# Reading information and drawing conclusions · Year 10

> Reading information and drawing conclusions, Year 10: Pictograms and more. Explanation, worked examples and free practice for the national curriculum in England.

In Reading information and drawing conclusions (Year 10) you practise 6 skills: Reading a graph · Two graphs on one grid · Step graphs and dot graphs · Pictograms · Pie charts · Changing the subject of a formula.

A graph, a table, a pictogram and a pie chart are different ways of showing the same information. To read a line graph, go up from a value on the horizontal axis to the line, and across to the vertical axis. When two graphs share one grid, the point where they cross is where both have the same value.

In a step graph each band has one price. At the end of a step there is a filled point and an empty point: the filled point belongs to the graph and the empty one does not. A dot graph has no line between its points, because there are no values in between.

In a pictogram every symbol is worth a fixed number, the key, and half a symbol is worth half of it. In a pie chart all the parts together make 100 percent, and to find the amount in one part you multiply the whole by the percent and divide by 100. Building a frequency table from a list: for the list 2, 3, 2, 1, 3, 2, write each value once, 1, 2 and 3, and count how often it appears. The value 1 appears once, 2 appears three times and 3 appears twice. The counts add up to 6, the number of values in the list.

A formula links several quantities. Put in what you know and solve the equation you get to find the missing quantity.

**Tip:** Before you answer, read the title, the axis labels and the key: they tell you what each point or symbol stands for.

## What you learn

### Reading a graph

- Example: Emma left home on her way to school. The graph shows how many metres from home she was at each minute. (A graph of Emma’s distance from home over time: a broken line from minute 0 to minute 10.) How many metres from home was Emma after 4 minutes?
- Answer: 400 m
- Solution: From minute 4 on the horizontal axis, go up to the graph, then across to the vertical axis. You reach 400. Emma was 400 metres from home.

### Two graphs on one grid

- Example: The graphs show the height of two plants, in cm, at the end of each month. The solid line is the first plant and the dashed line is the second plant. (Two graphs of the plants’ heights over eight months) Which was higher in month 6 ?
- Options: The second plant · The first plant
- Answer: The first plant
- Solution: In month 6 the first plant is at 14 and the second plant is at 12 .

### Step graphs and dot graphs

- Example: At a car park you pay for every hour begun: part of an hour costs the same as a whole hour. The graph shows the price by the time parked. (A step graph of the parking price by the number of hours) What is the price for 0.5 hours ?
- Answer: £12
- Solution: On the horizontal axis, 0.5 hours lie under the step at 12 .

### Pictograms

- Example: The pictogram shows how many people visited a nature reserve each year. Each symbol stands for 50,000 visitors, and half a symbol stands for half of that. (A pictogram of the number of visitors each year) How many visitors were there in 2021?
- Answer: 225000
- Solution: In the 2021 row there are 4.5 symbols, that is 4.5 × 50,000 = 225,000 .

### Pie charts

- Example: The pie chart shows how a family shares out its monthly budget. (A pie chart of the monthly budget. The value for transport is not known.) What percent does the transport slice stand for?
- Answer: 70%
- Solution: All the parts together make 100 percent, so the missing part is 100 − 20 − 10 = 70 percent.

### Changing the subject of a formula

- Example: The height of a plant, in cm, after x weeks is y = 2x + 8 . After how many weeks will the plant be 26 cm tall?
- Answer: 9
- Solution: Put in y = 26 : 26 = 2x + 8 , so 2x = 18 and x = 9

The exercises are made by rules and the answers are worked out in code. The topic follows the national curriculum in England: mathematics (key stages 3 and 4).

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