Perimeter of rectilinear shapes, time and money problems
By the end of this chapter you will be able to
- Find the perimeter of a rectilinear shape, working out missing sides
- Convert between hours, minutes and seconds
- Find a time or a duration across an hour or a day change
- Solve money problems with pounds and pence
- Choose the operation for a problem and explain the choice
You should already know
- Metric length and mass (chapter 8)
- Adding and subtracting money in pounds and pence (chapter 7)
- Time to the minute (Level 4, chapter 8)
Where this leads
- Area and perimeter of more shapes (a later level)
- Time in days, weeks, months and years (a later level)
Step-by-step practice: maths (Level 5). Small steps, repeated until fluent. Content: Measure and calculate the perimeter of composite rectilinear shapes in centimetres (Y5 paraphrase), Convert hours to minutes and minutes to seconds (Y5 paraphrase; hours, minutes and seconds only), Solve time problems across a change of hour or day (Y4 and Y5 paraphrase), Solve money problems in pounds and pence, including two-step problems with four operations (Y5 paraphrase).
Exercise P Do you remember?
Non-calculatorMethod. Count in fours seven times.
- Count in fours. Each count adds 4.4, 8, 12, 16, 20, 24, 28
- The last number we said is the answer. We counted seven groups of 4.4 × 7 = 28
- Write the answer. This is the total.28
Check. Check: 28 ÷ 4 = 7.
Watch out. Count the fours carefully.
Method. Multiply by 100.
- Use the rule. 1 m is 100 cm.1 m = 100 cm
- Multiply the metres by 100. Each metre has 100 centimetres.2 × 100 = 200
- Write the answer. The unit is centimetres.200 cm
Check. Check: 200 ÷ 100 = 2.
Watch out. A smaller unit gives a bigger number. Multiply.
Method. Add the tenths.
- Line up the decimal points. Add the tenths in the same column.5.5 + 0.3
- Add the tenths. Five tenths plus three tenths is eight tenths.5 + 3 = 8 tenths
- Write the answer. This is the total.5.8
Check. Check: 5.8 - 0.3 = 5.5.
Watch out. Keep the decimal points in a line.
Method. Take away the thousands, then the rest.
- Take away 1,000. Start with the thousands.3,000 - 1,000 = 2,000
- Take away 250. Take away the rest.2,000 - 250 = 1,750
- Write the answer. This is what is left.1,750
Check. Check: 1,750 + 1,250 = 3,000.
Watch out. Check the subtraction by adding back.
Method. Compare the tenths.
- Compare the whole numbers. Both are 0 whole.0 and 0
- Compare the tenths. 5 tenths is more than 4 tenths.5 and 4 tenths
- Choose the greater. 0.5 has more tenths than 0.45.0.5
Check. Check: 0.5 is 50 hundredths and 0.45 is 45 hundredths.
Watch out. Compare the tenths first.
Perimeter of rectilinear shapes
A rectilinear shape has only right-angled corners. The perimeter is the distance all the way round, so add every side.
Some sides are not given. Work them out first: a missing side is a longer side take away a shorter part.
Key ideas
- Perimeter = the sum of all the sides.
- Find each missing side by subtraction first.
- A rectangle: 2 × (length + width).
Method. Work out each missing side, then add all the sides of the shape.
- Find the missing sides. Missing sides come from the sides that are given: take away the shorter part.step = 10 - 4 = 6 cm; right side = 8 - 3 = 5 cm
- List all six sides. The perimeter is the distance all the way round.4 + 5 + 6 + 3 + 10 + 8 cm
- Add the sides. Add all the lengths together.36 cm
- Write the perimeter. Give the answer with the unit cm.36 cm
Check. Check: the perimeter of a shape like this is twice the width plus twice the height: 2 × (10 + 8) = 36 cm.
Watch out. Do not add only the sides you can see. Every side counts, including the ones you worked out.
Method. Work out each missing side, then add all the sides of the shape.
- Find the missing sides. Missing sides come from the sides that are given: take away the shorter part.step = 9 - 5 = 4 cm; right side = 7 - 2 = 5 cm
- List all six sides. The perimeter is the distance all the way round.5 + 5 + 4 + 2 + 9 + 7 cm
- Add the sides. Add all the lengths together.32 cm
- Write the perimeter. Give the answer with the unit cm.32 cm
Check. Check: the perimeter of a shape like this is twice the width plus twice the height: 2 × (9 + 7) = 32 cm.
Watch out. Do not add only the sides you can see. Every side counts, including the ones you worked out.
Method. Add one length and one width, then double the answer.
- Add the length and the width. One long side and one short side.7 + 4 = 11 cm
- Double the answer. A rectangle has two lengths and two widths.2 × 11 = 22 cm
- Write the perimeter. Give the unit cm.22 cm
Check. Check: 7 + 4 + 7 + 4 = 22 cm.
Watch out. Count all four sides. Do not forget the two sides you have not added yet.
Watch out
Watch out. Do not leave out a side. An L-shape has six sides, not four.
Exam tip
Grown-up tip. Ask the child to trace the shape with a finger, saying each side aloud, before adding.
Exercise 9A Practice: perimeter
Non-calculatorMethod. Work out each missing side, then add all the sides of the shape.
- Find the missing sides. Missing sides come from the sides that are given: take away the shorter part.step = 9 - 6 = 3 cm; right side = 7 - 5 = 2 cm
- List all six sides. The perimeter is the distance all the way round.6 + 2 + 3 + 5 + 9 + 7 cm
- Add the sides. Add all the lengths together.32 cm
- Write the perimeter. Give the answer with the unit cm.32 cm
Check. Check: the perimeter of a shape like this is twice the width plus twice the height: 2 × (9 + 7) = 32 cm.
Watch out. Do not add only the sides you can see. Every side counts, including the ones you worked out.
Method. Work out each missing side, then add all the sides of the shape.
- Find the missing sides. Missing sides come from the sides that are given: take away the shorter part.step = 7 - 2 = 5 cm; right side = 5 - 2 = 3 cm
- List all six sides. The perimeter is the distance all the way round.2 + 3 + 5 + 2 + 7 + 5 cm
- Add the sides. Add all the lengths together.24 cm
- Write the perimeter. Give the answer with the unit cm.24 cm
Check. Check: the perimeter of a shape like this is twice the width plus twice the height: 2 × (7 + 5) = 24 cm.
Watch out. Do not add only the sides you can see. Every side counts, including the ones you worked out.
Method. Work out each missing side, then add all the sides of the shape.
- Find the missing sides. Missing sides come from the sides that are given: take away the shorter part.step = 12 - 6 = 6 cm; right side = 8 - 5 = 3 cm
- List all six sides. The perimeter is the distance all the way round.6 + 3 + 6 + 5 + 12 + 8 cm
- Add the sides. Add all the lengths together.40 cm
- Write the perimeter. Give the answer with the unit cm.40 cm
Check. Check: the perimeter of a shape like this is twice the width plus twice the height: 2 × (12 + 8) = 40 cm.
Watch out. Do not add only the sides you can see. Every side counts, including the ones you worked out.
Method. Work out each missing side, then add all the sides of the shape.
- Find the missing sides. Missing sides come from the sides that are given: take away the shorter part.step = 10 - 2 = 8 cm; right side = 4 - 2 = 2 cm
- List all six sides. The perimeter is the distance all the way round.2 + 2 + 8 + 2 + 10 + 4 cm
- Add the sides. Add all the lengths together.28 cm
- Write the perimeter. Give the answer with the unit cm.28 cm
Check. Check: the perimeter of a shape like this is twice the width plus twice the height: 2 × (10 + 4) = 28 cm.
Watch out. Do not add only the sides you can see. Every side counts, including the ones you worked out.
Method. Work out each missing side, then add all the sides of the shape.
- Find the missing sides. Missing sides come from the sides that are given: take away the shorter part.step = 9 - 6 = 3 cm; right side = 6 - 4 = 2 cm
- List all six sides. The perimeter is the distance all the way round.6 + 2 + 3 + 4 + 9 + 6 cm
- Add the sides. Add all the lengths together.30 cm
- Write the perimeter. Give the answer with the unit cm.30 cm
Check. Check: the perimeter of a shape like this is twice the width plus twice the height: 2 × (9 + 6) = 30 cm.
Watch out. Do not add only the sides you can see. Every side counts, including the ones you worked out.
