# FS Calculating

Document Sample

```					FS Calculating
•   Begin to relate addition to combining two groups of objects and subtraction to ‘taking away’

There are four cups on the table.                         [Count 5 pennies into a purse and shut it.
Put two more cups on the table.                           Show 2 more pennies in your hand.]
How many cups altogether are on the table now?            How many pennies are there altogether?

There are nine biscuits on this plate.                    We have four easels.
Take three of the biscuits to eat.                        There are seven children who want to paint.
How many biscuits are left on the plate?                  How many more easels do we need?

•   In practical activities and discussion begin to use the vocabulary involved in adding and
subtracting
One, two, three, … What goes next?                        There are six toys in a box.
I take away three of the toys.
Hop three spaces on this number track. Now hop
How many toys are left in the box?
two more. Where are you now?

How many white rabbits are there?
I have two toys in a box.                                 How many rabbits are there altogether?
I add four more toys to the box.
How many toys are there in the box now?

Find all the dominoes that have a total of six spots.

Count 5 small toys into this cloth bag. How many
objects in the bag? Now count 2 more small toys
into the bag. How many small toys in the bag now?         What is the difference between the number of grey
rabbits and the number of white rabbits?
Show me 5 fingers on one hand. Show me 2 fingers
on the other hand. How many fingers altogether?           Here are five toy cars.
How many more cars are needed to make a set of
I have hidden two cubes in this box. There are three      eight cars?
cubes on the table. How many cubes are there
altogether?                                               John has four books.
Lisa has one book.
How many more books has John than Lisa?
•   Count repeated groups of the same size

Count these pairs of socks.                                                  How many buttons are there on this coat?
How many pairs are there?                                                    Count them in twos.
How many socks are there altogether?                                         Count them in fives.

Count the pairs of animals on the Ark.

Count the eggs in this egg box.                                              There are five paintbrushes in each jar.
Count the paintbrushes.

•   Share objects into equal groups and count how many in each group
Share these pencils equally between Asif and Ben.                            How many children can have two squares each of
How many pencils will each of them get.                                      this chocolate?
choco
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e         choco
at                  late
olate

col
choc

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choc

choco
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choco
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at e
choc

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cho                                            choco
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Put half of these ten animals in the ark. How many
of the animals are in the ark?
Y1 Calculating
•   Relate addition to counting on; recognise that addition can be done in any order; use
practical and informal written methods to support the addition of a one-digit number or a
multiple of 10 to a one- or two-digit number
Show me your arrow card which has numbers on it      Add these numbers:
that add up to three. Match the arrow card to the    5 and 6 and 2.
number 3 on your strip.                              KS1 2001 level 2c [oral]
2    1   3
2
[oral question]
7
4
[oral question]
10
Write the total.
6
35 + 40 =
Now do the same for the other cards.                 KS1 1998 level 2c
KS1 1998 level 1 [oral]

•   Understand subtraction as ‘take away’ and find a ‘difference’ by counting up; use practical
and informal written methods to support the subtraction of a one-digit number from a one- or
two-digit number and a multiple of 10 from a two-digit number
I'm giving each of you two number cards [from 0 to   What is the difference between twelve and sixteen?
5].                                                  KS1 1998 level 2b [oral]
What is the difference between your two numbers?
KS1 1999 level 1 [oral, adapted]                     What is left if five is subtracted from twelve?
Y4 optional test Mental test level 2
15 ducks are on the pond. 11 of them go away.
How many are left?                                   What is forty-eight subtract ten?
[oral question]

What is thirty-two subtract five?
KS1 1999 level 2c                                    [oral question]

72 – 8 =
KS1 1999 level 2c

65 – 40 =

Work out the difference between 80 and 20.
Show how you worked it out in the box.
•   Use the vocabulary related to addition and subtraction and symbols to describe and record
Write the total.
7+3+8+2=
KS1 2004 level 2c

25 – 12 =
KS1 2005 level 2c

Buy 2 different comics and spend 16p. Tick the 2   Match each subtraction to its answer.
comics.
16 – 6         8
Write an addition to show what you did.
