Rich Learning Tasks

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Pizza

Questions to facilitate the learning

•

Which number did you decide on first? Were you then free to make another number choice or not?

•

How did the numbers of those who liked mushrooms and those who liked extra cheese compare? Why

does that make sense?

•

Which was the most popular topping choice? Why does that make sense?

•

Suppose you wanted more people to like mushrooms than extra cheese—would you have to change both

pieces of information you were given or only one? How would you change it?

•

Are you sure of how many people participated in the survey? Why or why not?

Scaffolding the learning

•

Do more people like pepperoni or extra cheese? How do you know?

•

Do more people like mushrooms or pepperoni? How do you know?

What’s the point of this task?

This task requires students to sort objects into categories meeting given conditions. Students address not

only outcomes/expectations/standards that refer to sorting, but also ones involving number. The references

half

and

twice

informally serve as a prelude to fractional and proportional reasoning as well as to the

inverse relationship between multiplying and dividing. (You might need to define

twice

and

half

or remind

some students that twice means two of something and half means that it would take two to make

a number.)

Because students can choose the numbers with which to work, this task suits students at many levels. They

could choose numbers less than 10 or 20 or greater numbers—whichever is more comfortable. The choice

of using a graph is made optional; again, some students will be ready to and prefer that representation,

whereas others might not.

There can be discussion about why we cannot just add the totals in each category to get a total for how

many people were asked, since someone surveyed could have chosen one, two or all three toppings.

Extending the learning

Students might create new relationships among the three toppings and choose numbers for those new

relationships. For example, it might be that three more people liked pepperoni than extra cheese or maybe

that twice as many liked mushrooms as pepperoni.

Data