Year 5 Units, perimeter, area, volume and time: check-up and SATs-style questions

Key words. A unit is the size we measure with. Metric units go up in tens, hundreds and thousands, so we convert between them by multiplying or dividing. A smaller unit gives a bigger number.

Method. Use the rule to see how many of the new unit there are. Multiply for a smaller unit, and divide for a bigger unit.

1. Write the rule. This rule links the two units, so we know how many of the smaller one make the bigger one.
   1 km = 1,000 m
2. Multiply, because the new unit is smaller. A smaller unit fits in more times, so the number gets bigger.
   4.2 × 1,000 = 4,200
3. Write the answer with the new unit.
   4,200 m

Check. 4,200 ÷ 1,000 = 4.2, which is the number we started with. ✓

Watch out. Check the size: a smaller unit must give a bigger number, and a bigger unit must give a smaller number.

Key words. A unit is the size we measure with. Metric units go up in tens, hundreds and thousands, so we convert between them by multiplying or dividing. A smaller unit gives a bigger number.

Method. Use the rule to see how many of the new unit there are. Multiply for a smaller unit, and divide for a bigger unit.

1. Write the rule. This rule links the two units, so we know how many of the smaller one make the bigger one.
   100 cm = 1 m
2. Divide, because the new unit is bigger. A bigger unit fits in fewer times, so the number gets smaller.
   625 ÷ 100 = 6.25
3. Write the answer with the new unit.
   6.25 m

Check. 6.25 × 100 = 625, which is the number we started with. ✓

Watch out. Check the size: a smaller unit must give a bigger number, and a bigger unit must give a smaller number.

Key words. A unit is the size we measure with. Metric units go up in tens, hundreds and thousands, so we convert between them by multiplying or dividing. A smaller unit gives a bigger number.

Method. Use the rule to see how many of the new unit there are. Multiply for a smaller unit, and divide for a bigger unit.

1. Write the rule. This rule links the two units, so we know how many of the smaller one make the bigger one.
   1 inch ≈ 2.5 cm
2. Multiply, because the new unit is smaller. A smaller unit fits in more times, so the number gets bigger.
   3 × 2.5 = 7.5
3. Write the answer with the new unit.
   about 7.5 cm

Check. 7.5 ÷ 2.5 = 3, which is the number we started with. ✓

Watch out. Check the size: a smaller unit must give a bigger number, and a bigger unit must give a smaller number.

Key words. The perimeter is the distance all the way round the outside of a shape. A composite shape is made from two or more simple shapes, such as rectangles.

Method. Add the lengths of all the sides on the outside.

1. Find every side on the outside. The perimeter is the distance all the way round the outside, so each outside side counts once.
   4 sides: 6.5 cm, 4 cm, 6.5 cm, 4 cm
2. Add the lengths of the sides. Add one side at a time and keep the unit.
   6.5 + 4 + 6.5 + 4 = 21 cm
3. Write the answer.
   21 cm

Check. The shortcut gives the same answer: 2 × (6.5 + 4) = 21 cm. ✓

Watch out. A rectangle has two lengths and two widths. Add all four sides once each.

Key words. The area is the amount of surface inside a shape. We measure area in square units, such as cm² (square centimetres) or m² (square metres).

Method. Multiply the length by the width. The answer is in square units.

1. Write the rule. The area is the number of squares that cover the shape. For a rectangle we multiply the length by the width.
   Area = length × width
2. Multiply the length by the width. Each row has as many squares as the length, and there is one row for each unit of width.
   9 × 4 = 36
3. Write the answer with square units. We are counting squares, so the unit is squared.
   36 m²

Check. 4 × 9 gives the same answer, because the order does not matter. ✓

Watch out. Area is in square units (cm²). Do not add the lengths: adding them gives the perimeter.

Key words. The volume is the amount of space a solid takes up, measured in cubic units such as cm³. Capacity is how much a container can hold. 1 ml is the same as 1 cm³.

Method. Find the cubes in one layer, then multiply by the number of layers.

1. Count the cubes in one layer. One layer is a rectangle of cubes, so multiply its length by its width.
   5 × 2 = 10 cubes in one layer
2. Count the layers. The layers are stacked on top of each other.
   3 layers
3. Multiply the cubes in one layer by the number of layers. Every layer has the same number of cubes.
   10 × 3 = 30 cubes
4. Write the answer in cubic centimetres. Each cube is 1 cm long, 1 cm wide and 1 cm high, so the volume is in cm³.
   30 cm³

Check. 5 × 3 × 2 = 30 as well, so the answer does not depend on the order. ✓

Watch out. Volume is measured in cubic centimetres (cm³), not square centimetres.

Key words. A unit is the size we measure with. Metric units go up in tens, hundreds and thousands, so we convert between them by multiplying or dividing. A smaller unit gives a bigger number.

