content*

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- UNIT 1: Introduction to Functions
- UNIT 2: Expressions, Equations, and Inequalities
- UNIT 3: Linear Functions
- UNIT 4: Systems of Equations
- UNIT 5: Radical Expressions, Equations, and Rational Exponents
- UNIT 6: Exponential Functions
- UNIT 7: Polynomial Operations and Applications
- UNIT 8: Quadratic Functions
- UNIT 9: Statistics

- LESSON 1: Introduction to Polynomials
- LESSON 2: Classifying Polynomials
- LESSON 3: Adding and Subtracting Polynomials
- LESSON 4: Multiplying Polynomials
- LESSON 5: Factoring Binomials
- LESSON 6: Factoring Quadratic Trinomials (Day 1 of 2)
- LESSON 7: Factoring Quadratic Trinomials (Day 2 of 2)
- LESSON 8: Polynomials and Factor by Grouping
- LESSON 9: Finding Average Rate of Change of Polynomial and Non-Polynomial Functions