Year 6: Solving problems with line graphs
Part of the Year 6 pie charts, line graphs and the mean chapter. Chapter overview · whole chapter on one page
Solving problems with line graphs
Line graphs help you solve problems. Often a question asks you to compare two lines, to find the difference between two points, or to find the total of several points. Read each value carefully before you calculate.
A rise is how much a value goes up between two points. The biggest rise is the pair of neighbouring points where the line goes up the most. To find the average change for each hour, divide the total change by the number of hours. Count the gaps between the times, not the points.
When two lines are on the same graph, they are equal at any point where they meet at the same height.
Key ideas
- Read both values before you compare, and use the same round for both teams.
- The total is found by adding all the values you need.
- A rise is the value at the end minus the value at the start.
- Average change per hour = total change ÷ number of hours.
Key words. The change is how much a value has gone up or down. To find it, take the first value away from the second value.
Method. Read both values, then take the smaller one away from the bigger one.
- Read the first value. Red team is 60 points.Red team = 60
- Read the second value. Blue team is 55 points.Blue team = 55
- Find the difference. Red team is the bigger, so take the smaller value away.60 − 55 = 5
- Write the answer. 5
Check. 55 + 5 = 60, so the difference is right. ✓
Watch out. Subtract the smaller value from the bigger value. The answer is never negative.
Key words. A line graph marks a point for each time or week, and joins the points with straight lines. The scale is the numbers up the side. The lines across the graph are the gridlines.
Method. Read every value you need, then add them all together.
- Read each value you need. Find each point on the graph, one at a time.Round 1 40, Round 2 30, Round 3 45
- Add the values. Add them all together to find the total.40 + 30 + 45 = 115
- Write the answer. This is the total for the Blue team in rounds 1 to 3.115
Check. Add them in a different order to check: the total is still 115. ✓
Watch out. Make sure you have read every point, including the last one.
Key words. The change is how much a value has gone up or down. To find it, take the first value away from the second value.
Method. Divide the total change by the number of hours.
- Find the total change. The water level changed by this much.30 litres
- Write the number of hours. Count the gaps between the times, one hour for each gap.3 hours
- Divide the change by the hours. This gives the average change for each hour.30 ÷ 3 = 10
- Write the answer. This is the change for each hour, on average.10
Check. 10 × 3 = 30, so the answer is right. ✓
Watch out. Count the gaps, not the points. Five points make four gaps between them.
Watch out
Common mistake: counting the gaps wrong. From 08:00 to 12:00 there are four hours, so there are four gaps. Count the gaps, not the points on the graph.
Exercise 12E Practice: solving problems with line graphs
Non-calculatorKey words. The change is how much a value has gone up or down. To find it, take the first value away from the second value.
Method. Read both values, then take the smaller one away from the bigger one.
- Read the first value. Red team is 50 points.Red team = 50
- Read the second value. Blue team is 40 points.Blue team = 40
- Find the difference. Red team is the bigger, so take the smaller value away.50 − 40 = 10
- Write the answer. 10
Check. 40 + 10 = 50, so the difference is right. ✓
Watch out. Subtract the smaller value from the bigger value. The answer is never negative.
Key words. A line graph marks a point for each time or week, and joins the points with straight lines. The scale is the numbers up the side. The lines across the graph are the gridlines.
Method. Compare the two lines at every label, and find the one where they meet.
- Read both lines for each label. Find the values of the two lines at each point.Round 1: 20 and 40; Round 2: 30 and 30; Round 3: 35 and 45; Round 4: 50 and 40; Round 5: 60 and 55
- Find the label where they are equal. Red team and Blue team meet at one point, with the same value.30 = 30
- Write the answer. Round 2
Check. Only Round 2 has the same value for both lines. ✓
Watch out. Two lines can cross without being equal at a label. Check the values, not the picture.
Key words. A line graph marks a point for each time or week, and joins the points with straight lines. The scale is the numbers up the side. The lines across the graph are the gridlines.
Method. Read every value you need, then add them all together.
- Read each value you need. Find each point on the graph, one at a time.Round 1 20, Round 2 30, Round 3 35, Round 4 50, Round 5 60
- Add the values. Add them all together to find the total.20 + 30 + 35 + 50 + 60 = 195
- Write the answer. This is the total for the Red team.195
Check. Add them in a different order to check: the total is still 195. ✓
Watch out. Make sure you have read every point, including the last one.
Key words. A line graph marks a point for each time or week, and joins the points with straight lines. The scale is the numbers up the side. The lines across the graph are the gridlines.
Method. Read every value you need, then add them all together.
- Read each value you need. Find each point on the graph, one at a time.Round 1 40, Round 2 30, Round 3 45, Round 4 40, Round 5 55
- Add the values. Add them all together to find the total.40 + 30 + 45 + 40 + 55 = 210
- Write the answer. This is the total for the Blue team.210
Check. Add them in a different order to check: the total is still 210. ✓
Watch out. Make sure you have read every point, including the last one.
