Pizza Pieces

In question 1, the students need to equate ordinary fractions with decimal fractions so that the pieces can be combined to make two whole pizzas in as many ways as possible. They can probably guess some of the combinations by looking at the sizes and shapes of the pieces. For example, the half and 0.5 pieces look as though they would make a whole pizza; likewise the quarter and 0.75 pieces. However, they may find it helpful to make a chart of the amounts of pizza shown so they can work out all the possible combinations

Looking down the chart, there are six different ways a whole pizza can be made from two pieces, or two fractions, of pizza shown in the illustration. The students will need to play around with the fractions to find the ways that a whole pizza can be formed using three or more pieces. For example, the following three pieces could be used: 0.5, 0.4, and 0.1, as could the pieces 1/2, 2/10, and 3/10.
The answer lists all the possible ways of making a whole pizza, including those using four pieces. For question 2, probably the easiest way to make one and a half pizzas using just three pieces is to take one of the pairs that combine to make one pizza (other than the half and 0.5 piece combination itself) and then simply add either the half or 0.5 piece of pizza to this pair. The answer includes a solution that involves
using five pieces.

Answers to Activity

1. All the ways are:
0.5 + 1/2
0.5 + 0.4 + 0.1
0.5 + 2/5 + 0.1
0.5 + 3/10 + 2/10
1/2 + 0.4 + 0.1
1/2 + 2/5 + 0.1
1/2 + 3/10 + 2/10
0.6 + 0.4
0.6 + 2/5
0.6 + 3/10 + 0.1
7/8 + 0.125
0.666 + 1/3
0.75 + 1/4
0.4 + 2/10 + 3/10 + 0.1
0.4 + 2/5 + 2/10
2/5 + 2/10 + 3/10 + 0.1
2. a.–b. Concentrating on ways to make one-half is a good first strategy:
0.5 and 1/2 are equivalent.
2/5 plus 0.1 make one-half.
2/10 plus 3/10 make one-half.
Combining these with the ways to make one whole gives all the possible answers. For example:
0.5 or 1/2 with:
7/8 and 0.125
1/3 and 0.666
0.75 and 1/4
0.4 + 2/10 + 3/10 + 0.1