Method. Use the rule to see how many of the new unit there are. Multiply for a smaller unit, and divide for a bigger unit.

1. Write the rule. This rule links the two units, so we know how many of the smaller one make the bigger one.
   1 hour = 60 minutes
2. Multiply, because the new unit is smaller. A smaller unit fits in more times, so the number gets bigger.
   2.5 × 60 = 150
3. Write the answer with the new unit.
   150 minutes

Check. 150 ÷ 60 = 2.5, which is the number we started with. ✓

Watch out. Check the size: a smaller unit must give a bigger number, and a bigger unit must give a smaller number.

Key words. A unit is the size we measure with. Metric units go up in tens, hundreds and thousands, so we convert between them by multiplying or dividing. A smaller unit gives a bigger number.

Method. Use the rule to see how many of the new unit there are. Multiply for a smaller unit, and divide for a bigger unit.

1. Write the rule. This rule links the two units, so we know how many of the smaller one make the bigger one.
   1 litre = 1,000 ml
2. Multiply, because the new unit is smaller. A smaller unit fits in more times, so the number gets bigger.
   1.75 × 1,000 = 1,750
3. Write the answer with the new unit.
   1,750 ml

Check. 1,750 ÷ 1,000 = 1.75, which is the number we started with. ✓

Watch out. Check the size: a smaller unit must give a bigger number, and a bigger unit must give a smaller number.

Key words. The area is the amount of surface inside a shape. We measure area in square units, such as cm² (square centimetres) or m² (square metres).

Method. Count the whole squares, then count the part squares and make pairs. Each pair is one whole square.

1. Count the whole squares inside the shape. A whole square is completely inside the outline.
   10 whole squares
2. Count the part squares, then pair them up. Each part square is exactly half a square. Two of them make one whole square.
   3 part squares ÷ 2 = 1.5 whole squares
3. Add the two counts. The total is the area of the shape in squares.
   10 + 1.5 = 11.5
4. Write the answer with square units. This is an estimate, so we say about.
   about 11.5 cm²

Check. Count the shape again, row by row, to check you have not missed a square. ✓

Watch out. Do not count a part square as a whole square, and do not leave out the part squares.

Key words. The perimeter is the distance all the way round the outside of a shape. A composite shape is made from two or more simple shapes, such as rectangles.

Method. Find the hidden sides by subtracting, then add all the outside sides.

1. Find the missing top side. The top is shorter than the bottom by the width of the notch (2 cm).
   6 − 2 = 4 cm
2. Find the missing inside side. The left side is 4 cm tall. The lower right side is 3 cm, so the rest is the inside side.
   4 − 3 = 1 cm
3. Add all six outside sides. Go all the way round the shape once and add each side.
   6 + 3 + 2 + 1 + 4 + 4 = 20 cm
4. Write the answer.
   20 cm

Check. Shortcut for an L-shape: 2 × (6 + 4) = 20 cm, which matches. ✓

Watch out. Count each outside side once. The two short sides inside the notch are outside sides too.

Key words. A unit is the size we measure with. Metric units go up in tens, hundreds and thousands, so we convert between them by multiplying or dividing. A smaller unit gives a bigger number.

Method. Use the rule to see how many of the new unit there are. Multiply for a smaller unit, and divide for a bigger unit.

1. Write the rule. This rule links the two units, so we know how many of the smaller one make the bigger one.
   1 kg = 1,000 g
2. Multiply, because the new unit is smaller. A smaller unit fits in more times, so the number gets bigger.
   3.2 × 1,000 = 3,200
3. Write the answer with the new unit.
   3,200 g

Check. 3,200 ÷ 1,000 = 3.2, which is the number we started with. ✓

Watch out. Check the size: a smaller unit must give a bigger number, and a bigger unit must give a smaller number.

Key words. A unit is the size we measure with. Metric units go up in tens, hundreds and thousands, so we convert between them by multiplying or dividing. A smaller unit gives a bigger number.

Method. Use the rule to see how many of the new unit there are. Multiply for a smaller unit, and divide for a bigger unit.

1. Write the rule. This rule links the two units, so we know how many of the smaller one make the bigger one.
   1 litre = 1,000 ml
2. Multiply, because the new unit is smaller. A smaller unit fits in more times, so the number gets bigger.
   0.35 × 1,000 = 350
3. Write the answer with the new unit.
   350 ml

Check. 350 ÷ 1,000 = 0.35, which is the number we started with. ✓

Watch out. Check the size: a smaller unit must give a bigger number, and a bigger unit must give a smaller number.

Key words. A unit is the size we measure with. Metric units go up in tens, hundreds and thousands, so we convert between them by multiplying or dividing. A smaller unit gives a bigger number.

Method. Use the rule to see how many of the new unit there are. Multiply for a smaller unit, and divide for a bigger unit.

