##
* *Reflection: Developing a Conceptual Understanding
Polynomial Puzzles 2: Distributive Property - Section 2: Polynomial Puzzles

I had never used these polynomial puzzles in the past. I am really happy that I infused these lessons at key points in this unit. The type of thinking required to complete the puzzle is exactly the type of thinking you want from your students when examining any polynomial question. In order to complete the puzzle, students need to show a flexibility in thinking. They need to be able to work forward (multiply) and backwards (factor) interchangeably. Often when working in a polynomials unit students are either practicing all factoring or all multiplying but not both at the same time. This activity also has the built in benefit of being "self-checking." This way students will know whether or not they are completing the puzzle correctly.

*Thinking Flexibly*

*Developing a Conceptual Understanding: Thinking Flexibly*

# Polynomial Puzzles 2: Distributive Property

Lesson 10 of 18

## Objective: SWBAT multiply and factor expressions using the distributive property.

*40 minutes*

#### Warm Up

*10 min*

This is a fairly basic warm up. The idea is to let students get used to the structure of the polynomial puzzles. Students have solved another polynomial puzzle dealing with addition and subtraction but not with multiplication and factoring. I will go through the first polynomial puzzle with students. To speed up the process I simply have the students make a square in their notebooks and divide it up like a "tic-tac-toe" board (3 rows/3 columns). You could also print each of these slides and distribute them to students. On the second puzzle, I let students complete it with their partner and then we go over it to make sure all students understand how the puzzles work. Before starting the third puzzle, I encourage students that they are going to have to use the structure of each expression to determine how to fill in the missing boxes (MP7). After letting students try the third puzzle, I will look for a volunteer to explain their thinking to the class (MP3).

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#### Polynomial Puzzles

*25 min*

Allow students to work in partners to complete each polynomial puzzle. Some pairs of students may come close to finishing in the 25 minutes, others may not make as much progress. In either case, students are forced to think flexibly and abstractly in order to complete each puzzle (MP2). NOTE: Puzzle #3 is typically where students will struggle. Watch for students who are multiplying the binomials but simply multiplying the first and last terms of each expression (example: (x+3)(2x-2) = 2x^2-6). This is a conceptual misunderstanding that you will want to address immediately to prevent issues when factoring trinomials in future lessons.

Students may not realize that they are factoring to complete each puzzle. That is okay. The thinking required is what you want to focus on. For example, when you questions students about their thinking, you may hear them explain it as follows, "I needed to think, what times 15x+6 is going to give me 30x^2+6x?" This type of flexible thinking will really help students as they get further into the factoring portion of this unit.

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#### Closure

*5 min*

This ticket out is leveled so that students can work on a task they feel comfortable with. While neither of these options includes binomials, much of the thinking required will be the same. If you have some students that have been extremely successful with the polynomial puzzle activity, you could challenge them to make up a polynomial puzzle that included binomials or even trinomials.

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- LESSON 1: Adding and Subtracting Monomials
- LESSON 2: Adding and Subtracting Polynomials
- LESSON 3: More with Adding and Subtracting Polynomials
- LESSON 4: Polynomial Puzzles 1: Adding and Subtracting Polynomials
- LESSON 5: Multiply and Divide Monomials-Jigsaw day 1 of 2
- LESSON 6: Multiply and Divide Monomials-Jigsaw Day 2 of 2
- LESSON 7: Multiplying Higher Degree Polynomials
- LESSON 8: Multiplying Polynomials Investigation
- LESSON 9: Polynomial Vocabulary
- LESSON 10: Polynomial Puzzles 2: Distributive Property
- LESSON 11: Factoring Using a Common Factor
- LESSON 12: What if There is No Common Factor?
- LESSON 13: Factoring Trinomials
- LESSON 14: More with Factoring Trinomials
- LESSON 15: Polynomial Puzzles 3: Multiplying and Factoring Polynomials
- LESSON 16: Seeing Structure in Factoring the Difference of Squares
- LESSON 17: Factoring Completely
- LESSON 18: More with Factoring Completely