Factoring Day 1 of 2

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Objective

SWBAT understand how to solve factored quadratic equations by understanding the zero product rule. SWBAT distinguish between quadratic equations that are not factorable and still have x-intercepts with those that do not have x-intercepts.

Big Idea

Students develop an intuitive method to solve quadratic equations by factoring.

Opening

15 minutes

I begin class by asking students to summarize what key concepts they have learned about quadratics so far in this unit.  I want to elicit that they have learned how to put quadratics in vertex form in order to find the maximum or minimum of a quadratic and that they can set that vertex form equation equal to zero in order to solve for the x-intercept(s).

I explain to students that for some quadratics, there is an easier way to find x-intercepts. I let them know that today's class will focus on this new method.

We start class by reading Factor Fixin' together. I have them do the first 8 problems as a warm up and have students share out their answers.

 

Investigation

35 minutes

Next, students begin to work in the opposite direction. I like how the Factor Fixin' task sets up the problem with the customers giving their orders in standard form, but the manufacturer needs to know how much to add or subtract from the original x by x quilt square.  This analogy seems to make a lot of sense to students and gets buy in from them.  I also like how the first two problems show students the middle values of the standard form quadratic before the like terms are combined. This makes it really easy for students to find the binomials and scaffolds the factoring process for them.  

When students get to Questions #10 through #13, they are primed to recognize that they are looking for two numbers to multiply to the constant "c" term but add to the "b" term.  Usually, one of my students will say something exactly to this effect and I will stop class and make sure everyone has heard this key point. Students can also write down this pattern next to Question #14.

I let students work in small groups or individually on Questions #10 through #13 and then have them share out their answers in a whole group setting.

Lastly, we work on Questions #15 through #17 and discuss them together. In the next lesson, students will learn why factoring is useful and set the factored equations equal to zero. But for today's class, I really want to focus on breaking the standard form quadratics into binomials.

Closing

10 minutes

I will make sure to give students some time to process what they have learned today about factoring.  I will use an exit ticket strategy like the one below to help them process their understanding.

Exit ticket: Write to an absent student and explain how to factor a quadratic.

 

 

Citations

  1. Factor Fixin' is licensed by © 2012 Mathematics Vision Project | MVP In partnership with the Utah State Office of Education Licensed under the Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported license.

    http://www.mathematicsvisionproject.org/secondary-mathematics-ii.html