Students will explore multiplication through the array model.

In this task, students will determine the number of krispy kreme donuts in a large box given the dimensions of the box in donuts. Students will be multiplying 2-digit by 2-digit numbers without the use of a calculator. The arrangement of donuts in an array might encourage students to use the array model as a tool for determining the number of donuts. Students should be able to use the image in order to defend their calculations. Meaning, if students use a standard algorithm, are they able to see their partial products within the array?

Some of the big ideas that will likely emerge in this task include:

• Creating and/or flexibly redefining the unit (unitizing).
• Repeated additions can be regrouped.
• The relationship between rows and columns in an array.
• Numbers can be composed and decomposed.
• The distributive property of multiplication over addition and over subtraction.
• The associative property of multiplication.

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 the teacher writes their ideas down on the whiteboard.

Some noticings and wonderings that have come up when I’ve used the task with the huge box of donuts 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?

For those who wish to go there and extend the discussion around the noticing and wondering, you can check out this article that covers the event at which this donut box was prepared for.

While you might explore some other wonderings, the first question we 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 an estimate and discuss with their neighbours and/or group.

Encourage students to consider a number that they know is for sure too low, one that is definitely too high, and ultimately land on their best estimate and share out.

After students have shared out their estimates, give them more information so that they can make their answer more precise.

Now, share out the following image:

Follow up with:

Update your estimate.

How might we convince someone that the quantity you come up with is reasonable without the use of a calculator?

Students have now been given enough information to now make calculations using mental math to improve their estimates based on spatial reasoning and/or prior knowledge.

Students may work with a partner or in a small group to determine the number of donuts in the box, however they will do so without the use of a calculator. They must also be able to convince others of how their answer is true.

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After the consolidation of learning is complete, you might consider sharing the following animation that reveals a few common approaches using some important mathematical models and strategies:

Provide students an opportunity to reflect on their learning by offering this consolidation prompt to be completed independently.

Consolidation Prompt:

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We suggest collecting this consolidation prompt as a ticket out the door in order to determine who heard what and how to plan/modify your lesson for the next day to ensure we meet all students where they are.

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