Factoring Quadratic Equations: Paraphrased
Example: x2 + 6x + 8
Step 1: Locate the third term in the quadratic, and find all the factor pairs associated with that term.
Step 2: Identify the factor pairs that will give you a sum that’s equal to the number in the middle, or the second term.
Step 3: Factor the first term. If the first term is X², both binomials will start with X. For example, it would be (X )(X ) because X(X) = X².
Step 4: Since the factor pair (2, 4) has a sum of six, two will be added in the first binomial, and four will be added in the second binomial.
For example, (X + 2)(X + 4). Two and four are added because all of the terms in the original quadratic are positive.
By paraphrasing the steps, I was able to internalize the concepts more, because I had the opportunity to interpret and communicate the procedures in my own personal way. Decoding language is an integral part of the learning process; thus, summarizing and paraphrasing allowed me to express my understanding in a unique way that made sense to me. This type of lesson could be applied in class by having students paraphrase procedures that are difficult for them to understand; therefore, students will have the opportunity to “confront” difficult concepts and make sense out of them. Since communication is essential to student’s understanding, if they are given the opportunity to paraphrase & construct meaning for themselves, the they will enhance their ability to learn and understand the math. Even if students understand procedures without paraphrasing them, I would require them, for example, to explain the factoring process, so I could assess their understanding by having them answer questions similar to the ones below:
- Why are both binomials X?
- Why did you use the factor pair (2, 4)?
- Where there other options besides (2, 4)?
- How did you know that (2, 4) needed to be added?
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