Download maths practise questions - Fairhouse Junior School

Year 6
Using and applying mathematics
•
Solve multi-step problems, and problems involving fractions, decimals and percentages;
choose and use appropriate calculation strategies at each stage, including calculator use
Jemma thinks of a number. She says,
'Add 3 to my number and then multiply the result by
5. The answer is 35'.
What is Jemma's number?
Sapna and Robbie have some biscuits. Altogether
they have 14 biscuits.
Riaz thinks of a number. He says,
'Halve my number and then add 17. The answer is
23.'
What is Riaz's number?
KS2 2005 Paper B level 4
Sapna has 2 more biscuits than Robbie. How many
biscuits do Sapna and Robbie each have?
Parveen has the same number of 20p and 50p
coins. She has £7.00.
How many of each coin has she?
KS2 2002 Paper B level 4
Y4 optional test 2003 Paper B level 4
In a supermarket storeroom there are
7 boxes of tomato soup
5 boxes of pea soup
4 boxes of chicken soup
185 people go to the school concert.
They pay £1.35 each.
How much ticket money is collected?
There are 24 tins in every box. How many tins of
soup are there altogether?
Programmes cost 15p each.
Selling programmes raises £12.30.
How many programmes are sold?
KS2 2004 Paper B level 4
KS2 2002 Paper B level 4
Kim has some rectangular tiles. Each one is 4
centimetres by 9 centimetres.
Some children do a sponsored walk.
Jason is sponsored for £3.45 for each lap.
He does 23 laps. How much money does he raise?
4cm
Lynne wants to raise £100.
She is sponsored for £6.50 for each lap. What is the
least number of whole laps she must do?
9cm
She makes a design with them.
KS2 1997 Paper B level 4
This fence has three posts, equally spaced.
height
Not to scale
width
Calculate the width and height of her design.
KS2 2000 Paper A level 4
gap
15cm
gap
15cm
15cm
153cm
Each post is 15 centimetres wide. The length of the
fence is 153 centimetres. Calculate the length of
one gap between two posts.
KS2 2003 Paper B level 5
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Primary National Strategy
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•
Tabulate systematically the information in a problem or puzzle; identify and record the steps
or calculations needed to solve it, using symbols where appropriate; interpret solutions in the
original context and check their accuracy
 represents the number of books that Alice reads
each week. Which of these represents the total
number of books that Alice reads in 5 weeks?
How many triangles can you see in this diagram?
A 5+
B 5×
C ÷5
D 5÷
How can you make sure that you have counted
them all?
 and  each stand for a different number.
 = 34
Imagine you have 25 beads. You have to make a
three-digit number on an abacus. You must use all
25 beads for each number you make.
+=++
What is the value of ?
Y4 optional test 2003 Paper B level 4
Each shape stands for a number.
The numbers shown are the totals of the line of four
numbers in the row or column.
How many different three-digit numbers can you
make? Write them in order.
Two boys and two girls can play tennis.
Ali said: ‘I will only play if Holly plays.’
Holly said: ‘I won’t play if Ben is playing.’
Ben said: ‘I won’t play if Luke or Laura plays.’
Luke said: ‘I will only play if Zoe plays.’
Zoe said: ‘I don’t mind who I play with.’
Find the remaining totals.
Which two boys and which two girls play tennis?
Helping children to achieve age-related expectations:
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•
Suggest, plan and develop lines of enquiry; collect, organise and represent information,
interpret results and review methods; identify and answer related questions
Here are some digit cards.
The graph shows how the price of a chocolate bar
has changed.
30p
Write all the three-digit numbers, greater than 500,
that can be made using these cards.
KS2 2005 Paper A level 4
20p
Jason threw some darts at this board.
Every dart landed on the board.
Price
10p
1972
1977
1982
1987
1992
1997
2002
Year
Fill in the gaps below.
Between 1992 and 2002,
the price of the chocolate bar increased by … p
Jason scored exactly 100.
How many darts did he throw?
Which numbers did they land on?
In 1992, the price of the chocolate bar was 6 times
as much as in …
The smallest increase in price was in the five years
between … and …
Write three more questions you cold ask about the
numbers on the dartboard.
This pie chart shows how the children in Class 6
best like their potatoes cooked.
Write down two more statements you could make
about the information shown in the graph.
Y7 progress test Paper B level 4 [adapted]
Class 6 count how many seeds they find under two
trees. They show the data in a graph.
32 children took part in the survey.
Look at the four statements below. For each
statement put a tick () if it is correct. Put a cross
() if it is not correct.
10 children like chips best.

25% of the children like
mashed potatoes best.

1
5 of the children like roast
potatoes best.

12 children like jacket
potatoes best.

How many seeds did they find in week 3
altogether?
In how many weeks did they find more than 40
chestnut seeds?
Write down two different ways in which you could
extend this survey.
Write down two more questions you could ask
about the information shown in the graph.
KS2 2005 Paper A level 5 [adapted]
KS2 2005 Paper A level 4 [adapted]
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•
Represent and interpret sequences, patterns and relationships involving numbers and
shapes; suggest and test hypotheses; construct and use simple expressions and formulae in
words then symbols, e.g. the cost of c pens at 15 pence each is 15c pence
In this sequence each number is double the
previous number. Write in the missing numbers.


