##### Ontario Alignment By Overall Expectation

## Fractions as Quotient and Fraction as Operator

As I’ve mentioned before, working with **fractions** can be very difficult for both teachers to teach and students to understand. This reason could contribute to why so many math classrooms teach students fractions procedurally instead of building a conceptual understanding beforehand. My first attempt at tackling fractions in 3 acts was with the Gimme a Break task and I’ve since shared a Progression of Fractions post to help highlight some of the complexities and misconceptions.

In this task, we look at a situation we’ve all been in before. You cut yourself a few slices of cheese from the brick and grab a handful of crackers from the box. Let’s explore **fractions as quotient** and **fractions as operator** as we try to determine how we should split the cheese to ensure we have enough for our cheese and crackers craving.

## Act 1: Spark Curiosity

Show the students this video.

I then have students take 30 seconds to discuss with their elbow partners what they notice and wonder before sharing out with the group.

After students share out with the class, I tell a story about the situation from the video and how annoying it is when you just randomly break off pieces of cheese for your crackers and then end up with too many crackers left with not enough cheese. DOH!

So, the question we begin with is:

How could the cheese be cut to split evenly with the crackers?

## Act 2 – Revealing Some Information

It’s pretty difficult to see how many crackers there are. I’d wait until somebody raises a stink about it. Then, I’ll show them this video.

The video shows me rearranging the crackers into a 3 by 4 array. (Did you know I love arrays?)

In a perfect world, you have cheese and crackers for students to work with when doing this activity. However, I understand if you were too busy to pick up the goods or if you’re living in Canada and it’s just too expensive to buy cheese! In either case, I like to have square tiles and relational rods (or Cuisenaire Rods) on the table for students to manipulate and experience before diving into any visual and/or symbolic mathematical work.

Walking around the room to help sequence how you plan to have students share their thinking is really important here.

## Act 3: Reveal the Solution

After consolidating this task, I’ll then show them the 3rd act video.

## Sequel

Show students this image.

Give students time to work through this using manipulatives and/or any visual or symbolic representations they choose to use.

Then, show them the act 3, representation #1 video.

Another possible representation might be this one.

## Sequel #2

Show students this image.

Give students time to work through this using manipulatives and/or any visual or symbolic representations they choose to use.

Then, show them this video as a sample of a representation that leverages spatial reasoning.

## Make This 3 Act Math Task Interactive With PearDeck

There are a ton of interactive edtech tools out there that make it easy to take a 3 act math task like this one and transform it into something interactive. Whether you choose Knowledgehook Gameshow, Desmos Custom Activity Builder, Recap! or GoFormative, you have a ton of options to use based on what you intend to achieve. While I’d argue a 3 act math task is fine and dandy with a projector and whiteboards, I’ve taken this task and tossed it into PearDeck.

Access the PearDeck here and feel free to make a copy.

Hopefully you and your students enjoy this task as an entry point into exploring fractions as quotient and fractions as operator! I hope to provide some consolidation animations at some point, but I have yet to sit down and get them carved out. Let me know in the comments if this is something you might need/want for your practice.

Enjoy!

## Share With Your Tribe:

## About Kyle Pearce

I’m Kyle Pearce and I am a former high school math teacher. I’m now the K-12 Mathematics Consultant with the Greater Essex County District School Board, where I uncover creative ways to spark curiosity and fuel sense making in mathematics. Read more.

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