Statistics
By the end of this chapter you will be able to
- Read values from a line graph, and find the time or week for a value
- Compare two values on a line graph by finding how much more or less one is than the other
- Solve sum and difference problems using information from a line graph
- Read a table, find its totals, and complete a table with a missing value
- Read a timetable, and work out journey times, durations and times written with am or pm
You should already know
- Reading bar charts and simple tables of data (Year 4, Chapter 11)
- Adding and subtracting, and the 24-hour clock (Year 4, Chapter 8 and Year 5, Chapter 2)
- Hours, minutes and durations (Year 5, Chapter 8)
Where this leads
- Interpreting and constructing pie charts and line graphs, and calculating the mean (Year 6, Chapter 12)
- Using tables, timetables and graphs together in the SATs revision chapter (Year 6, Chapter 13)
National Curriculum for England, Key Stage 2 mathematics, Year 5. Content: Solve comparison, sum and difference problems using information presented in a line graph, Complete, read and interpret information in tables, Read and interpret information in timetables, including journey times and durations.
Exercise P Do you remember?
Non-calculatorMethod. Line up the decimal points, then add the pence and the pounds.
- Write the two amounts one under the other. Line up the decimal points.£3.50 + £2.75
- Add the pence. 50p + 75p = 125p, which is £1 and 25p. Write 25p and carry £1.50p + 75p = 125p
- Add the pounds, including the £1 we carried. Add the carried pound to the pounds.3 + 2 + 1 = 6
- Write the answer. £6.25
Check. £6.25 − £2.75 = £3.50, so the answer is right. ✓
Watch out. Line up the decimal points before you add.
Method. One hour is 60 minutes, so multiply the number of hours by 60.
- Write the number of hours. The question asks about 2 hours.2 hours
- Multiply by 60. Each hour has 60 minutes.2 × 60 = 120
- Write the answer. 120 minutes
Check. 60 + 60 = 120. ✓
Watch out. Do not write 2 hours as 200 minutes. Each hour is 60 minutes.
Method. Use column subtraction. Exchange a ten, hundred or thousand when the top digit is too small.
- Write the numbers one under the other. Line up the digits by place value.4 000 - 1 265
- Subtract the ones, then the tens, then the hundreds. Exchange where needed.4 000 - 1 265 = 2 735
- Write the answer. 2,735
Check. 2,735 + 1,265 = 4,000. ✓
Watch out. Check the answer by adding it back to the number you took away.
Method. Read the two bars, then subtract the smaller number from the bigger one.
- Read the bar for bananas. The bar for bananas reaches 8.8 children
- Read the bar for pears. The bar for pears reaches 3.3 children
- Subtract the smaller value from the bigger one. The difference is how many more.8 − 3 = 5
- Write the answer. 5 more children
Check. 3 + 5 = 8, so the difference is right. ✓
Watch out. Read the scale carefully: each square on the scale is one child.
Method. Count forwards on the 24-hour clock. Add 3 to the hours.
- Write the starting time. The time starts at 14:30.14:30
- Add 3 hours. Three hours later, the hour is 3 more. The minutes stay the same.14 + 3 = 17
- Write the answer. 17:30
Check. Three hours before 17:30 is 14:30. ✓
Watch out. The minutes do not change when you add whole hours.
Reading a line graph
A line graph shows how something changes over time. A point is marked for each time or week, and a line joins the points. You can see at a glance whether the value goes up, goes down or stays the same.
Before you read any value, look at three things: the title, the axis along the bottom (the time, the week or the day) and the scale up the side (the value, with its units).
To read a value: find the time or week along the bottom, go up to the line, then go across to the scale.
Key ideas
- Read the title, the axis and the scale before you read any value.
- To read a value: go along the bottom, up to the line, then across to the scale.
- To find the time for a value: start on the scale and work back to the bottom.
- A line that goes up means the value is increasing. A flat line means no change.
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 12:00 along the bottom of the graph. The bottom of the graph shows the time.12:00
- Go up from 12:00 to the Temperature 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 12 °C
- Write the answer. 12 °C
Check. The point sits on a gridline, so the reading is exact. ✓
Watch out. Each gridline is worth 2 °C, 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. Start at the value on the scale, go across to the line, then down to the time or week.
- Find 14 °C on the scale. The scale on the side tells you the height of each gridline.14 °C
- Go across to the Temperature line. Find the point at that height on the line.across to the point
- Go down to the bottom of the graph. The time or week under the point is the answer.down to 13:00
- Write the answer. 13:00
Check. Read 13:00 again and the value there is 14 °C. ✓
Watch out. Start from the scale, not from the bottom of the graph.
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 Week 3 along the bottom of the graph. The bottom of the graph shows the week.Week 3
- Go up from Week 3 to the Leo's plant 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 14 cm
- Write the answer. 14 cm
Check. The point sits on a gridline, so the reading is exact. ✓
Watch out. Each gridline is worth 2 cm, so count the gridlines carefully.
Watch out
Watch out: read the value at a point. The line between two points shows the change, but it does not give an exact value for a time between them. Also count the gridlines, because a label may be shown only on every second gridline.
Exercise 11A Reading values 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 Temperature 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 10 °C
- Write the answer. 10 °C
Check. The point sits on a gridline, so the reading is exact. ✓
Watch out. Each gridline is worth 2 °C, 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 09:00 along the bottom of the graph. The bottom of the graph shows the time.09:00
- Go up from 09:00 to the Temperature 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 6 °C
- Write the answer. 6 °C
Check. The point sits on a gridline, so the reading is exact. ✓
Watch out. Each gridline is worth 2 °C, 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 15:00 along the bottom of the graph. The bottom of the graph shows the time.15:00
- Go up from 15:00 to the Temperature 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 10 °C
- Write the answer. 10 °C
Check. The point sits on a gridline, so the reading is exact. ✓
Watch out. Each gridline is worth 2 °C, 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. Look for the highest point, then read along to the bottom.
- Find the highest point on the line. That point has the greatest value on the scale.highest point = 14 °C
- Go down from that point to the bottom of the graph. The time or week under the point is the answer.down to 13:00
- Write the answer. 13:00
Check. Every other point is lower than 14 °C. ✓
Watch out. Look at the height of the point, not the last point on the graph.
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. Start at the value on the scale, go across to the line, then down to the time or week.
- Find 12 °C on the scale. The scale on the side tells you the height of each gridline.12 °C
- Go across to the Temperature line. Find the point at that height on the line.across to the point
- Go down to the bottom of the graph. The time or week under the point is the answer.down to 12:00
- Write the answer. 12:00
Check. Read 12:00 again and the value there is 12 °C. ✓
Watch out. Start from the scale, not from the bottom of the graph.
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 Week 4 along the bottom of the graph. The bottom of the graph shows the week.Week 4
- Go up from Week 4 to the Aisha's plant 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 18 cm
- Write the answer. 18 cm
Check. The point sits on a gridline, so the reading is exact. ✓
Watch out. Each gridline is worth 2 cm, 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 Week 6 along the bottom of the graph. The bottom of the graph shows the week.Week 6
- Go up from Week 6 to the Leo's plant 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 24 cm
- Write the answer. 24 cm
Check. The point sits on a gridline, so the reading is exact. ✓
Watch out. Each gridline is worth 2 cm, 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. Start at the value on the scale, go across to the line, then down to the time or week.
- Find 14 cm on the scale. The scale on the side tells you the height of each gridline.14 cm
- Go across to the Leo's plant line. Find the point at that height on the line.across to the point
- Go down to the bottom of the graph. The time or week under the point is the answer.down to Week 3
- Write the answer. Week 3
Check. Read Week 3 again and the value there is 14 cm. ✓
Watch out. Start from the scale, not from the bottom of the graph.
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 Thursday along the bottom of the graph. The bottom of the graph shows the day.Thursday
- Go up from Thursday to the Steps 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 9,000 steps
- Write the answer. 9,000 steps
Check. The point sits on a gridline, so the reading is exact. ✓
Watch out. Each gridline is worth 1,000 steps, 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. Look for the lowest point, then read along to the bottom.
- Find the lowest point on the line. That point has the smallest value on the scale.lowest point = 5,000 steps
- Go down from that point to the bottom of the graph. The time or week under the point is the answer.down to Wednesday
- Write the answer. Wednesday
Check. Every other point is higher than 5,000 steps. ✓
Watch out. Look at the height of the point, not the last point on the graph.
