Key ideas
- Before you read a graph, work out the scale. Look at the numbers up the side and count the lines between them. If the numbers go up in 2s with one line between, each line is worth 1.
- To read a value, go to the top of the bar (or the point) and follow a line straight across to the scale.
- A bar graph compares separate things. The bars are the same width, with equal gaps between them.
- A line graph shows how something changes over time. Plot the points, then join them with straight lines using a ruler.
- A compound bar graph puts two (or more) bars side by side for each thing, so you can compare. Use the key to tell them apart.
- A multiple line graph has two or more lines on the same axes, with a key. Where the lines cross, the values are the same.
- Every graph you draw needs a title, labelled axes and an even scale.
- In a pie chart the whole circle is 360° and stands for everyone. A slice's angle as a fraction of 360 tells you the fraction of the total.
- Drawing a pie chart: angle = fraction × 360°. The angles must add up to 360°.
Bar graphs
(a) How many pupils take the bus?
(b) How many more pupils walk than go by car?(2 marks)
(b) How many more pupils walk than go by car?(2 marks)
Work out the scale.The numbers go up in 2sThere is 1 line between each number, so each line is worth 1
In plain EnglishBefore reading anything, look at the numbers up the side. They go up in 2s and there is one line in between, so each line is worth 1.
Read the bus bar.9 pupils take the bus✓1
In plain EnglishGo to the top of the bus bar and follow a line straight across to the scale. It lands on the line between 8 and 10, which is 9.
Find the difference.14 − 6 = 88 more pupils walk✓2
In plain EnglishRead both bars first: 14 walk and 6 go by car. "How many more" means take away.
Draw a bar graph to show this information.(3 marks)
| Sport | Football | Netball | Swimming | Rugby | Dance |
|---|---|---|---|---|---|
| Pupils | 8 | 5 | 7 | 4 | 6 |
Draw the axes and choose a scale.
In plain EnglishThe biggest number is 8, so the scale needs to go up to at least 8. Going up in 2s fits well. Label both axes and give the graph a title.
Draw the bars.Each bar goes up to its number✓3
In plain EnglishDraw each bar up to its number. Swimming is 7, so its bar stops on the line halfway between 6 and 8. All the bars are the same width with equal gaps between them.
Checklist for drawing a graph:
- a title
- both axes labelled, with units if there are any
- an even scale starting at 0
- bars the same width with equal gaps
Line graphs
(a) What was the temperature at 14:00?
(b) Between which two times did the temperature rise the most?(2 marks)
(b) Between which two times did the temperature rise the most?(2 marks)
Read the value at 14:00.15°C✓1
In plain EnglishFind 14:00 along the bottom, go up to the point, then straight across to the scale. Each line is worth 1, so it is 15°C.
Compare the rises.08:00 to 10:00: 9 − 6 = 3°C10:00 to 12:00: 13 − 9 = 4°C12:00 to 14:00: 15 − 13 = 2°CBetween 10:00 and 12:00, since 4 > 3 > 2✓2
In plain EnglishWork out each rise. The biggest rise is where the line is steepest going up. After 14:00 the temperature falls, so we stop there.
Draw a line graph to show the height of the plant.(3 marks)
| Week | 1 | 2 | 3 | 4 | 5 | 6 |
|---|---|---|---|---|---|---|
| Height (cm) | 2 | 4 | 7 | 9 | 12 | 13 |
Plot each point.
In plain EnglishGo along to the week, then up to the height, and mark a small dot or cross. Week 3 is 7 cm: halfway between 6 and 8.
Join the points with straight lines.Points joined with a ruler✓3
In plain EnglishUse a ruler to join each point to the next one. The line shows how the height changes over time.
Checklist for drawing a graph:
- a title
- both axes labelled, with units if there are any
- an even scale starting at 0
- points plotted carefully and joined with straight lines
Compound bar graphs
(a) How many girls chose Art?