Method. Add one length and one width, then double the answer.
- Add the length and the width. One long side and one short side.15 + 6 = 21 cm
- Double the answer. A rectangle has two lengths and two widths.2 × 21 = 42 cm
- Write the perimeter. Give the unit cm.42 cm
Check. Check: 15 + 6 + 15 + 6 = 42 cm.
Watch out. Count all four sides. Do not forget the two sides you have not added yet.
Method. Work out each missing side, then add all the sides of the shape.
- Find the missing sides. Missing sides come from the sides that are given: take away the shorter part.step = 12 - 6 = 6 cm; right side = 7 - 5 = 2 cm
- List all six sides. The perimeter is the distance all the way round.6 + 2 + 6 + 5 + 12 + 7 cm
- Add the sides. Add all the lengths together.38 cm
- Write the perimeter. Give the answer with the unit cm.38 cm
Check. Check: the perimeter of a shape like this is twice the width plus twice the height: 2 × (12 + 7) = 38 cm.
Watch out. Do not add only the sides you can see. Every side counts, including the ones you worked out.
Method. Work out each missing side, then add all the sides of the shape.
- Find the missing sides. Missing sides come from the sides that are given: take away the shorter part.step = 12 - 8 = 4 cm; right side = 9 - 6 = 3 cm
- List all six sides. The perimeter is the distance all the way round.8 + 3 + 4 + 6 + 12 + 9 cm
- Add the sides. Add all the lengths together.42 cm
- Write the perimeter. Give the answer with the unit cm.42 cm
Check. Check: the perimeter of a shape like this is twice the width plus twice the height: 2 × (12 + 9) = 42 cm.
Watch out. Do not add only the sides you can see. Every side counts, including the ones you worked out.
Method. Add one length and one width, then double the answer.
- Add the length and the width. One long side and one short side.14 + 8 = 22 cm
- Double the answer. A rectangle has two lengths and two widths.2 × 22 = 44 cm
- Write the perimeter. Give the unit cm.44 cm
Check. Check: 14 + 8 + 14 + 8 = 44 cm.
Watch out. Count all four sides. Do not forget the two sides you have not added yet.
Method. Work out each missing side, then add all the sides of the shape.
- Find the missing sides. Missing sides come from the sides that are given: take away the shorter part.step = 9 - 4 = 5 cm; right side = 8 - 6 = 2 cm
- List all six sides. The perimeter is the distance all the way round.4 + 2 + 5 + 6 + 9 + 8 cm
- Add the sides. Add all the lengths together.34 cm
- Write the perimeter. Give the answer with the unit cm.34 cm
Check. Check: the perimeter of a shape like this is twice the width plus twice the height: 2 × (9 + 8) = 34 cm.
Watch out. Do not add only the sides you can see. Every side counts, including the ones you worked out.
Method. Work out each missing side, then add all the sides of the shape.
- Find the missing sides. Missing sides come from the sides that are given: take away the shorter part.step = 5 - 2 = 3 cm; right side = 6 - 2 = 4 cm
- List all six sides. The perimeter is the distance all the way round.2 + 4 + 3 + 2 + 5 + 6 cm
- Add the sides. Add all the lengths together.22 cm
- Write the perimeter. Give the answer with the unit cm.22 cm
Check. Check: the perimeter of a shape like this is twice the width plus twice the height: 2 × (5 + 6) = 22 cm.
Watch out. Do not add only the sides you can see. Every side counts, including the ones you worked out.
Method. Add one length and one width, then double the answer.
- Add the length and the width. One long side and one short side.12 + 9 = 21 cm
- Double the answer. A rectangle has two lengths and two widths.2 × 21 = 42 cm
- Write the perimeter. Give the unit cm.42 cm
Check. Check: 12 + 9 + 12 + 9 = 42 cm.
Watch out. Count all four sides. Do not forget the two sides you have not added yet.
Method. Work out each missing side, then add all the sides of the shape.
- Find the missing sides. Missing sides come from the sides that are given: take away the shorter part.step = 7 - 5 = 2 cm; right side = 6 - 3 = 3 cm
- List all six sides. The perimeter is the distance all the way round.5 + 3 + 2 + 3 + 7 + 6 cm
- Add the sides. Add all the lengths together.26 cm
- Write the perimeter. Give the answer with the unit cm.26 cm
Check. Check: the perimeter of a shape like this is twice the width plus twice the height: 2 × (7 + 6) = 26 cm.
Watch out. Do not add only the sides you can see. Every side counts, including the ones you worked out.
Method. Add one length and one width, then double the answer.
- Add the length and the width. One long side and one short side.11 + 5 = 16 cm
- Double the answer. A rectangle has two lengths and two widths.2 × 16 = 32 cm
- Write the perimeter. Give the unit cm.32 cm
Check. Check: 11 + 5 + 11 + 5 = 32 cm.
Watch out. Count all four sides. Do not forget the two sides you have not added yet.
Method. Add one length and one width, then double the answer.
- Add the length and the width. One long side and one short side.15 + 9 = 24 cm
- Double the answer. A rectangle has two lengths and two widths.2 × 24 = 48 cm
- Write the perimeter. Give the unit cm.48 cm
Check. Check: 15 + 9 + 15 + 9 = 48 cm.
Watch out. Count all four sides. Do not forget the two sides you have not added yet.
Method. Add one length and one width, then double the answer.
- Add the length and the width. One long side and one short side.13 + 6 = 19 cm
- Double the answer. A rectangle has two lengths and two widths.2 × 19 = 38 cm
- Write the perimeter. Give the unit cm.38 cm
Check. Check: 13 + 6 + 13 + 6 = 38 cm.
Watch out. Count all four sides. Do not forget the two sides you have not added yet.
Hours, minutes and seconds
There are 60 minutes in 1 hour and 60 seconds in 1 minute. To change hours to minutes, multiply by 60.
To change minutes into hours and minutes, divide by 60. The remainder is the minutes left over: 95 minutes = 1 h 35 min.
Key ideas
- 1 hour = 60 minutes; 1 minute = 60 seconds.
- Hours to minutes: multiply by 60.
- Minutes to hours: divide by 60; the remainder is minutes.
Method. Multiply the hours by 60 to change them into minutes.
- Use the rule. There are 60 minutes in 1 hour.1 h = 60 min
- Multiply the hours by 60. Each hour has 60 minutes.3 × 60 = 180
- Write the answer. The unit is minutes.180 minutes
Check. Check: 180 ÷ 60 = 3.
Watch out. Going from hours to minutes gives a bigger number. Multiply by 60.
Method. Divide by 60 to find the hours; the remainder is the minutes.
- Share the minutes into groups of 60. Each group of 60 minutes is one hour.95 ÷ 60 = 1 r 35
- Write the hours and the minutes left. The remainder is the minutes that are left over.1 h and 35 min
- Write the answer. Use the units hours and minutes.1 h 35 min
Check. Check: 1 × 60 + 35 = 95.
Watch out. Do not write 1 h 95 min. The minutes must be less than 60.
Method. Divide by 60 to find the minutes; the remainder is the seconds.
- Share the seconds into groups of 60. Each group of 60 seconds is one minute.190 ÷ 60 = 3 r 10
- Write the minutes and the seconds left. The remainder is the seconds.3 min and 10 s
- Write the answer. Use the units minutes and seconds.3 min 10 s
Check. Check: 3 × 60 + 10 = 190.
Watch out. The seconds must be less than 60.
Watch out
Watch out. 95 minutes is 1 h 35 min, not 1 h 95 min. The minutes must be less than 60.
Exam tip
Grown-up tip. Use a clock face: ask how many minutes go round the clock in one hour.
Exercise 9B Practice: hours, minutes and seconds
Non-calculatorMethod. Multiply the minutes by 60 to change them into seconds.
- Use the rule. There are 60 seconds in 1 minute.1 min = 60 s
- Multiply the minutes by 60. Each minute has 60 seconds.6 × 60 = 360
- Write the answer. The unit is seconds.360 seconds
Check. Check: 360 ÷ 60 = 6.
Watch out. Multiply by 60, not by 100.
Method. Divide by 60 to find the minutes; the remainder is the seconds.
- Share the seconds into groups of 60. Each group of 60 seconds is one minute.571 ÷ 60 = 9 r 31
- Write the minutes and the seconds left. The remainder is the seconds.9 min and 31 s
- Write the answer. Use the units minutes and seconds.9 min 31 s
Check. Check: 9 × 60 + 31 = 571.
