Students will determine the number of servings of pizza in two and a half pizzas if each serving is one-fifth pizza per person.

In this task, students will observe servings of pizza being dished out onto a plate. Each person will receive one-fifth of a pizza. This quantity of pizza is considered one serving. If the party host has two and one-half pizzas left, how many servings can they make? In this context, students are dividing two and one-half pizzas by one-fifth pizza/person, this is a context that elicits quotative division.

The purpose is to reveal the number of iterations or parts of the rate (one-fifth pizza/person) in the other quantity of the same unit (two and one-half pizzas). Some of the big ideas that may emerge through this task include:

• There are two types of division;
• In quotative division, both the dividend and the divisor have the same unit (pizza and pizza).
• The divisor is a rate.
• The quotient can represent the number of parts or iterations of the rate.
• Quotative division can be accessed through skip counting, repeated addition, repeated subtraction or multiplication.

Show students the following video:

Then, ask students:

What do you notice?

What do you wonder?

Give students 60 seconds (or more) to do a rapid write on a piece of paper.

Replaying the video and/or leaving a screenshot from the video up can be helpful here.

Then, ask students to share with their neighbours for another 60 seconds.

Finally, allow students to share with the entire group. Be sure to write down these noticings and wonderings on the blackboard/whiteboard, chart paper, or some other means to ensure students know that their voice is acknowledged and appreciated.

Some of the noticing and wondering that may come up includes:

• There is a pizza.
• It looks like a homemade pizza.
• I wonder what brand of frozen pizza that is?
• It is burnt on some of the edges.
• I wonder how many people are going to be eating?
• The person only cut one part of the whole pizza.
• I wonder what fraction of the whole pizza that is?
• I think they are going to cut it into 6 equal strips.
• I wonder how long it took to cook?

At this point, you can answer any wonders that you can cross off the list right away and of course, you can create your own answers for some of these wonders. For example:

• You could explain that this is a specific brand of frozen pizza that you and your own family enjoy.
• You could share that while your family has ___ people in it, this pizza was being served at a birthday party.
• You could share that it took about 24 minutes to cook.
• And so on…

After we have heard students and demonstrated that we value their voice, we can land on the first question we will challenge them with:

What fraction of the pizza was sliced?

We can now ask students to make an estimate (not a guess) as we want them to be as strategic as they can possibly be. This will force them to determine a fraction of the pizza that would be reasonable before determining a more precise answer. Consider asking students to think about an estimate that would be “too low” and an estimate that would be “too high” before asking for their best estimate in order to help them come up with a more reasonable estimate.

It can be helpful to encourage students to draw a model of their thinking by creating a rectangle and partitioning the pizza to show the fraction of pizza that was sliced.

Encourage students to share their estimates, however avoid sharing their justification just yet. We do not want to rob other students of their thinking.

Facilitator Note:

You might consider intentionally omitting the word “fraction” from the prompt if you’d like to keep the initial conversation more open. By doing so, you might hear students describing the amount of pizza using fractional language, decimal language or standard units of measure. All descriptions of the amount are welcome. This could be a great opportunity to discuss equivalence.

Show students the following image:

Students can now see that the first slice that was cut in the spark video represented approximately 1 fifth of the pizza.

Show students this short silent animation clip to reveal how many pizzas are left to be sliced and served.

Prompt students by stating:

If the host intends to serve each guest at the party one-fifth of a pizza, how many servings can be made with the remaining two and one-half pizzas?

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Consider sharing the following reveal video with your students:

Consider leaving the following screenshot of the final frame up for students to reflect on.

Students will complete the following consolidation prompts 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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