Reading Proportions Game

About Fair Share

Fair Share draws a horizontal bar that is divided into slices, one for each choice of food, with a small legend underneath. The question names a total, such as 'Out of 360 people, how many chose sushi?'. You slide to the number of people in the sushi slice. The bar has no percentages, so you must read the share from its length and apply it to the total.

There are three slices on the first levels and up to six on the later ones. On level 1 the totals are small and round, such as 120, 150 or 200, and the shares are round fractions like a half or a quarter. On later levels the shares are arbitrary whole percentages and the totals reach 1,200 people.

How to play

1. Check the total in the question and find the slice in the legend.
2. Estimate how much of the whole bar the slice takes up, as a fraction or percent.
3. Multiply that share by the total, and slide to the number of people.
4. The note after your answer gives the exact percentage of the slice.

A bar is split in slices with a legend. You know how many people there are in total. Slide to how many belong to the slice you are asked about.

How scoring works

The score depends on how far your count is from the real count. A perfect answer gives 100, and the score falls to 0 at a distance of 20 percent of the total on level 1 and about 11 percent of the total on level 10. For a total of 500 on level 10 an error of 28 people still earns about 50 points.

The shares are whole percentages that add up to 100, each at least 6, and the real count is rounded to a whole person. The time limit is 14 seconds on level 1 and 11 seconds on level 10.

What it trains

The game trains proportional reasoning, the ability to turn a part-of-a-whole picture into a number. It is the basic skill behind reading graphs in a news article, a budget chart or a poll result.

It also checks your use of fractions in daily life. A quarter of 360 is 90, a tenth of 1,200 is 120, and being able to work with such fractions quickly helps whenever you meet charts and percentages.

Tips for a higher score

• Compare the slice with the whole bar: is it about a half, a third, a quarter, a fifth or a tenth? These fractions are easy to multiply.
• Use the other slices. If the slice is about twice as wide as the one next to it, and the neighbour is a fifth, then it is about two fifths.
• Estimate the percent first, and then calculate. Ten percent of the total is a good building block: move one decimal place.
• Mind the total. A quarter of 200 is a different number than a quarter of 1,200.
• Check the legend colours twice. Several slices look similar at a glance.

The idea behind it

The choice of a bar rather than a pie in this game is based on research. In 1984 William Cleveland and Robert McGill ranked the accuracy with which people extract numbers from graphs, and found that comparing positions along a common scale is much more accurate than judging angles or areas. A horizontal bar uses length, so you can judge it well.

Understanding proportions is also one of the central parts of numeracy. Surveys by the OECD on adult skills show that a large share of adults find it difficult to apply percentages to quantities, which is why daily practice with graphs is useful.

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