Watch out. The seconds must be less than 60.
Method. Multiply the hours by 60 to change them into minutes.
- Use the rule. There are 60 minutes in 1 hour.1 h = 60 min
- Multiply the hours by 60. Each hour has 60 minutes.7 × 60 = 420
- Write the answer. The unit is minutes.420 minutes
Check. Check: 420 ÷ 60 = 7.
Watch out. Going from hours to minutes gives a bigger number. Multiply by 60.
Method. Divide by 60 to find the minutes; the remainder is the seconds.
- Share the seconds into groups of 60. Each group of 60 seconds is one minute.537 ÷ 60 = 8 r 57
- Write the minutes and the seconds left. The remainder is the seconds.8 min and 57 s
- Write the answer. Use the units minutes and seconds.8 min 57 s
Check. Check: 8 × 60 + 57 = 537.
Watch out. The seconds must be less than 60.
Method. Divide by 60 to find the minutes; the remainder is the seconds.
- Share the seconds into groups of 60. Each group of 60 seconds is one minute.254 ÷ 60 = 4 r 14
- Write the minutes and the seconds left. The remainder is the seconds.4 min and 14 s
- Write the answer. Use the units minutes and seconds.4 min 14 s
Check. Check: 4 × 60 + 14 = 254.
Watch out. The seconds must be less than 60.
Method. Multiply the hours by 60 to change them into minutes.
- Use the rule. There are 60 minutes in 1 hour.1 h = 60 min
- Multiply the hours by 60. Each hour has 60 minutes.4 × 60 = 240
- Write the answer. The unit is minutes.240 minutes
Check. Check: 240 ÷ 60 = 4.
Watch out. Going from hours to minutes gives a bigger number. Multiply by 60.
Method. Divide by 60 to find the hours; the remainder is the minutes.
- Share the minutes into groups of 60. Each group of 60 minutes is one hour.236 ÷ 60 = 3 r 56
- Write the hours and the minutes left. The remainder is the minutes that are left over.3 h and 56 min
- Write the answer. Use the units hours and minutes.3 h 56 min
Check. Check: 3 × 60 + 56 = 236.
Watch out. Do not write 1 h 95 min. The minutes must be less than 60.
Method. Divide by 60 to find the minutes; the remainder is the seconds.
- Share the seconds into groups of 60. Each group of 60 seconds is one minute.312 ÷ 60 = 5 r 12
- Write the minutes and the seconds left. The remainder is the seconds.5 min and 12 s
- Write the answer. Use the units minutes and seconds.5 min 12 s
Check. Check: 5 × 60 + 12 = 312.
Watch out. The seconds must be less than 60.
Method. Multiply the hours by 60 to change them into minutes.
- Use the rule. There are 60 minutes in 1 hour.1 h = 60 min
- Multiply the hours by 60. Each hour has 60 minutes.2 × 60 = 120
- Write the answer. The unit is minutes.120 minutes
Check. Check: 120 ÷ 60 = 2.
Watch out. Going from hours to minutes gives a bigger number. Multiply by 60.
Method. Multiply the minutes by 60 to change them into seconds.
- Use the rule. There are 60 seconds in 1 minute.1 min = 60 s
- Multiply the minutes by 60. Each minute has 60 seconds.9 × 60 = 540
- Write the answer. The unit is seconds.540 seconds
Check. Check: 540 ÷ 60 = 9.
Watch out. Multiply by 60, not by 100.
Method. Divide by 60 to find the minutes; the remainder is the seconds.
- Share the seconds into groups of 60. Each group of 60 seconds is one minute.484 ÷ 60 = 8 r 4
- Write the minutes and the seconds left. The remainder is the seconds.8 min and 4 s
- Write the answer. Use the units minutes and seconds.8 min 4 s
Check. Check: 8 × 60 + 4 = 484.
Watch out. The seconds must be less than 60.
Method. Divide by 60 to find the hours; the remainder is the minutes.
- Share the minutes into groups of 60. Each group of 60 minutes is one hour.238 ÷ 60 = 3 r 58
- Write the hours and the minutes left. The remainder is the minutes that are left over.3 h and 58 min
- Write the answer. Use the units hours and minutes.3 h 58 min
Check. Check: 3 × 60 + 58 = 238.
Watch out. Do not write 1 h 95 min. The minutes must be less than 60.
Method. Divide by 60 to find the hours; the remainder is the minutes.
- Share the minutes into groups of 60. Each group of 60 minutes is one hour.127 ÷ 60 = 2 r 7
- Write the hours and the minutes left. The remainder is the minutes that are left over.2 h and 7 min
- Write the answer. Use the units hours and minutes.2 h 7 min
Check. Check: 2 × 60 + 7 = 127.
Watch out. Do not write 1 h 95 min. The minutes must be less than 60.
Method. Divide by 60 to find the hours; the remainder is the minutes.
- Share the minutes into groups of 60. Each group of 60 minutes is one hour.242 ÷ 60 = 4 r 2
- Write the hours and the minutes left. The remainder is the minutes that are left over.4 h and 2 min
- Write the answer. Use the units hours and minutes.4 h 2 min
Check. Check: 4 × 60 + 2 = 242.
Watch out. Do not write 1 h 95 min. The minutes must be less than 60.
Method. Multiply the hours by 60 to change them into minutes.
- Use the rule. There are 60 minutes in 1 hour.1 h = 60 min
- Multiply the hours by 60. Each hour has 60 minutes.9 × 60 = 540
- Write the answer. The unit is minutes.540 minutes
Check. Check: 540 ÷ 60 = 9.
Watch out. Going from hours to minutes gives a bigger number. Multiply by 60.
Method. Divide by 60 to find the hours; the remainder is the minutes.
- Share the minutes into groups of 60. Each group of 60 minutes is one hour.189 ÷ 60 = 3 r 9
- Write the hours and the minutes left. The remainder is the minutes that are left over.3 h and 9 min
- Write the answer. Use the units hours and minutes.3 h 9 min
Check. Check: 3 × 60 + 9 = 189.
Watch out. Do not write 1 h 95 min. The minutes must be less than 60.
Durations across an hour or a day change
Count on from the start time. First count to the next hour, then the whole hours, then the minutes to the end time.
Across midnight, count to 24:00 first, then on from 00:00.
Key ideas
- Count on, do not subtract the clock times.
- Count to the next hour first.
- Midnight is 24:00.
Method. Count on in steps from the start to the arrival time: first to the next hour, then whole hours, then minutes.
- Count the minutes to the next hour. Go from the start time to the next full hour.10:45 to 11:00 is 15 min
- Count the whole hours. Count each full hour after that.1 whole hours
- Count the minutes after the last whole hour. Count on to the arrival time.20 min
- Add the parts. Add all the parts for the total time.15 min + 1 h + 20 min = 1 h 35 min
- Write the answer. Give the journey time in hours and minutes.1 h 35 min
Check. Check: 1 h 35 min added to 10:45 gives 12:20.
Watch out. Do not subtract the times as if they were ordinary numbers. Count on across the hour.
Method. Count to midnight, then count on from midnight to the arrival time.
- Count to midnight. Midnight is 24:00, the start of the next day.22:30 to 24:00 is 1 h 30 min
- Count on from midnight. Add the time after midnight.00:00 to 01:15 is 1 h 15 min
- Add the two parts. The journey crosses midnight, so we add the two parts.1 h 30 min + 1 h 15 min = 2 h 45 min
- Write the answer. Give the journey time in hours and minutes.2 h 45 min
Check. Check: 2 h 45 min is the same as 165 minutes.
Watch out. When a journey crosses midnight, the arrival time is smaller than the start time. Count across the day change.
Method. Count on in steps from the start to the arrival time: first to the next hour, then whole hours, then minutes.
- Count the minutes to the next hour. Go from the start time to the next full hour.17:20 to 18:00 is 40 min
- Count the whole hours. Count each full hour after that.1 whole hours
- Count the minutes after the last whole hour. Count on to the arrival time.50 min
- Add the parts. Add all the parts for the total time.40 min + 1 h + 50 min = 2 h 30 min
- Write the answer. Give the journey time in hours and minutes.2 h 30 min
Check. Check: 2 h 30 min added to 17:20 gives 19:50.
Watch out. Do not subtract the times as if they were ordinary numbers. Count on across the hour.
