Objectives:
~Preknowledge:
The problems I chose (in order):
To start, I had all the students join me at the front of the room to discuss our plans. I told them that I was going to give them a problem that I want them to factor using "the box". When they are all done, we are going to discuss their solutions. Then I would give them two more problems to do. I handed out the cards that randomly groups them on the boards and they got to work on the first problem. 2x^2+14x+24 Since they have played a little bit with have an a-value other than 1, they went right to work factoring with a 2x and x on the outside of the box. There were two answers that came out of the groups: (2x+6)(x+4) and (2x+8)(x+3) Since some groups finished quicker than others, I challenged them to find another solution (I told them there were 3 solutions). When the groups finished with at least one solution, I called the class to look at two different groups' work. They decided that both solutions were done correctly. I questioned how there could be two answers and challenged them to return to their boards to make sense of it. Most groups connected that dividing the factor with the 2x by 2 would give the other factor. (see image below) I took this opportunity to explain that we will FACTOR out a 2 instead of divide by 2, which means we will write the two in front of the factorization. I then also showed them what would happen if we factored out the 2 right away, and then factored the quadratic. We discussed the efficiency in doing that first. To wrap up, we agreed that 2(x+4)(x+3) was the complete factorization. (I also connected it to prime factorization from grade school: 20=2*2*5)
3x^2+18x+24 The students went back to their boards and I wrote this quadratic on the board. I chose this one so that it wasn't a 2 that got factored out, but I thought having a constant of 24 again would be interesting. (It turns out to not be interesting). This went quickly, the students factored out the 3 and then quickly factored the quadratic into two binomials. 2x^2+19x+24 I purposely gave them this one that does not have a monomial to factor out. I wanted to see what they would do and make sure they saw that not all quadratics with a non-one a-value would factor out a monomial. They started by trying to factor out a 2, but I heard discussions about being uncomfortable with the decimal coefficient that remained. They quickly scrapped that method and went right back to factoring using the area model. The groups all got (2x+3)(x+8). We wrapped up the board work by discussing why this factorization was different than the ones they originally got with the first problem (how they could factor out a 2 from their linear factor, but can't with this one). The remainder of the hour was spent practicing different problems. It went smoothly and any of their questions were discussed in their groups and figured out on their own. It was fun to listen to their discussions and reasoning.
2 Comments
Cassandra Deering
10/16/2020 04:42:11 am
I am so excited to try this!!!! I attended your presentation yesterday through Fond du Lac CITS and I really want to turn my classroom into a Thinking Classroom. I'm currently teaching Algebra 2 so this fits right in. Thank you!
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Shane
10/27/2022 12:13:22 pm
I like this. My students rarely remember to factor out a common factor.
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AuthorI teach mathematics for grades 7-12. Teaching mathematics is my passion. Archives
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