3
6
12
24
The first two numbers in this sequence are 2.1 and
2.2. The sequence then follows the rule ‘to get the
next number, add the two previous numbers‘.

48
Write in the next two numbers in the sequence.
KS2 2003 Paper B level 4
2.1
17 multiplied by itself gives a 3-digit answer.
2.2
4.3

6.5

KS2 2003 Paper A level 4
11
10
What is the smallest 2-digit number that can be
multiplied by itself to give a 4-digit answer?
9
(7, 8)
8
7
(4, 6)
C
6
5
(1, 4)
3
Here is a repeating pattern of shapes. Each shape
is numbered.
1
2
3
4
5
6
7
8
9
1
(4, 3)
A
2
(7, 5)
B
4
KS2 2005 Paper B level 4
(1, 1)
(9, 5)
(6, 3)
(3, 1)
0
0
1
2
3
4
5
6
7
8
9
10
11 12
13
Write the co-ordinates of the next triangle in the
sequence.
10
The pattern continues in the same way. Write the
numbers of the next two stars in the pattern.
Y4 optional test Paper B level 4
Complete this sentence.
Halid makes a sequence of 5 numbers. The first
number is 2. The last number is 18. His rule is to
add the same amount each time.
Shape number 35 will be a circle because ...
KS2 2003 Paper A level 4
Write in the missing numbers.
What is the value of 4x + 7 when x = 5?
2



18
Y5 optional test 1998 Paper B level 4
KS2 1999 Paper B level 5
Take three shapes like this.
The rule for this sequence of numbers is ‘add 3
each time’.
1......4......7......10......13......16......…
Use the three shapes to make a symmetrical shape.
How many different symmetrical shapes can you
make using the three shapes?
The sequence continues in the same way. Mary
says, ‘No matter how far you go there will never be
a multiple of 3 in the sequence.’
Is she correct? Circle Yes or No.
Explain how you know.
How many of the shapes have only one line of
symmetry? How many have two lines of symmetry?
KS2 2001 Paper B level 5
Sam says: ‘In a triangle, each angle must be 90
degrees or less, because the three angles add up to
270 degrees.’
Is Sam correct? Ring YES or NO.
Explain how you know.
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•
Explain reasoning and conclusions, using words, symbols or diagrams as appropriate
The spinner is divided into nine equal sections.
Nadia is working with whole numbers. She says, 'If
you add a two-digit number to a two-digit number
you cannot get a four-digit number.’
2
Which two different numbers on the spinner are
equally likely to come up?
Meera says, ‘2 has a greater than even chance of
coming up’. Explain why she is correct.
PAVING SLABS
£3.50 each
2
2
Mr Singh buys paving slabs to go around his pond.
Square slabs
3
1
KS2 2000 Paper B level 4
50cm by 50cm
2
2
Is she correct? Circle Yes or No.
Explain why.
£1.95 each
1
4
50cm
KS2 2000 Paper A level 4
100cm
Pond
The diagram shows a square.
Rectangular slabs
100cm by 50cm
He buys 4 rectangular slabs and 4 square slabs.
What is the total cost of the slabs he buys?
'It would cost more to use square slabs all the way
round.' Explain why he is correct.
KS2 2002 Paper A level 4
How many degrees is angle a?
Explain how you know.
Y7 progress test 2005 Paper B [adapted]
Counting and understanding number
•
Find the difference between a positive and a negative integer, or two negative integers, in
context
The temperature starts at four degrees and goes
down by ten degrees. What is the temperature
now?
What temperature is twenty degrees lower than six
degrees Celsius?
KS2 2004 Mental test level 5
Y5 optional test 1998 Mental test level 4
Megan makes a sequence of numbers starting with
100. She subtracts 45 each time.
The temperatures were:
inside
outside
–1°C
–8°C
Write the next two numbers in the sequence.
100
55
10


KS2 1999 Paper A level 5
What is the difference between these two
temperatures?
A sequence starts at 500 and 80 is subtracted each
time.
KS2 2002 Paper B level 4
500
420
340 ...
The temperature inside an aeroplane is 20 °C. The
temperature outside the aeroplane is –30 °C. What
is the difference between these temperatures?
The sequence continues in the same way. Write the
first two numbers in the sequence which are less
than zero.
KS2 2003 Paper B level 4
KS2 2002 Paper A level 5
The temperature in York is 4°C. Rome is 7 degrees
colder than York. What is the temperature in Rome?
Circle two numbers which have a difference of 2.
KS2 2000 Paper A level 4
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–1
–0.5
0
0.5
1
1.5
KS2 2001 Paper B level 4
5
00028-2007CDO-EN
© Crown copyright 2007
•
Use decimal notation for tenths, hundredths and thousandths, partition, round and order
decimals with up to three places, and position them on the number line
Write a number in the box to make this correct.
Write these numbers in order.
One has been done for you.
0.627 = 0.6 + 0.02 + 
In the number 5.375, what does the digit 7
represent?
A
B
C
D
7
1000
7
100
7
10
Y5 optional test 2003 Paper A level 5
7
Put a ring around the smallest number.
0.27
What number is exactly halfway between one point
one and one point two?
0.207
0.027 2.07
2.7
KS2 2001 Mental test level 4
KS2 2005 Mental test level 4
Here are three supermarket bills.