Watch out
Watch out. 10:45 to 12:20 is 1 h 35 min, not 1 h 25 min. Count across the hour carefully.
Exam tip
Grown-up tip. Use a clock or a timetable. Ask: “How long until the next hour? How long after it?”
Exercise 9C Practice: durations across the hour and the day
Non-calculatorMethod. Count on in steps from the start to the arrival time: first to the next hour, then whole hours, then minutes.
- Count the minutes to the next hour. Go from the start time to the next full hour.08:53 to 09:00 is 7 min
- Count the whole hours. Count each full hour after that.1 whole hours
- Count the minutes after the last whole hour. Count on to the arrival time.36 min
- Add the parts. Add all the parts for the total time.7 min + 1 h + 36 min = 1 h 43 min
- Write the answer. Give the journey time in hours and minutes.1 h 43 min
Check. Check: 1 h 43 min added to 08:53 gives 10:36.
Watch out. Do not subtract the times as if they were ordinary numbers. Count on across the hour.
Method. Count on in steps from the start to the arrival time: first to the next hour, then whole hours, then minutes.
- Count the minutes to the next hour. Go from the start time to the next full hour.08:07 to 09:00 is 53 min
- Count the whole hours. Count each full hour after that.1 whole hours
- Count the minutes after the last whole hour. Count on to the arrival time.57 min
- Add the parts. Add all the parts for the total time.53 min + 1 h + 57 min = 2 h 50 min
- Write the answer. Give the journey time in hours and minutes.2 h 50 min
Check. Check: 2 h 50 min added to 08:07 gives 10:57.
Watch out. Do not subtract the times as if they were ordinary numbers. Count on across the hour.
Method. Count on in steps from the start to the arrival time: first to the next hour, then whole hours, then minutes.
- Count the minutes to the next hour. Go from the start time to the next full hour.13:29 to 14:00 is 31 min
- Count the whole hours. Count each full hour after that.3 whole hours
- Count the minutes after the last whole hour. Count on to the arrival time.38 min
- Add the parts. Add all the parts for the total time.31 min + 3 h + 38 min = 4 h 9 min
- Write the answer. Give the journey time in hours and minutes.4 h 9 min
Check. Check: 4 h 9 min added to 13:29 gives 17:38.
Watch out. Do not subtract the times as if they were ordinary numbers. Count on across the hour.
Method. Count on in steps from the start to the arrival time: first to the next hour, then whole hours, then minutes.
- Count the minutes to the next hour. Go from the start time to the next full hour.17:20 to 18:00 is 40 min
- Count the whole hours. Count each full hour after that.2 whole hours
- Count the minutes after the last whole hour. Count on to the arrival time.8 min
- Add the parts. Add all the parts for the total time.40 min + 2 h + 8 min = 2 h 48 min
- Write the answer. Give the journey time in hours and minutes.2 h 48 min
Check. Check: 2 h 48 min added to 17:20 gives 20:08.
Watch out. Do not subtract the times as if they were ordinary numbers. Count on across the hour.
Method. Count on in steps from the start to the arrival time: first to the next hour, then whole hours, then minutes.
- Count the minutes to the next hour. Go from the start time to the next full hour.20:08 to 21:00 is 52 min
- Count the whole hours. Count each full hour after that.2 whole hours
- Count the minutes after the last whole hour. Count on to the arrival time.34 min
- Add the parts. Add all the parts for the total time.52 min + 2 h + 34 min = 3 h 26 min
- Write the answer. Give the journey time in hours and minutes.3 h 26 min
Check. Check: 3 h 26 min added to 20:08 gives 23:34.
Watch out. Do not subtract the times as if they were ordinary numbers. Count on across the hour.
Method. Count on in steps from the start to the arrival time: first to the next hour, then whole hours, then minutes.
- Count the minutes to the next hour. Go from the start time to the next full hour.09:04 to 10:00 is 56 min
- Count the whole hours. Count each full hour after that.1 whole hours
- Count the minutes after the last whole hour. Count on to the arrival time.10 min
- Add the parts. Add all the parts for the total time.56 min + 1 h + 10 min = 2 h 6 min
- Write the answer. Give the journey time in hours and minutes.2 h 6 min
Check. Check: 2 h 6 min added to 09:04 gives 11:10.
Watch out. Do not subtract the times as if they were ordinary numbers. Count on across the hour.
Method. Count on in steps from the start to the arrival time: first to the next hour, then whole hours, then minutes.
- Count the minutes to the next hour. Go from the start time to the next full hour.16:37 to 17:00 is 23 min
- Count the whole hours. Count each full hour after that.2 whole hours
- Count the minutes after the last whole hour. Count on to the arrival time.33 min
- Add the parts. Add all the parts for the total time.23 min + 2 h + 33 min = 2 h 56 min
- Write the answer. Give the journey time in hours and minutes.2 h 56 min
Check. Check: 2 h 56 min added to 16:37 gives 19:33.
Watch out. Do not subtract the times as if they were ordinary numbers. Count on across the hour.
Method. Count on in steps from the start to the arrival time: first to the next hour, then whole hours, then minutes.
- Count the minutes to the next hour. Go from the start time to the next full hour.18:04 to 19:00 is 56 min
- Count the whole hours. Count each full hour after that.0 whole hours
- Count the minutes after the last whole hour. Count on to the arrival time.51 min
- Add the parts. Add all the parts for the total time.56 min + 0 h + 51 min = 1 h 47 min
- Write the answer. Give the journey time in hours and minutes.1 h 47 min
Check. Check: 1 h 47 min added to 18:04 gives 19:51.
Watch out. Do not subtract the times as if they were ordinary numbers. Count on across the hour.
Method. Count on in steps from the start to the arrival time: first to the next hour, then whole hours, then minutes.
- Count the minutes to the next hour. Go from the start time to the next full hour.18:53 to 19:00 is 7 min
- Count the whole hours. Count each full hour after that.4 whole hours
- Count the minutes after the last whole hour. Count on to the arrival time.0 min
- Add the parts. Add all the parts for the total time.7 min + 4 h + 0 min = 4 h 7 min
- Write the answer. Give the journey time in hours and minutes.4 h 7 min
Check. Check: 4 h 7 min added to 18:53 gives 23:00.
Watch out. Do not subtract the times as if they were ordinary numbers. Count on across the hour.
Method. Count to midnight, then count on from midnight to the arrival time.
- Count to midnight. Midnight is 24:00, the start of the next day.22:31 to 24:00 is 1 h 29 min
- Count on from midnight. Add the time after midnight.00:00 to 02:14 is 2 h 14 min
- Add the two parts. The journey crosses midnight, so we add the two parts.1 h 29 min + 2 h 14 min = 3 h 43 min
- Write the answer. Give the journey time in hours and minutes.3 h 43 min
Check. Check: 3 h 43 min is the same as 223 minutes.
Watch out. When a journey crosses midnight, the arrival time is smaller than the start time. Count across the day change.
Method. Count on in steps from the start to the arrival time: first to the next hour, then whole hours, then minutes.
- Count the minutes to the next hour. Go from the start time to the next full hour.19:02 to 20:00 is 58 min
- Count the whole hours. Count each full hour after that.0 whole hours
- Count the minutes after the last whole hour. Count on to the arrival time.56 min
- Add the parts. Add all the parts for the total time.58 min + 0 h + 56 min = 1 h 54 min
- Write the answer. Give the journey time in hours and minutes.1 h 54 min
Check. Check: 1 h 54 min added to 19:02 gives 20:56.
Watch out. Do not subtract the times as if they were ordinary numbers. Count on across the hour.
Method. Count on in steps from the start to the arrival time: first to the next hour, then whole hours, then minutes.
- Count the minutes to the next hour. Go from the start time to the next full hour.15:31 to 16:00 is 29 min
- Count the whole hours. Count each full hour after that.0 whole hours
- Count the minutes after the last whole hour. Count on to the arrival time.23 min
- Add the parts. Add all the parts for the total time.29 min + 0 h + 23 min = 52 min
- Write the answer. Give the journey time in hours and minutes.52 min
Check. Check: 52 min added to 15:31 gives 16:23.
Watch out. Do not subtract the times as if they were ordinary numbers. Count on across the hour.
Method. Count on in steps from the start to the arrival time: first to the next hour, then whole hours, then minutes.
