Fraction of an Amount
Fractions · Year 3–Year 6
Three quarters of twenty, in two steps with counters.
About the fraction of
Counters on the board, a fraction above them, and two presses. The first splits the counters into equal groups and writes the division; the second takes as many groups as the top number says and writes the multiplication. The answer arrives in words with the last press.
The second step is the one a class skips. Ask for three quarters of twenty and the commonest wrong answer is five, which is what you get by dividing by four and stopping. The other one is twenty divided by three, from dividing by the top number instead of the bottom. So the board never shows an answer without both steps, and it opens on the question with the counters in one block.
The counters do not move except when a class would move them. Splitting them into equal groups is a thing you do with real counters, and it is what the first press draws: the same counters, in groups, with a ring round each one.
The amount is always a multiple of the bottom number, because a third of twenty counters is six and two thirds of a counter, which is not something you can put on a board. Changing the number of parts moves the amount to the nearest one that works rather than leaving an impossible question up.
Taking every group is allowed, and worth doing once: four quarters of twenty is twenty, and hearing that said is how a class comes to see that a fraction can be a whole.
How to use it on your whiteboard
- 1Set the amount and the fraction with the toolbar.
- 2Ask the class how many counters will be in each group.
- 3Press Next. The counters go into equal groups and the board writes the division.
- 4Ask how many are in the groups you are taking, then press Next again.
- 5Change one number and the working clears, because it is a new question.
Questions
- Why divide by the bottom number?
- Because the bottom number says how many equal parts the whole is split into. Four quarters means four equal groups, so twenty counters go into four groups of five. The top number then says how many of those groups to take.
- Why can I not take a third of 20?
- Because twenty counters do not split into three equal groups. The amount always stays a multiple of the number of parts, so the question on the board can always be answered with whole counters.
- Is this the same as the bar model?
- It is the same idea with objects rather than lengths, which is where a class meets it first. The bar model tool is the version for word problems, and it is worth moving to once a class can do this one.