This year, I am taking a big risk with my Algebra 1 kiddos. I taught them to factor quadratic trinomials with a leading coefficient greater than one before we ever discussed solving equations. Last year, I crammed in factoring quadratics at the very end of the school year. I was feeling rushed, and I needed to cover factoring quadratics and simplifying radicals before the end-of-instruction exam. I didn't feel like I really did either topic justice because I was so rushed.
This year is different. Really different. My Algebra 1 students came in at a much lower level than my students last year. After spending weeks on integer operations and the order of operations and all that fun stuff that students should already know from middle school, I still had a lot of kids who were just not getting it. That was nothing new. Last year, my students struggled with these topics, too. And, last year, I moved on to solving equations and HOPED that the rules for dealing with integers and all that good stuff would "click" when they started seeing it in equations. That worked to a certain extent.
This year, I could tell I was more frustrated and my students were more frustrated than normal. The kids who understood integer operations were bored out of their minds. They wanted to move onto something new. The kids who didn't understand integer operations still didn't quite know that they didn't understand them. So, my constant review as futile. My students had solved equations in middle school, so that wouldn't be something new and exciting. After teaching them the distributive property, I had an epiphany.
Okay. I need to pause the story. Yes, I know you're wanting to know what my epiphany was. But, you're just going to have to wait. If you're protesting with me in your mind right now, I'll tell you what I tell my kids a lot. You'll live. Is that a little harsh? I probably say that more in my classroom than I should. Anyway... I made a commitment to myself last year that I would stop teaching students to FOIL. I learned to multiply binomials by FOILing. But, I'm learning that some of the tricks that I was taught in Algebra are just that. They are tricks that work, but students don't quite know why they work. If my students can see a problem as an extension of the distributive property, they can solve a myriad of problems in different forms. If students only know how to FOIL, they are going to be stuck and not know what to do when they are asked to multiply a trinomial and a binomial. Last year, instead of teaching students to FOIL, I taught students what I called "The Double Distributive Property." This could be extended to the triple distributive property as well. And, it worked out pretty well.
Back to my epiphany. What if didn't teaching the double distributive property as a separate property? What if just told my students that when they see two polynomials being multiplied together that it is a distributive property problem? So, I did just that. Day one of the distributive property featured monomials times binomials. Day two of the distributive property featured polynomials times polynomials. I made no distinction between the two. When my students see two polynomials being multiplied, they automatically think distributive property. And, that makes me insanely happy.
After teaching students to distribute, the natural thing to teach students is to undistribute, or factor. When my students were first reviewing integer operations, I gave them a sheet of diamond puzzles or X-puzzles to complete. I taught my students to factor quadratics with a leading coefficient of 1 using the X-puzzle.
Then, we moved onto factoring quadratics with a leading coefficient greater than 1. Again, I changed my teaching approach from last year. Last year, I taught my students to do the Airplane Method. This worked. But, I still had a few students who never caught on. This summer, at the Common Core conference I went to, I was introduced to the Slide and Divide method of factoring. Another teacher mentioned that she called it the Bottoms Up Method. I combined these two ideas to create the "Slide, Divide, Bottoms Up!" Method. My students LOVE it.
Yes, this is a trick. But, I haven't figured out a better way to teach it. When I took Algebra 1, I learned the guess and check method. And, I found that method to be torturous. But, I didn't know there was a better, faster, easier way. Now that I do know there is a better way, I would never go back.
So, without further ado, I think I've given you enough back story to help you understand the context behind these foldables and interactive notebook pages for Algebra 1.
Last year, I had a conversation with a student that changed my outlook on vocabulary. This was not my own student but the child of a coworker. Before tutoring him one day, he was sitting in his mom's office, discussing why he was having so much trouble in algebra. He said, "My teacher just keeps going on and on and on. And, he keeps saying this word that nobody knows what it means. And, the whole class is lost." Naturally, I wanted to know what the word was. "I don't know. I think it starts with a b." Since they were working on polynomials and factoring, I took an educated guess: "binomial." Yes, that was the word. Once I described to this student what a binomial was, he began to realize that maybe this wasn't as hard as he had made it out to be.
This year, I am emphasizing vocabulary more. I don't want students to think that I use words without ever telling them what they mean. At the very least, they should know that the vocabulary word should be in their interactive notebook somewhere.
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| Polynomial Frayer Model |
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| Rules for Naming Polynomials |
I told my students that when polynomial parents have children, they don't get to choose their names like human parents do. Instead, polynomial parents must follow strict naming rules. I lamented about how sad this was. I mean, what if the parents wanted to be creative? What if the parents wanted their child to have the same last name as them? The first name of any polynomial child is determined by its degree. The last name of any polynomial child is determined by its number of terms.
One of my students asked me if I was going to use these rules to name my own children. Apparently, I seem like the type of person who would name my child "Cubic Trinomial." I guess I should take that as a compliment...
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| Introduction to Polynomials Interactive Notebook Pages |
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| Factoring Quadratic Trinomials with a Leading Coefficient of 1 |
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| Examples of Factoring Quadratic Trinomials with a Leading Coefficient of 1 |
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| Basic Factoring Interactive Notebook Pages |
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| Factoring Quadratic Trinomials with a Leading Coefficient Greater than One (More Affectionately Known as: Slide, Divide, Bottoms Up!) |
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| Examples of Factoring Quadratic Trinomials with a Leading Coefficient Greater than One |
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| Slide, Divide, Bottoms Up Factoring INB Pages |
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| Factoring Difference of Squares |
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| Factoring Difference of Squares Examples |
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| Factoring Difference of Squares INB Pages |
If you have trouble viewing these files, please send me an e-mail. I would be more than happy to attach the files and send them to you.
Naming Polynomials Graphic Organizer
Blank Frayer Models
Factoring Quadratic Trinomials with a Leading Coefficient of 1 Graphic Organizer
Factoring Quadratic Trinomials with a Leading Coefficient Greater Than 1 Graphic Organizer
Factoring Difference of Squares Graphic Organizer