- Count the minutes to the next hour. Go from the start time to the next full hour.17:35 to 18:00 is 25 min
- Count the whole hours. Count each full hour after that.1 whole hours
- Count the minutes after the last whole hour. Count on to the arrival time.24 min
- Add the parts. Add all the parts for the total time.25 min + 1 h + 24 min = 1 h 49 min
- Write the answer. Give the journey time in hours and minutes.1 h 49 min
Check. Check: 1 h 49 min added to 17:35 gives 19:24.
Watch out. Do not subtract the times as if they were ordinary numbers. Count on across the hour.
Method. Count to midnight, then count on from midnight to the arrival time.
- Count to midnight. Midnight is 24:00, the start of the next day.23:35 to 24:00 is 25 min
- Count on from midnight. Add the time after midnight.00:00 to 01:40 is 1 h 40 min
- Add the two parts. The journey crosses midnight, so we add the two parts.25 min + 1 h 40 min = 2 h 5 min
- Write the answer. Give the journey time in hours and minutes.2 h 5 min
Check. Check: 2 h 5 min is the same as 125 minutes.
Watch out. When a journey crosses midnight, the arrival time is smaller than the start time. Count across the day change.
Method. Count to midnight, then count on from midnight to the arrival time.
- Count to midnight. Midnight is 24:00, the start of the next day.22:52 to 24:00 is 1 h 8 min
- Count on from midnight. Add the time after midnight.00:00 to 01:55 is 1 h 55 min
- Add the two parts. The journey crosses midnight, so we add the two parts.1 h 8 min + 1 h 55 min = 3 h 3 min
- Write the answer. Give the journey time in hours and minutes.3 h 3 min
Check. Check: 3 h 3 min is the same as 183 minutes.
Watch out. When a journey crosses midnight, the arrival time is smaller than the start time. Count across the day change.
Method. Count on in steps from the start to the arrival time: first to the next hour, then whole hours, then minutes.
- Count the minutes to the next hour. Go from the start time to the next full hour.18:16 to 19:00 is 44 min
- Count the whole hours. Count each full hour after that.3 whole hours
- Count the minutes after the last whole hour. Count on to the arrival time.53 min
- Add the parts. Add all the parts for the total time.44 min + 3 h + 53 min = 4 h 37 min
- Write the answer. Give the journey time in hours and minutes.4 h 37 min
Check. Check: 4 h 37 min added to 18:16 gives 22:53.
Watch out. Do not subtract the times as if they were ordinary numbers. Count on across the hour.
Two-step money problems
Money in pounds and pence is worked out in the same way as decimals to hundredths. Line up the decimal points.
In a two-step problem, add the costs first, then take the total from the money at the start.
Key ideas
- Line up the decimal points.
- Work out the total cost first.
- Keep two places for the pence.
Method. Add the costs, then subtract the total from the money at the start.
- Add the two costs. Add the pounds and the pence together.£4.35 + £0.85 = £5.20
- Take the total away from the money Sam has. Subtract the total cost.£10.00 - £5.20 = £4.80
- Write the answer. Give the amount left with the pound sign.£4.80
Check. Check: £4.80 + £5.20 = £10.00.
Watch out. Keep the pence in two places: £0.85 and £2.40, not £0.85 and £2.4.
Method. Add the costs, then subtract the total from the money at the start.
- Add the two costs. Add the pounds and the pence together.£12.50 + £3.75 = £16.25
- Take the total away from the money Sam has. Subtract the total cost.£20.00 - £16.25 = £3.75
- Write the answer. Give the amount left with the pound sign.£3.75
Check. Check: £3.75 + £16.25 = £20.00.
Watch out. Keep the pence in two places: £0.85 and £2.40, not £0.85 and £2.4.
Method. Find the total of all the items, then take it from the money paid.
- Work out the cost of the cups. Multiply the price by the number of cups.3 × £1.25 = £3.75
- Add the cost of the cake. Add all the items to find the total.£3.75 + £2.40 = £6.15
- Work out the change. Change is what is left from the money paid.£10.00 - £6.15 = £3.85
- Write the answer. Give the change with the pound sign.£3.85
Check. Check: £6.15 + £3.85 = £10.00.
Watch out. Add all the items before you take anything away.
Watch out
Watch out. Do not subtract each cost one at a time from the wrong amount. Work out the total of the costs first.
Exam tip
Grown-up tip. Use real coins and notes. Ask the child to pay the total, then count the change back to the amount paid.
Exercise 9D Practice: two-step money problems
Non-calculatorMethod. Add the costs, then subtract the total from the money at the start.
- Add the two costs. Add the pounds and the pence together.£5.43 + £0.76 = £6.19
- Take the total away from the money Sam has. Subtract the total cost.£19.35 - £6.19 = £13.16
- Write the answer. Give the amount left with the pound sign.£13.16
Check. Check: £13.16 + £6.19 = £19.35.
Watch out. Keep the pence in two places: £0.85 and £2.40, not £0.85 and £2.4.
Method. Add the costs, then subtract the total from the money at the start.
- Add the two costs. Add the pounds and the pence together.£1.70 + £0.98 = £2.68
- Take the total away from the money Sam has. Subtract the total cost.£16.09 - £2.68 = £13.41
- Write the answer. Give the amount left with the pound sign.£13.41
Check. Check: £13.41 + £2.68 = £16.09.
Watch out. Keep the pence in two places: £0.85 and £2.40, not £0.85 and £2.4.
Method. Add the costs, then subtract the total from the money at the start.
- Add the two costs. Add the pounds and the pence together.£1.87 + £2.43 = £4.30
- Take the total away from the money Sam has. Subtract the total cost.£14.51 - £4.30 = £10.21
- Write the answer. Give the amount left with the pound sign.£10.21
Check. Check: £10.21 + £4.30 = £14.51.
Watch out. Keep the pence in two places: £0.85 and £2.40, not £0.85 and £2.4.
Method. Add the costs, then subtract the total from the money at the start.
- Add the two costs. Add the pounds and the pence together.£3.52 + £1.18 = £4.70
- Take the total away from the money Sam has. Subtract the total cost.£10.40 - £4.70 = £5.70
- Write the answer. Give the amount left with the pound sign.£5.70
Check. Check: £5.70 + £4.70 = £10.40.
Watch out. Keep the pence in two places: £0.85 and £2.40, not £0.85 and £2.4.
Method. Add the costs, then subtract the total from the money at the start.
- Add the two costs. Add the pounds and the pence together.£1.42 + £1.39 = £2.81
- Take the total away from the money Sam has. Subtract the total cost.£14.03 - £2.81 = £11.22
- Write the answer. Give the amount left with the pound sign.£11.22
Check. Check: £11.22 + £2.81 = £14.03.
Watch out. Keep the pence in two places: £0.85 and £2.40, not £0.85 and £2.4.
Method. Add the costs, then subtract the total from the money at the start.
- Add the two costs. Add the pounds and the pence together.£2.05 + £1.54 = £3.59
- Take the total away from the money Sam has. Subtract the total cost.£14.41 - £3.59 = £10.82
- Write the answer. Give the amount left with the pound sign.£10.82
Check. Check: £10.82 + £3.59 = £14.41.
Watch out. Keep the pence in two places: £0.85 and £2.40, not £0.85 and £2.4.
Method. Add the costs, then subtract the total from the money at the start.
- Add the two costs. Add the pounds and the pence together.£3.80 + £0.59 = £4.39
- Take the total away from the money Sam has. Subtract the total cost.£15.81 - £4.39 = £11.42
- Write the answer. Give the amount left with the pound sign.£11.42
Check. Check: £11.42 + £4.39 = £15.81.
Watch out. Keep the pence in two places: £0.85 and £2.40, not £0.85 and £2.4.
Method. Add the costs, then subtract the total from the money at the start.
- Add the two costs. Add the pounds and the pence together.£2.88 + £2.61 = £5.49
- Take the total away from the money Sam has. Subtract the total cost.£11.93 - £5.49 = £6.44
- Write the answer. Give the amount left with the pound sign.£6.44
Check. Check: £6.44 + £5.49 = £11.93.
Watch out. Keep the pence in two places: £0.85 and £2.40, not £0.85 and £2.4.
Method. Add the costs, then subtract the total from the money at the start.
- Add the two costs. Add the pounds and the pence together.£2.48 + £2.28 = £4.76
- Take the total away from the money Sam has. Subtract the total cost.£18.75 - £4.76 = £13.99
- Write the answer. Give the amount left with the pound sign.£13.99
Check. Check: £13.99 + £4.76 = £18.75.