Write the number that is exactly halfway between
eight point six and eight point seven.
Y5 optional test 1998 Mental test level 4
Write a number that is bigger than nought point
three but smaller than nought point four.
Total £74.68
Total £65.90
Total £59.05
KS3 2003 Mental test level 4
Tom rounds each bill to the nearest £10 and adds
them up. What is the total amount that Tom gets?
Write each of these numbers to the nearest whole
number.
13.7
is nearest to
...............
Mary adds up the three bills exactly. What is the
total difference between her total and Tom’s total?
8 ⁄8
3
is nearest to
...............
KS2 2004 Paper B level 4
3.38
is nearest to
...............
Circle the number closest in value to 0.1.
Y5 Optional test Paper B level 3
0.01
Round each decimal to the nearest whole number.
0.05
0.11
0.2
0.9
KS2 2002 Paper B level 5
6.01  
9.51  
Round two point six nine four to one decimal place.
7.75  
KS3 2005 Mental test level 6
Y5 optional test 2003 Paper B level 4 [adapted]
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•
Express a larger whole number as a fraction of a smaller one e.g. recognise that 8 slices of a
8
3
5-slice pizza represents 5 or 1 5 pizzas; simplify fractions by cancelling common factors;
order a set of fractions by converting them to fractions with a common denominator
Look at these fractions.
Draw one line to join two fractions which have the
same value.
1
2
4
7
5
6
Mark each fraction on the number line. The first one
is done for you.
2
8
1
2
1
3
0
2
5
1
1
3
1
2
KS3 2001 level 4
1
4
4
Write a fraction that is larger than ⁄5.
1
Write a fraction that is smaller than ⁄5.
KS2 1998 Paper A level 4
1
3
Write a fraction that lies between ⁄4 and ⁄8.
Karen makes a fraction using two number cards.
She says,
1
‘My fraction is equivalent to ⁄2. One of the number
cards is 6’
Which is larger,
What could Karen’s fraction be?
Give both possible answers.
KS2 2002 Paper A level 5
1
2
or ?
3
5
Explain how you know.
Here are some number cards.
or
7
5
9
3
11
Use two of the cards to make a fraction which is
1
less than 2.
KS2 2003 Paper B level 4
Complete these fractions to make each equivalent
to
3
.
5
How much less than 1 is your fraction?
KS2 1996 Paper B level 5
10
15
12
KS2 2001 Paper A level 5
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•
Express one quantity as a percentage of another, e.g. express £400 as a percentage of
£1000; find equivalent percentages, decimals and fractions
Write these decimals as percentages.
Put a ring around the fraction which is equivalent to
forty per cent.
0.25  …%
1
40
0.6  …%
40
60
4
10
1
4
1
400
KS2 1999 Mental test level 4
Write these percentages as decimals.
42%  …
Circle the two fractions that are equivalent to 0.6.
5%  …
6
10
What is seven-tenths as a percentage?
1
60
60
100
1
6
Y5 optional test 2003 Paper B level 4
KS2 2005 Mental test level 4
Put a ring around the decimal which is equal to onefifth.
Write 80% as a fraction in its simplest form.
What is twenty out of forty as a percentage?
0.1
0.2
0.3
0.4
0.5
KS2 2004 Mental test level 4
KS2 2003 Mental test level 5
A class is collecting money for charity. They want a
total of £1000. By the end of April, they have
collected £400.
Some of the statements below are correct.
Tick () the correct ones.
What percentage of their total have they collected
by the end of April?
Tick ( ) if correct
Y7 progress test Paper A level 4
1
2
=
0.5
9
30
=
3
10
0.75
=
3
4
1
2
is equivalent to 10%
1
5
is equivalent to 5%
Y7 optional test Paper A level 4
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•
Solve simple problems involving direct proportion by scaling quantities up or down
Two letters have a total weight of 120 grams
On a school trip each teacher can take no more
than 20 pupils. Three teachers go on a school trip.
What is the greatest number of pupils they can take
with them?
Complete the table to show the least number of
teachers that must go with each school trip.
Number
of pupils
One letter weighs twice as much as the other. Write
the weight of the heavier letter.
Number
of teachers
Y4 optional test 2003 Paper B level 4
100
Peanuts cost 60p for 100 grams.
What is the cost of 350 grams of peanuts?
104
Raisins cost 80p for 100 grams.
Jack pays £2 for a bag of raisins.
How many grams of raisins does he get?
199
KS2 2000 Paper A level 4
KS3 2002 Paper A level 3
Here is part of a number line. Write the two missing
numbers in the boxes.
Jenny is going to make some cordial. The finished
1
2
drink should be 3 cordial and 3 water.
Jenny puts 100 ml of cordial in a glass.
How much water should she put with it?
KS3 2004 Paper A level 4
Four biscuits cost twenty pence altogether.
How much do twelve biscuits cost?
KS2 2005 Paper A level 4
KS2 2005 Mental test level 4
Here is part of a number line. Write the missing
numbers in the boxes.
Two rulers cost eighty pence.
How much do three rulers cost?
KS3 2005 Mental test level 4
Six cakes cost one pound eighty.
How much do ten cakes cost?
KS2 2002 Mental test level 5
Here is a recipe for pasta sauce.
