Fractions in Simplest Form

Do your math backwards: A math hack for teaching fractions.

Here's how I taught today's math lesson...

First of all, I hate the way Fractions in Simplest Form is presented in the math textbook my school uses (Envision for 4th grade). Here's why: the banner problem (a.k.a. the example) is reduce 4/12 to simplest form. The banner problem tells students that because 4 and 12 are even you can divide both the numerator and denominator by 2, get 2/6, then divide 2/6 by 2 again.

If students aren't ready to learn how to find all the factors of a number so they can then find the greatest common factor, we shouldn't be teaching this concept yet. We should teach student how to reduce fractions to their simplest forms when students are ready to find the GCF.

Instead of teaching students the book's way, I reviewed the meanings of Factor, Product, and Greatest Common Factor. Then I reviewed how to find the factors of a number. I say "reviewed" because I've informally showed them this before, just for fun, for students who were ready for the concept. Then we found the factors of 24 (I like 24 as an example). But then-

And this was the part of the lesson that got me really excited. It was so simple, but I had never done it this way. I hadn't been taught to do it this way, and I haven't seen other teachers explicitly teach it this way (I'm sure some must!).

I had students fold their papers hot dog (lengthwise). I explained that the problems would go in the right column, but the factors (the show-your-work part) would go in the left column.

Doing it this way is backwards to the way students instinctively go about writing math problems. We write left to right, but I told them to write on the right and then the left. Backwards.

We did the first problem together and the students oohed and said  how it made so much sense.

Stuff making sense. Little victories. Yay!