Watch out. Keep the pence in two places: £0.85 and £2.40, not £0.85 and £2.4.
Method. Add the costs, then subtract the total from the money at the start.
- Add the two costs. Add the pounds and the pence together.£4.88 + £1.74 = £6.62
- Take the total away from the money Sam has. Subtract the total cost.£15.02 - £6.62 = £8.40
- Write the answer. Give the amount left with the pound sign.£8.40
Check. Check: £8.40 + £6.62 = £15.02.
Watch out. Keep the pence in two places: £0.85 and £2.40, not £0.85 and £2.4.
Method. Add the costs, then subtract the total from the money at the start.
- Add the two costs. Add the pounds and the pence together.£5.16 + £2.18 = £7.34
- Take the total away from the money Sam has. Subtract the total cost.£17.92 - £7.34 = £10.58
- Write the answer. Give the amount left with the pound sign.£10.58
Check. Check: £10.58 + £7.34 = £17.92.
Watch out. Keep the pence in two places: £0.85 and £2.40, not £0.85 and £2.4.
Method. Add the costs, then subtract the total from the money at the start.
- Add the two costs. Add the pounds and the pence together.£3.74 + £0.81 = £4.55
- Take the total away from the money Sam has. Subtract the total cost.£12.90 - £4.55 = £8.35
- Write the answer. Give the amount left with the pound sign.£8.35
Check. Check: £8.35 + £4.55 = £12.90.
Watch out. Keep the pence in two places: £0.85 and £2.40, not £0.85 and £2.4.
Method. Add the costs, then subtract the total from the money at the start.
- Add the two costs. Add the pounds and the pence together.£5.69 + £2.89 = £8.58
- Take the total away from the money Sam has. Subtract the total cost.£11.84 - £8.58 = £3.26
- Write the answer. Give the amount left with the pound sign.£3.26
Check. Check: £3.26 + £8.58 = £11.84.
Watch out. Keep the pence in two places: £0.85 and £2.40, not £0.85 and £2.4.
Method. Add the costs, then subtract the total from the money at the start.
- Add the two costs. Add the pounds and the pence together.£4.47 + £0.72 = £5.19
- Take the total away from the money Sam has. Subtract the total cost.£19.48 - £5.19 = £14.29
- Write the answer. Give the amount left with the pound sign.£14.29
Check. Check: £14.29 + £5.19 = £19.48.
Watch out. Keep the pence in two places: £0.85 and £2.40, not £0.85 and £2.4.
Method. Add the costs, then subtract the total from the money at the start.
- Add the two costs. Add the pounds and the pence together.£1.23 + £2.49 = £3.72
- Take the total away from the money Sam has. Subtract the total cost.£14.32 - £3.72 = £10.60
- Write the answer. Give the amount left with the pound sign.£10.60
Check. Check: £10.60 + £3.72 = £14.32.
Watch out. Keep the pence in two places: £0.85 and £2.40, not £0.85 and £2.4.
Method. Add the costs, then subtract the total from the money at the start.
- Add the two costs. Add the pounds and the pence together.£1.40 + £0.69 = £2.09
- Take the total away from the money Sam has. Subtract the total cost.£14.66 - £2.09 = £12.57
- Write the answer. Give the amount left with the pound sign.£12.57
Check. Check: £12.57 + £2.09 = £14.66.
Watch out. Keep the pence in two places: £0.85 and £2.40, not £0.85 and £2.4.
Change from a total, and choosing the operation
To find the change, first find the total of all the items. Then take the total from the money paid.
Key words help you choose: spent and left mean take away; altogether and total mean add.
Key ideas
- Find the total of all the items first.
- Change = money paid − total.
- Explain the operation with a reason from the story.
Method. Find the total of all the items, then take it from the money paid.
- Work out the cost of the cups. Multiply the price by the number of cups.3 × £1.25 = £3.75
- Add the cost of the cake. Add all the items to find the total.£3.75 + £2.40 = £6.15
- Work out the change. Change is what is left from the money paid.£10.00 - £6.15 = £3.85
- Write the answer. Give the change with the pound sign.£3.85
Check. Check: £6.15 + £3.85 = £10.00.
Watch out. Add all the items before you take anything away.
Method. Choose the operation from what happens in the story, and say why.
- Read the story. Money is spent, so some of it goes away.£15.00 spent £3.50
- Choose the operation. When an amount goes away, we take it away.Subtract
- Give the reason. The money left is what is left after the spending.Accept any answer that says subtract and gives a reason, such as: the money is taken away
Check. Accept any answer that names the operation and gives a sensible reason, such as the one shown.
Watch out. Read the key words: spent, left, altogether, total, change, and each.
Method. Choose the operation from what happens in the story, and say why.
- Read the story. Two costs are put together for a total.£12.00 and £4.50
- Choose the operation. When amounts are combined, we add them.Add
- Give the reason. The total is the sum of the amounts.Accept any answer that says add and gives a reason, such as: the costs are put together
Check. Accept any answer that names the operation and gives a sensible reason, such as the one shown.
Watch out. Read the key words: spent, left, altogether, total, change, and each.
Watch out
Watch out. Change is found by subtracting only after the total is worked out. Do not take one item away from the money paid.
Exam tip
Grown-up tip. Ask: “Is the money going away, or are we putting amounts together?” before the child calculates.
Exercise 9E Practice: change and choosing the operation
Non-calculatorMethod. Choose the operation from what happens in the story, and say why.
- Read the story. Two costs are put together for a total.£20.34 and £7.97
- Choose the operation. When amounts are combined, we add them.Add
- Give the reason. The total is the sum of the amounts.Accept any answer that says add and gives a reason, such as: the costs are put together
Check. Accept any answer that names the operation and gives a sensible reason, such as the one shown.
Watch out. Read the key words: spent, left, altogether, total, change, and each.
Method. Find the total of all the items, then take it from the money paid.
- Work out the cost of the cups. Multiply the price by the number of cups.3 × £1.31 = £3.93
- Add the cost of the cake. Add all the items to find the total.£3.93 + £2.23 = £6.16
- Work out the change. Change is what is left from the money paid.£10.00 - £6.16 = £3.84
- Write the answer. Give the change with the pound sign.£3.84
Check. Check: £6.16 + £3.84 = £10.00.
Watch out. Add all the items before you take anything away.
Method. Choose the operation from what happens in the story, and say why.
- Read the story. Money is spent, so some of it goes away.£28.80 spent £1.60
- Choose the operation. When an amount goes away, we take it away.Subtract
- Give the reason. The money left is what is left after the spending.Accept any answer that says subtract and gives a reason, such as: the money is taken away
Check. Accept any answer that names the operation and gives a sensible reason, such as the one shown.
Watch out. Read the key words: spent, left, altogether, total, change, and each.
Method. Find the total of all the items, then take it from the money paid.
- Work out the cost of the cups. Multiply the price by the number of cups.3 × £1.65 = £4.95
- Add the cost of the cake. Add all the items to find the total.£4.95 + £2.07 = £7.02
- Work out the change. Change is what is left from the money paid.£15.00 - £7.02 = £7.98
- Write the answer. Give the change with the pound sign.£7.98
Check. Check: £7.02 + £7.98 = £15.00.
Watch out. Add all the items before you take anything away.
Method. Find the total of all the items, then take it from the money paid.
- Work out the cost of the cups. Multiply the price by the number of cups.3 × £1.71 = £5.13
- Add the cost of the cake. Add all the items to find the total.£5.13 + £2.59 = £7.72
- Work out the change. Change is what is left from the money paid.£20.00 - £7.72 = £12.28
- Write the answer. Give the change with the pound sign.£12.28
Check. Check: £7.72 + £12.28 = £20.00.
Watch out. Add all the items before you take anything away.
Method. Find the total of all the items, then take it from the money paid.
- Work out the cost of the cups. Multiply the price by the number of cups.2 × £1.76 = £3.52
- Add the cost of the cake. Add all the items to find the total.£3.52 + £1.59 = £5.11
- Work out the change. Change is what is left from the money paid.£20.00 - £5.11 = £14.89
- Write the answer. Give the change with the pound sign.£14.89
Check. Check: £5.11 + £14.89 = £20.00.
Watch out. Add all the items before you take anything away.
Method. Find the total of all the items, then take it from the money paid.