KS1 1999 level 1 [oral]                                                               9
15 – 10
13
Look at the numbers.                                                   19 – 11
15 7 16 8                                                         10

Use two of these numbers to make this correct.                         18 – 9         5
–=7
KS1 1999 level 2c
KS1 2004 level 2c
Put a number in the box to make this correct.
Write a number in the box to make this correct.                        3 +  + 9 = 17
16 –  = 10                    KS1 1998 level 2b
KS1 2000 level 2c

Write numbers in the shapes to add to 12.
 +  = 12
KS1 1996 level 2c
•   Solve practical problems that involve combining groups of 2, 5 or 10, or sharing into equal
groups
Add these three numbers: five and five and five.   Four children share these shells.
KS1 2003 level 2c [oral]                           They each get the same number of shells.

There are 10 crayons in each box.

How many crayons are there altogether?
KS1 2000 level 2c
How many shells does each child get?
KS1 2005 level 2c

How many pairs of socks are there?

KS1 2000 level 2b

How many               coins make 20p?

KS1 2005 level 2b
Y2 Calculating
•   Add or subtract mentally a single-digit number or a multiple of 10 to or from any two-digit
number; use practical and informal written methods to add and subtract two-digit numbers
Write the answers.                                    Write the total.
5 + 10 =                                             61 + 11 =
15 + 10 =                                             KS1 2004 level 3
25 + 10 =
KS1 2001 level 2c                                     Write the total.
36 + 29 =
Write the total.
KS1 2002 level 2a
35 + 40 =
KS1 1998 level 2c                                     Write the answer
79 – 34 =
KS1 1996 level 2a
72 – 8 =
KS1 1999 level 2c                                     Write the answer.
82 – 45 =
Write the total.
KS1 2004 level 3
58 + 9 =
KS1 2000 level 2c                                     Write the answer.
63 – 37 =
KS1 2002 level 3
30 – 15 =
KS1 2003 level 2b                                     Write the number which is 11 less than 40.
KS1 2004 level 2a
25 + 10 + 9 =                                         Work out the difference between 46 and 18.
KS1 1997 level 2a                                     KS1 2000 level 3

Tick () the two numbers which total 50.              Write the answer.
150 + 56 =
24 15
KS1 2005 level 3
38        26
What is twenty-seven subtract nine?
19
Y3 optional test 2003 Mental test level 3
KS1 2002 level 2a

•   Understand that subtraction is the inverse of addition and vice versa and use this to derive
and record related addition and subtraction number sentences
Twenty-three children are on the bus.                 Put a number in the box to make this correct.
Four children get off and four children get on. How   38 –  = 11
many children are on the bus now?                     KS1 1997 level 2a
KS1 2005 level 2c [oral]
Write numbers in the boxes to make this correct.
Look at the numbers in this addition.                 18 +  –  = 18
9   +    5      =   14             KS1 2003 level 3

Use the same numbers to make these correct.

–           =   9

+    9      =
KS1 2005 level 2b
•   Represent repeated addition and arrays as multiplication, and sharing and repeated
subtraction (grouping) as division; use practical and informal written methods and related
vocabulary to support multiplication and division, including calculations with remainders
Some children share 12 strawberries. Each child                     4 + 4 + 4 +4 + 4 = 20
gets 3 strawberries.                               Write this addition fact as a multiplication fact.
_____ × _____ = _____

Look at each number sentence. Put a tick () if it is
correct. Put a cross () if it is not correct.
8×2=8+8                     
How many children are there?
3 × 10 = 3 + 3 + 3          
Y3 optional test 2003 level 2
5×4=5+5+5+5                 
John puts these apples in bags.                    Y3 optional test 2003 level 2

Match each addition to a multiplication.
One is done for you.
3×4

4+4+4+4+4
6×5
He puts 5 apples in each bag. How many apples
will be left over?
KS1 1997 level 2b
3+3+3                        3×3
Ella has 12 counters.
She puts them into threes like this.
6+6+6+6+6                       6×4

How many threes can she make altogether?                                                      4×5
6+6+6
She puts the same number of counters into fours.
How many fours can she make altogether?
KS1 2004 level 2b                                                                             6×3
KS1 2004 level 3
There are 4 apples in each pack.