Y5 optional test 2003 Paper A level 4
In a country dance there are 3 boys and 2 girls in
every line.
Josh makes the pasta sauce using 900g of
tomatoes. What weight of onions should he use?
42 boys take part in the dance.
How many girls take part?
Y5 optional test 2003 Paper B level 5
KS2 1996 Paper B level 5
Helping children to achieve age-related expectations:
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Primary National Strategy
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Knowing and using number facts
•
Use knowledge of place value and multiplication facts to 10 × 10 to derive related
multiplication and division facts involving decimals, e.g. 0.8 × 7, 4.8 ÷ 6
What is nought point four multiplied by nine?
Divide four point eight by eight.
KS2 2005 Mental test level 4 [adapted]
KS2 2004 Mental test level 4 [adapted]
What is nought point three multiplied by four?
Divide four point two by six.
KS2 2004 Mental test level 5 [adapted]
Y4 optional test 1998 Mental test level 4 [adapted]
What is four multiplied by nought point nine?
What number multiplied by eight equals four point
eight?
KS2 2005 Mental test level 4 [adapted]
KS3 2005 Mental test level 4 [adapted]
Multiply seven by nought point six.
Divide four point two by seven.
KS2 2003 Mental test level 4 [adapted]
KS3 2004 Mental test level 4 [adapted]
What is nought point eight multiplied by six?
Y3 optional test 2003 Mental test level 3 [adapted]
Multiply nought point seven by nine.
KS2 1999 Mental test level 4 [adapted]
•
Use knowledge of multiplication facts to derive quickly squares of numbers to 12 × 12 and
the corresponding squares of multiples of 10
What is five squared?
What is the next square number after thirty-six?
KS3 2001 Mental test level 4
Y7 progress test 2005 Mental test level 4
Explain why 16 is a square number.
What is the next number in the sequence of square
numbers?
One, four, nine, sixteen ...
Y5 optional test 1998 Paper B level 3
KS3 2004 Mental test level 5
Here is a sorting diagram for numbers. Write a
number less than 100 in each space.
Find two square numbers that total 45
even
not even
 +  = 45
a square
number
KS2 2005 Paper A level 5
not a square
number
What is thirty multiplied by thirty?
[oral question]
KS2 2004 Paper A level 4
•
Recognise that prime numbers have only two factors and identify prime numbers less than
100; find the prime factors of two-digit whole numbers
Millie and Ryan play a number game.
Is it under 20?
Is it under 25?
Is it odd?
Is it a prime number?
Write the three prime numbers which multiply to
make 231.
No
Yes
Yes
Yes
×  ×  = 231
KS2 2001 Paper B level 5
What is the number?
The three numbers missing from these boxes are all
prime numbers greater than 3. Write in the missing
prime numbers.
KS2 1999 Paper B level 3
 ×  ×  = 1001
KS2 1996 Paper C level 6
Helping children to achieve age-related expectations:
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•
Use approximations, inverse operations and tests of divisibility to estimate and check results
A car park has 76 rows for parking. There are 52
car spaces in each row. Which of these is the BEST
way to estimate how many cars can park
altogether?
A 100 × 50 = 5000
B 90 × 60 = 5400
Julie says, ‘I added three odd numbers and my
answer was 50.’
Explain why Julie cannot be correct.
KS2 2004 Paper A level 5
C 80 × 60 = 4800
This sequence of numbers goes up by 40 each
time.
D 80 × 50 = 4000
40
E 70 × 60 = 4200
This sequence continues.
Will the number 2140 be in the sequence?
Circle Yes or No.
Explain how you know.
80
120
160
200
…
KS2 2000 Paper A level 5
Estimate the value of nine point two multiplied by
two point nine.
KS3 2005 Mental test level 5
Circle the best estimate of the answer to
72.34 ÷ 8.91
6
7
8
9
10
11
KS3 2002 Paper A level 5
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Calculating
•
Calculate mentally with integers and decimals: U.t ± U.t, TU × U, TU ÷ U, U.t × U, U.t ÷ U
What number is halfway between thirty and eighty?
What is the sum of eight point five and eight point
six?
KS2 2004 Mental test level 4
KS2 2002 Mental test level 4
Tick () the two numbers which have a total of 10.
Add three point five to four point eight.
KS2 1999 Mental test level 4
Subtract one point nine from two point seven.
KS2 2003 Mental test level 4
Subtract nought point seven five from six.
KS3 2003 Mental test level 4
KS2 2005 Paper A level 4
Add together nought point two, nought point four
and nought point six.
Circle two numbers which add to make 0.12.
0.1
KS2 2005 Mental test level 4
0.5
0.05
0.7
0.07
0.2
KS2 2000 Paper A level 4
What is four multiplied by three point five?
Circle the two numbers which add up to 1.
KS2 2000 Mental test level 4
0.1
0.65
0.99
0.45
0.35
KS2 1999 Paper A level 5
In a café I buy two cups of coffee and a sandwich.
Altogether I pay three pounds.
The sandwich costs one pound sixty.
What is the cost of one cup of coffee?
The first two numbers in this sequence are 2.1 and
2.2. The sequence then follows the rule ‘to get the
next number, add the two previous numbers‘.
Y7 progress test 2003 Mental test level 3
Write in the next two numbers in the sequence.
