x^2 + 6x + 8
First, look at the last term (8). Determine the factors of the numbers.
The factors of 8 are 1 and 8 or 2 and 4.
Next, look at the second term (6x). Use the factors from above (1 and 8 or 2 and 4) and add or subtract them until you get the number in the second term (6).
1 + 8 = 9
1 – 8 = -7
8 + 1 = 9
8 – 1 = 7
2 + 4 = 6
Look at the first term (x^2) and write its factors out.
The factors are x and x.
Finally, let’s put it all together. Make two sets of parentheses and put a “x” in each so that it looks like:
(x )(x )
The factors that we previously found (2 and 4) are what will go inside the parenthesis. They were both positive numbers so we will put plus signs in the parentheses as well.
Our final answer will look like.
(x + 2)(x + 4)
Did paraphrasing the words help you internalize the concepts more?
Honestly, it was a huge help. I’ve never directly taught quadratic equations and I’ve personally hated the way that some of the math teachers try to teach it so I never fully understood how to do it and explain it to students. Thanks to this activity, I now totally remember how to do it and feel confident in teaching it to others.
How can you apply this type of exercise in a lesson for your own students?
My students really struggle with paraphrasing how to solve problems so I could have students paraphrase every concept once they had practiced it enough. They could then write it out in an easy to read visual and present it to the class.