Mrs Pullen buys 3 packs of apples.                 23 children are coming to John’s party.
How many apples does she buy?                      Each child will get 1 ice cream.
KS1 2001 level 2b                                  There are 10 ice creams in a box.
How many boxes does John need to buy?
Alex buys 6 packets of stickers.                   KS1 2001 level 2a
There are 5 stickers in each packet.
How many stickers does he buy?                     Desi needs 18 balloons. The shop sells balloons in
KS1 1999 level 2a                                  packs of 5. How many packs does he need to buy?
KS1 2003 level 2a
20 children sit at tables in groups of 4.
How many groups will there be?
There are 20 eggs.
KS1 1999 level 2a                                  A box holds 6 eggs.
How many boxes are needed to hold all the eggs?
KS1 2000 level 2a
•   Use the symbols +, –, ×, ÷ and = to record and interpret number sentences involving all four
operations; calculate the value of an unknown in a number sentence, e.g.  ÷ 2 = 6,
30 –  = 24,
Write four different numbers to make these correct.   Write the same number in each triangle to make the
multiplication correct.
 +  = 17
 ×  = 100
 +  = 17                           KS1 2004 level 2b [oral]
KS1 2003 level 2c
Write the missing number in the box.
Write numbers in the boxes to make this correct.
5 × 4 = 10 × 
13 +  +  = 23
KS1 2002 level 3
KS1 2005 level 2c
Write the missing number in the box.
Look at these signs.
÷2=7
+     ×   –      =
KS1 2001 level 2a
Use one of the signs to make this correct.
9  2 = 11                     Put a number in the box to make this correct.
Now use the signs to make this one correct.                               100 =  + 42
14  2  12                       KS1 1998 level 3
KS1 1997 level 2c
Y3 Calculating
•   Add or subtract mentally combinations of one- and two-digit numbers
What is twenty-seven subtract nine?                      Each side of this square must add up to 80.
Y5 optional test 2003 Mental test level 3                Write in the missing numbers.

30     40
KS2 2002 Mental test level 3                                                              50

What is twenty-six more than fifty?                                          20     40    20
KS2 1998 Mental test level 3
KS2 1998 Paper A level 3
Subtract thirty-two from seventy.
This is a number triangle with some numbers
KS2 2004 Mental test level 3                             missing. The numbers along each edge must add
up to 90.
The difference between a number and twenty-nine
Put all the numbers 20, 30, 50 and 60 in the circles
is ten. What could the number be?
to make the totals correct.
KS2 1998 Mental test level 3
10
What is the sum of twenty-three and twenty-seven?
KS2 2000 Mental test level 3                                                        40

In a large fish tank there are twenty-one red fish and   KS2 1995 Paper A level 3
nine blue fish. How many fish are there altogether?
Y3 optional test 1998 Mental test level 3                This table shows the increase in bus fares.

Bus fares
In a class there are thirty-two children. If there are
old fare        new fare
twenty-three girls, how many boys are there?
42p             48p
Y4 optional test 1998 Mental test level 3
52p             57p
In a class of thirty-two children, fourteen walked to                      60p             72p
school and the rest came by bus.                                           75p             85p
How many came by bus?                                                      90p            £1.05
Y4 optional test 1999 Mental test level 3                                 £1.20           £1.28

Sohan’s new bus fare is 72p.
How much has his bus fare gone up?
Millie says, ‘My bus fare has gone up by 10p’. How
much is Millie’s new bus fare?
KS2 2001 Paper A level 3
•   Develop and use written methods to record, support or explain addition and subtraction of
two- and three-digit numbers
Add together 24, 67 and 45.                       Work out the difference between 147 and 205.
KS1 2001 level 2a
Write the answer in the box.
Write in the missing numbers.
KS1 2005 level 3
 + 79 = 91
60 –  = 26                                       Write the total.
KS2 1996 Paper A level 3                          256 + 172 =
KS1 2001 level 3
Write the total.                                  .
156 + 83 =                                        Calculate 309 –198.
KS1 2004 level 3                                  KS2 2003 Paper A level 3

176 – 49 =                                        1000 – 143 =
KS1 2003 level 3                                  KS1 2004 level 3

Write in the missing number.                      Write the missing number in the box.