A packet of crisps costs thirty-two pence.
Josh buys three packets. How much change does
he get from one pound?
2.1
2.2
4.3
6.5


KS2 2003 Paper A level 4
KS2 2005 Mental test level 4
A magazine costs one pound forty pence.
I buy two of them and pay with a five pound note.
How much change should I get?
KS3 2003 Mental test level 4
Two rulers cost eighty pence.
How much do three rulers cost?
KS3 2005 Mental test level 4
A bag of four oranges costs thirty seven pence.
How much do twelve oranges cost?
KS2 2000 Mental test level 5
Helping children to achieve age-related expectations:
securing Level 4 by the end of Key Stage 2
Primary National Strategy
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00028-2007CDO-EN
© Crown copyright 2007
•
Use efficient written methods to add and subtract integers and decimals, to multiply
and divide integers and decimals by a one-digit integer, and to multiply two-digit and
three-digit integers by a two-digit integer
Calculate 2307 × 8.
Calculate 15.05 – 14.84.
KS2 2003 Paper A level 4
KS2 2002 Paper A level 5
Write in the missing digits.
Calculate 8.6 – 3.75.
4  4 + 38  = 851
KS2 2000 paper A level 5
KS2 2004 Paper A level 4
In the chart any three numbers in a line, across or
down, have a total of 18.45. Write the missing
number.
Write in the missing digit.
 7 × 9 = 333
KS2 1996 Paper A level 4
2.46
Write in the missing digit.
11.07
5  × 8 = 456
4.92
8.61
7.38
1.23
3.69
9.84
KS2 1995 Paper A level 4
KS2 1997 Paper A level 4
Write in the missing number.
 ÷ 5 = 22
Calculate 31.6 × 7.
KS2 1995 Paper A level 4
KS2 2004 Paper A level 5
Eggs are put in trays of 12.
The trays are packed in boxes.
Each box contains 180 eggs.
How many trays are in each box?
Calculate 123 ÷ 5.
KS2 1999 Paper A level 4
Calculate 27.6 ÷ 8.
Some children go camping.
It costs £2.20 for each child to camp each night.
They go for 6 nights. How much will each child have
to pay for the 6 nights?
Shenaz buys a pack of 24 cans of cola for £6.00.
Calculate 16.5 ÷ 3.
There are 70 children.
Each tent takes up to 6 children.
What is the least number of tents they will need?
What is the cost of each can?
KS2 1998 Paper A level 4
Helping children to achieve age-related expectations:
securing Level 4 by the end of Key Stage 2
Primary National Strategy
KS2 1998 Paper A level 5
13
00028-2007CDO-EN
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•
Relate fractions to multiplication and division, e.g. 6 ÷ 2 = 2 of 6 = 6 × 2; express a quotient
2
as a fraction or decimal, e.g. 67 ÷ 5 = 13.4 or 13 5; find fractions and percentages of whole5
number quantities, e.g. 8 of 96, 65% of £260
1
1
Calculate 60% of 765.
One third of a number is twelve. What is the
number?
KS2 2000 Paper B level 4
KS2 1997 Mental test level 4
In a sale, there is fifty per cent off all prices.
A chair costs forty-five pounds in the sale.
How much was it before the sale?
What is three-quarters of two hundred?
KS2 2000 Mental test level 4
KS2 1999 Mental test level 4
What is three-fifths of forty pounds?
KS3 2003 Mental test level 5
John had £5. He gave 25% of it to charity. How
much did he give?
Joe has some pocket money. He spends threequarters of it. He has fifty pence left. How much
pocket money did he have?
Y4 optional test Paper B level 4
Sophie poured some water out of a litre jug. Look
how much is left in the jug. Estimate how many
millilitres of water are left.
Y5 optional test 2003 Mental test level 4
Calculate 4 of 840.
3
KS2 2000 Paper A level 4
Fill in the missing numbers.
1
1
of 20 =
of …
2
4
3
1
of 100 =
of …
4
2
Y5 optional test 2003 Paper A level 4
1
2
of 60 =
of …
3
3
KS3 2003 Paper 1 level 5
Helping children to achieve age-related expectations:
securing Level 4 by the end of Key Stage 2
Primary National Strategy
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© Crown copyright 2007
•
Use a calculator to solve problems involving multi-step calculations
Three pupils answered different questions. This is
what each pupil’s calculator showed:
Emma saves £3.50 each week. How much has she
saved after 16 weeks?
Y5 optional test Paper B level 4
Asim’s question was about money. Complete the
sentence:
Sima thinks of a number.
She divides it by 12. Her answer is 26.
What is the number Sima thinks of?
3.5 means £3 and ……pence.
KS2 1998 Paper B level 5
Ben’s question was about time. Complete the
sentence:
Nicola has £50. She buys 3 flowerpots at £12.75
each and a spade at £9.65. How much money does
she have left?
3.5 means 3 hours and …… minutes.
Charlie’s question was about length. Complete the
sentence:
3.5 means 3 metres and …… centimetres.
Seeds are £1.45 for a packet. Steffan has £10 to
spend on seeds. What is the greatest number of
packets he can buy?
Y7 progress test Paper B level 4
KS2 1999 Paper B level 5
Here is a picture of three people.
Mrs Jones prints books.
Jon pays £4.35 for his book, including the cover.
