Help your upper elementary students understand the concept of **simplest form** using these simple strategies.

## Fraction Tiles Are Essential!

My students are wrapping up our study of fractions next week. This year my goal was to use our class set of fraction tiles *every single day* in order to really develop a concrete understanding of fractions. There were many days when all we did was work with those tiles. (Don’t get me started on how we managed to collect those little things day after day that would somehow get left on the floor!) However, the longer we studied fractions, and especially when we got to operations with fractions, the less some of my students needed them. They had started to rely on their schema in their minds and realized that was a more efficient way to solve their problems. Of course, some students still want the assurance that comes with checking their work with the fraction tiles, and I’m cool with that approach, too. Everyone learns at a different rate. If you don’t have a set of foam fraction tiles, I would strongly encourage you to actively try to get your class a set. Here’s a paper version that will do in a pinch.

## Fewer Tiles = Simplest Form

Way before we ever got to solving problems with fractions and reducing them to simplest form, we used our fraction tiles to generate equivalent fractions. Students quickly caught on that creating an equivalent fraction with our tiles meant that we would need more tiles to represent the same amount. When it came time to introduce simplest form, I started first with our fraction tiles. Only this time, instead of using MORE tiles, I told students that simplest form meant we needed to use FEWER tiles because that was SIMPLER. We had to repeat this many, many times with our tiles before the idea transferred – that’s normal, of course. So my second recommendation when teaching fractions would be to give yourself plenty of time to teach it. I know that’s not always easy, but rushing students through this concept won’t save you time in the long run.

## Checking for Simplest Form

Once we had developed a concrete understanding of simplest form, it was time to develop a set of criteria for determining if a fraction was in simplest form. That’s not easy because there are several you need to check for, and – as you know – kids sometimes like to rush through their work to get “done.” Getting students to learn and actually check all of these criteria won’t be easy, but it’s a good start and will give them some specific actions they can do to reduce a fraction to simplest form.

- Are the numerator and denominator both even numbers? If they are, that means they can both be divided by 2, maybe even more than once. We like to just say, “Divide them both in half” and see what that leaves us as our fraction. If the answer is no, then go to the next question…
- Is the numerator a multiple of the denominator? We translate that to, “Can I say the denominator if I count by the numerator?” If the answer is yes, divide both numbers by the numerator. If the answer is no, go to the next question…
- Is the numerator half of the denominator? We catch on to this question quickly as students seem to recognize fraction halves more easily. If the answer is yes, great! The simplest form is 1/2. If the answer is no, your fraction is already in simplest form.

Other ways to check if a fraction is in simplest form include…

- If the fraction is a unit fraction (meaning it has a one as the numerator), your fraction is already in simplest form. This is a great time to get out those fraction tiles again and confirm this fact.
- If the numerator is “one away” from the denominator, your fraction is already in simplest form. Practice identifying fractions where this is the case – 1/2, 2/3, 3/4, etc.

I hope this helps you and your students determine simplest form. Click on the link below if you want a printable that lists the above strategies, which you can have students glue into their math notebooks. Happy teaching!

~ Sally

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