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 10:00 along the bottom of the graph. The bottom of the graph shows the time.10:00
- Go up from 10:00 to the Temperature 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 8 °C
- Write the answer. 8 °C
Check. The point sits on a gridline, so the reading is exact. ✓
Watch out. Each gridline is worth 2 °C, 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 Temperature 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 14 °C
- Write the answer. 14 °C
Check. The point sits on a gridline, so the reading is exact. ✓
Watch out. Each gridline is worth 2 °C, 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 15:00 along the bottom of the graph. The bottom of the graph shows the time.15:00
- Go up from 15:00 to the Temperature 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 10 °C
- Write the answer. 10 °C
Check. The point sits on a gridline, so the reading is exact. ✓
Watch out. Each gridline is worth 2 °C, 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 Week 2 along the bottom of the graph. The bottom of the graph shows the week.Week 2
- Go up from Week 2 to the Aisha's plant 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 8 cm
- Write the answer. 8 cm
Check. The point sits on a gridline, so the reading is exact. ✓
Watch out. Each gridline is worth 2 cm, 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 Week 2 along the bottom of the graph. The bottom of the graph shows the week.Week 2
- Go up from Week 2 to the Leo's plant 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 6 cm
- Write the answer. 6 cm
Check. The point sits on a gridline, so the reading is exact. ✓
Watch out. Each gridline is worth 2 cm, 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 Week 5 along the bottom of the graph. The bottom of the graph shows the week.Week 5
- Go up from Week 5 to the Leo's plant 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 16 cm
- Write the answer. 16 cm
Check. The point sits on a gridline, so the reading is exact. ✓
Watch out. Each gridline is worth 2 cm, so count the gridlines carefully.
Method. Find the two plants in Week 3 and Week 4, then compare the heights.
- Read Aisha's plant in Week 4. Go up from Week 4 to the top line of the plant graph.18 cm
- Read Leo's plant in Week 4. Do the same for Leo's plant.16 cm
- Compare the two heights. The taller plant has the bigger height.18 cm is more than 16 cm, so Aisha's plant is taller
- Write the answer. No, Sam is not right. In Week 4 Aisha's plant was taller.
Check. 16 cm + 2 cm = 18 cm, so Aisha's plant was 2 cm taller. ✓
Watch out. Read both lines in the same week before you say which plant is taller.
Method. Read the steps for each day in order, then check whether each day goes up from the day before.
- Read the steps for Monday to Wednesday. Go up from each day to the line.Monday 6,000, Tuesday 8,000, Wednesday 5,000
- Compare Tuesday with Wednesday. A line that goes down shows a fall.8,000 is more than 5,000, so the steps fell
- Decide. The steps did not go up every day, so the statement is not true.No
Check. Monday to Tuesday goes up, but Tuesday to Wednesday goes down. ✓
Watch out. A line that goes up and then down is not steadily rising. Check every pair of days.
Comparing two values on a line graph
A comparison problem asks how much more or how much less one value is than another. Read both values from the graph, then subtract the smaller value from the bigger one.
When a graph has two lines, compare the two points at the same time or week. Look at the key to see which line is which.
Key ideas
- A comparison asks how much more or how much less: subtract to find the difference.
- Compare the two lines at the same time or week, then say which value is bigger.
- Read the key before you read the graph, so you know which line belongs to which name.
- The difference is always found by taking the smaller value away from the bigger one.
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 Aisha's plant in Week 4. Find the point on the line and read across to the scale.18 cm
- Read the value for Leo's plant in Week 4. Do the same for the second point.16 cm
- Subtract the smaller value from the bigger value. The difference tells you how much more one value is than the other.18 − 16 = 2
- Write the answer. 2 cm
Check. 16 + 2 = 18, 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.14 °C
- Read the value for 09:00. Do the same for the second point.6 °C
- Subtract the smaller value from the bigger value. The difference tells you how much more one value is than the other.14 − 6 = 8
- Write the answer. 8 °C
Check. 6 + 8 = 14, 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 Saturday. Find the point on the line and read across to the scale.11,000 steps
- Read the value for Wednesday. Do the same for the second point.5,000 steps
- Subtract the smaller value from the bigger value. The difference tells you how much more one value is than the other.11,000 − 5,000 = 6,000
- Write the answer. 6,000 steps
Check. 5,000 + 6,000 = 11,000, so the difference is right. ✓
Watch out. Always subtract the smaller value from the bigger one, so the answer is not negative.
Watch out
Watch out: the bigger value goes first in your subtraction, so the answer is never negative. Also check that you have compared the same week on both lines, not two different weeks.
Exercise 11B Comparing values on a line graph
Non-calculatorKey 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 Leo's plant in Week 3. Find the point on the line and read across to the scale.14 cm
- Read the value for Aisha's plant in Week 3. Do the same for the second point.12 cm
- Subtract the smaller value from the bigger value. The difference tells you how much more one value is than the other.14 − 12 = 2
- Write the answer. 2 cm
Check. 12 + 2 = 14, 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 Aisha's plant in Week 6. Find the point on the line and read across to the scale.26 cm
- Read the value for Leo's plant in Week 6. Do the same for the second point.24 cm
- Subtract the smaller value from the bigger value. The difference tells you how much more one value is than the other.26 − 24 = 2
- Write the answer. 2 cm
Check. 24 + 2 = 26, 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 Aisha's plant in Week 5. Find the point on the line and read across to the scale.22 cm
- Read the value for Leo's plant in Week 5. Do the same for the second point.16 cm
- Subtract the smaller value from the bigger value. The difference tells you how much more one value is than the other.22 − 16 = 6
- Write the answer. 6 cm
Check. 16 + 6 = 22, 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. Work out the gap for every week, then choose the biggest one.
- Find the gap in each week. The gap is the bigger height minus the smaller height.Week 1: 2 cm, Week 2: 2 cm, Week 3: 2 cm, Week 4: 2 cm, Week 5: 6 cm, Week 6: 2 cm
- Find the biggest gap. Only Week 5 has a gap of 6 cm. Every other week has a smaller gap.biggest gap = 6 cm
- Write the answer. Week 5, a gap of 6 cm
Check. In Week 5, 22 − 16 = 6. ✓
Watch out. The gap is always a positive number. Do not say a gap is negative.
Method. Compare the two heights in each week, then count the weeks when Aisha's plant is taller.
- Compare the two plants in each week. Look for the weeks when Aisha's line is higher.Week 1: 4 > 2, Week 2: 8 > 6, Week 3: 12 < 14, Week 4: 18 > 16, Week 5: 22 > 16, Week 6: 26 > 24
- Count the weeks when Aisha was taller. Count only the weeks where her value is the bigger one.1, 2, 4, 5, 6
- Write the answer. 5 weeks
Check. The weeks when Leo was taller are the ones left, so 5 + 1 = 6 weeks. ✓
Watch out. Compare the two plants in the same week. A week is not counted twice.
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.14 °C
- Read the value for 10:00. Do the same for the second point.8 °C
- Subtract the smaller value from the bigger value. The difference tells you how much more one value is than the other.14 − 8 = 6
- Write the answer. 6 °C
Check. 8 + 6 = 14, 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 temperatures, then compare them.
- Read the temperature at 11:00. Go up from 11:00 to the line.10 °C
- Read the temperature at 15:00. Go up from 15:00 to the line.10 °C
- Compare them. If the two values are the same, neither is warmer.10 − 10 = 0
- Write the answer. The two temperatures are the same, so there is no difference.0 °C
Check. The line is at the same height at both times. ✓
Watch out. A difference of 0 means the two values are equal.
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 Friday. Find the point on the line and read across to the scale.7,000 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.7,000 − 6,000 = 1,000
- Write the answer. 1,000 steps
Check. 6,000 + 1,000 = 7,000, 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 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. Start from Wednesday, add 2,000, then find the day with that many steps.
- Read the steps on Wednesday. Go up from Wednesday to the line.5,000 steps
- Add 2,000 steps. We want a day with 2,000 more steps than Wednesday.5,000 + 2,000 = 7,000
- Find 7,000 steps on the scale. Go across from 7,000 to the line, then down to the bottom.the point at 7,000 is on Friday
- Write the answer. Friday
Check. Friday is the only point at 7,000 steps, and 7,000 − 5,000 = 2,000. ✓
Watch out. To find a value that is 2,000 more, add 2,000 to the starting value. Then check the line at that height.
