How Important Is Factoring?

 

As I wrote the blog on the importance of fractions, it made me wonder how important it was for students to be able to factor in both elementary and in the upper grades.  We know that factoring helps students simplify fractions,  find lowest common multiples or lowest common denominators, ratios, and so much more. Unfortunately, we tend to teach factoring as something that is mostly done on worksheets with much less connection to how it could be used in a much more interesting manner.

In addition, factoring which is the breaking down of a number or mathematical expression or equation into smaller parts.  It allows people to reverse engineer equations and this skill is used in many careers including data analysis and application. So factoring is extremely important to teach but not everyone has learned the skill.

Often factoring is taught as an extension of multiplication by asking a student who is trying to figure out the factors of 6 - "What two numbers do you multiply together to get 6?".  If a student is not good at multiplication, they will struggle to figure out the answer and this struggle continue into high school where they are expected to know how to factor more complex terms.

I've found, it is worth taking time to teach students different ways of factoring when they get to high school.  I am a firm believer in using the rectangle as a visual to show how to factor numbers.  I am not sure what else it is called except the area model where you draw a rectangle using the factors that make the number.  If you have 6, then you arrange it as either one by six or two by three.  If you have 24, you might arrange it as six by four, eight by three, two by twelve or twenty-four by one.  So if you want to find the greatest common factor it would be six because there is a six by one in both examples.

Then when moving to binomials and trinomials, I have a method of binomial multiplication has students use a visualization, the same visualization I've used to teach elementary children two digit by two digit multiplication. (I will see if I can cover that in another entry).  The terms go on the outside and the product on the inside. When it comes to factoring I start with the visualization by drawing the products inside and working outward.  From here, I can move the students to the grouping method since that is one of the best ways to teach factorization of quadratics and some polynomials.  The visualization actually shows the grouping so it is easier to see. The visual step is important because it helps tie standard multiplication to binomial multiplication

If students can find connections between multiplication and factoring visually, they often find it easier to transfer knowledge from one concept to the next. Let me know what you think, I'd love to hear.  Have a great day.