## Donut Delight 3 Act Math Task Resources

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## Sparking Curiosity to Promote Conceptual Understanding of Multiplication and Division

When one of our district math leads, Brennan Jones asked me to brainstorm some ways we could help his staff engage in some professional development around division and incorporate a 3 act math task into the learning, I immediately thought of some contexts where arrays, base ten blocks and area models could be used to help attack this concept. I was thinking about a box of Coca-Cola, jars of peppers and many other ideas prior to settling on the idea of donuts in a box. It was then that I remembered that Graham Fletcher, Mike Wiernicki, YummyMath and others had explored the Krispy Kreme Double Hundred Dozen box of doughnuts in the past (read about it here). However, these innovative mathletes had approached the problem from the angle of multiplication and possibly some extension questions related to proportional reasoning. Brennan and I thought that we might be able to take that idea and make some connections to division.

This **3 act math task** was designed with the idea of accessing student prior knowledge of multiplication and then connecting that knowledge to division including the use of open area models, repeated subtraction and then connecting these to a flexible division algorithm that is considered to be a more accessible algorithm for use by students with varying abilities.

## Curriculum Connections:

### Junior

- Grade 6 – NS1 – solve problems involving the multiplication and division of whole numbers (four-digit by two-digit), using a variety of tools (e.g., concrete materials, drawings, calculators) and strategies (e.g., estimation, algorithms);

### Intermediate

- Grade 7 – NS3 – demonstrate an understanding of rate as a comparison, or ratio, of two measurements with different units (e.g., speed is a rate that compares distance to time and that can be expressed as kilometres per hour);
- Grade 8 – NS3 – identify and describe real-life situations involving two quantities that are directly proportional (e.g., the number of servings and the quantities in a recipe, mass and volume of a substance, circumference and diameter of a circle);
- Grade 9 Applied – NA1 – solve for the unknown value in a proportion, using a variety of methods (e.g., concrete materials, algebraic reasoning, equivalent ratios, constant of proportionality);
- Grade 9 Academic – NA2 – solve problems requiring the manipulation of expressions arising from applications of percent, ratio, rate, and proportion;;

## Act 1: Introduce the Task

Consider showing students the act 1 video from an episode of Fast Food Mania. The original, longer version is here.

Once the video is complete, show students this image.

Then ask students to do a rapid write of what they notice and what they wonder.

Students will then share out their noticings and wonderings while I jot their ideas down on the whiteboard.

Some noticings and wonderings that have come up when I’ve used this task include:

- How many donuts are in that box?
- How heavy is the box?
- Those people look really small.
- Is this a real picture?
- How many calories are in that box?

While we may explore some other wonderings, the first question I intend to address is:

How many donuts are in that box?

With manipulatives and/or paper/whiteboards already out on their tables, I would then give students some time to make a prediction and discuss with their neighbours and/or group.

## Act 2: Reveal Some Information

After students have shared out their predictions, I would show them some information, depending on the group I’m working with.

If I want to use friendly numbers for students who are just beginning to multiply two-digit by two-digit numbers, I might use this image:

If students are ready for more of a challenge (and the actual dimensions of this box of Krispy Kreme doughnuts), I might use this image:

With these dimensions, you will offer students an opportunity to utilize multiplication strategies that might differ from student to student. Depending on where students are relative to concreteness fading, they may choose to concrete materials like base ten blocks; a visual representation such as drawing base ten blocks, an area model, or Japanese multiplication; or a symbolic representation such as partial products or the standard algorithm.

## Act 3, Version 1: Reveal “Friendly Number” Solution

While many students will arrive at the answer of 600 donuts, I’ll then take a moment and show them this image which shows a zoomed in photo of the box that states: “DOUBLE HUNDRED DOZEN”.

Then, I let kids discuss and decide if they want to take some time to update their answers.

## Sequel #1, How Many Layers?

The best part is that the fun has just begun.

If you chose **friendly numbers** for this task, I’ll show students this image:

If you chose the **actual dimensions** (less friendly numbers), I’d show students this image:

Next, I challenge them to determine how many layers of donuts their must be based on what they have done so far. Students already know that one layer is 600 (if friendly numbers were used) or 800 (if the actual dimensions were used), so now they must determine how many layers there are.

So while we know that the double hundred dozen box has 2,400 donuts in it, the number of layers will be different in the friendly number case and in the actual dimensions case.

If students are quite fluent with division and/or the long division algorithm, then the solutions will likely be less than fun to explore. However, if you hit students with this task before introducing long division, it could be a great way to build conceptual understanding using repeated subtraction and open area models:

**Version #1: Friendly Number Animated Gif:**

Or, consider checking out the friendly number animated gif as a silent solution video here.

**Version #2: Actual Dimensions Animated Gif:**

## Sequel #2: Fair Share Amongst 8 Classes

Next, we ask students:

If your school bought this box of doughnuts to split between 8 classes, how many would each class get?

If you used friendly numbers for this task, here are some possible strategies that students might consider including using an open area model and flexible division:

If you chose the actual dimensions in order to raise the floor on this task with less friendly numbers, the extension question will result in the same number of donuts for each of the 8 classes. However, some of the representations may look the same, while others may not.

For example, if a student chooses to use repeated subtraction, flexible division or the long division algorithm, both the process and result may look the same.

However, if the student approached the problem by visually dividing each layer into parts, the process may look significantly different than if a student were to use a similar approach in the friendly numbers case.

In the animated gif below, you’ll see an example where a student might attempt dividing each layer into smaller and smaller pieces until there are enough pieces to fair share with all 8 classes.

## Sequel #3: How Many Calories in the Box?

## Sequel #4: How Many Calories in the Box?

## Download Resources For This Math Task

Click on the button below to grab all the media files for use in your own classroom:

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