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 Thursday. Find the point on the line and read across to the scale.9,000 steps
- Read the value for Tuesday. Do the same for the second point.8,000 steps
- Subtract the smaller value from the bigger value. The difference tells you how much more one value is than the other.9,000 − 8,000 = 1,000
- Write the answer. 1,000 steps
Check. 8,000 + 1,000 = 9,000, 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 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 Wednesday. Do the same for the second point.5,000 steps
- Subtract the smaller value from the bigger value. The difference tells you how much more one value is than the other.10,000 − 5,000 = 5,000
- Write the answer. 5,000 steps
Check. 5,000 + 5,000 = 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 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 Saturday. Find the point on the line and read across to the scale.11,000 steps
- Read the value for Thursday. Do the same for the second point.9,000 steps
- Subtract the smaller value from the bigger value. The difference tells you how much more one value is than the other.11,000 − 9,000 = 2,000
- Write the answer. 2,000 steps
Check. 9,000 + 2,000 = 11,000, 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 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 difference that Ali is talking about, then check his number.
- Read the temperature at 10:00. Ali is comparing 13:00 with 10:00.8 °C
- Read the temperature at 13:00. Go up from 13:00 to the line.14 °C
- Find the real difference. Subtract the smaller value from the bigger one.14 − 8 = 6
- Compare with Ali's number. Ali said 4, but the difference is 6.6 is not 4
Check. 8 + 6 = 14, so the difference is 6 °C. ✓
Watch out. Check your subtraction by adding the difference to the smaller value.
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 both plants in Week 3 and compare them.
- Read Leo's plant in Week 3. Go up from Week 3 to Leo's line.14 cm
- Read Aisha's plant in Week 3. Go up from Week 3 to Aisha's line.12 cm
- Subtract the smaller value from the bigger one. The difference is how much taller Leo's plant was.14 − 12 = 2
- Write the answer. Yes, Leo is right: 2 cm taller
Check. 12 + 2 = 14, so Leo's plant was 2 cm taller. ✓
Watch out. Read the line for each plant, not the line above or below.
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. Look for a week where the gap is more than 2 cm.
- Look at Week 5. Week 5 is a week where the two lines are far apart.22 cm and 16 cm
- Subtract the smaller value from the bigger one. The gap is the difference.22 − 16 = 6
- Decide. A gap of 6 cm is more than 2 cm, so Aisha is wrong.No
Check. 16 + 6 = 22, so the gap in Week 5 is 6 cm. ✓
Watch out. One week is enough to show a statement is false.
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.
Reading and completing tables
A table puts information in rows and columns. Read across a row to find the information for one item, and down a column for one category. A total adds up a row or a column.
To complete a table, work out the missing number from the total and the numbers you already know. Use the subtraction to find the missing part, or addition to find a total.
Points scored at the sports day.
| Class | Races | Relay | Tug of war | Total points |
|---|---|---|---|---|
| 5A | 14 | 9 | 7 | 30 |
| 5B | 11 | 12 | 8 | 31 |
| 5C | 9 | 10 | 13 | 32 |
| 5D | 12 | 6 | 11 | 29 |
Key ideas
- Read across a row for one item, and down a column for one category.
- A total is the sum of the numbers in its row or column.
- To find a missing number, take the known numbers away from the total.
- Check that the numbers in each row add up to its total.
| Class | Races | Relay | Tug of war | Total points |
|---|---|---|---|---|
| 5A | 14 | 9 | 7 | 30 |
| 5B | 11 | 12 | 8 | 31 |
| 5C | 9 | 10 | 13 | 32 |
| 5D | 12 | 6 | 11 | 29 |
Key words. A table puts information in rows and columns. Read along a row for one item and down a column for one category. A total is the sum of a row or a column.
Method. Read along the row for 5C, then add the three numbers in that row.
- Find the row for 5C. Each row is one class.5C
- Read the three events. The races, relay and tug of war are the three numbers in the row.9 + 10 + 13
- Add the three numbers. The total is the sum of the three events.9 + 10 + 13 = 32
- Write the answer. 32 points
Check. The total column also shows 32 for 5C. ✓
Watch out. Use the numbers in the same row. Do not mix up two classes.
| Day | Lemon sales | Chocolate sales | Total sales |
|---|---|---|---|
| Monday | £36 | £48 | £84 |
| Tuesday | £42 | £39 | £81 |
| Wednesday | £30 | £51 | £81 |
| Thursday | £45 | £44 | £89 |
| Friday | £58 | £62 | £120 |
| Whole week | £211 | £244 | £455 |
Key words. A table puts information in rows and columns. Read along a row for one item and down a column for one category. A total is the sum of a row or a column.
Method. Add all five daily lemon sales, reading down the lemon column.
- Find the lemon column. The lemon sales are in the second column.lemon sales
- Read each day. Read the five numbers from the table.£36, £42, £30, £45, £58
- Add the five numbers. The total for the week is the sum of the column.36 + 42 + 30 + 45 + 58 = 211
- Write the answer. £211
Check. The whole-week row of the table also shows £211. ✓
Watch out. Add the column, not the row. Each row is one day.
| Pet | Number |
|---|---|
| Dogs | 4 |
| Cats | ? |
| Fish | 3 |
| Rabbits | 2 |
| Total | 14 |
Key words. A table puts information in rows and columns. Read along a row for one item and down a column for one category. A total is the sum of a row or a column.
Method. Subtract the known values from the total to find the missing one.
- Look at the total. The total of all the pets is 14.total = 14
- Add the numbers we know. These are the values that are in the table.4 + 3 + 2 = 9
- Take the known total away from the total. The missing number is what is left over.14 − 9 = 5
- Write the answer. Cats = 5
Check. 9 + 5 = 14, so the total is right. ✓
Watch out. A missing value is not a total: work it out from the total and the other values.
Watch out
Watch out: a total at the bottom of a column adds up the numbers above it. Do not add the numbers in the total column when you are asked for the total of one column, and do not mix up rows and columns.
Exercise 11D Reading and completing tables
Non-calculator| Class | Races | Relay | Tug of war | Total points |
|---|---|---|---|---|
| 5A | 14 | 9 | 7 | 30 |
| 5B | 11 | 12 | 8 | 31 |
| 5C | 9 | 10 | 13 | 32 |
| 5D | 12 | 6 | 11 | 29 |
Key words. A table puts information in rows and columns. Read along a row for one item and down a column for one category. A total is the sum of a row or a column.
Method. Find the row for 5D, then read across to the races column.
- Find the row for 5D. Each row is one class.5D
- Find the Races column. The races column has the number of points from the races.Races
- Read the number where they meet. The number in that cell is the answer.12
- Write the answer. 12 points
Check. The table has 12 for 5D in the races column. ✓
Watch out. Use the Races column, not the Total column.
| Class | Races | Relay | Tug of war | Total points |
|---|---|---|---|---|
| 5A | 14 | 9 | 7 | 30 |
| 5B | 11 | 12 | 8 | 31 |
| 5C | 9 | 10 | 13 | 32 |
| 5D | 12 | 6 | 11 | 29 |
Key words. A table puts information in rows and columns. Read along a row for one item and down a column for one category. A total is the sum of a row or a column.
Method. Find the row for 5C, then read across to the relay column.
- Find the row for 5C. Each row is one class.5C
- Find the Relay column. The relay column has the points from the relay.Relay
- Read the number where they meet. The number in that cell is the answer.10
- Write the answer. 10 points
Check. 9 + 10 + 13 = 32 is the total for 5C, so 10 is one of its three events. ✓
Watch out. Read along the row for 5C only.
| Class | Races | Relay | Tug of war | Total points |
|---|---|---|---|---|
| 5A | 14 | 9 | 7 | 30 |
| 5B | 11 | 12 | 8 | 31 |
| 5C | 9 | 10 | 13 | 32 |
| 5D | 12 | 6 | 11 | 29 |
Key words. A table puts information in rows and columns. Read along a row for one item and down a column for one category. A total is the sum of a row or a column.
Method. Find the row for 5A, then read the number in the total column.
- Find the row for 5A. Each row is one class.5A
- Find the Total points column. The last column adds up all three events.Total points
- Read the number. The total is already in the table.30
- Write the answer. 30 points
Check. 14 + 9 + 7 = 30, which matches the table. ✓
Watch out. Read the total column, not one of the events.
| Class | Races | Relay | Tug of war | Total points |
|---|---|---|---|---|
| 5A | 14 | 9 | 7 | 30 |
| 5B | 11 | 12 | 8 | 31 |
| 5C | 9 | 10 | 13 | 32 |
| 5D | 12 | 6 | 11 | 29 |
Key words. A table puts information in rows and columns. Read along a row for one item and down a column for one category. A total is the sum of a row or a column.
Method. Look down the tug of war column for the biggest number.