- Work out the cost of the cups. Multiply the price by the number of cups.4 × £1.18 = £4.72
- Add the cost of the cake. Add all the items to find the total.£4.72 + £1.43 = £6.15
- Work out the change. Change is what is left from the money paid.£15.00 - £6.15 = £8.85
- Write the answer. Give the change with the pound sign.£8.85
Check. Check: £6.15 + £8.85 = £15.00.
Watch out. Add all the items before you take anything away.
Method. Choose the operation from what happens in the story, and say why.
- Read the story. Money is spent, so some of it goes away.£28.09 spent £2.94
- Choose the operation. When an amount goes away, we take it away.Subtract
- Give the reason. The money left is what is left after the spending.Accept any answer that says subtract and gives a reason, such as: the money is taken away
Check. Accept any answer that names the operation and gives a sensible reason, such as the one shown.
Watch out. Read the key words: spent, left, altogether, total, change, and each.
Method. Find the total of all the items, then take it from the money paid.
- Work out the cost of the cups. Multiply the price by the number of cups.4 × £1.47 = £5.88
- Add the cost of the cake. Add all the items to find the total.£5.88 + £1.41 = £7.29
- Work out the change. Change is what is left from the money paid.£15.00 - £7.29 = £7.71
- Write the answer. Give the change with the pound sign.£7.71
Check. Check: £7.29 + £7.71 = £15.00.
Watch out. Add all the items before you take anything away.
Method. Choose the operation from what happens in the story, and say why.
- Read the story. Two costs are put together for a total.£16.28 and £5.17
- Choose the operation. When amounts are combined, we add them.Add
- Give the reason. The total is the sum of the amounts.Accept any answer that says add and gives a reason, such as: the costs are put together
Check. Accept any answer that names the operation and gives a sensible reason, such as the one shown.
Watch out. Read the key words: spent, left, altogether, total, change, and each.
Method. Choose the operation from what happens in the story, and say why.
- Read the story. Money is spent, so some of it goes away.£25.76 spent £2.91
- Choose the operation. When an amount goes away, we take it away.Subtract
- Give the reason. The money left is what is left after the spending.Accept any answer that says subtract and gives a reason, such as: the money is taken away
Check. Accept any answer that names the operation and gives a sensible reason, such as the one shown.
Watch out. Read the key words: spent, left, altogether, total, change, and each.
Method. Choose the operation from what happens in the story, and say why.
- Read the story. Two costs are put together for a total.£26.57 and £3.63
- Choose the operation. When amounts are combined, we add them.Add
- Give the reason. The total is the sum of the amounts.Accept any answer that says add and gives a reason, such as: the costs are put together
Check. Accept any answer that names the operation and gives a sensible reason, such as the one shown.
Watch out. Read the key words: spent, left, altogether, total, change, and each.
Method. Find the total of all the items, then take it from the money paid.
- Work out the cost of the cups. Multiply the price by the number of cups.3 × £0.88 = £2.64
- Add the cost of the cake. Add all the items to find the total.£2.64 + £1.29 = £3.93
- Work out the change. Change is what is left from the money paid.£20.00 - £3.93 = £16.07
- Write the answer. Give the change with the pound sign.£16.07
Check. Check: £3.93 + £16.07 = £20.00.
Watch out. Add all the items before you take anything away.
Method. Choose the operation from what happens in the story, and say why.
- Read the story. Money is spent, so some of it goes away.£23.67 spent £5.93
- Choose the operation. When an amount goes away, we take it away.Subtract
- Give the reason. The money left is what is left after the spending.Accept any answer that says subtract and gives a reason, such as: the money is taken away
Check. Accept any answer that names the operation and gives a sensible reason, such as the one shown.
Watch out. Read the key words: spent, left, altogether, total, change, and each.
Method. Find the total of all the items, then take it from the money paid.
- Work out the cost of the cups. Multiply the price by the number of cups.2 × £1.23 = £2.46
- Add the cost of the cake. Add all the items to find the total.£2.46 + £2.25 = £4.71
- Work out the change. Change is what is left from the money paid.£15.00 - £4.71 = £10.29
- Write the answer. Give the change with the pound sign.£10.29
Check. Check: £4.71 + £10.29 = £15.00.
Watch out. Add all the items before you take anything away.
Method. Choose the operation from what happens in the story, and say why.
- Read the story. Money is spent, so some of it goes away.£13.88 spent £3.50
- Choose the operation. When an amount goes away, we take it away.Subtract
- Give the reason. The money left is what is left after the spending.Accept any answer that says subtract and gives a reason, such as: the money is taken away
Check. Accept any answer that names the operation and gives a sensible reason, such as the one shown.
Watch out. Read the key words: spent, left, altogether, total, change, and each.
Chapter summary
| Skill | Method |
|---|---|
| Perimeter | Add all the sides; find missing sides by subtraction first |
| Hours and minutes | 1 h = 60 min; hours × 60; minutes ÷ 60, remainder is minutes |
| Durations | Count to the next hour, then whole hours, then minutes; across midnight, count to 24:00 |
| Money | Line up the points; total the costs first; keep two places for pence |
| Change and operations | Change = paid − total; choose the operation from the key words and explain |
Can you…?
- I can find the perimeter of a rectilinear shape, including missing sides
- I can convert between hours, minutes and seconds
- I can find a time or a duration across an hour or midnight
- I can solve two-step money problems in pounds and pence
- I can give change from a total, and choose and explain the operation
Key terms
- rectilinear
- a shape made only of straight sides with right angles
- perimeter
- the distance all the way round a shape
- duration
- how long something lasts
- change
- the money given back when you pay more than the cost
Exercise 9Z Check-up
Non-calculatorMethod. Work out each missing side, then add all the sides of the shape.
- Find the missing sides. Missing sides come from the sides that are given: take away the shorter part.step = 5 - 2 = 3 cm; right side = 4 - 2 = 2 cm
- List all six sides. The perimeter is the distance all the way round.2 + 2 + 3 + 2 + 5 + 4 cm
- Add the sides. Add all the lengths together.18 cm
- Write the perimeter. Give the answer with the unit cm.18 cm
Check. Check: the perimeter of a shape like this is twice the width plus twice the height: 2 × (5 + 4) = 18 cm.
Watch out. Do not add only the sides you can see. Every side counts, including the ones you worked out.
Method. Find the total of all the items, then take it from the money paid.
- Work out the cost of the cups. Multiply the price by the number of cups.4 × £0.88 = £3.52
- Add the cost of the cake. Add all the items to find the total.£3.52 + £2.10 = £5.62
- Work out the change. Change is what is left from the money paid.£10.00 - £5.62 = £4.38
- Write the answer. Give the change with the pound sign.£4.38
Check. Check: £5.62 + £4.38 = £10.00.
Watch out. Add all the items before you take anything away.
Method. Count on in steps from the start to the arrival time: first to the next hour, then whole hours, then minutes.
- Count the minutes to the next hour. Go from the start time to the next full hour.14:24 to 15:00 is 36 min
- Count the whole hours. Count each full hour after that.0 whole hours
- Count the minutes after the last whole hour. Count on to the arrival time.42 min
- Add the parts. Add all the parts for the total time.36 min + 0 h + 42 min = 1 h 18 min
- Write the answer. Give the journey time in hours and minutes.1 h 18 min
Check. Check: 1 h 18 min added to 14:24 gives 15:42.
Watch out. Do not subtract the times as if they were ordinary numbers. Count on across the hour.
Method. Count on in steps from the start to the arrival time: first to the next hour, then whole hours, then minutes.
- Count the minutes to the next hour. Go from the start time to the next full hour.17:20 to 18:00 is 40 min
- Count the whole hours. Count each full hour after that.3 whole hours
- Count the minutes after the last whole hour. Count on to the arrival time.50 min
- Add the parts. Add all the parts for the total time.40 min + 3 h + 50 min = 4 h 30 min
- Write the answer. Give the journey time in hours and minutes.4 h 30 min
Check. Check: 4 h 30 min added to 17:20 gives 21:50.
Watch out. Do not subtract the times as if they were ordinary numbers. Count on across the hour.
Method. Add the costs, then subtract the total from the money at the start.
- Add the two costs. Add the pounds and the pence together.£4.89 + £0.81 = £5.70
- Take the total away from the money Sam has. Subtract the total cost.£16.89 - £5.70 = £11.19
- Write the answer. Give the amount left with the pound sign.£11.19
Check. Check: £11.19 + £5.70 = £16.89.