How many pages are in his book?
KS2 1996 Paper B level 5
Lisa’s height is half-way between Julie’s height and
Tom’s height. Calculate Lisa’s height.
KS2 1998 Paper B level 4
Helping children to achieve age-related expectations:
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Understanding shape
•
Describe, identify and visualise parallel and perpendicular edges or faces; use these
properties to classify 2-D shapes and 3-D solids
These two shaded triangles are each inside a
regular hexagon. Under each hexagon, put a ring
around the correct name of the shaded triangle.
Imagine a triangular prism.
How many faces does it have?
KS2 1999 Mental test level 4
Imagine a cube. How many vertices does it have?
KS2 2000 Mental test level 4
Here are five shapes on a square grid.
equilateral
equilateral
isosceles
isosceles
scalene
scalene
A
B
KS2 2001 Paper B level 4
C
Here are six triangles. One of them is an equilateral
triangle. Put a tick () in the equilateral triangle.
D
E
Write in the missing letters.
Shape  has two pairs of parallel sides.
Shape  is a pentagon.
Shape  has reflective symmetry.
Write one property which makes equilateral
triangles different from all other triangles.
KS2 1999 Paper B level 4
KS2 1998 Paper A level 4
Here is a shape on a square grid.
These diagrams show the diagonals of three
quadrilaterals. Write the names of the quadrilaterals
in the boxes.
A
D
C
B
For each sentence, put a tick () if it is true. Put a
cross () if it is not true.
Angle C is an obtuse angle.
Angle D is an acute angle.
Line AD is parallel to line BC.
Line AB is perpendicular to line AD.
KS2 2000 Paper B level 5
KS2 2003 Paper A level 4
Helping children to achieve age-related expectations:
securing Level 4 by the end of Key Stage 2
Primary National Strategy
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© Crown copyright 2007
•
Make and draw shapes with increasing accuracy and apply knowledge of their properties
Draw two straight lines from point A to divide the
shaded shape into a square and two triangles.
Here is the net of a cube with no top. The shaded
square shows the bottom of the cube. Draw an
extra square to make the net of a cube which does
have a top.
A
KS2 2003 Paper B level 4
KS2 2003 Paper B level 4
Here are five shapes on a square grid.
A cube has shaded triangles on three of its faces.
B
A
C
E
Here is the net of the cube. Draw in the two missing
shaded triangles.
D
Which two shapes fit together to make a square?
KS2 2001 Paper B level 4
Here are some shaded shapes on a grid.
A
B
C
KS2 2002 Paper B level 5
On the grid below, use a ruler to draw a pentagon
that has three right angles.
D
E
F
Which three shapes have reflective symmetry?
KS2 2000 Paper A level 4
Helping children to achieve age-related expectations:
securing Level 4 by the end of Key Stage 2
Primary National Strategy
KS2 1998 Paper B level 5
17
00028-2007CDO-EN
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•
Visualise and draw on grids of different types where a shape will be after reflection,
after translations, or after rotation through 90° or 180° about its centre or one of its
vertices
Kyle has drawn triangle ABC on this grid.
Here is a shaded shape on a grid. The shape is
rotated 90° clockwise about point A. Draw the
shape in its new position on the grid. You may use
tracing paper.
A
KS2 2000 Paper B level 4
The rectangle is rotated 90° clockwise about point
A. Draw the rectangle in its new position. You may
use tracing paper.
Holly has started to draw an identical triangle DEF.
What will be the coordinates of point F?
Y5 optional test 2003 Paper B level 4
Draw the reflection of this shape.
A
Y5 optional test 1998 Paper B level 4
This pattern is made by turning a shape clockwise
through 90° each time.
Draw the two missing triangles on the last shape.
Y3 optional test 2003 Paper B level 4
KS2 2005 Paper B level 4
Helping children to achieve age-related expectations:
securing Level 4 by the end of Key Stage 2
Primary National Strategy
18
00028-2007CDO-EN
© Crown copyright 2007
•
Use coordinates in the first quadrant to draw, locate and complete shapes that meet given
properties
The diagram shows two identical squares.
Here is a graph.
y
B
(6,3)
(4,2)
A
0
x
A is the point (10,10).
What are the coordinates of B and C?
The dots on the line are equally spaced. What are
the coordinates of the point A?
KS2 2005 Paper B level 4
Megan says, ‘The point B has coordinates (11,5).’
Use the graph to explain why she cannot be correct.
KS2 1997 Paper B level 4
Here is a pentagon drawn on a coordinate grid. The
pentagon is symmetrical.
y
B (7,10)
A
C
(4,9)
A, B and C are three corners of a rectangle. What
are the coordinates of the fourth corner?
E
(2,0)
(12,0) D
0
x
Y4 optional test 2003 Paper B level 4
What are the coordinates of point C?
KS2 2003 Paper A level 5
Helping children to achieve age-related expectations:
securing Level 4 by the end of Key Stage 2
Primary National Strategy
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00028-2007CDO-EN
© Crown copyright 2007
•
Estimate angles, and use a protractor to measure and draw them, on their own and in
shapes; calculate angles in a triangle or around a point
Look at the triangle. Angle x is fifty-five degrees.
Calculate the size of angle y.
x
x
y
KS2 2001 Mental test level 5
Measure angle x accurately. Use a protractor (angle
measurer).