- Find the tug of war column. Look at the points for the tug of war.Tug of war
- Find the biggest number. 5C has the biggest number, 13.biggest = 13
- Write the answer. 5C
Check. Every other class scored fewer than 13 in the tug of war. ✓
Watch out. Look for the biggest number in one column, not the biggest total.
| Class | Races | Relay | Tug of war | Total points |
|---|---|---|---|---|
| 5A | 14 | 9 | 7 | 30 |
| 5B | 11 | 12 | 8 | 31 |
| 5C | 9 | 10 | 13 | 32 |
| 5D | 12 | 6 | 11 | 29 |
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 two totals, then subtract the smaller one from the bigger one.
- Read the total for 5B. Use the total points column.31
- Read the total for 5D. Use the total points column.29
- Subtract the smaller total from the bigger total. The difference is how many more points 5B scored.31 − 29 = 2
- Write the answer. 2 points
Check. 29 + 2 = 31. ✓
Watch out. Subtract the smaller total from the bigger one.
| Day | Lemon sales | Chocolate sales | Total sales |
|---|---|---|---|
| Monday | £36 | £48 | £84 |
| Tuesday | £42 | £39 | £81 |
| Wednesday | £30 | £51 | £81 |
| Thursday | £45 | £44 | £89 |
| Friday | £58 | £62 | £120 |
| Whole week | £211 | £244 | £455 |
Key words. A table puts information in rows and columns. Read along a row for one item and down a column for one category. A total is the sum of a row or a column.
Method. Read the Thursday row, then read the lemon column.
- Find the Thursday row. Each row is one day.Thursday
- Read the lemon sales. The lemon column is the second column.£45
- Write the answer. £45
Check. £45 is in the Thursday row and the lemon column. ✓
Watch out. Use the lemon column, not the chocolate column.
| Day | Lemon sales | Chocolate sales | Total sales |
|---|---|---|---|
| Monday | £36 | £48 | £84 |
| Tuesday | £42 | £39 | £81 |
| Wednesday | £30 | £51 | £81 |
| Thursday | £45 | £44 | £89 |
| Friday | £58 | £62 | £120 |
| Whole week | £211 | £244 | £455 |
Key words. A table puts information in rows and columns. Read along a row for one item and down a column for one category. A total is the sum of a row or a column.
Method. Add all five daily chocolate sales, reading down the chocolate column.
- Find the chocolate column. Chocolate sales are the third column.chocolate sales
- Read each day. Read the five numbers.£48, £39, £51, £44, £62
- Add the five numbers. The total is the sum of the column.48 + 39 + 51 + 44 + 62 = 244
- Write the answer. £244
Check. The whole-week row also shows £244 for chocolate. ✓
Watch out. Add the column, not the row.
| Day | Lemon sales | Chocolate sales | Total sales |
|---|---|---|---|
| Monday | £36 | £48 | £84 |
| Tuesday | £42 | £39 | £81 |
| Wednesday | £30 | £51 | £81 |
| Thursday | £45 | £44 | £89 |
| Friday | £58 | £62 | £120 |
| Whole week | £211 | £244 | £455 |
Key words. A table puts information in rows and columns. Read along a row for one item and down a column for one category. A total is the sum of a row or a column.
Method. Look down the total sales column for the biggest number.
- Read the total sales for each day. Each day total is the lemon and chocolate sales added together.Monday £84, Tuesday £81, Wednesday £81, Thursday £89, Friday £120
- Find the biggest total. Friday has the biggest total, £120.biggest = £120
- Write the answer. Friday
Check. Friday's total is £58 + £62 = £120. ✓
Watch out. Use the total sales column, not just the lemon column.
| Day | Lemon sales | Chocolate sales | Total sales |
|---|---|---|---|
| Monday | £36 | £48 | £84 |
| Tuesday | £42 | £39 | £81 |
| Wednesday | £30 | £51 | £81 |
| Thursday | £45 | £44 | £89 |
| Friday | £58 | £62 | £120 |
| Whole week | £211 | £244 | £455 |
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 the Wednesday row, then subtract the lemon sales from the chocolate sales.
- Find the Wednesday row. Each row is one day.Wednesday
- Read the two numbers. Chocolate sales are the third column, and lemon sales are the second column.chocolate £51, lemon £30
- Subtract the smaller number from the bigger one. The difference is how many more chocolate sales there were.£51 − £30 = £21
- Write the answer. £21
Check. £30 + £21 = £51. ✓
Watch out. Subtract the lemon sales from the chocolate sales, so the answer is positive.
| Class | Dogs | Cats | Fish | Rabbits | All pets |
|---|---|---|---|---|---|
| 5A | 3 | 5 | 8 | 2 | 18 |
| 5B | 4 | 6 | 3 | 1 | 14 |
| 5C | 2 | 7 | 6 | 4 | 19 |
| 5D | 5 | 4 | 9 | 3 | 21 |
| Whole school | 14 | 22 | 26 | 10 | 72 |
Key words. A table puts information in rows and columns. Read along a row for one item and down a column for one category. A total is the sum of a row or a column.
Method. Read the total cats row for the whole school, from the bottom row of the table.
- Find the bottom row. The bottom row is the total for the whole school.Whole school
- Find the Cats column. It is the third number column.Cats
- Read the number. The total for cats is already added up for you.22
- Write the answer. 22 cats
Check. 5 + 6 + 7 + 4 = 22, which matches the table. ✓
Watch out. Check the total with the four classes.
| Pet | Number |
|---|---|
| Dogs | ? |
| Cats | 6 |
| Fish | 2 |
| Rabbits | 5 |
| Total | 19 |
Key words. A table puts information in rows and columns. Read along a row for one item and down a column for one category. A total is the sum of a row or a column.
Method. Subtract the known values from the total to find the missing one.
- Look at the total. The total of all the pets is 19.total = 19
- Add the numbers we know. These are the values that are in the table.6 + 2 + 5 = 13
- Take the known total away from the total. The missing number is what is left over.19 − 13 = 6
- Write the answer. Dogs = 6
Check. 13 + 6 = 19, so the total is right. ✓
Watch out. A missing value is not a total: work it out from the total and the other values.
| Day | Lemon sales | Chocolate sales | Total sales |
|---|---|---|---|
| Monday | £36 | £48 | £84 |
| Tuesday | £42 | £39 | £81 |
| Wednesday | £30 | £51 | £81 |
| Thursday | £45 | £44 | £89 |
| Friday | £58 | £62 | £120 |
| Whole week | £211 | £244 | £455 |
Key words. A table puts information in rows and columns. Read along a row for one item and down a column for one category. A total is the sum of a row or a column.
Method. Compare the two columns in every row, then pick out the days where lemon is bigger.
- Compare lemon and chocolate on each day. Look for the days when the lemon number is bigger.Monday: 36 vs 48, Tuesday: 42 vs 39, Wednesday: 30 vs 51, Thursday: 45 vs 44, Friday: 58 vs 62
- Pick out the days where lemon is bigger. Lemon is bigger on Tuesday (42 is more than 39) and Thursday (45 is more than 44).Tuesday and Thursday
- Write the answer. Tuesday and Thursday
Check. On Monday, Wednesday and Friday chocolate sales were bigger. ✓
Watch out. Compare the two numbers in the same row.
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. Work out the difference between chocolate and lemon on each day, then pick the biggest.
- Find the difference on each day. Subtract lemon from chocolate in each row.Monday: 48 − 36 = 12, Tuesday: 39 − 42 = -3, Wednesday: 51 − 30 = 21, Thursday: 44 − 45 = -1, Friday: 62 − 58 = 4
- Find the biggest difference. Wednesday has the biggest difference, 21.biggest = 21
- Write the answer. Wednesday
Check. The other days have differences of 12, -3, -1, 4. ✓
Watch out. A negative difference means lemon was bigger. Look at the size of the difference.
| Class | Dogs | Cats | Fish | Rabbits | All pets |
|---|---|---|---|---|---|
| 5A | 3 | 5 | 8 | 2 | 18 |
| 5B | 4 | 6 | 3 | 1 | 14 |
| 5C | 2 | 7 | 6 | 4 | 19 |
| 5D | 5 | 4 | 9 | 3 | 21 |
| Whole school | 14 | 22 | 26 | 10 | 72 |
Key words. A table puts information in rows and columns. Read along a row for one item and down a column for one category. A total is the sum of a row or a column.
Method. Add the total pets for each class, then check whether each total is more than 15.
- Find the total for each class. Add the four animals in each row.5A 18, 5B 14, 5C 19, 5D 21
- Check each total against 15. Ali says every class has more than 15 pets.5B has 14, which is not more than 15
- Decide. Ali is not right, because one class has fewer than 15 pets.No
Check. 14 is less than 15, so the statement is false. ✓
Watch out. One class with fewer than 15 pets is enough to show the statement is false.
