Year 5: Sums and differences from a line graph
Part of the Year 5 statistics chapter. Chapter overview · whole chapter on one page
Sums and differences from a line graph
Some line graphs show a running total, such as the money raised so far. The line only goes up or stays flat, because the total never goes down.
To find the money raised between two times, read the value at each time and subtract the earlier one from the later one. To find a total of several values, read each value and add them.
Key ideas
- A difference between two times is the later reading minus the earlier reading.
- A total of several values is found by reading each value and adding them.
- A running total never goes down, so the line never falls on this kind of graph.
- Write down each reading before you calculate, so you can check your working.
Key words. A comparison says how much more or how much less one value is than another. The difference is found by subtracting the smaller value from the bigger one.
Method. Read both values, then subtract the smaller one from the bigger one.
- Read the value for 10:30. Find the point on the line and read across to the scale.£20
- Read the value for 11:30. Do the same for the second point.£80
- Subtract the smaller value from the bigger value. The difference tells you how much more one value is than the other.80 − 20 = 60
- Write the answer. £60
Check. 20 + 60 = 80, so the difference is right. ✓
Watch out. Always subtract the smaller value from the bigger one, so the answer is not negative.
Key words. A sum is the total of several values, found by adding them. On a graph or a table, read each value first, then add.
Method. Read each value from the graph, then add them all together.
- Read the value for each time or day. We need every value in the list.Monday: 6,000 steps, Tuesday: 8,000 steps, Wednesday: 5,000 steps
- Add the values. A sum is the total of all the values.6,000 + 8,000 + 5,000 = 19,000
- Write the answer. 19,000 steps
Check. Add the values in a different order and you get 19,000 again. ✓
Watch out. Check that you have added every value in the list, and no others.
Key words. A sum is the total of several values, found by adding them. On a graph or a table, read each value first, then add.
Method. Read both heights for the same week, then add them.
- Read Aisha's plant in Week 3. Go up from the week to the blue line.12 cm
- Read Leo's plant in Week 3. Go up from the same week to the orange line.14 cm
- Add the two heights. The total height is the sum of the two values.12 + 14 = 26
- Write the answer. 26 cm
Check. 26 − 14 = 12, so the total is right. ✓
Watch out. Add the two plants in the same week, not two different weeks.
Watch out
Watch out: for a difference, subtract the earlier value from the later one. For a total, you add. Do not mix the two up: "how much was raised between" means subtract, and "how much was raised altogether" means use the last reading.
Exercise 11C Sums and differences from a line graph
Non-calculatorKey words. A line graph joins points with lines. The scale up the side shows the value of each gridline. The axis along the bottom shows the time, the week or the day.
Method. Find the time or week, go up to the line, then across to the scale.
- Find 11:00 along the bottom of the graph. The bottom of the graph shows the time.11:00
- Go up from 11:00 to the Total raised so far line. The point on the line shows the value at that time or week.up to the point
- Go across to the scale on the side. The scale tells you how big the value is.reads £50
- Write the answer. £50
Check. The point sits on a gridline, so the reading is exact. ✓
Watch out. Each gridline is worth £10, so count the gridlines carefully.
Key words. A line graph joins points with lines. The scale up the side shows the value of each gridline. The axis along the bottom shows the time, the week or the day.
Method. Find the time or week, go up to the line, then across to the scale.
- Find 13:00 along the bottom of the graph. The bottom of the graph shows the time.13:00
- Go up from 13:00 to the Total raised so far line. The point on the line shows the value at that time or week.up to the point
- Go across to the scale on the side. The scale tells you how big the value is.reads £160
- Write the answer. £160
Check. The point sits on a gridline, so the reading is exact. ✓
Watch out. Each gridline is worth £10, so count the gridlines carefully.
Key words. A comparison says how much more or how much less one value is than another. The difference is found by subtracting the smaller value from the bigger one.
Method. Read both values, then subtract the smaller one from the bigger one.
- Read the value for 11:00. Find the point on the line and read across to the scale.£50
- Read the value for 10:00. Do the same for the second point.£0
- Subtract the smaller value from the bigger value. The difference tells you how much more one value is than the other.50 − 0 = 50
- Write the answer. £50
Check. 0 + 50 = 50, so the difference is right. ✓
Watch out. Always subtract the smaller value from the bigger one, so the answer is not negative.
Key words. A comparison says how much more or how much less one value is than another. The difference is found by subtracting the smaller value from the bigger one.
Method. Read both values, then subtract the smaller one from the bigger one.
- Read the value for 12:00. Find the point on the line and read across to the scale.£120
- Read the value for 11:00. Do the same for the second point.£50
- Subtract the smaller value from the bigger value. The difference tells you how much more one value is than the other.120 − 50 = 70
- Write the answer. £70
Check. 50 + 70 = 120, so the difference is right. ✓
Watch out. Always subtract the smaller value from the bigger one, so the answer is not negative.
Key words. A comparison says how much more or how much less one value is than another. The difference is found by subtracting the smaller value from the bigger one.
Method. Read both values, then subtract the smaller one from the bigger one.
- Read the value for 13:00. Find the point on the line and read across to the scale.£160
- Read the value for 12:00. Do the same for the second point.£120
- Subtract the smaller value from the bigger value. The difference tells you how much more one value is than the other.160 − 120 = 40
- Write the answer. £40
Check. 120 + 40 = 160, so the difference is right. ✓
Watch out. Always subtract the smaller value from the bigger one, so the answer is not negative.
