# QTS Numeracy Model Solutions – Test 2, Q14

In this series of blog posts, we look at some of the detailed methods that you could use to tackle the questions on the QTS Numeracy practice papers from the **Department for Education**.

In this post, we look at question 14 from practice test 2. The full practice paper can be downloaded **here**.

## The Question

To inform her choice of reading materials, a primary teacher looked at the spread of reading ages in her class. The scatter graph shows the actual age and reading age of 21 pupils in the class.

Circle the pupil who has the greatest difference between their reading age and actual age.

## Worked Solution

This is another **scatter graphs** question that is based on the same graph as we have previously considered in **question 13**. On the scatter graph, you see 21 points, each representing one of the 21 pupils in the class. To answer this question you will need to figure out which of these pupils has the greatest difference between the reading age and the actual age and circle the point that represents that pupil.

You can use the scatter graph to work out the reading age and actual age of each pupil, by reading off values for each point on both of the axes. If you draw a vertical line straight down to the horizontal axis, this will show you the **actual age** of the pupil (as this axis is labelled ‘actual age’). The bold lines labelled 5, 6, 7 and 8 show you the number of years and the thinner lines in between them show you the number of months. In a similar way, you can draw a horizontal line across from the point to the vertical axis to find the reading age (as this axis is labelled ‘reading age’). Again, the bold lines represent the number of years and the thinner lines between them represent the number of months.

For example, the point furthest to the left on the scatter graph represents one of the pupils. You can find the actual age of the pupil by drawing a line down to the horizontal axis. This crosses the axis 9 of the thinner lines after the bold line labelled ‘5’, so the actual age of the pupil is 5 years and 9 months. To find the reading age, draw a horizontal line across to the vertical axis. This crosses the axis 5 of the thinner lines above the bold line labelled ‘6’, so the reading age is 6 years and 5 months.

To work out the **difference** between these values, you need to count up the number of the months from the lower value to the next whole number of years (i.e. 6 years). You need another 3 months to reach from 5 years 9 months to 6 years, and then an additional 5 months to reach 6 years 5 months. This makes a total difference of 8 months.

The question wants to know which of the points has the **greatest difference**. One approach would be to read off values for each of the points one by one, and manually work out the difference. This would take a long time and there is a much quicker approach available.

There is a blue diagonal line that has been drawn from the bottom left to the top right of the scatter graph. Points on this line represent pupils who have **exactly the same** reading age and actual age. Points that are closer to the line have reading ages that are close to each other, and the further away a point is from the line the more difference there will be between the reading age and the actual age.

This means that to answer the question you will need to find the point that is furthest away from the diagonal line. The question does not specify whether the reading age or the actual age should be highest, so you need to look both above the diagonal line (points representing pupils with a higher reading age) and below the diagonal line (points representing pupils with a higher actual age).

When you look at the scatter graph, you can see that all of the points below the line are clustered fairly close to the line, whereas the points above the line are spread a bit further away from the line – and one of these points is clearly a greater distance from the line than any of the others.

This is the point that represents a pupil with an actual age of 6 years 1 month and a reading age of 7 years 7 months.

To find the difference between these ages count up from the lower value (6 years 1 month) to the next whole number of years (7 years), which will be 11 months. You then need to add a further 7 months to reach 7 years 7 months. This makes a total of 11 + 7 = 18 months, or 1 year 6 months. This is a bigger difference than any other pupil, so you need to circle this point.

## Final Answer

*Note – I have made a point of being thorough in this method to ensure you understand each point as we go. When you sit your QTS Skills Tests, your process will probably be much quicker as these techniques start to become second nature to you.*

## Further Help

If you require any further help with questions like this, we have created a selection of resources to provide all the help you need.

**Revision Book** – The Guide to the QTS Skills Tests book devotes a whole chapter to each QTS numeracy topic, with detailed methods, worked examples and plenty of practice questions for you to have a go at. The book also includes three practice tests and fully worked solutions to every question.

**Practice Tests** – Want more practice tests to see how ready you are? Take a look at our selection of practice papers for the QTS numeracy test (including some totally free papers as our gift to you).

**Revision Cheat Sheets** – Our cheat sheets boil down everything you need to know to just the key points on the topic. They are a perfect resource for your last minute revision!