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SATs practice · Year 6Chapter 4 · Measures in context
Year 6 · Chapter 4

Measures in context

By the end of this chapter you will be able to

  • Change a measure from one unit to another, including decimals
  • Work out how long something takes from a start and an end time
  • Use an approximate conversion between miles and kilometres, or pounds and kilograms
  • Find the area of a rectangle, a triangle or a parallelogram, and of a shape made of rectangles
  • Explain why two shapes with the same area can have different perimeters

You should already know

  • Metric units and the four operations with decimals (Year 5 measures)
  • Area of a rectangle and the times tables (Year 5 measures)

Where this leads

  • Position and coordinates (Chapter 6 of this book)

KS2 SATs practice for reasoning (Year 6). Original questions in the style of the national tests. Content: Convert between metric units of length, mass and capacity, including decimals (Year 5-6), Use, read, write and convert between standard units, using decimal notation (Year 6), Convert between miles and kilometres, and use approximate imperial equivalents (Year 5-6), Solve problems involving the calculation and conversion of units of measure (Year 6), Convert between units of time, including timetables and durations (Year 5-6), Calculate the perimeter of composite rectilinear shapes and the area of rectangles, triangles and parallelograms (Year 5-6), Recognise that shapes with the same area can have different perimeters, and compare the volumes of cubes and cuboids (Year 6).

Exercise P  Do you remember?

Non-calculator
1
FChange 3 m to cm.
2
FHow many minutes are there in 2 hours?
3
FA rectangle is 5 cm long and 4 cm wide. What is its area? Write the answer with square units.
4
FChange 0.5 kg to g.
5
FWrite 0.4 of a metre as a number of centimetres.
4.1

Metric units of length, mass and capacity

Year 6
Convert between metric units of length, mass and capacity, including decimals (Year 5-6), Use, read, write and convert between standard units, using decimal notation (Year 6)
Video lesson: Metric units of length, mass and capacityComing soon
Practice material. Do this without a calculator. This is practice in the style of the Year 6 maths reasoning test. It is not the official test, and no official test item is used. Marks and timings are a practice guide only.
Story. The school garden club measures rainwater in a barrel, weighs the compost in bags and measures the lengths of the beds. Their notes mix metres, centimetres, litres and millilitres, so they must change them to the same unit before they compare.

Rule

Length: 10 mm = 1 cm, 100 cm = 1 m, 1000 m = 1 km. Mass: 1000 g = 1 kg. Capacity: 1000 ml = 1 litre.

Changing to a smaller unit gives a bigger number: multiply. Changing to a bigger unit gives a smaller number: divide.

Key ideas

  • Smaller unit: multiply. Bigger unit: divide.
  • 1 kg = 1000 g, so 2.5 kg = 2500 g.
  • Check the answer: a bigger unit should give a smaller number.
Worked example 4.1.1
Change 2.5 km to m.

Method. Find the number of smaller units in one bigger unit, then multiply or divide.

  1. Find how many m make one km. There are 1000 m in 1 km.
    1 km = 1000 m
  2. Multiply by 1000. Changing to a smaller unit needs more of them, so the number gets bigger: multiply.
    2.5 x 1000 = 2500
  3. Write the answer with the new unit. Keep the same measure, in the new unit.
    2500 m
  4. Write the answer.
    2500 m

Check. 2500 m is the same length, mass or volume as 2.5 km. ✓

Watch out. Going from a bigger unit to a smaller one makes the number bigger.

Worked example 4.1.2
Change 4500 g to kg.

Method. Find the number of smaller units in one bigger unit, then multiply or divide.

  1. Find how many g make one kg. There are 1000 g in 1 kg.
    1 kg = 1000 g
  2. Divide by 1000. Changing to a bigger unit needs fewer of them, so the number gets smaller: divide.
    4500 / 1000 = 4.5
  3. Write the answer with the new unit. Keep the same measure, in the new unit.
    4.5 kg
  4. Write the answer.
    4.5 kg

Check. 4.5 kg is the same length, mass or volume as 4500 g. ✓

Watch out. Going from a bigger unit to a smaller one makes the number bigger.

Worked example 4.1.3
Change 0.75 l to ml.