 + 85 = 200                                      456 +  = 710
120 – 51 =                                       KS1 2003 level 3
KS2 2004 Paper A level 3

•   Multiply one- and two-digit numbers by 10 or 100, and describe the effect
What is fifty-six multiplied by ten?              What is sixty-five multiplied by one hundred?
KS2 1997 Mental test level 3                      Y4 optional test 2003 Mental test level 3

Write the answer.                                 Write what the missing numbers could be.
37 × 10 =                                          ×  = 150
Y4 Optional test Paper A level 3                  Y4 optional test 2003 Paper A level 3

Put a ring around the number which cannot be      Harry multiplied two numbers together.
divided exactly by 10.                            His answer was 120.
60   110    80    120        90   101   Which two numbers could he have multiplied
together?
KS1 1999 level 2a
KS1 2004 level 3
Write the missing number in the box.
Ben saved twenty-four 10p coins and ten 20p coins.
 × 10 = 50
How much money has Ben saved?
KS1 2001 level 2b
Y3 optional test 2003 Paper A level 3
•   Use practical and informal written methods to multiply and divide two-digit numbers (e.g.
13 × 3, 50 ÷ 4); round remainders up or down, depending on the context
Calculate 13 × 3.                                  What is the remainder when twenty-seven is divided
Y3 optional test 2003 Paper A level 3              by five?
KS2 2005 Mental test level 3
24 × 4 =                                           Circle the two divisions which have an answer of 5
remainder 2
KS1 2005 level 3
17 ÷ 5       17 ÷ 3       22 ÷ 4      22 ÷ 5
Ella’s dad washes some cars.                       Y5 optional test 2003 Paper A level 3
He uses 12 buckets of water.
Each bucket has 5 litres of water.                 Ten children can sit at one table.
How many litres of water does he use altogether?   There are 43 children.
KS1 2004 level 2a                                  How many tables are needed so that each child can
sit at a table?
A bus ticket costs 25p.                            KS1 2005 level 3
How much will 5 of these tickets cost?
KS1 1998 level 3                                   A carton of orange fills 6 cups.
Mrs Green wants to fill 50 cups with orange.
Nutty lollies cost 35p each.                       How many cartons of orange does she need to
How much do 3 Nutty lollies cost?                  buy?
KS1 1997 level 3 [adapted]                         KS1 2003 level 3

It costs 75p for a child to go swimming.           Sadi needs 26 cartons of juice for her party.
How much does it cost for 2 children?              There are four cartons in a pack.
How many packs does she need to buy?
KS1 2001 level 3
Alan has 45 beans.
He plants 3 beans in each of his pots.
How many pots does he need?
KS2 2004 Paper A level 3

•   Understand that division is the inverse of multiplication and vice versa and use to derive and
record related multiplication and division number sentences
Here are 3 numbers.                                Write a number in each box to make this correct.
5   30     6                 300 ÷ 2 =  × 
Use all the numbers each time to complete these.   KS1 2003 level 3
5 × 6 = 30
Write a number in each box to make this correct.
6 ×  = 30
÷=6
÷6=5
KS1 2000 level 3                                   KS1 2005 level 3

When I doubled a number, the answer was 16.
Which number did I double?
KS1 2001 level 2b
Find unit fractions of numbers and quantities, e.g. ½, ⅓, ¼ and 6 of 12 litres
1
•
Jack ate half the cherries on the plate. These are    Here are 21 apples. Put a ring around one third of
the cherries that were left.                          them.

How many cherries were on Jack’s plate before he
ate half of them?                                     Y4 optional test level 3
Y4 optional test 2003 Paper A level 3
What is one-fifth of twenty-five?
Lucy has 16 cards. She gives a quarter of her cards   Y4 optional test 2003 Mental test level 3
to Kiran. How many cards does Lucy give to Kiran?
Five is a quarter of a number.
KS2 2003 Paper A level 3
What is the number?
Write the number which is half of 38.                 KS1 2003 level 3
KS1 2001 level 3

Y4 Calculating
•   Add or subtract mentally pairs of two-digit whole numbers, e.g. 47 + 58, 91 – 35
Add seventeen and fourteen.                           Jenny thought of a number.
