### Where Is The Power?

I've started focusing on**three powerful fraction concepts**that students need. Students need to clearly understand each concept and be able to explain each one in words and modeling. The

**power**comes when students can integrate the concepts, model all three, and explain the differences between all three

*at the same time.*### Finding The Power

When we begin our fraction work, identifying a unit fraction like 1/4, or one out of four pieces, seemed to come relatively easily. We use manipulatives, colored area models, and number lines.Next, we look at 4/4, or four out of four pieces. That's the whole one. This was a little tougher because one is usually written as "1" and we tend to neglect seeing that it can be 3/3, 5/5, 10/10, or any other whole fraction.

When we're well into fraction studies, we talk about

__fractions greater than one whole,__often called improper fractions. That's what 4/1 looks like - and is - to my students...an improper fraction. What we were forgetting to emphasize was that 4/1 is four whole, individual things: 4 pizzas, 4 books, or 4 days. We all got that 4 means four wholes. It's the format 4/1 that kicked us a little.

My mistake was in always teaching these three concepts in isolation from each other. Students could show an understanding of each one individually, but to compare even two caused some confusion.

One day, almost in desperation, I wrote these exact fractions on the board: 1/4, 4/4, and 4/1. I directed students to explain the differences between the three, using pictures, words, area models, or whatever worked for them.

"Can I use a number line?", one student immediately asked. I answered, "Absolutely", and off we went.

As I expected, modeling and explaining 1/4 was pretty easy. Most students quickly used one of the area models you see in the first column above.

Modeling 4/4 made a few pause to think, but most moved on quickly. Yep, it's the whole thing.

The format of the third fraction, 4/1, slowed down almost everyone. I could almost hear students thinking, "I know that's four separate things...I think..." As I peered over shoulders to see how we were doing, I got a number of those hopeful looks that ask, "Is this right?"

When we pulled everyone back together to share, I actually saw the relief on students' faces - the same relief I was feeling! Yes, they knew what each fraction was in isolation and could define and model them. More importantly, I was sure that they knew the differences between the less familiar fractions and

__Whew! What power!__

**how they relate to each other.**### Why We Should Use This Activity

I love this no-prep activity because of its low floor and high ceiling. We can repeat it with different fractions from time to time to keep skills sharp. I especially value it because it reaches down and builds foundational math concepts that are essential to student mastery.Consider trying this activity with your students. Begin with unit fractions that have smaller denominators, such as 1/3, 3/3, 3/1 or perhaps the example of fourths used in the image above. If you'd like to challenge students, move away from unit fractions and see what happens!

I'd love to know how working with these

**three powerful fraction concepts**works in your classroom!

See other products that support fractions at

**Growing Grade By Grade**!