Method. Find the number of smaller units in one bigger unit, then multiply or divide.

  1. Find how many ml make one l. There are 1000 ml in 1 l.
    1 l = 1000 ml
  2. Multiply by 1000. Changing to a smaller unit needs more of them, so the number gets bigger: multiply.
    0.75 x 1000 = 750
  3. Write the answer with the new unit. Keep the same measure, in the new unit.
    750 ml
  4. Write the answer.
    750 ml

Check. 750 ml is the same length, mass or volume as 0.75 l. ✓

Watch out. Going from a bigger unit to a smaller one makes the number bigger.

Watch out

Watch out. 0.5 km is 500 m, not 50 m. Move the decimal point the right number of places.

Exam tip

Practice guide. Write both units in the question first, then decide whether to multiply or divide.

Exercise 4A  Practice: metric units

Non-calculator
1
FChange 1.199999999999999955591079015 m to cm.
2
FChange 3500 ml to l.
3
FChange 2.45000000000000017763568394 kg to g.
4
FChange 480 cm to m.
5
FChange 0.05999999999999999777955395075 km to m.
6
FChange 750 mm to cm.
7
FChange 6.5 l to ml.
8
FChange 1250 g to kg.
9
PSA jug holds 1.5 litres. How many 250 ml glasses can be filled from the full jug?
10
PSA bag of flour has a mass of 2.4 kg. A cake uses 150 g. How many whole cakes can be made from the bag?
11
RSam says 0.5 km is 50 m. Is he right? Choose one: Yes, 0.5 km is 50 m or No, 0.5 km is 500 m.
12
FTick the statements that are true. Options: 1 m = 100 cm | 1 kg = 100 g | 1 litre = 100 ml | 1 km = 100 m | 1 cm = 10 mm. Write the options you would tick, in the order given.
13
FA rope is 3.25 m long. Write its length in centimetres.
14
PSA rain gauge collects 2 l 350 ml of water. Write this in litres.
15
RA builder needs 4 m of pipe. Pipes are sold in lengths of 80 cm. Explain how many pipes are needed.
16
PSMia has 0.8 kg of grapes and 650 g of cherries. How many grams of fruit does she have altogether?
17
RSam says that 2.4 litres is more than 2400 ml. Is he right? Explain.
4.2

Time, durations and timetables

Year 6
Convert between units of time, including timetables and durations (Year 5-6)
Video lesson: Time, durations and timetablesComing soon
Story. A bus timetable for the school trip shows when the coach leaves the car park and when it reaches the museum. Mr Hall needs to work out the time each journey takes so that the class arrives on time.

Rule

There are 60 minutes in an hour, 24 hours in a day and 60 seconds in a minute.

To find a duration, work out the time in minutes for each time, then subtract. Change the answer back to hours and minutes.

Key ideas

  • 1 hour = 60 minutes; 1 minute = 60 seconds.
  • To find a duration, subtract the start time from the end time.
  • Do not write 1 h 75 min: that is 2 h 15 min.
Worked example 4.2.1
A journey starts at 09:15 and ends at 11:50. How long does it take? Write hours and minutes.

Method. Find the difference between the two times in minutes, then change to hours and minutes.

  1. Change both times to minutes past midnight. 09:15 is 555 minutes and 11:50 is 710 minutes.
    555 and 710
  2. Subtract the start from the end. 710 - 555 = 155 minutes.
    155 minutes
  3. Change back to hours and minutes. 155 minutes is 2 hour(s) and 35 minutes.
    2 h 35 min
  4. Write the answer.
    2 h 35 min

Check. 09:15 + 2 h 35 min = 11:50. ✓

Watch out. Do not count 60 minutes as 100 when you change between hours and minutes.

Worked example 4.2.2
A journey starts at 08:40 and ends at 12:05. How long does it take? Write hours and minutes.

Method. Find the difference between the two times in minutes, then change to hours and minutes.

  1. Change both times to minutes past midnight. 08:40 is 520 minutes and 12:05 is 725 minutes.
    520 and 725
  2. Subtract the start from the end. 725 - 520 = 205 minutes.
    205 minutes
  3. Change back to hours and minutes. 205 minutes is 3 hour(s) and 25 minutes.
    3 h 25 min
  4. Write the answer.
    3 h 25 min

Check. 08:40 + 3 h 25 min = 12:05. ✓

Watch out. Do not count 60 minutes as 100 when you change between hours and minutes.

