Thin Slicing: Solve By Factoring

Grade 10s are working on applying their factoring skills. We have looked at how we can graph parabolas from factored form, and now we are looking at how to solve quadratic equations by factoring. This is the sequence I used to develop the skills today.

(x)(6)=0 and (8)(x)=0

Then we included coefficients. Some groups really clicked into the idea that if the product is 0 one of the factors must be 0.

The next question was interesting, as there were 3 representations of solutions.
(11)(x+1)=0

One group did the area model to expand, another used the distributive property without the area model to expand then solve, and there was one group who knew that (x+1) would need to be 0 and solved quickly.

We practiced a few more examples and many groups latched onto the idea of solving without expanding.

The next introduced a coefficient, and it was interesting to see how students approached it. Some realized that we multiply 2 by 2.5 to get 5 which is the zero pair of -5 which is in the bracket. Others approached it as if it was x-5 in the bracket the x would be 5. Since it’s 2x in the bracket then the x must be 2.5.

Our next step happened after students were comfortable solving by setting brackets equal to 0. We tried (x-1)(x+2)=0

It was neat to see how they were ok with their being 2 answers. We made the connection to a parabola passing through the x axis twice, so it’s ok to have 2 answers.

I wanted to avoid students always thinking that the constant in the brackets is connected to the answer, so I introduced coefficients quite quickly to enforce the idea that we need to fin the x which makes the bracket equal to 0.

Next we looked at what happens if we are not given factored form, but instead a trinomial equal to 0. We need to factor first and from there it’s all the same as before. We use the area model for factoring because it connects so well to algebra tiles and how we expand polynomials too.

The next step sequentially was to start with an equation without 0 on one side. Students knew to use zero pairs to create an equation equal to 0 and then to factor and solve.

The sequence worked really well, and I hope that students will continue to be able to apply their skills to solve quadratic word problems next!