After the students in the school eat all 2 400 donuts (each donut containing 200 calories), students will determine how many kilometres they will need to run collectively to burn off the calories.

Students will be asked to divide a six-digit number by a two or three-digit number (depending on their approach). The nature of the context will elicit quotative division, and students will be asked to use proportional reasoning. Students will likely reveal this quotative division quotient through multiplicative thinking, particularly scaling in tandem.

Some of the big ideas that may emerge through today’s task include:

• Numbers can be composed and decomposed;
• Multiplication and division are related;
• The distributive property of multiplication over addition;
• Quotative division can be accessed through skip counting, repeated addition, multiplication and/or repeated subtraction;
• The result of multiplying a number by the base;
• Ratio reasoning through scaling in tandem;
• A composed unit is one way of defining the relationship that exists in a ratio;
• When you divide the two quantities within a ratio, the quotient is a single quantity that represents a rate.

Revisit the context from Day 4, where students were asked to determine the total number of calories in 2 400 donuts. The big idea that will be elicited through today’s math talk is the result of multiplying by the base. Engage students in the following string of related facts and record the products horizontally on the board. The goal of today’s lesson is to confirm that multiplying a number by 1 000  is the same as multiplying the number by 10 three times.

250 x 10

2 500 x 10

250 x 1 000

160 x 10 

1 600 x 10

16 000 x 10

160 x 1000

You might consider phrasing these number sentences with the number of donuts in each box, multiplied by the number of boxes.

For example:

“How many donuts would there be in total if there were 250 donuts in a box and you brought 10 boxes to a party?”

Craft a productive struggle by sharing the following prompt with students:

By eating all 2 400 donuts in the box, you collectively consumed 480 000 calories. In order to burn off those calories, you decide to go for a school wide run. If you can burn 400 calories by running 5 km, how many kilometres will your school population have to run collectively to burn off all 480 000 calories?

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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 reflection as an additional opportunity to engage in the formative assessment process to inform next steps for individual students as well as how the whole class will proceed.

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