Worked example 4.2.3
A journey starts at 13:20 and ends at 15:05. How long does it take? Write hours and minutes.

Method. Find the difference between the two times in minutes, then change to hours and minutes.

  1. Change both times to minutes past midnight. 13:20 is 800 minutes and 15:05 is 905 minutes.
    800 and 905
  2. Subtract the start from the end. 905 - 800 = 105 minutes.
    105 minutes
  3. Change back to hours and minutes. 105 minutes is 1 hour(s) and 45 minutes.
    1 h 45 min
  4. Write the answer.
    1 h 45 min

Check. 13:20 + 1 h 45 min = 15:05. ✓

Watch out. Do not count 60 minutes as 100 when you change between hours and minutes.

Watch out

Watch out. From 10:45 to 11:20 is 35 minutes, not 75 minutes. Count the minutes after the hour.

Exam tip

Practice guide. Count on from the start time to the next hour, then to the end time.

Exercise 4B  Practice: time and durations

Non-calculator
1
FA journey starts at 07:35 and ends at 10:10. How long does it take? Write hours and minutes.
2
FA journey starts at 14:25 and ends at 16:00. How long does it take? Write hours and minutes.
3
FA journey starts at 06:50 and ends at 09:05. How long does it take? Write hours and minutes.
4
FA journey starts at 10:45 and ends at 11:20. How long does it take? Write hours and minutes.
5
PSA bus leaves at 08:25 and the journey takes 47 minutes. What time does it arrive? Write the time in the 24-hour clock.
6
PSA film starts at 19:40 and lasts 2 hours 15 minutes. What time does it finish? Write the time in the 24-hour clock.
7
FWrite 3 hours 20 minutes as a number of minutes.
8
FHow many seconds are there in 4 minutes?
9
PSA train was 35 minutes late. It was due at 13:50. What time did it arrive? Write the time.
10
RAli says 1 hour 30 minutes is 130 minutes. Is he right? Explain.
11
PSA swimming lesson starts at 16:10 and finishes at 17:05. How long is the lesson, in minutes?
12
PSA timetable shows a bus at 07:50 and another at 08:15. Which is the gap between the buses? Choose one: 25 minutes, 35 minutes or 65 minutes.
13
PSA school day runs from 08:50 to 15:20, with a break of 1 hour 20 minutes. How many minutes of lessons are there, not counting the break?
14
PSWrite the time 2 hours and 45 minutes after 11:30 in the 24-hour clock.
4.3

Miles, kilometres and approximate imperial units

Year 6
Convert between miles and kilometres, and use approximate imperial equivalents (Year 5-6)
Video lesson: Miles, kilometres and approximate imperial unitsComing soon
Story. A family is driving to a holiday cottage. The map shows the distance in miles, but the car satnav and the camera use kilometres, so the family works out the approximate distance in both.

Rule

Approximate conversions: 1 mile is about 1.6 km. 1 kg is about 2.2 pounds (lb). 1 inch is about 2.5 cm. 1 litre is about 1.75 pints.

These are estimates, so the answer is about a number. Multiply by the rule, then round.

Key ideas

  • 5 miles is about 8 km, so 10 miles is about 16 km.
  • An approximate conversion gives an answer with about in front.
  • Round to a sensible number of whole units.
Worked example 4.3.1
Roughly how many km is 5 miles? Use the rule: 1 mile is about 1.6 km.

Method. Multiply by the approximate conversion factor, then round.

  1. Use the approximate rule: 1 mile is about 1.6 km. The rule is only an estimate, so the answer is about this amount.
    5 miles x 1.6 = 8.00
  2. Round to the nearest whole number. Round to the nearest whole number for a sensible answer.
    about 8 km
  3. Write the answer.
    about 8 km

Check. 5 x 1.6 is about 8. ✓

Watch out. Imperial and metric conversions are approximate. Write about in your answer.

Worked example 4.3.2
Roughly how many pounds is 60 kg? Use the rule: 1 kg is about 2.2 pounds.

