##
* *Reflection: Diverse Entry Points
Factoring Completely - Section 3: Create a Diagram

The chart activity in this lesson is a great formative assessment on factoring. Students need to understand the separate methods of factoring well enough to be able to categorize and represent them in a visual model. I walked around and got a good idea of where each student was by looking at their charts (or occasionally lack thereof). By discussing them in groups and choosing their favorite, this enabled students to improve their model. Here is an example of a nice Sample Chart.

I also use the chart to help the students focus their thinking as they are faced with factoring polynomials completely. In past years, I have seen so many students freeze over what type of factoring to use for a given problem. The chart can provide some extra support until they are confident enough not to need it any more.

*Diverse Entry Points: Creating a Chart as a Formative Assessment*

# Factoring Completely

Lesson 10 of 15

## Objective: Students will be able to factor polynomials completely.

#### 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 homogeneous pairs provides an opportunity for appropriately differentiated math conversations. The Video Narrative specifically explains this lesson’s Warm Up- Factoring Completely which asks students to determine which of two answers is the proper factored form of a polynomial.

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

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I begin this lesson with the polynomial 2x^{2} + 6x + 4. The students are going to factor this problem. They get either (2x+2)(x+2) or (x+1)(2x+4). I get a volunteer to share their answer and then ask if everyone got that solution. Someone else shares the other factored form or, given a shy class, I note that I saw the second form on someone’s paper. I ask if they are both correct or if one is a mistake. The students will check and see that they are both correct. I then ask WHY (**Math Practice 7**). One of the students should note that there is a factor of two which means is can also be factored as 2(x+1)(x+2). I ask which form is best. This leads us to the fact that our new rule is that you always look for a greatest common factor first.

#### Resources

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#### Create a Diagram

*15 min*

As pairs, students come up with a list of the types of factoring that we have talked about as well as their traits. This list gets discussed as a class.

I then ask them to create their own flow chart or diagram describing what type of factoring to use given a polynomial. This is the key activity of the day. Students need to be able to take any polynomial and factor it without specific directions on which technique to use. Rather than making a chart FOR the students, they make one for themselves (**Math Practice 7**). I have them work individually checking with their partner as needed for feedback. They then get together with another pair and each person share’s their chart. They select the best chart of the four and that person gets to share his/her chart describe and why it was chosen with the class.

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#### Guided Practice

*15 min*

The remainder of the lesson is Guided Practice. This gives the students an opportunity to use the diagrams that they created to factor these appropriately (**Math Practice 5**). I verbally model how to use their diagram in the beginning extending to having students explain to each other as we progress.

#### Resources

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#### Exit Ticket

*3 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 completely factor a polynomial.

#### Resources

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This Assignment allows students to practice using all the factoring skills together. These are eight of these types of problems. The final two problems are extension problems (**Math Practice 1**). Rather than a single variable, these problems must be factored using an expression.

#### Resources

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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