Watch out. Keep the pence in two places: £0.85 and £2.40, not £0.85 and £2.4.
Method. Add the costs, then subtract the total from the money at the start.
- Add the two costs. Add the pounds and the pence together.£1.49 + £2.65 = £4.14
- Take the total away from the money Sam has. Subtract the total cost.£17.83 - £4.14 = £13.69
- Write the answer. Give the amount left with the pound sign.£13.69
Check. Check: £13.69 + £4.14 = £17.83.
Watch out. Keep the pence in two places: £0.85 and £2.40, not £0.85 and £2.4.
Method. Work out each missing side, then add all the sides of the shape.
- Find the missing sides. Missing sides come from the sides that are given: take away the shorter part.step = 11 - 3 = 8 cm; right side = 7 - 3 = 4 cm
- List all six sides. The perimeter is the distance all the way round.3 + 4 + 8 + 3 + 11 + 7 cm
- Add the sides. Add all the lengths together.36 cm
- Write the perimeter. Give the answer with the unit cm.36 cm
Check. Check: the perimeter of a shape like this is twice the width plus twice the height: 2 × (11 + 7) = 36 cm.
Watch out. Do not add only the sides you can see. Every side counts, including the ones you worked out.
Method. Work out each missing side, then add all the sides of the shape.
- Find the missing sides. Missing sides come from the sides that are given: take away the shorter part.step = 12 - 6 = 6 cm; right side = 4 - 2 = 2 cm
- List all six sides. The perimeter is the distance all the way round.6 + 2 + 6 + 2 + 12 + 4 cm
- Add the sides. Add all the lengths together.32 cm
- Write the perimeter. Give the answer with the unit cm.32 cm
Check. Check: the perimeter of a shape like this is twice the width plus twice the height: 2 × (12 + 4) = 32 cm.
Watch out. Do not add only the sides you can see. Every side counts, including the ones you worked out.
Method. Work out each missing side, then add all the sides of the shape.
- Find the missing sides. Missing sides come from the sides that are given: take away the shorter part.step = 9 - 6 = 3 cm; right side = 5 - 3 = 2 cm
- List all six sides. The perimeter is the distance all the way round.6 + 2 + 3 + 3 + 9 + 5 cm
- Add the sides. Add all the lengths together.28 cm
- Write the perimeter. Give the answer with the unit cm.28 cm
Check. Check: the perimeter of a shape like this is twice the width plus twice the height: 2 × (9 + 5) = 28 cm.
Watch out. Do not add only the sides you can see. Every side counts, including the ones you worked out.
Method. Multiply the hours by 60 to change them into minutes.
- Use the rule. There are 60 minutes in 1 hour.1 h = 60 min
- Multiply the hours by 60. Each hour has 60 minutes.9 × 60 = 540
- Write the answer. The unit is minutes.540 minutes
Check. Check: 540 ÷ 60 = 9.
Watch out. Going from hours to minutes gives a bigger number. Multiply by 60.
Total 19 marks. Allow about 19 minutes.
Exercise 9X Practice test questions
Non-calculatorMethod. Work out each missing side, then add all the sides of the shape.
- Find the missing sides. Missing sides come from the sides that are given: take away the shorter part.step = 7 - 2 = 5 cm; right side = 4 - 2 = 2 cm
- List all six sides. The perimeter is the distance all the way round.2 + 2 + 5 + 2 + 7 + 4 cm
- Add the sides. Add all the lengths together.22 cm
- Write the perimeter. Give the answer with the unit cm.22 cm
Check. Check: the perimeter of a shape like this is twice the width plus twice the height: 2 × (7 + 4) = 22 cm.
Watch out. Do not add only the sides you can see. Every side counts, including the ones you worked out.
Method. Work out each missing side, then add all the sides of the shape.
- Find the missing sides. Missing sides come from the sides that are given: take away the shorter part.step = 12 - 4 = 8 cm; right side = 8 - 4 = 4 cm
- List all six sides. The perimeter is the distance all the way round.4 + 4 + 8 + 4 + 12 + 8 cm
- Add the sides. Add all the lengths together.40 cm
- Write the perimeter. Give the answer with the unit cm.40 cm
Check. Check: the perimeter of a shape like this is twice the width plus twice the height: 2 × (12 + 8) = 40 cm.
Watch out. Do not add only the sides you can see. Every side counts, including the ones you worked out.
Method. Work out each missing side, then add all the sides of the shape.
- Find the missing sides. Missing sides come from the sides that are given: take away the shorter part.step = 8 - 4 = 4 cm; right side = 9 - 4 = 5 cm
- List all six sides. The perimeter is the distance all the way round.4 + 5 + 4 + 4 + 8 + 9 cm
- Add the sides. Add all the lengths together.34 cm
- Write the perimeter. Give the answer with the unit cm.34 cm
Check. Check: the perimeter of a shape like this is twice the width plus twice the height: 2 × (8 + 9) = 34 cm.
Watch out. Do not add only the sides you can see. Every side counts, including the ones you worked out.
Method. Work out each missing side, then add all the sides of the shape.
- Find the missing sides. Missing sides come from the sides that are given: take away the shorter part.step = 8 - 2 = 6 cm; right side = 6 - 2 = 4 cm
- List all six sides. The perimeter is the distance all the way round.2 + 4 + 6 + 2 + 8 + 6 cm
- Add the sides. Add all the lengths together.28 cm
- Write the perimeter. Give the answer with the unit cm.28 cm
Check. Check: the perimeter of a shape like this is twice the width plus twice the height: 2 × (8 + 6) = 28 cm.
Watch out. Do not add only the sides you can see. Every side counts, including the ones you worked out.
Method. Divide by 60 to find the hours; the remainder is the minutes.
- Share the minutes into groups of 60. Each group of 60 minutes is one hour.96 ÷ 60 = 1 r 36
- Write the hours and the minutes left. The remainder is the minutes that are left over.1 h and 36 min
- Write the answer. Use the units hours and minutes.1 h 36 min
Check. Check: 1 × 60 + 36 = 96.
Watch out. Do not write 1 h 95 min. The minutes must be less than 60.
Method. Add one length and one width, then double the answer.
- Add the length and the width. One long side and one short side.9 + 6 = 15 cm
- Double the answer. A rectangle has two lengths and two widths.2 × 15 = 30 cm
- Write the perimeter. Give the unit cm.30 cm
Check. Check: 9 + 6 + 9 + 6 = 30 cm.
Watch out. Count all four sides. Do not forget the two sides you have not added yet.
Method. Choose the operation from what happens in the story, and say why.
- Read the story. Two costs are put together for a total.£19.05 and £8.48
- Choose the operation. When amounts are combined, we add them.Add
- Give the reason. The total is the sum of the amounts.Accept any answer that says add and gives a reason, such as: the costs are put together
Check. Accept any answer that names the operation and gives a sensible reason, such as the one shown.
Watch out. Read the key words: spent, left, altogether, total, change, and each.
Method. Divide by 60 to find the hours; the remainder is the minutes.
- Share the minutes into groups of 60. Each group of 60 minutes is one hour.233 ÷ 60 = 3 r 53
- Write the hours and the minutes left. The remainder is the minutes that are left over.3 h and 53 min
- Write the answer. Use the units hours and minutes.3 h 53 min
Check. Check: 3 × 60 + 53 = 233.
Watch out. Do not write 1 h 95 min. The minutes must be less than 60.
Method. Add one length and one width, then double the answer.
- Add the length and the width. One long side and one short side.6 + 4 = 10 cm
- Double the answer. A rectangle has two lengths and two widths.2 × 10 = 20 cm
- Write the perimeter. Give the unit cm.20 cm
Check. Check: 6 + 4 + 6 + 4 = 20 cm.
Watch out. Count all four sides. Do not forget the two sides you have not added yet.
Method. Choose the operation from what happens in the story, and say why.
- Read the story. Money is spent, so some of it goes away.£17.57 spent £3.52
- Choose the operation. When an amount goes away, we take it away.Subtract
- Give the reason. The money left is what is left after the spending.Accept any answer that says subtract and gives a reason, such as: the money is taken away
Check. Accept any answer that names the operation and gives a sensible reason, such as the one shown.
Watch out. Read the key words: spent, left, altogether, total, change, and each.