Method. Multiply by the approximate conversion factor, then round.

  1. Use the approximate rule: 1 kg is about 2.2 pounds. The rule is only an estimate, so the answer is about this amount.
    60 kg x 2.2 = 132.00
  2. Round to the nearest whole number. Round to the nearest whole number for a sensible answer.
    about 132 pounds
  3. Write the answer.
    about 132 pounds

Check. 60 x 2.2 is about 132. ✓

Watch out. Imperial and metric conversions are approximate. Write about in your answer.

Worked example 4.3.3
Roughly how many cm is 20 inches? Use the rule: 1 inch is about 2.5 cm.

Method. Multiply by the approximate conversion factor, then round.

  1. Use the approximate rule: 1 inch is about 2.5 cm. The rule is only an estimate, so the answer is about this amount.
    20 inches x 2.5 = 50.00
  2. Round to the nearest whole number. Round to the nearest whole number for a sensible answer.
    about 50 cm
  3. Write the answer.
    about 50 cm

Check. 20 x 2.5 is about 50. ✓

Watch out. Imperial and metric conversions are approximate. Write about in your answer.

Watch out

Watch out. A mile is longer than a kilometre. 10 miles is about 16 km, not 10 km.

Exam tip

Practice guide. Use 5 miles = 8 km as a check when you are not sure of the rule.

Exercise 4C  Practice: miles, kilometres and imperial units

Non-calculator
1
FRoughly how many km is 10 miles? Use the rule: 1 mile is about 1.6 km.
2
FRoughly how many km is 26 miles? Use the rule: 1 mile is about 1.6 km.
3
FRoughly how many pounds is 4 kg? Use the rule: 1 kg is about 2.2 pounds.
4
FRoughly how many pints is 3 litres? Use the rule: 1 litre is about 1.75 pints.
5
FRoughly how many cm is 2 inches? Use the rule: 1 inch is about 2.5 cm.
6
PSWhich is the best estimate of 10 km in miles? Choose one: about 6 miles, about 16 miles or about 10 miles.
7
PSA cyclist rides 20 miles. Roughly how far is this in kilometres? Use 1 mile = 1.6 km.
8
RExplain why a 10 km race is much shorter than a 10 mile race.
9
PSA baby weighs 3.5 kg. Roughly how many pounds is this? Use 1 kg = 2.2 pounds and round to the nearest pound.
10
PSA hiker walks 15 miles on Saturday and 8 miles on Sunday. Roughly how many kilometres does she walk in total? Use 1 mile = 1.6 km.
11
RTick the statements that are reasonable approximations. Options: 5 miles is about 8 km | 1 kg is about 10 pounds | 2 inches is about 5 cm | 1 litre is about 5 pints. Write the options you would tick, in the order given.
12
PSA car travels 80 km. Roughly how many miles is this? Use 8 km = 5 miles.
4.4

Perimeter and area of rectangles, triangles, parallelograms and composite shapes

Year 6
Calculate the perimeter of composite rectilinear shapes and the area of rectangles, triangles and parallelograms (Year 5-6)
Video lesson: Perimeter and area of rectangles, triangles, parallelograms and composite shapesComing soon
Story. Ravi is fencing and painting a garden shed. He needs the area of the front wall, which is a rectangle with a triangle on top, and the perimeter of the garden shape to order the fencing.

Rule

Rectangle: area = length x width. Triangle: area = base x perpendicular height / 2. Parallelogram: area = base x perpendicular height.

For a shape made of rectangles, find each area and add them. For perimeter, add all the outside sides.

Key ideas

  • Use the perpendicular height for triangles and parallelograms.
  • A triangle is half of a rectangle with the same base and height.
  • The perimeter of a rectilinear shape is the total length of its outside edges.
Worked example 4.4.1
A rectangle is 12 cm long and 7 cm wide. What is its area? Write the answer with square units.

Method. Multiply the length by the width.

  1. Write the formula. Area of a rectangle = length x width.
    12 x 7
  2. Multiply. Multiply the length by the width.
    12 x 7 = 84
  3. Write the units as square units. The area is measured in square cm.
    84 cm²
  4. Write the answer.
    84 cm²

Check. 84 / 12 = 7. ✓

Watch out. Area is measured in square units, so the answer ends with a small 2, such as cm².

