This problem solving activity has a number (multiplication and division) focus.
Pizza Place has just two big tables.
If 7 people can sit around each table, how many people can be seated altogether?
Chicken N Chips also has two big tables.
If 16 people altogether are seated, how many people are at each table?
This problem explores doubling and halving.
Doubling is the first step towards finding any multiple of a number and halving is the beginning of work with fractions.
Doubling and halving are inverse operations. Students need opportunities to see and understand that one operation cancels out the other. Multiplying by four and finding quarters is another example of inverse operations.
Much of mathematics is based around inverse operations. They are important, for instance, in solving equations. One side of an equation can be simplified by using an inverse operation to cancel out the operation on that side. For example, if four times something equals 12, then we can undo the ‘four times’ by applying its inverse – ‘taking a quarter’. So a quarter of four times something is the something itself. And a quarter of 12 is 3. The something then, is 3.
This application of inverses occurs at every level including calculus at Levels 7 and 8 (the inverse of differentiation is integration) and things called matrices at university level.
Pizza Place has just two big tables. If 7 people can sit around each table, how many people can be seated altogether?
Chicken N Chips also has two big tables. If 16 people altogether are seated, how many people are at each table?
Vary the number of people.
Pose problems with 4 tables and smaller numbers of people at each. Students might use half and half again, or double and double again strategies for these problems.
Students might use a range of representations to show that Pizza Place can hold 14 people, and that 8 people sit at each of the Chicken N Chips tables.
Printed from https://nzmaths.co.nz/resource/pizzas-and-things at 10:29pm on the 23rd April 2024