Factoring (Day 3 of 3)

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SWBAT factor trinomial expressions where the leading coefficient is not 1.

Big Idea

Students will investigate the relationship between factoring and polynomial multiplication. Students will factor complex expressions by grouping.


10 minutes

Students will complete the Do-Now in 5 minutes. While students are working, I will pass back the graded exit cards from our last class, and ask students to review any answers that they may have gotten incorrect.

Five student volunteers will come up to the board to share their answers with the class. I will ask students to verify their classmates’ answers by multiplying the binomials pairs together, to see if we end up at our starting point.

Next, a student will read the objective, “SWBAT factor trinomials where the leading coefficient is not 1.”

I will ask students to recap what it means to factor in Algebra. I will also ask students to think about the phrase, “leading coefficient”, and to make a prediction about its meaning. Once we establish the definition of leading coefficient, I will ask students what the leading coefficient has been in the trinomials we factored during our last class.


10 minutes

Students will work in pairs on the Factoring Investigation. This activity is similar to the last investigation we completed in class, and builds off student’s prior knowledge of factoring and polynomial multiplication. Students will use Algebra Tiles to build the model of a polynomial, and then find its factors by identifying the length and the width.

After about 7 minutes we will come back together as a whole group for a brief reflection. I will ask students to describe how the leading coefficient of the trinomial changed the factors, and if they were able to identify any patterns. I will then ask students to describe the connection between the unsimplified terms that result after you FOIL the factors, and the Algebra Tiles.

Guided Notes + Practice

30 minutes

Next we transition to the Guided Notes and Presentation. I will ask students to brainstorm how we can apply what we learned about the factors of a trinomial where a1 to a situation where Algebra Tiles are not present.

There are many methods to factor a trinomial, but the one that find the most successful for my students is the AC Method.  I will model the AC method for the first three problems, then invite students to factor the fourth example with me. It is also helpful for students to factor a trinomial where a = 1 with the this method to help them solidify the steps involved.

Students who struggled with factoring trinomials enjoyed the AC method more because it does not rely on number intuition as much, and has a set process. For these students, I will give them the option of factoring all trinomials using this method.

Finally, students will work independently on the practice problems on the back of their notes. We will then review answers as a whole group.

Partner Activity: Matching Cards

20 minutes

 ***Instructor note** these cards must be cut out and paper clipped together before class begins***

In order to give students an opportunity to practice skills that we have learned over the past few classes, students will work on a Review Activity. While students are working, I will pull a small group of students to practice factoring trinomials with the AC method.


10 minutes

I will ask students to describe what we learned in class today, and to describe how changing the leading coefficient in a trinomial affects its visual representation and its binomial factors.

Students will then complete an Exit Card.