Worked example 4.4.2
A triangle has a base of 10 cm and a perpendicular height of 6 cm. What is its area?

Method. Multiply the base by the height, then halve.

  1. Write the formula. Area of a triangle = base x height / 2.
    10 x 6 / 2
  2. Multiply the base and the height. Multiply first.
    10 x 6 = 60
  3. Halve the answer. A triangle is half of a rectangle with the same base and height.
    60 / 2 = 30
  4. Write the answer. Square units for area.
    30 cm²
  5. Write the answer.
    30 cm²

Check. A rectangle 10 by 6 has area 60, and half of it is 30. ✓

Watch out. Use the perpendicular height, not the slanted side.

Worked example 4.4.3
A shape is made from two rectangles. One is 6 cm by 4 cm, and the other is 3 cm by 2 cm. What is the total area?

Method. Split the shape into rectangles, find each area, then add.

  1. Split the shape into two rectangles. Rectangle 1 is 6 cm by 4 cm; rectangle 2 is 3 cm by 2 cm.
    6 x 4 and 3 x 2
  2. Find each area. Multiply the length and width of each rectangle.
    24 and 6
  3. Add the areas. The total area is the sum of the two parts.
    24 + 6 = 30
  4. Write the answer. Square units for area.
    30 cm²
  5. Write the answer.
    30 cm²

Check. 24 + 6 = 30. ✓

Watch out. Check that the two rectangles do not overlap.

Watch out

Watch out. Do not use the slanted side of a triangle or a parallelogram. Use the perpendicular height.

Exam tip

Practice guide. Draw the shape and label the lengths before you multiply.

Exercise 4D  Practice: perimeter and area

Non-calculator
1
FA rectangle is 15 m long and 8 m wide. What is its area? Write the answer with square units.
2
FA triangle has a base of 7 cm and a perpendicular height of 4 cm. What is its area?
3
FA triangle has a base of 9 cm and a perpendicular height of 6 cm. What is its area?
4
FA parallelogram has a base of 11 cm and a perpendicular height of 5 cm. What is its area?
5
FA shape is made from two rectangles. One is 8 m by 5 m, and the other is 4 m by 3 m. What is the total area?
6
PSA shape is made from two rectangles. One is 10 cm by 3 cm, and the other is 4 cm by 6 cm. What is the total area?
7
FA rectangle has a length of 9 cm and a width of 4 cm. What is its perimeter, in cm?
8
PSAn L-shaped room fits inside a rectangle that is 10 m long and 6 m wide. A corner of size 4 m by 2 m is cut out. What is the perimeter of the L-shaped room, in metres?
9
PSA poster is 40 cm long and 30 cm wide. A border 5 cm wide is added all the way round the outside. What is the area of the border, in square cm?
10
RSam says the area of a triangle with base 8 cm and height 5 cm is 40 square cm. Is he right? Write the correct area.
11
RA triangle and a parallelogram have the same base and the same perpendicular height. Which has the bigger area? Choose one: the parallelogram, the triangle or they are the same.
12
PSA triangle has an area of 30 square cm and a base of 10 cm. What is its perpendicular height, in cm?
13
RExplain why a parallelogram with a base of 6 cm and a slanted side of 9 cm might have a height of 5 cm.
14
PSA shape is made from two rectangles. One is 12 cm by 2 cm, and the other is 5 cm by 3 cm. What is the total area?
15
PSA rectangle is 14 cm by 6 cm. A triangle is cut from one corner with base 6 cm and height 4 cm. What is the area left, in square cm?
4.5

Same area, different perimeters, and volume of cuboids

Year 6
Recognise that shapes with the same area can have different perimeters, and compare the volumes of cubes and cuboids (Year 6)
Video lesson: Same area, different perimeters, and volume of cuboidsComing soon
Story. A gardener has 24 square metres of space for a vegetable bed. She can make it long and thin, or short and wide. The bed needs a fence around its edge, so the shape with the smaller perimeter needs less wood.

Rule

Rectangles with the same area can have different perimeters. The closer the length and width, the smaller the perimeter.

Volume of a cuboid = length x width x height. Cubic units are written as cm3.