1. Write the rule. This rule links the two units, so we know how many of the smaller one make the bigger one.
   1 inch ≈ 2.5 cm
2. Multiply, because the new unit is smaller. A smaller unit fits in more times, so the number gets bigger.
   6 × 2.5 = 15
3. Write the answer with the new unit.
   about 15 cm

Check. 15 ÷ 2.5 = 6, which is the number we started with. ✓

Watch out. Check the size: a smaller unit must give a bigger number, and a bigger unit must give a smaller number.

Key words. The perimeter is the distance all the way round the outside of a shape. A composite shape is made from two or more simple shapes, such as rectangles.

Method. Find the hidden sides by subtracting, then add all the outside sides.

1. Find the missing top side. The top is shorter than the bottom by the width of the notch (3 cm).
   7 − 3 = 4 cm
2. Find the missing inside side. The left side is 5 cm tall. The lower right side is 3 cm, so the rest is the inside side.
   5 − 3 = 2 cm
3. Add all six outside sides. Go all the way round the shape once and add each side.
   7 + 3 + 3 + 2 + 4 + 5 = 24 cm
4. Write the answer.
   24 cm

Check. Shortcut for an L-shape: 2 × (7 + 5) = 24 cm, which matches. ✓

Watch out. Count each outside side once. The two short sides inside the notch are outside sides too.

Key words. The volume is the amount of space a solid takes up, measured in cubic units such as cm³. Capacity is how much a container can hold. 1 ml is the same as 1 cm³.

Method. Find the cubes in one layer, then multiply by the number of layers.

1. Count the cubes in one layer. One layer is a rectangle of cubes, so multiply its length by its width.
   5 × 3 = 15 cubes in one layer
2. Count the layers. The layers are stacked on top of each other.
   2 layers
3. Multiply the cubes in one layer by the number of layers. Every layer has the same number of cubes.
   15 × 2 = 30 cubes
4. Write the answer in cubic centimetres. Each cube is 1 cm long, 1 cm wide and 1 cm high, so the volume is in cm³.
   30 cm³

Check. 5 × 2 × 3 = 30 as well, so the answer does not depend on the order. ✓

Watch out. Volume is measured in cubic centimetres (cm³), not square centimetres.

Key words. A unit is the size we measure with. Metric units go up in tens, hundreds and thousands, so we convert between them by multiplying or dividing. A smaller unit gives a bigger number.

Method. Change the litres to millilitres, then divide by the size of one jug.

1. Change 4.5 litres to millilitres. There are 1,000 ml in 1 litre.
   4.5 × 1,000 = 4,500 ml
2. Divide by the size of one jug. Count how many 750 ml jugs fill 4,500 ml.
   4,500 ÷ 750 = 6
3. Write the answer. The tank is filled exactly, with no part jug left over.
   6 jugs

Check. 6 × 750 ml = 4,500 ml. ✓

Watch out. Change the litres to millilitres first. Do not divide 4.5 by 750.

Key words. A duration is how long something lasts. There are 60 minutes in 1 hour, 60 seconds in 1 minute, 24 hours in 1 day and 7 days in 1 week.

Method. Change 1 hour 45 minutes to minutes, then to seconds.

1. Change the hour and the minutes to minutes. One hour is 60 minutes. Add the 45 minutes.
   60 + 45 = 105 minutes
2. Change minutes to seconds. One minute is 60 seconds.
   105 × 60 = 6,300 seconds
3. Write the answer.
   6,300 seconds

Check. 6,300 ÷ 60 = 105 minutes. ✓

Watch out. Change to minutes first, then to seconds. Check the number is bigger in seconds.

Key words. To scale a quantity is to multiply or divide it by a number, for example to make a recipe for 6 people instead of 4.

Method. Find the amount for 1 person first, then multiply by 5.

1. Find the amount for 1 person. The recipe serves 3 people, so share 240 g between 3 people.
   240 ÷ 3 = 80 g
2. Multiply by 5 people. Five people each need 80 g.
   80 × 5 = 400 g
3. Write the answer.
   400 g

Check. 400 g ÷ 5 = 80 g, the same as 1 person. ✓

Watch out. Scaling up: find 1 first, then multiply.

Key words. The perimeter is the distance all the way round the outside of a shape. A composite shape is made from two or more simple shapes, such as rectangles.

Method. Find the perimeter of the garden, then multiply by the cost per metre.

1. Find the perimeter. The fence goes all the way round the garden.
   2 × (12.5 + 8) = 41 m
2. Multiply by the cost of one metre. Each metre costs £4.50.
   41 × 4.50 = 184.50
3. Check the size of the answer. About 40 m at about £4.50 a metre is about £180, which is close.
   £184.50 is about right.
4. Write the answer with £.
   £184.50

Check. £184.50 ÷ 41 = £4.50. ✓

Watch out. Find the perimeter first. Multiplying by the length of only one side gives the wrong answer.