Reflection: Staircase of Complexity Factoring Day 1 of 2  Section 1: Opening
Students have already seen the first few problems in this task, but I really like how this activity has students go from binomials to standard form first and then asks them work backwards. I have found this approach to factoring and the context of the quilt squares to be extremely helpful in getting students to see the structure of quadratics in the two forms.
Factoring Day 1 of 2
Lesson 12 of 18
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 xintercepts with those that do not have xintercepts.
Opening
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 xintercept(s).
I explain to students that for some quadratics, there is an easier way to find xintercepts. 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.
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Investigation
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.
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Closing
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.

Factor Fixin' is licensed by © 2012 Mathematics Vision Project  MVP In partnership with the Utah State Office of Education Licensed under the Creative Commons AttributionNonCommercialShareAlike 3.0 Unported license.
http://www.mathematicsvisionproject.org/secondarymathematicsii.html
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