Key ideas

  • Same area, different perimeter: a square has the smallest perimeter for a given area.
  • Perimeter = 2 x (length + width).
  • Volume is the number of unit cubes that fill the box.
Worked example 4.5.1
Rectangles with a whole-number length and width have an area of 24 square cm. Which rectangle has the smallest perimeter? Write the sides and the perimeter.

Method. List the pairs that multiply to the area, then find each perimeter.

  1. List the whole-number pairs that multiply to the area. Each pair of sides gives area 24.
    1 x 24; 2 x 12; 3 x 8; 4 x 6
  2. Work out each perimeter. Perimeter = 2 x (length + width).
    1 by 24 gives 50; 2 by 12 gives 28; 3 by 8 gives 22; 4 by 6 gives 20
  3. Choose the smallest perimeter. The smallest perimeter is the one with the sides closest in length.
    4 by 6 (perimeter 20)
  4. Write the answer.
    4 by 6 (perimeter 20)

Check. The closest pair of sides gives the smallest perimeter. ✓

Watch out. The same area can have very different perimeters: a long thin rectangle has a bigger perimeter than a square.

Worked example 4.5.2
A box is 4 cm long, 3 cm wide and 5 cm high. What is its volume? Write the answer in cubic centimetres.

Method. Multiply the length, width and height.

  1. Write the formula. Volume of a cuboid = length x width x height.
    4 x 3 x 5
  2. Multiply. Multiply the three lengths.
    4 x 3 = 12, then 12 x 5 = 60
  3. Write the units. Cubic units for volume.
    60 cm³
  4. Write the answer.
    60 cm³

Check. 4 x 3 x 5 = 60. ✓

Watch out. Volume is measured in cubic units, so the answer ends with a small 3, such as cm³.

Worked example 4.5.3
A cube has sides of 4 cm. A cuboid is 6 cm long, 4 cm wide and 3 cm high. Which has the bigger volume? Write cube or cuboid.

Method. Work out the volume of each shape.

  1. Cube. Volume = 4 x 4 x 4 = 64 cm3.
    64 cm³
  2. Cuboid. Volume = 6 x 4 x 3 = 72 cm3.
    72 cm³
  3. Compare. 72 is more than 64, so the cuboid has the bigger volume.
    cuboid
  4. Write the answer.
    cuboid

Check. 72 > 64. ✓

Watch out

Watch out. A long thin rectangle can have a much bigger perimeter than a square with the same area.

Exam tip

Practice guide. List the pairs of sides that multiply to the area, then work out each perimeter.

Exercise 4E  Practice: same area and volume

Non-calculator
1
FRectangles with a whole-number length and width have an area of 36 square cm. Which rectangle has the smallest perimeter? Write the sides and the perimeter.
2
FRectangles with a whole-number length and width have an area of 20 square cm. Which rectangle has the smallest perimeter? Write the sides and the perimeter.
3
FA box is 6 cm long, 2 cm wide and 5 cm high. What is its volume? Write the answer in cubic centimetres.
4
FA box is 3 cm long, 3 cm wide and 3 cm high. What is its volume? Write the answer in cubic centimetres.
5
FA box is 10 cm long, 4 cm wide and 2 cm high. What is its volume? Write the answer in cubic centimetres.
6
RWhich box holds more: a cube of side 5 cm, or a cuboid 4 cm by 6 cm by 4 cm? Write the name of the box.
7
PSA cuboid has a volume of 48 cm3. Its length is 6 cm and its width is 4 cm. What is its height, in cm?
8
RTwo rectangles both have an area of 12 square cm. Which pair of sides could make the rectangle with the smallest perimeter? Choose one: 3 cm by 4 cm, 2 cm by 6 cm or 1 cm by 12 cm.
9
RExplain why a rectangle 6 cm by 2 cm and a rectangle 4 cm by 3 cm both have an area of 12 square cm, but different perimeters.
10
PSA box is 10 cm long, 5 cm wide and 2 cm high. How many cubes of side 1 cm fill the box?
11
PSRectangles with a whole-number length and width have an area of 16 square cm. Which rectangle has the smallest perimeter? Write the sides and the perimeter.
12
PSA rectangle has an area of 30 square cm. Its length is 6 cm. What is its width, in cm, and its perimeter, in cm? Write the width first.
13
RWhich rectangle would need the least fencing for an area of 25 square metres: 25 m by 1 m or 5 m by 5 m? Explain.

