##
* *Reflection: Developing a Conceptual Understanding
Factoring (Day 2 of 3) - Section 2: Investigation

This lesson is similar to lesson 3 in that using algebra tiles is essential in aiding student understanding. Again, although cumbersome, the tiles are well worth the time. During the investigation it is powerful for the kids to make the connection on their own. Instead of the teacher telling the students exactly what to do, they are able to come to the “ah ha” moment on their own. This is much more powerful and lasting than simply memorizing steps. The self discovery makes it stick. This is a one day lesson but it may be worth 2 days. Due to the weight of the standard and the length of the lesson, if there is time, I recommend spending the 2 days on it.

*Algebra Tiles, Cont.*

*Developing a Conceptual Understanding: Algebra Tiles, Cont.*

# Factoring (Day 2 of 3)

Lesson 7 of 9

## Objective: SWBAT factor trinomial expressions.

#### Do-Now

*10 min*

Students will complete the Do-Now in 5 minutes. The purpose of today's Do-Now is for students to practice multiplying polynomials, since this skill will be utilized in today's lesson. As students are working, I will pass back the graded exit cards back from our last class. I will then call on student volunteers to come up to the board to show their work to the class.

We will then review the Exit Card from our last class since this skill is a prerequisite topic for today's activity. Next, a student will read the objective, **"SWBAT factor trinomial expressions".**

I will ask students to recall what it means to "factor" in Algebra, and to give a brief summary of what we learned about factoring Algebraic expressions.

#### Resources

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#### Investigation

*15 min*

As we continue to work through Factoring Trinomials.pptx, this section begins on **Slide 5**. I will show students the polynomial on the screen, x^2 + 3x + 4, and ask them to factor the polynomials using the same process that we did previously. Students will quickly see that the three terms in the trinomial have no common monomial factor, so we must figure out another way to factor the expression.

Using the Factoring Trinomials Investigation handout, students will discover the relationship between the visual representation of a trinomial, and its binomial factors. Students will work in pairs during this self guided activity, while I circulate around the room guiding students as they work.

After 10 minutes, we will come together as a whole group to summarize what students learned during the investigation. I will ask students the following questions to help them devise their own shortcut:

- What patterns did you start to see as your started to find the factors of the trinomials?
- Did this make the process easier or harder as you worked?
- Could finding a pattern help you factor a trinomial without Algebra Tiles?
- How did the use of the FOIL or Box method assist you in finding the factors of each problem?

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#### Guided Notes + Practice

*20 min*

The class will continue to follow along with this Presentation using Guided Notes.

Students will dominate the majority of the conversation going forward, as we will be using the "shortcut" that they discovered to factor the rest of the problems in their notes. Some of my students struggle with integer operations, so I will encourage them to use the Algebra Tiles or integer chips for assistance as they work.

After completing the **Example Problems** together, students will spend a few minutes working on the **Practice Problems**. After a quick review, we will complete the **Check For Understanding** questions (see Slide 13 of Factoring trinomials.pptx) using clickers to asses the progress the group has made with today's lesson.

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Students will complete a station activity entitled, Crack the Code. Each student will need an Answer Sheet to record their answers.

The Factoring Stations in this activity form a loop. Each question/answer combo will guide students through a set sequence. It does not matter where students start.

**Station Instructions:**

- Stand at a station. You can start at any station.
- Write down the station number you are standing at on your answer sheet.
- Record the code that is inside of the black box on your answer sheet.
- Solve the problem at the station. Then, write down your answer.
- Look around the room. Find the station on the wall that has the answer you got in step 4.
- Repeat the cycle (starting at step 2) until you have all 13 codes written down.
- When you are finished, unscramble all 13 codes to reveal a secret message.

After 20 minutes students will return to their seat, and I will reveal the secret message (a Math riddle) using Slide 16.

**Instructor Note:** These stations need to be taped to the wall prior to the start of class.

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#### Closing

*5 min*

I will ask a student to summarize what we learned today in class and to decide if we have mastered our objective. I will also ask students to reflect on the significance of the Algebra Tiles that we used when factoring trinomials. Lastly, I will invite students to brainstorm a method to factor trinomial with Algebra Tiles that includes negative numbers.

Students will then complete an Exit Card.

#### Resources

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- UNIT 1: Welcome Back! - The First Week of School
- UNIT 2: Linear & Absolute Value Functions
- UNIT 3: Numeracy
- UNIT 4: Linear Equations
- UNIT 5: Graphing Linear Functions
- UNIT 6: Systems of Linear Equations
- UNIT 7: Linear Inequalities
- UNIT 8: Polynomials
- UNIT 9: Quadratics
- UNIT 10: Bridge to 10th Grade

- LESSON 1: Properties of Exponents (Day 1 of 2)
- LESSON 2: Properties of Exponents (Day 2 of 2)
- LESSON 3: Adding and Subtracting Polynomials
- LESSON 4: Multiplying Polynomials - Part I
- LESSON 5: Multiplying Polynomials - Part II
- LESSON 6: Factoring (Day 1 of 3)
- LESSON 7: Factoring (Day 2 of 3)
- LESSON 8: Factoring (Day 3 of 3)
- LESSON 9: Review Day