Step-by-step Maths Level 5 Perimeter of rectilinear shapes, time and money problems: check-up and practice test questions

Method. Work out each missing side, then add all the sides of the shape.

1. 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
2. List all six sides. The perimeter is the distance all the way round.
   2 + 2 + 3 + 2 + 5 + 4 cm
3. Add the sides. Add all the lengths together.
   18 cm
4. 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.

1. Work out the cost of the cups. Multiply the price by the number of cups.
   4 × £0.88 = £3.52
2. Add the cost of the cake. Add all the items to find the total.
   £3.52 + £2.10 = £5.62
3. Work out the change. Change is what is left from the money paid.
   £10.00 - £5.62 = £4.38
4. 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.

1. 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
2. Count the whole hours. Count each full hour after that.
   0 whole hours
3. Count the minutes after the last whole hour. Count on to the arrival time.
   42 min
4. Add the parts. Add all the parts for the total time.
   36 min + 0 h + 42 min = 1 h 18 min
5. 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.

1. 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
2. Count the whole hours. Count each full hour after that.
   3 whole hours
3. Count the minutes after the last whole hour. Count on to the arrival time.
   50 min
4. Add the parts. Add all the parts for the total time.
   40 min + 3 h + 50 min = 4 h 30 min
5. 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.

1. Add the two costs. Add the pounds and the pence together.
   £4.89 + £0.81 = £5.70
2. Take the total away from the money Sam has. Subtract the total cost.
   £16.89 - £5.70 = £11.19
3. 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.

1. Add the two costs. Add the pounds and the pence together.
   £1.49 + £2.65 = £4.14
2. Take the total away from the money Sam has. Subtract the total cost.
   £17.83 - £4.14 = £13.69
3. 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.

1. 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
2. List all six sides. The perimeter is the distance all the way round.
   3 + 4 + 8 + 3 + 11 + 7 cm
3. Add the sides. Add all the lengths together.
   36 cm
4. 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.

1. 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
2. List all six sides. The perimeter is the distance all the way round.
   6 + 2 + 6 + 2 + 12 + 4 cm
3. Add the sides. Add all the lengths together.
   32 cm
4. 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.

1. 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
2. List all six sides. The perimeter is the distance all the way round.
   6 + 2 + 3 + 3 + 9 + 5 cm
3. Add the sides. Add all the lengths together.
   28 cm
4. 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.

1. Use the rule. There are 60 minutes in 1 hour.
   1 h = 60 min
2. Multiply the hours by 60. Each hour has 60 minutes.
   9 × 60 = 540
3. 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. Work out each missing side, then add all the sides of the shape.

1. 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
2. List all six sides. The perimeter is the distance all the way round.
   2 + 2 + 5 + 2 + 7 + 4 cm
3. Add the sides. Add all the lengths together.
   22 cm
4. 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.

1. 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
2. List all six sides. The perimeter is the distance all the way round.
   4 + 4 + 8 + 4 + 12 + 8 cm
3. Add the sides. Add all the lengths together.
   40 cm
4. 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.

1. 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
2. List all six sides. The perimeter is the distance all the way round.
   4 + 5 + 4 + 4 + 8 + 9 cm
3. Add the sides. Add all the lengths together.
   34 cm
4. 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.

1. 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
2. List all six sides. The perimeter is the distance all the way round.
   2 + 4 + 6 + 2 + 8 + 6 cm
3. Add the sides. Add all the lengths together.
   28 cm
4. 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.

1. Share the minutes into groups of 60. Each group of 60 minutes is one hour.
   96 ÷ 60 = 1 r 36
2. Write the hours and the minutes left. The remainder is the minutes that are left over.
   1 h and 36 min
3. 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.

1. Add the length and the width. One long side and one short side.
   9 + 6 = 15 cm
2. Double the answer. A rectangle has two lengths and two widths.
   2 × 15 = 30 cm
3. 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.

1. Read the story. Two costs are put together for a total.
   £19.05 and £8.48
2. Choose the operation. When amounts are combined, we add them.
   Add
3. 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.

1. Share the minutes into groups of 60. Each group of 60 minutes is one hour.
   233 ÷ 60 = 3 r 53
2. Write the hours and the minutes left. The remainder is the minutes that are left over.
   3 h and 53 min
3. 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.

1. Add the length and the width. One long side and one short side.
   6 + 4 = 10 cm
2. Double the answer. A rectangle has two lengths and two widths.
   2 × 10 = 20 cm
3. 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.

1. Read the story. Money is spent, so some of it goes away.
   £17.57 spent £3.52
2. Choose the operation. When an amount goes away, we take it away.
   Subtract
3. 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.