Key words. A comparison says how much more or how much less one value is than another. The difference is found by subtracting the smaller value from the bigger one.
Method. Read both values, then subtract the smaller one from the bigger one.
- Read the value for 13:00. Find the point on the line and read across to the scale.£160
- Read the value for 12:30. Do the same for the second point.£140
- Subtract the smaller value from the bigger value. The difference tells you how much more one value is than the other.160 − 140 = 20
- Write the answer. £20
Check. 140 + 20 = 160, so the difference is right. ✓
Watch out. Always subtract the smaller value from the bigger one, so the answer is not negative.
Key words. A sum is the total of several values, found by adding them. On a graph or a table, read each value first, then add.
Method. Work out the amount raised in each half hour, then choose the biggest.
- Find the amount raised in each half hour. Subtract each reading from the reading after it.10:00–10:30: £20, 10:30–11:00: £30, 11:00–11:30: £30, 11:30–12:00: £40, 12:00–12:30: £20, 12:30–13:00: £20
- Find the biggest amount. Only the half hour from 11:30 to 12:00 raised £40. Every other half hour raised less.biggest = £40
- Write the answer. Between 11:30 and 12:00, £40
Check. 120 − 80 = 40, so the amount for 11:30 to 12:00 is right. ✓
Watch out. Compare the amounts raised in each half hour, not the total at each time.
Key words. A sum is the total of several values, found by adding them. On a graph or a table, read each value first, then add.
Method. Read both heights for the same week, then add them.
- Read Aisha's plant in Week 2. Go up from the week to the blue line.8 cm
- Read Leo's plant in Week 2. Go up from the same week to the orange line.6 cm
- Add the two heights. The total height is the sum of the two values.8 + 6 = 14
- Write the answer. 14 cm
Check. 14 − 6 = 8, so the total is right. ✓
Watch out. Add the two plants in the same week, not two different weeks.
Key words. A sum is the total of several values, found by adding them. On a graph or a table, read each value first, then add.
Method. Read each value from the graph, then add them all together.
- Read the value for each time or day. We need every value in the list.Thursday: 9,000 steps, Friday: 7,000 steps, Saturday: 11,000 steps
- Add the values. A sum is the total of all the values.9,000 + 7,000 + 11,000 = 27,000
- Write the answer. 27,000 steps
Check. Add the values in a different order and you get 27,000 again. ✓
Watch out. Check that you have added every value in the list, and no others.
Key words. A comparison says how much more or how much less one value is than another. The difference is found by subtracting the smaller value from the bigger one.
Method. Read both values, then subtract the smaller one from the bigger one.
- Read the value for Sunday. Find the point on the line and read across to the scale.10,000 steps
- Read the value for Monday. Do the same for the second point.6,000 steps
- Subtract the smaller value from the bigger value. The difference tells you how much more one value is than the other.10,000 − 6,000 = 4,000
- Write the answer. 4,000 steps
Check. 6,000 + 4,000 = 10,000, so the difference is right. ✓
Watch out. Always subtract the smaller value from the bigger one, so the answer is not negative.
Key words. A sum is the total of several values, found by adding them. On a graph or a table, read each value first, then add.
Method. Read each value from the graph, then add them all together.
- Read the value for each time or day. We need every value in the list.Monday: 6,000 steps, Tuesday: 8,000 steps, Wednesday: 5,000 steps, Thursday: 9,000 steps, Friday: 7,000 steps, Saturday: 11,000 steps, Sunday: 10,000 steps
- Add the values. A sum is the total of all the values.6,000 + 8,000 + 5,000 + 9,000 + 7,000 + 11,000 + 10,000 = 56,000
- Write the answer. 56,000 steps
Check. Add the values in a different order and you get 56,000 again. ✓
Watch out. Check that you have added every value in the list, and no others.
Key words. A comparison says how much more or how much less one value is than another. The difference is found by subtracting the smaller value from the bigger one.
Method. Find each amount separately, then subtract the smaller amount from the bigger one.
- Find the amount raised from 11:00 to 12:30. Subtract the reading at 11:00 from the reading at 12:30.£140 − £50 = £90
- Find the amount raised from 10:00 to 10:30. Subtract the reading at 10:00 from the reading at 10:30.£20 − £0 = £20
- Find how much more. Subtract the smaller amount from the bigger one.£90 − £20 = £70
- Write the answer. £70
Check. £20 + £70 = £90. ✓
Watch out. Find each amount first, then compare them.
Key words. A comparison says how much more or how much less one value is than another. The difference is found by subtracting the smaller value from the bigger one.
Method. Find the amount raised between 11:00 and 12:30, then compare it with Ruby's number.
- Read the amount at 11:00. Go up from 11:00 to the line.£50
- Read the amount at 12:30. Go up from 12:30 to the line.£140
- Subtract to find the amount raised in that time. The difference is the money raised between the two times.£140 − £50 = £90
- Compare with Ruby's number. Ruby said £100, but the answer is £90.£90 is not £100
Check. £50 + £90 = £140, so the amount is £90. ✓
Watch out. Check each reading on the line, not the labels alone.