Two of the angles in a triangle are sixty degrees
and seventy degrees. What is the size of the third
angle?
KS2 2004 Paper B level 5
KS3 2005 Mental test level 5
Complete the drawing below to show an angle of
157°. Label the angle 157°.
A pupil measured the angles in a triangle.
She said: ‘The angles are 30°, 60° and 100°.’
Could she be correct? Tick () Yes or No.
Explain your answer.
______________
KS3 2004 Paper A level 5
KS3 2000 Paper A level 5
What is the angle between the hands of a clock at
four o ’clock?
Look at these angles.
KS2 2003 Mental test level 5
This diagram is not drawn accurately. Calculate the
size of angle m
angle P
angle Q
angle R
angle S
angle T
One of the angles measures 30°. Write its letter.
KS3 2000 Paper A level 5
70º
Look at the angle.
m
Put a ring around the number which is the
approximate size of the angle.
60°
90°
110°
135°
70º
KS3 2004 Paper A level 5
240°
KS2 2000 Mental test level 5
Helping children to achieve age-related expectations:
securing Level 4 by the end of Key Stage 2
Primary National Strategy
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00028-2007CDO-EN
© Crown copyright 2007
Measuring
•
Select and use standard metric units of measure and convert between units using
decimals to two places, e.g. change 2.75 litres to 2750 ml, or vice versa
How many millilitres are there in three-quarters of a
litre?
Look at the diagram. It shows how to change
metres into centimetres and millimetres.
Y4 optional test 2003 Mental test level 4
×100
Change sixty millimetres to centimetres.
number of
metres
×10
number of
centimetres
number of
millimetres
KS3 2001 Mental test level 4
×1000
A table is two hundred centimetres long. How many
metres is that?
Change 5 metres into centimetres.
Change 9 centimetres into millimetres.
KS3 1999 Mental test level 4
Change 8000 millimetres into metres.
This table shows the weight of some fruits and
vegetables. Complete the table.
potatoes
grams
kilograms
3500
3.5
A bottle holds 1 litre of lemonade.
Rachel fills 5 glasses with lemonade.
3
She puts 150
in each glass.
2 millilitres
4
How much
is left in the bottle?
1 lemonade
5
6
KS2 2003 0Paper
kg A level 4
1.2
apples
grapes
Y7 progress test 2003 level 4
Put a ring round the number which is the
approximate weight of a thirty-centimetre plastic
ruler.
250
ginger
0.03
2g
Primary National Strategy
200 g
2 kg
20 kg
KS2 2001 Mental test level 5
KS2 2002 Paper A level 4 [adapted]
Helping children to achieve age-related expectations:
securing Level 4 by the end of Key Stage 2
20 g
21
00028-2007CDO-EN
© Crown copyright 2007
•
Read and interpret scales on a range of measuring instruments, recognising that the
measurement made is approximate and recording results to a required degree of accuracy;
compare readings on different scales, for example when using different instruments
Here are a pencil sharpener, a key and a rubber.
The diagrams in this question are not drawn
accurately. The diagram shows Jo’s key.
Actual size
Use the scale to find the length of Jo’s key.
0
This time you cannot see all of Jo’s key.
1
2
3
4
5
6
7
8
9 cm
What is the length of all three things together? Give
your answer in millimetres.
What is the length of the key? Give your answer in
millimetres.
KS2 2002 Paper A level 4
One end is at 2.8cm on the scale.
Where is the other end on the scale?
This scale shows the weight of Fred’s cat.
Y7 progress test 2005 level 4
All the water in these two containers is to be poured
into the empty container below.
5kg
4kg
500 ml
500 ml
What is the weight of Fred’s cat?
400 ml
400 ml
This scale shows the weight of Fred’s dog.
300 ml
300 ml
200 ml
200 ml
100 ml
100 ml
6kg
5kg
Draw where the water level will be in the container.
How much more does Fred’s dog weigh than his
cat?
1 litre
KS2 2004 Paper B level 4
On this scale, the arrow (↑) shows the weight of a
pineapple.
1/2 litre
0
1
2
Y4 optional test Paper B level 4
kg
The diagram shows the volume of water in two
measuring jugs.
Here is a different scale.
500
Mark with an arrow (↑) the weight of the same
pineapple.
400
300
0
1
2
3
4
1000
200
kg
500
0
100
ml
Jug A
0
KS2 2001 Paper B level 4
ml
Jug B
Which jug contains more water? Tick () A or B.
How much more does it contain?
2003 Y7 progress test Paper B level 4
Helping children to achieve age-related expectations:
securing Level 4 by the end of Key Stage 2
Primary National Strategy
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00028-2007CDO-EN
© Crown copyright 2007
•
Calculate the perimeter and area of rectilinear shapes; estimate the area of an irregular
shape by counting squares
Calculate the perimeter of a rectangle which is
eleven metres long and four metres wide.
Millie has some star-shaped tiles. Each edge of a
tile is 5 centimetres long.
KS2 2003 Mental test level4
5 cm
Not actual size
2
The area of a rectangle is 16 cm .
One of the sides is 2 cm long.
What is the perimeter of the rectangle?
She puts two tiles together to make this shape.
Y4 optional test 1999 Paper B level 4
Here are some shapes drawn on a grid.