Chapter summary

SkillMethod
Metric conversionsSmaller unit: multiply. Bigger unit: divide. 1 km = 1000 m; 1 kg = 1000 g; 1 l = 1000 ml.
TimeChange to minutes, subtract, then change back. 1 hour = 60 minutes.
Miles and kilometresAbout 1.6 km to 1 mile; 5 miles is about 8 km.
Area of a rectangleLength x width.
Area of a triangleBase x perpendicular height / 2.
Area of a parallelogramBase x perpendicular height.
PerimeterThe total length of the outside edges.
Volume of a cuboidLength x width x height, in cubic units.

Can you…?

  • I can convert between metric units, including decimals
  • I can work out a duration and read a timetable
  • I can use an approximate conversion between miles and kilometres
  • I can find the area of a rectangle, triangle, parallelogram and composite shape
  • I can explain why shapes with the same area can have different perimeters
  • I can find the volume of a cuboid and compare two volumes

Key terms

perpendicular height
the straight height at right angles to the base
perimeter
the total distance around the outside of a shape
composite shape
a shape made from two or more simpler shapes
volume
the amount of space inside a 3-D shape, measured in cubic units
approximately
close to, but not exactly equal to
duration
the length of time between a start and an end

Exercise 4Z  Check-up

Non-calculator
1
Change 4.25 kg to g.
2
Change 3600 ml to l.
3
A journey starts at 15:30 and ends at 17:05. How long does it take? Write hours and minutes.
4
Roughly how many km is 15 miles? Use the rule: 1 mile is about 1.6 km.
5
A rectangle is 14 cm long and 9 cm wide. What is its area? Write the answer with square units.
6
A triangle has a base of 12 m and a perpendicular height of 5 m. What is its area?
7
A parallelogram has a base of 8 cm and a perpendicular height of 7 cm. What is its area?
8
A shape is made from two rectangles. One is 7 cm by 3 cm, and the other is 5 cm by 2 cm. What is the total area?
9
A box is 5 cm long, 4 cm wide and 3 cm high. What is its volume? Write the answer in cubic centimetres.
10
Rectangles with a whole-number length and width have an area of 18 square cm. Which rectangle has the smallest perimeter? Write the sides and the perimeter.

Total 24 marks. Allow about 24 minutes.

Exercise 4X  Practice test questions

Non-calculator
1
FChange 0.3499999999999999777955395075 l to ml.[1 mark]
2
FA journey starts at 11:40 and ends at 13:15. How long does it take? Write hours and minutes.[1 mark]
3
PSRoughly how many pounds is 12 kg? Use the rule: 1 kg is about 2.2 pounds.[2 marks]
4
FA triangle has a base of 14 cm and a perpendicular height of 9 cm. What is its area?[2 marks]
5
PSA shape is made from two rectangles. One is 9 m by 4 m, and the other is 6 m by 2 m. What is the total area?[2 marks]
6
FA box is 8 cm long, 3 cm wide and 2 cm high. What is its volume? Write the answer in cubic centimetres.[2 marks]
7
PSA coach leaves school at 08:20. The journey is 1 hour 50 minutes, and the coach stops for a 25 minute break in the middle. What time does the coach arrive? Write the time.[2 marks]
8
RExplain why a 2 metre length of rope and a 200 centimetre length of rope are the same length.[2 marks]
9
PSA cuboid has a volume of 60 cm3. Its height is 5 cm and its width is 3 cm. What is its length, in cm?[2 marks]
10
RA rectangle has an area of 16 square cm. Write the dimensions of two different rectangles with this area, and their perimeters.[3 marks]
11
PSRoughly how many km is 50 miles? Use the rule: 1 mile is about 1.6 km.[2 marks]
12
PSA door is 2 m high. Write its height in centimetres, and then say how many 25 cm strips would fit one above the other, to the nearest whole number.[3 marks]
← Chapter 3: Ratio and proportion reasoningChapter 5: Geometry: angles and shapes →

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