(b) How many pupils chose PE altogether?
(c) For which subject was the difference between boys and girls the greatest?(3 marks)
(b) How many pupils chose PE altogether?
(c) For which subject was the difference between boys and girls the greatest?(3 marks)
Use the key.9 girls chose Art✓1
In plain EnglishThe key shows the girls' bars are orange. Find the orange bar for Art and go straight across: 9.
Add both bars.PE: 11 boys + 8 girls= 19 pupils✓2
In plain English"Altogether" means add the boys and the girls.
Compare each pair.Maths: 10 − 8 = 2Art: 9 − 5 = 4PE: 11 − 8 = 3Music: 6 − 4 = 2Art, since 4 is the biggest difference✓3
In plain EnglishTake away the smaller bar from the bigger one for each subject. Art has the biggest gap between its two bars.
Multiple line graphs
(a) In which month did the café sell the same number of each?
(b) How many more hot chocolates than ice creams were sold in February?
(c) Describe how the ice cream sales changed.(3 marks)
(b) How many more hot chocolates than ice creams were sold in February?
(c) Describe how the ice cream sales changed.(3 marks)
Find where the lines cross.April: 22 of each✓1
In plain EnglishWhere the two lines cross, the values are the same. They cross in April, at 22.
Read both lines for February.Hot chocolate: 36, ice cream: 1036 − 10 = 26 more✓2
In plain EnglishEach line on the scale is worth 2. Read both points above February, then take away.
Describe the trend, with numbers.Ice cream sales went up every month,from 6 in January to 38 in June✓3
In plain EnglishSay what happened (went up) and quote numbers from the graph to back it up.
Reading pie charts
60 pupils were asked to name their favourite pet.
(a) How many chose a cat?
(b) How many chose fish?(2 marks)
(a) How many chose a cat?
(b) How many chose fish?(2 marks)
A right angle is a quarter.90° is 14 of 360°14 of 60 = 60 ÷ 4 = 15✓1
In plain EnglishThe whole circle is 360° and stands for all 60 pupils. The cat slice has the right-angle symbol, so it is 90°: a quarter of the circle. So a quarter of the pupils chose a cat.
Use the angle as a fraction of 360.72360 × 60= 12 pupils✓2
In plain EnglishThe fish slice is 72 out of the 360 degrees, so it is 72/360 of the pupils. Multiply by the total, 60.
Check: the numbers for every slice should add up to the total. Here: 20 + 15 + 12 + 13 = 60.
Drawing pie charts
30 pupils chose their favourite fruit. Draw a pie chart to show this information.(3 marks)
| Fruit | Number |
|---|---|
| Apple | 6 |
| Banana | 9 |
| Orange | 5 |
| Grapes | 10 |
| Total | 30 |
Work out each angle.
Angle = fraction × 360°✓1
| Fruit | Number | Angle |
|---|---|---|
| Apple | 6 | 630 × 360 = 72° |
| Banana | 9 | 930 × 360 = 108° |
| Orange | 5 | 530 × 360 = 60° |
| Grapes | 10 | 1030 × 360 = 120° |
| Total | 30 | 360° |
In plain EnglishEach fruit is a fraction of the 30 pupils: 6 out of 30 chose apple, so that is 6/30. Multiply each fraction by 360° to get its angle.
Check the total.72 + 108 + 60 + 120 = 360°
In plain EnglishThe angles must add up to 360°. If they don't, check your working before you start drawing.
Draw and label.Each slice measured from the last line✓2Every slice labelled✓3
In plain EnglishDraw a circle and a line from the centre straight up. Put the protractor on that line and measure 72° clockwise for Apple. Then measure 108° from the new line, and so on. The last slice is whatever is left: check it is 120°.
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Your turn
To draw a graph, tap above each label at the right height, or drag. To draw a pie chart, slide to the angle and press Draw line. Stuck? Tap Need a hint?