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## Solving Problems Involving Area of Composite Figures

In this 3 act math task, we will explore the measurement strand of the Ontario mathematics curriculum. Specifically, we will look at the area of composite figures including the area of a rectangle and the area of a circle.

## Act 1: Introducing the Problem

In the first act of this real world math problem, we show students the video of cookie dough being mixed and rolled with a rolling pin. The cookies are then cut using a circular cookie cutter in a very particular fashion.

After showing the video, give students some time to brainstorm the possible questions that we could ask in this situation.

At our recent MYCI Learning Fair professional development sessions, we had some great questions come from the participating teachers including:

• How many more cookies can we make with the dough that is left over?
• What is the area of the wasted dough?
• What is the surface area of the granite countertop?
• How much more ingredients do you need if you tripled the recipe?
• If this recipe serves ____, then what must we do to serve 25?
• What is the cost of 1 cookie?
• If you’re selling these cookies at a bake sale, how much should you charge to ensure you earn 40% profit?
• How many calories are in the left-over dough?
• How long did it take to make the cookies?
• What size box do you need to ship x cookies?
• What is the optimal shape box to ship x cookies?
• What shape and dimensions would be the most efficient for the cookies?

After having students share out their ideas and celebrating some of the creative thinking, we then narrow the question down to:

## Act 2: Revealing Some Information

### Dimensions of the Cookie Cutter

Have your students brainstorm to decide what information they need to determine how many more cookies can be cut from the leftover dough. I find it really fun to get kids taking guesses using a high/low strategy to set a range and then have them narrow down to a specific prediction. Great way to get all learners involved, regardless of their level of comfort with math.

After sharing out predictions and hearing what students feel they need in terms of given information, you can show them the following video or image:

Now that students have some information to work with, they can get to it! Sharing and celebrating different strategies to solve the problem can really help elevate the lesson to a dynamic and innovative learning experience! I try to find a really “messy” solution to celebrate the need for students to brainstorm by writing anything and everything they are thinking rather than worrying about their work being a perfectly organized process.

## Act 3: Reveal the Answer

Once students have shared out, it is time to experience the solution of this real world problem:

If you would prefer to show an image over the video, here it is:

I really like this task because students should come up with an answer of just over 3 additional cookies from the remaining dough, whereas the Act 3 video shows a little more than 5. Some great discussion comes from this surrounding the extraneous variables that could cause this to happen. Some students will notice immediately as the video plays that the cookie dough looks “thinner” and thus more cookies could be the result. Others may notice that some of the corners of the rectangular dough was missing and should yield less than 3 cookies. With many other variables to take into consideration, this is a great task to get students talking and engaged in your room!

## New to Using 3 Act Math Tasks?

Download the 2-page printable 3 Act Math Tip Sheet to ensure that you have the best start to your journey using 3 Act math Tasks to spark curiosity and fuel sense making in your math classroom!

## Share With Your Learning Community:

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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