Today we trialed it with Year 11 middle ability students in a small group intervention sessions to add fractions with different denominators. The question was 1/3 + 4/5.
Firstly, get two different coloured Play Doh of the same amount. Each ball represents 1 whole:
Split the Pay Doh into thirds to eventually represent the 1/3 fraction, and into fifths to represent the 4/5 fraction. This helps students appreciate the fractions are different sizes as the parts of the different fractions are not the same. You can see in the image below the thirds are larger than the fifths:
Take one of the thirds (1/3), and 4 of the fifths (4/5). This is what we need to add together:
But you can see the fractions are different sizes. Firstly, we need to split all of the Play Doh into equal parts so to get them all the same size we split into fifteenths:
Once the thirds have been split into fifteen, we need to divide these fifteen into three groups again; 5 in each group. We need 1/3 of these which is equivalent to 5/15 (see above). The fifths also are split into fifteenths but in this case we need four out of the 5 groups (12/15).
We now have the sum 5/15 + 12/15, and all the balls are the same size, so we can add them together to make 17/15:
You can see we have 12 pink balls of Play Doh, and 5 blue balls of Play Doh. You can also see we have the left over fifteenths at the top. The three pink fifteenths can be swapped with three of the blue fifteenths as they are all the same size, meaning we have used all of the pink fifteenths which represents a whole one:
The answer is then one whole (represented by the pink Play Doh), and leftover we have 2 fifteenths:
This is how using Play Doh 1/3 + 4/5 = 17/15 = 1 1/15! It was great to hear the Year 11 students saying "I think I understand this now" as they could see what was happening with the fractions and gained an appreciation of their different sizes.