![]() ![]() My personal preferred method is Guess and Check, but for my students, I will be teaching the "Splitting the b" method in the future. They can avoid this issue by ensuring that the Area Model works when multiplying. The issue occurs if they blindly take out the GCF and forget to check the multiplication. Students must take out the GCF before jumping into factoring to avoid issues. What if a student forgets to take out the GCF first? I tried to discourage them since it's more time-consuming, but not all of them listened. I also noticed that some students became too attached to the Area Model and used it for factoring easier trinomials such as $x^2+12x+35$. In 2022-2023, I found that when we had not done factoring for some time, students had forgotten how to set up the box. It's still a *method* and requires students to remember the steps of the method. Teaching this method also paves the way for dividing polynomials using the Area Model, which I successfully taught in lieu of the Long Division algorithm during the 2022-2023 school year. Students will hopefully see the connection between multiplying and factoring. If you have taught the students how to multiply polynomials using the Area Model, this method is a smooth transition into factoring. When factoring, the trinomial represents the area, and students must find the two factors (length and width) that were multiplied to get the area/trinomial. The idea behind this is based on the area of a rectangle being length times width. I kept calling it the X Box method, and it wasn't until May that I realized I was saying the name of a gaming system! Hahaha! I used this method almost exclusively during the 2022-2023 school year with my Algebra 2 classes. As a result, I penalize them for failing to follow the proper process. ![]() They end up saying that $2x^2+3x-2$ is equivalent to $(x+2)(x-1/2)$, which it is not (see image below). Some realize they don't need to fully factor before arriving at the answer. More on that below.Īnother issue arises when students learn to solve quadratic equations by factoring. If the trinomial has a GCF and students forget to take it out first, they will have the wrong answer if they use this method. For example, in my work above, students often stopped when they reached $(x+4)(x-1)$. If students forget the last few steps, it's not an effective method. This is one reason why I stopped teaching it. Students often forget a crucial step in this method-the "divide" step. It requires no deep understanding of what the students are actually doing, and explaining why the method works is not easy. It's more of a trick than a mathematically correct process. When using this method correctly (and taking out the GCF first), it will always lead to the correct answer. If they cannot be reduced or a denominator remains after reducing, move the denominator to the front of the x in the factor. Then, since I multiplied by the "a" value (2 in this case), I now go back and divide by the "a" value. Then I factored "like normal" - looking for two numbers whose product is -4 and whose sum or difference is 3. In the example above, I started by multiplying the "a" value by the "c" value and rewriting the problem. ![]() My preferred method is "splitting the b." However, my opinion has since changed, and I no longer advocate for teaching this method. I first learned this method from a fellow teacher in the late 90s and taught it for years. Many people □♀️ have taught this method but called it by a different name. ![]() The Slide and Divide method has gained popularity in recent years, though it has its fair share of critics. Try it with $6x^2+9x-6$! Slide and Divide (a.k.a. What if a student forgets to take out the GCF first?įortunately, if students forget to take out the Greatest Common Factor first, they can take it out at the end. Checking all of these options can take several minutes. If you were trying to factor $12x^2-19x-18$ through guess and check, you must consider all factors of 12 and all factors of 18. Students often give up if they can't get the answer after two or three tries.Īnother issue is that it can be time-consuming. In the example above, there are a handful of ways to get a product of $6x^2$ and likewise for $8$. One issue with this method is that students must have a high tolerance for frustration and fairly good number sense. A significant advantage is that students are constantly checking their answers, which means they will know if they are right and they will be improving their ability to multiply binomials quickly. ![]()
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