Work out the perimeter of Millie’s shape.
KS2 2004 Paper A level 4
Lauren has three small equilateral triangles and one
large equilateral triangle. The small triangles have
sides of 7 centimetres. Lauren makes this shape.
7 cm
Write the letters of the two shapes that are equal in
area.
Y4 optional test 2003 Paper B level 4
Here is a 1cm square grid. Some of the grid is
shaded.
Not actual size
Calculate the perimeter of the shape.
KS2 2001 Paper B level 4
Liam has two rectangular tiles like this.
11cm
What is the area that is shaded?
5cm
KS2 2005 Paper B level 4
He makes this L shape.
Here is a map of an island.
Church
What is the perimeter of Liam’s L shape?
Cave
KS2 2000 Paper A level 5
Wood
What is the area of this shape?
4cm
Lighthouse
Not to scale
Estimate the area of the Wood.
10cm
KS2 1995 Paper B level 4
7cm
10cm
KS2 2002 Paper B level 5
Helping children to achieve age-related expectations:
securing Level 4 by the end of Key Stage 2
Primary National Strategy
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00028-2007CDO-EN
© Crown copyright 2007
Handling data
•
Describe and predict outcomes from data using the language of chance or likelihood
Shade this spinner so that there is a 50% chance
that the arrow will land on shaded.
Here are two spinners, A and B. Each one is a
regular hexagon.
1
2
3
2
1
1
1
3
2
A
Y7 progress test Paper A level 4
Here is a spinner which is a regular octagon. Write
1, 2 or 3 in each section of the spinner so that 1 and
2 are equally likely to come up and 3 is the least
likely to come up.
B
For each statement, put a tick () if it is true. Put a
cross () if it is not true.
Scoring ‘1’ is more likely on A than on B.
Scoring ‘2’ is more likely on A than on B.
Scoring ‘3’ is as equally likely on A as on B.
Zara spins both spinners. The score on A is added
to the score on B. She says, ’The sum of the scores
on both spinners is certain to be less than 7’ .
Is she correct? Circle Yes or No.
Explain how you know.
KS2 2001 Paper A level 4
KS2 2005 Paper B level 4
Helping children to achieve age-related expectations:
securing Level 4 by the end of Key Stage 2
Primary National Strategy
24
00028-2007CDO-EN
© Crown copyright 2007
•
Solve problems by collecting, selecting, processing, presenting and interpreting data,
using ICT where appropriate; draw conclusions and identify further questions to ask
Table and pie chart of favourite boy bands
Table and pie chart of favourite sport of Year 6 girls,
produced in Microsoft Excel
http://www.standards.dfes.gov.uk/primary/teachingr
esources/mathematics/nns_itps/data_handling/
Table and conversion graph for euros to pounds,
produced in Microsoft Excel
Table, dual bar chart and stacked bar chart showing
favourite colours of two Year 6 classes, produced in
MicrosoftExcel
Helping children to achieve age-related expectations:
securing Level 4 by the end of Key Stage 2
Primary National Strategy
25
00028-2007CDO-EN
© Crown copyright 2007
•
Construct and interpret frequency tables, bar charts with grouped discrete data, and line
graphs; interpret pie charts
A school has a quiz each year. There are two
teams. Here are their results.
North
The pie chart shows information about children who
go to a nursery school.
South
300
250
two
years old
four
years old
200
Points
three
years old
150
100
50
0
1999
2000
2001
Year
2002
Altogether, 80 children go to the nursery school.
How many of the 80 children are two years old?
2003
How many of the 80 children are four years old?
In which year did North beat South by 100 points?
Y7 progress test Paper A level 4
In which year did South beat North by the greatest
amount?
This graph shows the cost of phone calls in the
daytime and in the evening.
KS2 2004 Paper B level 4
60p
Some children do a sponsored walk. The graph
shows their results.
da
50p
e
ytim
40p
Cost
of call 30p
20p
evening
10p
0p
0
2
4
6
8
10
12
Length of call in minutes
How much does it cost to make a 9 minute call in
the daytime?
How much more does it cost to make a 6 minute
call in the daytime than in the evening?
KS2 2002 Paper A level 4
How many children walked 21 laps or more?
Y5 optional test 2003 Paper A level 4
•
Describe and interpret results and solutions to problems using the mode, range, median and
mean
These are the marks from a spelling test.
Jay
Karen
Dominic
Tariq
Lara
Oliver
Gemma
Rob runs 100 metres ten times.
These are his times in seconds.
16
13
18
13
12
14
19
13.4
13.5
13.0
14.0
13.9
14.4
13.7
13.8
13.3
14.0
What is his mean (average) time?
KS2 1995 level 5
Write a different number in each of these boxes so
that the mean of the three numbers is 9.
What is the median number of marks?
Y5 optional test Paper B level 4
Write a number in each of these boxes so that the
mode of the five numbers is 11.
KS2 1997 Paper A level 5
Helping children to achieve age-related expectations:
securing Level 4 by the end of Key Stage 2
Primary National Strategy
26
00028-2007CDO-EN
© Crown copyright 2007
Helping children to achieve age-related expectations:
securing Level 4 by the end of Key Stage 2
Primary National Strategy
27
00028-2007CDO-EN
© Crown copyright 2007