Reading and using timetables
A timetable shows when things happen, such as when a bus leaves and arrives, when a swimming session starts, or when a lesson begins and ends. Each row or column is one bus, one stop or one lesson.
To find when a bus reaches a stop, find the row for that bus, then read across to the column for the stop. To find how long something lasts, subtract the start time from the finish time.
Bus timetable: buses that leave Hilltop.
| Bus | Hilltop | Mill Lane | The Green | Station |
|---|---|---|---|---|
| Bus 1 | 07:40 | 07:46 | 07:55 | 08:02 |
| Bus 2 | 08:10 | 08:16 | 08:25 | 08:32 |
| Bus 3 | 08:40 | 08:46 | 08:55 | 09:02 |
| Bus 4 | 09:20 | 09:26 | 09:35 | 09:42 |
| Bus 5 | 10:00 | 10:06 | 10:15 | 10:22 |
Key ideas
- Find the row for the bus, then read across to the stop.
- Each bus keeps its row: do not mix two buses.
- A duration is the finish time minus the start time, counted in minutes.
- Use the 24-hour clock in timetables, and be ready to write the time with am or pm.
| Bus | Hilltop | Mill Lane | The Green | Station |
|---|---|---|---|---|
| Bus 1 | 07:40 | 07:46 | 07:55 | 08:02 |
| Bus 2 | 08:10 | 08:16 | 08:25 | 08:32 |
| Bus 3 | 08:40 | 08:46 | 08:55 | 09:02 |
| Bus 4 | 09:20 | 09:26 | 09:35 | 09:42 |
| Bus 5 | 10:00 | 10:06 | 10:15 | 10:22 |
Key words. A timetable shows when things happen. A duration is how long something lasts: the finish time minus the start time.
Method. Subtract the start time from the finish time to find how long it lasts.
- Write the start time. The bus journey starts at 08:10.08:10
- Write the finish time. The bus journey finishes at 08:32.08:32
- Find the length of time. Subtract the start time from the finish time, counting in minutes.512 − 490 = 22 minutes
- Write the answer in hours and minutes. 22 minutes is 22 minutes.22 minutes
Check. 490 + 22 = 512, which is the finish time. ✓
Watch out. Do not subtract the hours and the minutes separately when the minutes go past 60.
| Session | Day | Starts | Finishes |
|---|---|---|---|
| Early swim | Monday | 06:45 | 07:45 |
| Lunchtime swim | Tuesday | 12:15 | 13:00 |
| Junior club | Wednesday | 16:30 | 17:45 |
| Family swim | Saturday | 10:30 | 12:00 |
| Adult lengths | Sunday | 08:00 | 09:15 |
Key words. A timetable shows when things happen. A duration is how long something lasts: the finish time minus the start time.
Method. Subtract the start time from the finish time to find how long it lasts.
- Write the start time. The family swim starts at 10:30.10:30
- Write the finish time. The family swim finishes at 12:00.12:00
- Find the length of time. Subtract the start time from the finish time, counting in minutes.720 − 630 = 90 minutes
- Write the answer in hours and minutes. 90 minutes is 1 hour 30 minutes.1 hour 30 minutes
Check. 630 + 90 = 720, which is the finish time. ✓
Watch out. Do not subtract the hours and the minutes separately when the minutes go past 60.
| Lesson | Starts | Ends |
|---|---|---|
| Register | 08:50 | 09:00 |
| Maths | 09:00 | 10:00 |
| Break | 10:00 | 10:20 |
| English | 10:20 | 11:20 |
| Science | 11:20 | 12:05 |
| Lunch | 12:05 | 13:05 |
| Topic | 13:05 | 14:05 |
| Music | 14:05 | 15:00 |
Key words. A timetable shows when things happen. A duration is how long something lasts: the finish time minus the start time.
Method. Subtract the start time from the finish time to find how long it lasts.
- Write the start time. The lessons from maths to topic starts at 09:00.09:00
- Write the finish time. The lessons from maths to topic finishes at 14:05.14:05
- Find the length of time. Subtract the start time from the finish time, counting in minutes.845 − 540 = 305 minutes
- Write the answer in hours and minutes. 305 minutes is 5 hours 5 minutes.5 hours 5 minutes
Check. 540 + 305 = 845, which is the finish time. ✓
Watch out. Do not subtract the hours and the minutes separately when the minutes go past 60.
Watch out
Watch out: do not mix up two buses. Take the time from the row of the bus you are asked about. Also, a time after 12 is still on the same 24-hour clock: 13:05 is 1:05 pm.
Exercise 11E Reading and using timetables
Non-calculator| Bus | Hilltop | Mill Lane | The Green | Station |
|---|---|---|---|---|
| Bus 1 | 07:40 | 07:46 | 07:55 | 08:02 |
| Bus 2 | 08:10 | 08:16 | 08:25 | 08:32 |
| Bus 3 | 08:40 | 08:46 | 08:55 | 09:02 |
| Bus 4 | 09:20 | 09:26 | 09:35 | 09:42 |
| Bus 5 | 10:00 | 10:06 | 10:15 | 10:22 |
Key words. A timetable shows when things happen. A duration is how long something lasts: the finish time minus the start time.
Method. Find the 08:40 bus, read across to Mill Lane, then add 6 minutes.
- Find the 08:40 bus. It leaves Hilltop at 08:40.Bus 3, 08:40
- Read across to Mill Lane. Mill Lane is the second stop.Mill Lane column
- Read the time. The bus takes 6 minutes from Hilltop to Mill Lane.08:40 + 6 minutes = 08:46
- Write the answer. 08:46
Check. 08:40 + 6 minutes = 08:46. ✓
Watch out. Read along the 08:40 row, not the 08:10 row.
| Bus | Hilltop | Mill Lane | The Green | Station |
|---|---|---|---|---|
| Bus 1 | 07:40 | 07:46 | 07:55 | 08:02 |
| Bus 2 | 08:10 | 08:16 | 08:25 | 08:32 |
| Bus 3 | 08:40 | 08:46 | 08:55 | 09:02 |
| Bus 4 | 09:20 | 09:26 | 09:35 | 09:42 |
| Bus 5 | 10:00 | 10:06 | 10:15 | 10:22 |
Key words. A timetable shows when things happen. A duration is how long something lasts: the finish time minus the start time.
Method. Find the bus, then read along to the The Green.
- Find the row for the bus that leaves Hilltop at 09:20. Each row is one bus.Bus 4
- Read across to The Green. Find the column for the stop.The Green
- Read the time where they meet. The time in that box is when the bus reaches the stop.09:35
- Write the answer. 09:35
Check. Start at 09:20 and add 15 minutes: 09:35. ✓
Watch out. Read along the same row for the same bus, so the times belong together.
| Bus | Hilltop | Mill Lane | The Green | Station |
|---|---|---|---|---|
| Bus 1 | 07:40 | 07:46 | 07:55 | 08:02 |
| Bus 2 | 08:10 | 08:16 | 08:25 | 08:32 |
| Bus 3 | 08:40 | 08:46 | 08:55 | 09:02 |
| Bus 4 | 09:20 | 09:26 | 09:35 | 09:42 |
| Bus 5 | 10:00 | 10:06 | 10:15 | 10:22 |
Key words. A timetable shows when things happen. A duration is how long something lasts: the finish time minus the start time.
Method. Find the Station column, then find the buses that arrive by 08:45.
- Read the Station times. Each bus arrives at Station at the time in the last column.07:40 bus 08:02, 08:10 bus 08:32, 08:40 bus 09:02, 09:20 bus 09:42, 10:00 bus 10:22
- Find the buses that arrive by 08:45. Priya needs to arrive by 08:45, so the bus must arrive at or before 08:45.07:40 bus (08:02), 08:10 bus (08:32)
- Choose the latest one. The latest of these buses is the one that leaves Hilltop last.latest = 08:10 bus
- Write the answer. The 08:10 bus, which arrives at 08:32
Check. The 08:40 bus arrives at 09:02, which is after 08:45, so it is too late. ✓
Watch out. The latest bus that is still on time is the best one to catch.
| Bus | Hilltop | Mill Lane | The Green | Station |
|---|---|---|---|---|
| Bus 1 | 07:40 | 07:46 | 07:55 | 08:02 |
| Bus 2 | 08:10 | 08:16 | 08:25 | 08:32 |
| Bus 3 | 08:40 | 08:46 | 08:55 | 09:02 |
| Bus 4 | 09:20 | 09:26 | 09:35 | 09:42 |
| Bus 5 | 10:00 | 10:06 | 10:15 | 10:22 |
Key words. A timetable shows when things happen. A duration is how long something lasts: the finish time minus the start time.
