Pizzas And Things
Count groups of two to 6
Use equipment to model and add sets of twos.
Devise and use problem solving strategies (draw a picture, use equipment, guess and check, be systematic).
This is a simple problem about doubling and halving. These are important basic skills as they can be used to estimate numbers of objects and some students use them as the basis for their own non-standard number algorithms.
Doubling is the first step towards finding any multiple of a number and halving is the beginning of work with fractions.
At this stage it is useful to use the two things together as they are inverse operations. This means that one operation will cancel out the other. If students can operate comfortably with inverses then they have a really good understanding of the process involved. Hence it is useful, where possible, to develop the operation and it’s inverse, side by side.
Other examples of inverse operations are multiplying by four and finding quarters. A lot 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. In a simple 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.
Our local Pizza Place has only two tables but they are quite big. If each table holds 7 people, how many people can be seated altogether?
The Chicken N Chips next door to the Pizza Place also has two identical tables. The Chicken N Chips can seat 16 people. How many people can sit at each table?
- Introduce the lesson with some guessing games, for example,
I am a number which is half of 10 what number am I?
I am a number which 4 more than 3 what number am I?
I am a number which is 5 less than 10 what number am I?
- Read the problem to the class.
- Brainstorm for ways to solve the problem.
- As the students work on the problem ask questions that focus on the number strategies that they are using.
Tell me how you got your answer?
Can you think of a way to check that you are correct?
- Share solutions.
This problem can be done in the context of animals (how many legs have two dogs?), people in two cars, or even just guessing games (half the number I’m thinking of is 6, what am I thinking of?).
Extension to the Problem
You could try using more than one table.
Perhaps the students will do this by using blocks to represent the people. Putting down 7 blocks for each table gives 14 blocks altogether. Therefore the Pizza Place can hold 14 people.
Now put 16 blocks down. Share them out equally into two piles. Each pile holds 8 blocks. So the tables at The Chicken N Chips can seat 8 people.