The following examples show how understanding the compare pattern can help students to solve number and measurement problems.
Compare problems involve comparisons (differences). In number, the comparison is between two disjoint sets (groups of objects), in measurement it is between two quantities (for example, lengths).
Comparing sets: Number
There are 18 baboons at the zoo and 25 zookeepers.
How many more zookeepers are there than baboons?
How can students identify that this is a compare problem?
There are two separate groups (baboons and zookeepers), the problem doesn’t involve action (the groups are not being joined or separated), and the problem involves “how many more” (a comparison).
Compare problems can be modelled using two bars:
The model can help students to recognise that there are two ways to find the solution:
- 25 – 18 = ?
- 18 + ? = 25
Comparing quantities: Measurement
Measurements can be (and often are) used to make comparisons. For example, consider the difference in length between these two pencils.
As can be seen from the visual models, this problem is identical in structure to the baboon and zookeeper problem. The difference can be found in two ways:
- measuring each pencil and subtracting one length from the other
- lining the pencils up at one end and working out how much is needed to make the two lengths equivalent.