Method. Read the 08:40 bus at Mill Lane and at Station, then find the time between them.
- Read the bus at Mill Lane. Find the 08:40 bus in the Mill Lane column.08:46
- Read the bus at Station. Find the 08:40 bus in the Station column.09:02
- Find the time between them. Subtract the earlier time from the later time, in minutes.542 − 526 = 16 minutes
- Write the answer. 16 minutes
Check. The whole journey from Hilltop is 22 minutes, and 22 − 6 = 16 minutes is the part from Mill Lane. ✓
Watch out. Count only the time from Mill Lane to Station, not from Hilltop.
| Bus | Hilltop | Mill Lane | The Green | Station |
|---|---|---|---|---|
| Bus 1 | 07:40 | 07:46 | 07:55 | 08:02 |
| Bus 2 | 08:10 | 08:16 | 08:25 | 08:32 |
| Bus 3 | 08:40 | 08:46 | 08:55 | 09:02 |
| Bus 4 | 09:20 | 09:26 | 09:35 | 09:42 |
| Bus 5 | 10:00 | 10:06 | 10:15 | 10:22 |
Key words. A timetable shows when things happen. A duration is how long something lasts: the finish time minus the start time.
Method. Find the two departure times from Hilltop, then find the time between them.
- Read the first departure. The 08:10 bus leaves Hilltop at 08:10.08:10
- Read the second departure. The 08:40 bus leaves Hilltop at 08:40.08:40
- Find the difference. Subtract the earlier time from the later time.520 − 490 = 30
- Write the answer. 30 minutes
Check. 08:10 + 30 minutes = 08:40. ✓
Watch out. Count the minutes between the two times, not the hours.
| Bus | Hilltop | Mill Lane | The Green | Station |
|---|---|---|---|---|
| Bus 1 | 07:40 | 07:46 | 07:55 | 08:02 |
| Bus 2 | 08:10 | 08:16 | 08:25 | 08:32 |
| Bus 3 | 08:40 | 08:46 | 08:55 | 09:02 |
| Bus 4 | 09:20 | 09:26 | 09:35 | 09:42 |
| Bus 5 | 10:00 | 10:06 | 10:15 | 10:22 |
Key words. A timetable shows when things happen. A duration is how long something lasts: the finish time minus the start time.
Method. Look down the Station column for 08:32, then read across to the bus name.
- Find 08:32 in the Station column. The bus reaches Station at 08:32.08:32
- Read across to the bus name. The bus name is at the start of the same row.Bus 2
- Check the Hilltop time. That row says the bus leaves Hilltop at 08:10.leaves Hilltop at 08:10
- Write the answer. Bus 2
Check. 08:10 + 22 minutes = 08:32. ✓
Watch out. Find the time in the correct column, then read along to the bus name.
| Session | Day | Starts | Finishes |
|---|---|---|---|
| Early swim | Monday | 06:45 | 07:45 |
| Lunchtime swim | Tuesday | 12:15 | 13:00 |
| Junior club | Wednesday | 16:30 | 17:45 |
| Family swim | Saturday | 10:30 | 12:00 |
| Adult lengths | Sunday | 08:00 | 09:15 |
Key words. A timetable shows when things happen. A duration is how long something lasts: the finish time minus the start time.
Method. Subtract the start time from the finish time to find how long it lasts.
- Write the start time. The lunchtime swim starts at 12:15.12:15
- Write the finish time. The lunchtime swim finishes at 13:00.13:00
- Find the length of time. Subtract the start time from the finish time, counting in minutes.780 − 735 = 45 minutes
- Write the answer in hours and minutes. 45 minutes is 45 minutes.45 minutes
Check. 735 + 45 = 780, which is the finish time. ✓
Watch out. Do not subtract the hours and the minutes separately when the minutes go past 60.
| Session | Day | Starts | Finishes |
|---|---|---|---|
| Early swim | Monday | 06:45 | 07:45 |
| Lunchtime swim | Tuesday | 12:15 | 13:00 |
| Junior club | Wednesday | 16:30 | 17:45 |
| Family swim | Saturday | 10:30 | 12:00 |
| Adult lengths | Sunday | 08:00 | 09:15 |
Key words. A timetable shows when things happen. A duration is how long something lasts: the finish time minus the start time.
Method. Find the length of each session, then add them together.
- Find the Early swim. It starts at 06:45 and finishes at 07:45.60 minutes
- Find the Junior club. It starts at 16:30 and finishes at 17:45.75 minutes
- Add the two lengths. Add the minutes together.60 + 75 = 135 minutes
- Write the answer in hours and minutes. 135 minutes is 2 hours 15 minutes.2 hours 15 minutes
Check. 60 + 75 = 135, and 2 hours is 120 minutes, so 15 more minutes makes 2 hours 15 minutes. ✓
Watch out. Add the minutes, then change the total to hours and minutes.
| Session | Day | Starts | Finishes |
|---|---|---|---|
| Early swim | Monday | 06:45 | 07:45 |
| Lunchtime swim | Tuesday | 12:15 | 13:00 |
| Junior club | Wednesday | 16:30 | 17:45 |
| Family swim | Saturday | 10:30 | 12:00 |
| Adult lengths | Sunday | 08:00 | 09:15 |
Key words. A timetable shows when things happen. A duration is how long something lasts: the finish time minus the start time.
Method. Find the length of every session, then choose the longest.
- Find the length of each session. Subtract the start time from the finish time.Early swim 60 minutes, Lunchtime swim 45 minutes, Junior club 75 minutes, Family swim 90 minutes, Adult lengths 75 minutes
- Choose the longest. Family swim is the longest, at 90 minutes.longest = 90 minutes
- Write the answer. Family swim, 1 hour 30 minutes
Check. 10:30 to 12:00 is 1 hour 30 minutes. ✓
Watch out. Compare the lengths, not the start times.
| Session | Day | Starts | Finishes |
|---|---|---|---|
| Early swim | Monday | 06:45 | 07:45 |
| Lunchtime swim | Tuesday | 12:15 | 13:00 |
| Junior club | Wednesday | 16:30 | 17:45 |
| Family swim | Saturday | 10:30 | 12:00 |
| Adult lengths | Sunday | 08:00 | 09:15 |
Key words. A timetable shows when things happen. A duration is how long something lasts: the finish time minus the start time.
Method. Change the 12-hour clock: 16:30 is 4:30 in the afternoon, so write pm.
- Write the time in 24-hour form. The Junior club starts at 16:30.16:30
- Take 12 from the hours. Times after 12 noon use the afternoon, so take away 12 hours.16 − 12 = 4
- Add am or pm. Times from midday until midnight are pm.4:30 pm
- Write the answer. 4:30 pm
Check. 4:30 pm is 4 and a half hours after 12 noon. ✓
Watch out. Times after 12 noon are pm, and the hour is 12 less than on the 24-hour clock.
Key words. A timetable shows when things happen. A duration is how long something lasts: the finish time minus the start time.
Method. Times before 12 noon are am. Write 08:00 as a 12-hour time.
- Write the time in 24-hour form. The Adult lengths start at 08:00.08:00
- Keep the hour, because it is before 12 noon. Morning times do not change, but drop the 0.8
- Add am. Times before 12 noon are am.8:00 am
- Write the answer. 8:00 am
Check. 8:00 am is in the morning, before midday. ✓
Watch out. Drop the 0 in front of the hour in the 12-hour time.
| Lesson | Starts | Ends |
|---|---|---|
| Register | 08:50 | 09:00 |
| Maths | 09:00 | 10:00 |
| Break | 10:00 | 10:20 |
| English | 10:20 | 11:20 |
| Science | 11:20 | 12:05 |
| Lunch | 12:05 | 13:05 |
| Topic | 13:05 | 14:05 |
| Music | 14:05 | 15:00 |
Key words. A timetable shows when things happen. A duration is how long something lasts: the finish time minus the start time.
Method. Subtract the start time from the finish time to find how long it lasts.
- Write the start time. Break starts at 10:00.10:00
- Write the finish time. Break finishes at 10:20.10:20
- Find the length of time. Subtract the start time from the finish time, counting in minutes.620 − 600 = 20 minutes
- Write the answer in hours and minutes. 20 minutes is 20 minutes.20 minutes
Check. 600 + 20 = 620, which is the finish time. ✓
Watch out. Do not subtract the hours and the minutes separately when the minutes go past 60.
| Lesson | Starts | Ends |
|---|---|---|
| Register | 08:50 | 09:00 |
| Maths | 09:00 | 10:00 |
| Break | 10:00 | 10:20 |
| English | 10:20 | 11:20 |
| Science | 11:20 | 12:05 |
| Lunch | 12:05 | 13:05 |
| Topic | 13:05 | 14:05 |
| Music | 14:05 | 15:00 |
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 how long English lasts, then how long Science lasts, and subtract.
