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Either paper 3 marks
Here are four metric units of length.
mm cm m km
Circle the unit that is most suitable for each measurement.
(a)Which unit is most suitable for measuring the length of a pencil?
(b)Which unit is most suitable for measuring the thickness of a coin?
(c)Which unit is most suitable for measuring the length of a tennis court?
Show answer
(a) cm
(b) mm
(c) mThe length of a pencil is about 18 cm. That is a small length that fits in the hand, so centimetres are sensible.
The most suitable unit is cm.
The thickness of a coin is about 2 mm. That is a very small length, so millimetres are sensible.
The most suitable unit is mm.
The length of a tennis court is about 24 m. That is a length a few strides long, so metres are sensible.
The most suitable unit is m.
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Either paper 1 markHere are four lengths.
Circle the shortest length.4.6 cm 0.074 km 0.38 m 63 mm Show answer
4.6 cmThe lengths are in different units, so the numbers cannot be compared as they stand. Change each length to metres.
4.6 cm: \(4.6 \div 100 = 0.046\) m
0.074 km: \(0.074 \times 1000 = 74\) m
0.38 m: already 0.38 m
63 mm: \(63 \div 1000 = 0.063\) m
In metres the lengths are 0.046, 74, 0.38 and 0.063, so the shortest is 0.046 m.
Circle 4.6 cm.
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Either paper 1 mark
Change 30 metres into centimetres.
Show answer
\(3000\)\(1\) metre is \(100\) centimetres.
Changing metres into centimetres gives a bigger number, so multiply by \(100\).
\(30 × 100 = 3000\)
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Either paper 1 mark
Write \(2\frac{1}{4}\) hours in minutes.
Show answer
\(135\)There are \(60\) minutes in 1 hour.
Minutes are smaller units than hours, so the number gets bigger: multiply by \(60\).
\(2\frac{1}{4} \times 60 = 135\)
So \(2\frac{1}{4}\) hours is \(135\) minutes.
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Either paper 4 marks
The graph can be used to change between miles and kilometres.
(a)Use the graph to change \(20\) miles into kilometres.
(b)Use the graph to change \(8\) kilometres into miles.
Show answer
(a) \(32\ \text{km}\)
(b) \(5\ \text{miles}\)Find \(20\) on the miles axis, go up to the line, then across to the kilometres axis.
The kilometres axis is numbered every \(10\) km and ruled every \(2\) km in between, and the line meets it at \(32\).
Every \(5\) miles is \(8\) km, so
\(20 \div 5 \times 8 = 32\) km
This time start on the kilometres axis. Find \(8\), go across to the line, then straight down to the miles axis.
\(8 \div 8 \times 5 = 5\) miles
- (a) M1reads or scales from the line: \(20\) ÷ 5 × 8
- (a) A1\(32\) km
- (b) M1reads or scales from the line: \(8\) ÷ 8 × 5
- (b) A1\(5\) miles
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Either paper 4 marks
Priya has an old cookery book that measures liquids in pints, but the jug she owns is marked in litres.
The graph can be used to change between litres and pints.
(a)Use the graph to change \(20\) litres into pints.
(b)Use the graph to change \(21\) pints into litres.
Show answer
(a) \(35\ \text{pints}\)
(b) \(12\ \text{litres}\)Both axes are numbered every \(5\) and ruled every \(1\) in between.
Find \(20\) on the litres axis, go up to the line, then across to the pints axis.
Every \(4\) litres across the graph is \(7\) pints up, so
\(20 \div 4 \times 7 = 35\) pints
Start on the pints axis this time. Find \(21\), go across to the line, then straight down to the litres axis.
\(21 \div 7 \times 4 = 12\) litres
- (a) M1reading up from \(20\) litres to the line
- (a) A1\(35\) pints
- (b) M1reading across from \(21\) pints to the line
- (b) A1\(12\) litres
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Either paper 3 marks(a)
Leila has \(3.3\) m of cord.
She cuts as many \(25\) cm pieces from it as she can.
Calculate how many pieces she cuts.
(b)Calculate the length of cord left over.
Give your answer in centimetres.
Show answer
(a) \(13\)
(b) \(5\ \text{cm}\)The two lengths are in different units, so change one of them. There are \(100\) cm in a metre.
\(3.3 \times 100 = 330\) cm
Now divide by the length of one piece.
\(330 \div 25 = 13\) remainder \(5\)
So she cuts \(13\) whole pieces.
The pieces use up \(13 \times 25 = 325\) cm.
\(330 - 325 = 5\) cm is left over.
- (a) M1changing to centimetres: \(330\) cm
- (a) A1\(330 \div 25\) giving \(13\) pieces
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Either paper 3 marks
The diagram shows a loaf of bread.
Find the total length of the loaf of bread.
Give your answer in centimetres.
Show answer
\(33.6\ \text{cm}\)The slices are all the same size, so multiply.
\(12 \times 25 = 300\) mm
There are two crusts, each \(18\) mm.
\(2 \times 18 = 36\) mm
The total length in millimetres is
\(300 + 36 = 336\) mm
There are \(10\) mm in \(1\) cm, so divide by \(10\).
\(336 \div 10 = 33.6\) cm
- M112 slices \(300\) mm
- M1plus two crusts, total \(336\) mm
- A1\(33.6\) cm
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Either paper 3 marks
A drum holds \(6.7\) litres of paint.
\(3\) pots of paint are filled from the drum.
Each pot holds \(130\) millilitres of paint.
What volume of paint is left in the drum?
State the units of your answer.
Show answer
\(6.31\) litresThe amount of paint at the start and the size of each of the pots are in different units, so write them in the same one. There are \(1000\) ml in \(1\) litres.
\(6.7 \times 1000 = 6700\) ml
The pots together use
\(3 \times 130 = 390\) ml
Take that away from the total.
\(6700 - 390 = 6310\) ml
In litres this is \(6310 \div 1000 = 6.31\) litres. Either \(6310\) ml or \(6.31\) litres is right, as long as the number and the unit match.
- M1both amounts in the same unit, total \(6700\) ml
- M1\(3\) pots use \(390\) ml
- A1\(6310\) ml or \(6.31\) litres, number and unit together
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Either paper 4 marks(a)
\(1\) mile is the same as \(1.6\) kilometres.
Work out the number of kilometres in \(75\) miles.
(b)Work out the number of miles in \(24\) kilometres.
Show answer
(a) \(120\ \text{kilometres}\)
(b) \(15\ \text{miles}\)Each mile is \(1.6\) kilometres, so \(75\) of them is \(75\) lots of \(1.6\).
\(75 \times 1.6 = 120\) kilometres
This is the other way round, so divide instead of multiplying.
\(24 \div 1.6 = 15\) miles
Check it: \(15 \times 1.6 = 24\) kilometres.
- (a) M1multiplying \(75\) by \(1.6\)
- (a) A1\(120\) kilometres
- (b) M1dividing \(24\) by \(1.6\)
- (b) A1\(15\) miles