Teaching students how to convert improper fractions to mixed numbers can feel like teaching a foreign language…numbers that are part whole and part-part?!? But just like with everything else we teach in math, we want to bring it to life and make sense of the math, not just teach a quick trick. Let’s talk about how to use fraction mats and manipulatives to do just that!
Starting Simple: Building Regular Fractions
First things first, I always start with the basics: building “regular” fractions with students. Give every student a copy of this fraction mat and some fraction pieces. I love to print the mat on card stock and place it into a plastic sleeve so students can easily write on and erase. Have students create a fraction using fraction pieces on their mat. Once they’ve done this, ask them to decompose the fraction into unit fractions. 3/4 can be broken down to ¼ + ¼ + ¼. They should also notice that ¾ does not take up the whole fraction bar space, because it is less than 1 whole.
Having students break down fractions into unit fractions builds a visual understanding of what each fraction represents. It sets them up for the next step: handling improper fractions!
The Curveball: Introducing Improper Fractions
Now that students are comfortable with simple fractions, it’s time for a twist. Ask them to create an improper fraction, like 5/4, on their mats. The key is don’t tell them it’s an improper fraction yet. Just continue on with your routine that you were doing in part 1. Watch the wheels inside their brain turn when they fill up the first fraction bar and realize 5/4 is a little bit different than what they are used to seeing.
Let them write this out as a sum of unit fractions: 1/4 + 1/4 + 1/4 + 1/4 + 1/4. Discuss how this fraction needed more pieces than would fit in the whole because it is a fraction that is greater than 1. Sometimes we call fractions greater than 1 improper fractions.
When they see it visually, most students will start to notice a pattern: they can group four of those fourths together to make one whole, with 1/4 left over.
The magic moment? They realize 5/4 can also be written as 1 and 1/4! We’ve just introduced the concept of converting from an improper fraction to a mixed number—and they’ve discovered it themselves. And there were zero cartwheels involved 🤸
Continue giving students improper fractions to create with tiles, decompose and unit fractions, and rewrite as mixed numbers. You can also play around with doing it in reverse. Give students a mixed number, have them build it and figure out what the improper fraction would be.
Resources for Fractions Greater than One
I’ve linked some free fraction mats to help you get started. Use these as a foundation for your own fraction explorations. Let’s build that conceptual understanding for students and watch those lightbulb moments unfold! 💡
Improper Fractions to Mixed Numbers Fraction Mat
Fractions greater than 1 Slides
Watch the mat in action here on Instagram
Looking to conceptually teach comparing fractions and grab even more free fraction resources? Head to this blog post.