- Find the length of English. English starts at 10:20 and finishes at 11:20.60 minutes
- Find the length of Science. Science starts at 11:20 and finishes at 12:05.45 minutes
- Subtract the shorter time from the longer time. The difference tells you how much longer English is.60 − 45 = 15 minutes
- Write the answer. 15 minutes
Check. 45 + 15 = 60. ✓
Watch out. Subtract the smaller length from the bigger one.
| Lesson | Starts | Ends |
|---|---|---|
| Register | 08:50 | 09:00 |
| Maths | 09:00 | 10:00 |
| Break | 10:00 | 10:20 |
| English | 10:20 | 11:20 |
| Science | 11:20 | 12:05 |
| Lunch | 12:05 | 13:05 |
| Topic | 13:05 | 14:05 |
| Music | 14:05 | 15:00 |
Key words. A timetable shows when things happen. A duration is how long something lasts: the finish time minus the start time.
Method. Find the whole time from Maths to Music, then take away Break and Lunch.
- Find the whole time from the start of Maths to the end of Music. Subtract 09:00 from 15:00.900 − 540 = 360 minutes
- Find the time for Break and Lunch. Break is 20 minutes and Lunch is 60 minutes.20 + 60 = 80 minutes
- Take the breaks away. The time left is the time in lessons.360 − 80 = 280 minutes
- Write the answer in hours and minutes. 280 minutes is 4 hours 40 minutes.4 hours 40 minutes
Check. 4 hours 40 minutes plus 1 hour 20 minutes is 6 hours. ✓
Watch out. Take the breaks away first. Do not forget Lunch, which is the longest break.
Chapter summary
| Skill | Method |
|---|---|
| Read a line graph | Find the time or week along the bottom, go up to the line, then across to the scale. |
| Find a time for a value | Start at the value on the scale, go across to the line, then down to the bottom. |
| Compare two values | Read both values, then subtract the smaller from the bigger one to find how much more. |
| Money between two times | Subtract the earlier reading from the later reading on a running total. |
| Total of several values | Read each value, then add them all together. |
| Complete a table | Use the total and the known values: subtract the known values from the total to find the missing one. |
| Read a table | Read across a row for one item, and down a column for one category. |
| Read a timetable | Find the row for the bus, then read across to the stop. Do not mix up two buses. |
| Duration | Subtract the start time from the finish time, counting in minutes, then write it in hours and minutes. |
| 12-hour time | Times after 12 noon are pm, and times before 12 noon are am. |
Can you…?
- I can read values from a line graph by going along, up and then across to the scale.
- I can find the time or week for a value on a line graph.
- I can solve comparison problems, using the difference between two values on a line graph.
- I can solve sum and difference problems using information from a line graph.
- I can read a row or a column of a table, and find totals.
- I can complete a table by finding a missing value from its total.
- I can read a timetable and find when a bus or a session arrives or ends.
- I can work out how long something lasts, in hours and minutes.
Key terms
- Line graph
- A graph that joins points with lines, to show how a value changes over time.
- Scale
- The numbers up the side of a graph that show the value of each gridline.
- Axis
- A line along the side or bottom of a graph that shows the value or the time.
- Gridline
- A faint line across a graph that helps you read the value.
- Comparison
- Finding how much more or how much less one value is than another.
- Difference
- The amount between two values, found by subtracting the smaller from the bigger.
- Sum
- The total when you add several values together.
- Table
- Information arranged in rows and columns.
- Total
- The sum of a row or a column in a table.
- Timetable
- A list of times that shows when buses, trains or activities happen.
- Duration
- How long something lasts, from the start time to the finish time.
- am and pm
- am is the time before 12 noon, and pm is the time after 12 noon.
Exercise 11Z Check-up (non-calculator)
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. Start at the value on the scale, go across to the line, then down to the time or week.
- Find 10 °C on the scale. The scale on the side tells you the height of each gridline.10 °C
- Go across to the Temperature line. Find the point at that height on the line.across to the point
- Go down to the bottom of the graph. The time or week under the point is the answer.down to 11:00
- Write the answer. 11:00
Check. Read 11:00 again and the value there is 10 °C. ✓
Watch out. Start from the scale, not from the bottom of the graph.
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 Aisha's plant in Week 5. Find the point on the line and read across to the scale.22 cm
- Read the value for Leo's plant in Week 5. Do the same for the second point.16 cm
- Subtract the smaller value from the bigger value. The difference tells you how much more one value is than the other.22 − 16 = 6
- Write the answer. 6 cm
Check. 16 + 6 = 22, 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 11:30. Find the point on the line and read across to the scale.£80
- 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.140 − 80 = 60
- Write the answer. £60
Check. 80 + 60 = 140, 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, Sunday: 10,000 steps
- Add the values. A sum is the total of all the values.6,000 + 10,000 = 16,000
- Write the answer. 16,000 steps
Check. Add the values in a different order and you get 16,000 again. ✓
Watch out. Check that you have added every value in the list, and no others.
| Class | Races | Relay | Tug of war | Total points |
|---|---|---|---|---|
| 5A | 14 | 9 | 7 | 30 |
| 5B | 11 | 12 | 8 | 31 |
| 5C | 9 | 10 | 13 | 32 |
| 5D | 12 | 6 | 11 | 29 |
Key words. A table puts information in rows and columns. Read along a row for one item and down a column for one category. A total is the sum of a row or a column.
Method. Look down the total points column for the biggest number.
- Read the total points for each class. The last column is the total for each class.5A 30, 5B 31, 5C 32, 5D 29
- Find the biggest total. 5C has the biggest total, 32 points.biggest = 32
- Write the answer. 5C
Check. 32 is bigger than every other total in the column. ✓
Watch out. Look at the total points column, not the races or the relay column.
| Day | Lemon sales | Chocolate sales | Total sales |
|---|---|---|---|
| Monday | £36 | £48 | £84 |
| Tuesday | £42 | £39 | £81 |
| Wednesday | £30 | £51 | £81 |
| Thursday | £45 | £44 | £89 |
| Friday | £58 | £62 | £120 |
| Whole week | £211 | £244 | £455 |
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 the whole-week row, then subtract the lemon total from the chocolate total.
- Read the whole-week lemon sales. This is the bottom row of the lemon column.£211
- Read the whole-week chocolate sales. This is the bottom row of the chocolate column.£244
- Subtract the smaller value from the bigger value. The difference is how many more chocolate sales there were.£244 − £211 = £33
- Write the answer. £33
Check. £211 + £33 = £244. ✓
Watch out. Use the whole-week row, not one day.
| Class | Dogs | Cats | Fish | Rabbits | All pets |
|---|---|---|---|---|---|
| 5A | 3 | 5 | 8 | 2 | 18 |
| 5B | 4 | 6 | 3 | 1 | 14 |
| 5C | 2 | 7 | 6 | 4 | 19 |
| 5D | 5 | 4 | 9 | 3 | 21 |
| Whole school | 14 | 22 | 26 | 10 | 72 |
Key words. A table puts information in rows and columns. Read along a row for one item and down a column for one category. A total is the sum of a row or a column.
Method. Read the Rabbits column in the bottom row, which is the total for the whole school.
- Find the Rabbits column. It is the fifth column of the table.Rabbits
- Read the whole-school total. The bottom row adds up all four classes.2+1+4+3 = 10
- Write the answer. 10 rabbits
Check. The four classes have 2, 1, 4, 3 rabbits. ✓
Watch out. Add the four classes to check the total.
| Bus | Hilltop | Mill Lane | The Green | Station |
|---|---|---|---|---|
| Bus 1 | 07:40 | 07:46 | 07:55 | 08:02 |
| Bus 2 | 08:10 | 08:16 | 08:25 | 08:32 |
| Bus 3 | 08:40 | 08:46 | 08:55 | 09:02 |
| Bus 4 | 09:20 | 09:26 | 09:35 | 09:42 |
| Bus 5 | 10:00 | 10:06 | 10:15 | 10:22 |
Key words. A timetable shows when things happen. A duration is how long something lasts: the finish time minus the start time.
Method. Find the bus, then read along to the Station.