Key words. The change is how much a value has gone up or down. To find it, take the first value away from the second value.
Method. Read both values, then take the smaller one away from the bigger one.
- Read the first value. The Blue team total is 210 points.the Blue team total = 210
- Read the second value. The Red team total is 195 points.the Red team total = 195
- Find the difference. The Blue team total is the bigger, so take the smaller value away.210 − 195 = 15
- Write the answer. 15
Check. 195 + 15 = 210, so the difference is right. ✓
Watch out. Subtract the smaller value from the bigger value. The answer is never negative.
Key words. The change is how much a value has gone up or down. To find it, take the first value away from the second value.
Method. Find the rise between every pair of neighbouring points, then pick the biggest.
- Find the rise between each pair of points. Take each value away from the value after it.Round 1 to Round 2: 10; Round 2 to Round 3: 5; Round 3 to Round 4: 15; Round 4 to Round 5: 10
- Find the biggest rise. Look for the biggest number in the list of rises.biggest rise = 15
- Write the answer. Name the two points the biggest rise is between.Round 3 to Round 4
Check. The rise from Round 3 to Round 4 is 15, and no other rise is as big. ✓
Watch out. Compare the rises, not the values. A high point can have a small rise.
Key words. The change is how much a value has gone up or down. To find it, take the first value away from the second value.
Method. Take the start value away from the end value.
- Read the value at the start. The first point is 08:00.08:00 = 10
- Read the value at the end. The second point is 12:00.12:00 = 50
- Find the rise. Take the start value away from the end value.50 − 10 = 40
- Write the answer. 40
Check. 10 + 40 = 50. ✓
Watch out. Start with the earlier point. A rise is positive, and a fall would be the other way round.
Key words. The change is how much a value has gone up or down. To find it, take the first value away from the second value.
Method. Divide the total change by the number of hours.
- Find the total change. The water level changed by this much.40 litres
- Write the number of hours. Count the gaps between the times, one hour for each gap.4 hours
- Divide the change by the hours. This gives the average change for each hour.40 ÷ 4 = 10
- Write the answer. This is the change for each hour, on average.10
Check. 10 × 4 = 40, so the answer is right. ✓
Watch out. Count the gaps, not the points. Five points make four gaps between them.
Key words. The change is how much a value has gone up or down. To find it, take the first value away from the second value.
Method. Find the rise between every pair of neighbouring points, then pick the biggest.
- Find the rise between each pair of points. Take each value away from the value after it.08:00 to 09:00: 15; 09:00 to 10:00: 10; 10:00 to 11:00: 5; 11:00 to 12:00: 10
- Find the biggest rise. Look for the biggest number in the list of rises.biggest rise = 15
- Write the answer. Name the two points the biggest rise is between.08:00 to 09:00
Check. The rise from 08:00 to 09:00 is 15, and no other rise is as big. ✓
Watch out. Compare the rises, not the values. A high point can have a small rise.
Key words. The change is how much a value has gone up or down. To find it, take the first value away from the second value.
Method. Read both values, then take the smaller one away from the bigger one.
- Read the first value. The Blue team is 45 points.the Blue team = 45
- Read the second value. The Red team is 35 points.the Red team = 35
- Find the difference. The Blue team is the bigger, so take the smaller value away.45 − 35 = 10
- Write the answer. 10
Check. 35 + 10 = 45, so the difference is right. ✓
Watch out. Subtract the smaller value from the bigger value. The answer is never negative.
Key words. A line graph marks a point for each time or week, and joins the points with straight lines. The scale is the numbers up the side. The lines across the graph are the gridlines.
Method. Count only the rounds where the Red team has more points.
- Compare the two teams in each round. Read both values for every round.Round 1: 20 and 40; Round 2: 30 and 30; Round 3: 35 and 45; Round 4: 50 and 40; Round 5: 60 and 55
- Count the rounds where the Red team scored more. Only count the rounds where the Red team is higher.Round 4, Round 5
- Write the answer. 2
Check. Every round was checked, and the rounds where the other team scored more are not counted. ✓
Watch out. Count the rounds, not the points. Check each round one at a time.
Key words. The change is how much a value has gone up or down. To find it, take the first value away from the second value.
Method. Find the rise between each pair of times, and check whether each rise is the same.
- Find the rises. Take each value away from the value after it.25 − 10 = 15; 35 − 25 = 10; 40 − 35 = 5; 50 − 40 = 10
- Compare the rises. If the water filled at the same speed, every rise would be the same.15, 10, 5, 10 are not all the same
- Decide. So the water did not rise at the same speed each hour.No
Check. The total rise is 40 litres, but the rises for each hour are not equal. ✓
Watch out. An average rate can hide changes. Check the rises between each pair of times.
Watch out
Watch out: a line that goes up is not always going up steadily. Check each pair of neighbouring points before you say a line rises the same amount each time.
Exam tip
Write down each value you read before you calculate. It is easy to mix up two lines on the same graph.