Teaching ratio using pizza

Last week Ann ran a three day transition project across Parafield Gardens High School and its feeder primary schools. The teachers involved were open to ideas and sharing in the interests of improving understanding and continuity between primary and high school maths and pedagogy.

Each day, Ann ran a demonstration lesson which the teachers then unpacked with student work samples to guide them. On the third day, Ann took the teachers into a year 7 class to give the students a problematised situation involving ratio. The class teacher was a bit alarmed as she hadn't introduced ratio yet.

“All the better for our purposes,” thought Ann, “...we should see students struggle with the problem!” The following problem is loosely true.

The Problem

Thomas has surveyed the 18 teachers here today to find their pizza preferences.
He says that ham and pineapple, supreme and vegetarian were selected in the following ratio, 3:2:1, and that everyone would be happy if they had three eighths of a pizza. Amanda says she is going to get six pizzas two of each flavour. 

I think this is going to be a poor decision. Please work out what our pizza order should be.

The Sting

We are on a limited budget so need to buy the least number of pizzas. They are $7.50. What should we order to get the best deal?

As it turned out, the students got straight into making sense of the problem, often by drawing, as the following example shows.

Although the students had not been formally introduced to ratio, they made a great job of interpreting what the question meant. In less time than Ann thought possible, the problem was solved and the sting-in-the-tail was required. Here the students brought their own understanding of what would constitute a ‘good deal’ and many of them focused on minimising wastage.