- Find the row for the bus that leaves Hilltop at 09:20. Each row is one bus.Bus 4
- Read across to Station. Find the column for the stop.Station
- Read the time where they meet. The time in that box is when the bus reaches the stop.09:42
- Write the answer. 09:42
Check. Start at 09:20 and add 22 minutes: 09:42. ✓
Watch out. Read along the same row for the same bus, so the times belong together.
| Session | Day | Starts | Finishes |
|---|---|---|---|
| Early swim | Monday | 06:45 | 07:45 |
| Lunchtime swim | Tuesday | 12:15 | 13:00 |
| Junior club | Wednesday | 16:30 | 17:45 |
| Family swim | Saturday | 10:30 | 12:00 |
| Adult lengths | Sunday | 08:00 | 09:15 |
Key words. A timetable shows when things happen. A duration is how long something lasts: the finish time minus the start time.
Method. Find the length of each session, then add them together.
- Find the Family swim. It starts at 10:30 and finishes at 12:00.90 minutes
- Find the Adult lengths. It starts at 08:00 and finishes at 09:15.75 minutes
- Add the two lengths. Add the minutes together.90 + 75 = 165 minutes
- Write the answer in hours and minutes. 165 minutes is 2 hours 45 minutes.2 hours 45 minutes
Check. 2 hours is 120 minutes, and 120 + 45 = 165. ✓
Watch out. Change the total minutes into hours and minutes.
| Lesson | Starts | Ends |
|---|---|---|
| Register | 08:50 | 09:00 |
| Maths | 09:00 | 10:00 |
| Break | 10:00 | 10:20 |
| English | 10:20 | 11:20 |
| Science | 11:20 | 12:05 |
| Lunch | 12:05 | 13:05 |
| Topic | 13:05 | 14:05 |
| Music | 14:05 | 15:00 |
Key words. A timetable shows when things happen. A duration is how long something lasts: the finish time minus the start time.
Method. Find the time from the start of Maths to the start of Science.
- Read the start of Maths. Maths starts at 09:00.09:00
- Read the start of Science. Science starts at 11:20.11:20
- Find the time between the two starts. Subtract in minutes.680 − 540 = 140 minutes
- Write the answer in hours and minutes. 140 minutes is 2 hours 20 minutes.2 hours 20 minutes
Check. 2 hours 20 minutes after 09:00 is 11:20. ✓
Watch out. Count from the start of Maths to the start of Science.
Total 24 marks. Allow about 24 minutes.
Exercise 11X SATs-style questions
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 14:00 along the bottom of the graph. The bottom of the graph shows the time.14:00
- Go up from 14:00 to the Temperature 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 12 °C
- Write the answer. 12 °C
Check. The point sits on a gridline, so the reading is exact. ✓
Watch out. Each gridline is worth 2 °C, 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. Look for the highest point, then read along to the bottom.
- Find the highest point on the line. That point has the greatest value on the scale.highest point = 11,000 steps
- Go down from that point to the bottom of the graph. The time or week under the point is the answer.down to Saturday
- Write the answer. Saturday
Check. Every other point is lower than 11,000 steps. ✓
Watch out. Look at the height of the point, not the last point on the graph.
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 Aisha's plant in Week 4. Find the point on the line and read across to the scale.18 cm
- Read the value for Leo's plant in Week 4. Do the same for the second point.16 cm
- Subtract the smaller value from the bigger value. The difference tells you how much more one value is than the other.18 − 16 = 2
- Write the answer. 2 cm
Check. 16 + 2 = 18, 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 11:30. Find the point on the line and read across to the scale.£80
- Read the value for 13:00. Do the same for the second point.£160
- Subtract the smaller value from the bigger value. The difference tells you how much more one value is than the other.160 − 80 = 80
- Write the answer. £80
Check. 80 + 80 = 160, so the difference is right. ✓
Watch out. Always subtract the smaller value from the bigger one, so the answer is not negative.
| Class | Races | Relay | Tug of war | Total points |
|---|---|---|---|---|
| 5A | 14 | 9 | 7 | 30 |
| 5B | 11 | 12 | 8 | 31 |
| 5C | 9 | 10 | 13 | 32 |
| 5D | 12 | 6 | 11 | 29 |
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 the total points for 5C and 5D, then subtract.
- Read the total for 5C. Use the total points column.32
- Read the total for 5D. Use the total points column.29
- Subtract the smaller total from the bigger total. The difference is how many more points 5C scored.32 − 29 = 3
- Write the answer. 3 points
Check. 29 + 3 = 32. ✓
Watch out. Subtract the smaller total from the bigger one.
| Day | Lemon sales | Chocolate sales | Total sales |
|---|---|---|---|
| Monday | £36 | £48 | £84 |
| Tuesday | £42 | £39 | £81 |
| Wednesday | £30 | £51 | £81 |
| Thursday | £45 | £44 | £89 |
| Friday | £58 | £62 | £120 |
| Whole week | £211 | £244 | £455 |
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. Work out the difference between the lemon and chocolate sales on each day, then pick the biggest.
- Find the difference on each day. Subtract the smaller number from the bigger one in each row.Monday 12, Tuesday 3, Wednesday 21, Thursday 1, Friday 4
- Find the biggest difference. Wednesday has the biggest difference, £21.biggest = £21
- Write the answer. Wednesday
Check. Lemon sales were £30 and chocolate sales were £51, so the difference is £21. ✓
Watch out. Use the size of the difference, not which column is bigger.
| Session | Day | Starts | Finishes |
|---|---|---|---|
| Early swim | Monday | 06:45 | 07:45 |
| Lunchtime swim | Tuesday | 12:15 | 13:00 |
| Junior club | Wednesday | 16:30 | 17:45 |
| Family swim | Saturday | 10:30 | 12:00 |
| Adult lengths | Sunday | 08:00 | 09:15 |
Key words. A timetable shows when things happen. A duration is how long something lasts: the finish time minus the start time.
Method. Find the length of each session, then add them together.
- Find the Early swim. It starts at 06:45 and finishes at 07:45.60 minutes
- Find the Lunchtime swim. It starts at 12:15 and finishes at 13:00.45 minutes
- Add the two lengths. Add the minutes together.60 + 45 = 105 minutes
- Write the answer in hours and minutes. 105 minutes is 1 hour 45 minutes.1 hour 45 minutes
Check. 60 + 45 = 105, and 60 + 45 = 105. ✓
Watch out. Change the minutes into hours and minutes at the end.
| Bus | Hilltop | Mill Lane | The Green | Station |
|---|---|---|---|---|
| Bus 1 | 07:40 | 07:46 | 07:55 | 08:02 |
| Bus 2 | 08:10 | 08:16 | 08:25 | 08:32 |
| Bus 3 | 08:40 | 08:46 | 08:55 | 09:02 |
| Bus 4 | 09:20 | 09:26 | 09:35 | 09:42 |
| Bus 5 | 10:00 | 10:06 | 10:15 | 10:22 |
Key words. A timetable shows when things happen. A duration is how long something lasts: the finish time minus the start time.
Method. Find the buses that reach Station before 09:00, then choose the latest one.
- Read the Station times. Each bus arrives at Station at the time in the last column.07:40 bus 08:02, 08:10 bus 08:32, 08:40 bus 09:02, 09:20 bus 09:42, 10:00 bus 10:22
- Find the buses that arrive before 09:00. Leo must arrive before 09:00.07:40 bus (08:02), 08:10 bus (08:32)
- Choose the latest of these buses. The 08:10 bus leaves Hilltop last of these buses.latest = 08:10 bus
- Write the answer. The 08:10 bus, which arrives at 08:32
Check. The 08:40 bus reaches Station at 09:02, which is too late. ✓
Watch out. Check the arrival time of every bus, not only the first one.
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. Check each hour of the temperature graph, first from 09:00 to 13:00, then after 13:00.
- Look at the rise from 09:00 to 13:00. Each hour the value goes up.6 → 8 → 10 → 12 → 14
- Look at what happens after 13:00. The line goes down after 13:00.14 → 12 → 10
- Decide. Ruby is right: the temperature rose every hour until 13:00 and then fell.Yes
Check. The line goes up at every point from 09:00 to 13:00, then down. ✓
Watch out. Check each pair of times in the order they happen.
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. Find the total for the whole week, then compare it with the target.
- Read the steps for every day. We need every day from Monday to Sunday.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 seven days. The total is the sum of every value.6,000 + 8,000 + 5,000 + 9,000 + 7,000 + 11,000 + 10,000 = 56,000
- Compare with the target. Her target is 40,000 steps.56,000 − 40,000 = 16,000
- Write the answer. Yes, by 16,000 steps
Check. 40,000 + 16,000 = 56,000. ✓
Watch out. Add all seven days, not just the weekdays.