Y3 optional test 1998 Mental test level 3             She doubled it and then added four. The answer
was eighty-eight. Which number did she think of?
How many less than forty-one is seventeen?            KS2 2002 Mental test level 4
Y4 optional test 2003 Mental test level 3
Add together thirteen, forty-seven and twenty-one.
Add together twenty-three and forty-eight.            Y5 optional test 2003 Mental test level 3
KS2 2005 Mental test level 3
Add together twenty-three, thirty-three and forty-
What number is thirty-four more than fifty-eight?     three.
KS2 2003 Mental test level 3                          KS2 2004 Mental test level 3

How many less than forty-one is seventeen?            Add together fifty-three, fifty-five and fifty-seven.
Y4 optional test 2003 Mental test level 3             KS2 2002 Mental test level 3

An apple costs eighteen pence, and an orange          Add together fourteen, twenty-three and forty-one.
costs nineteen pence. How much are they               KS2 2001 Mental test level 3
altogether?
KS2 1998 Mental test level 3                          Add together thirty-eight, twenty-three and forty-
four.
In a bag there are eighty-one red counters and        KS2 1999 Mental test level 3
thirty-seven yellow counters. How many counters
are there altogether?                                 Subtract one hundred and five from two hundred.
Y5 optional test 1998 Mental test level 3             KS2 2004 Mental test level 3

Emma is 21 years old today. Her father is 24 years    Calculate the difference between five hundred and
older. How old is Emma’s father?                      two hundred and thirty.
KS1 2005 level 3 [oral]                               KS2 2000 Mental test level 4
•   Refine and use efficient written methods to add and subtract two- and three-digit whole
numbers and £.p
Calculate 584 + 79.                                  These are the prices of sandwiches, drinks and fruit.
Y5 optional test 2003 Paper A level 3
Sandwiches        Drinks         Fruit
Calculate 137 – 65.                                        ham     £1.45   milk     55p   apple      15p
Y5 optional test 2003 Paper A level 3                      tuna    £1.70   cola     45p   pear       20p
salad   £1.20   juice    65p   melon      25p
Calculate 369 + 251.
KS2 2000 Paper A level 3                             Shereen buys a tuna sandwich, milk and a pear.
How much does she pay?
Calculate 309 –198.                                  Mike has 80p to spend on a fruit and a drink. What
KS2 2003 Paper A level 3                             two things can he buy for exactly 80p?
KS2 2004 Paper A level 3
Calculate 438 – 296.
KS2 1999 Paper A level 4                             Write in the missing digits.
1  7 + 6  = 200
Calculate 808 – 512.                                 Y4 optional test 2003 Paper A level 3
KS2 1998 Paper A level 4
Write what the two missing digits could be.
A shop sells three types of sunglasses.               62 +  95 = 757
KS2 1997 Paper A level 4

What is the difference in price between the most
expensive and least expensive sunglasses?
KS2 2004 Paper A level 4

•   Multiply and divide numbers to 1000 by 10 and then 100 (whole number answers),
understanding the effect; relate to scaling up or down
What is fifty-six multiplied by ten?                 Write in the missing number.
KS2 1997 Mental test level 3                         56 × 100 = 
Y4 Optional test 1998 Paper A level 4
If one hundred and seventy children are put into
groups of ten children, how many groups will there   What is sixty-five multiplied by one hundred?
be?
Y4 optional test 2003 Mental test level 4
Y4 optional test 1998 Mental test level 3
How many hundreds are there altogether in two
Divide three hundred and ninety by ten.
thousand four hundred?
KS2 2001 Mental test level 4
Y5 optional test 2003 Mental test level 4
Write in the missing number.
 ÷ 10 = 20
KS2 1996 Paper A level 3

Circle all the multiples of 10.
640      500      404
170             26            195
30                  531
Y3 optional test Paper B level 3
•    Develop and use written methods to record, support and explain multiplication and division
of two-digit numbers by a one-digit number, including division with remainders, e.g. 15 × 9,
98 ÷ 6
Write in the missing number.                          Write the answer.
5 × 70 =                                             84 ÷ 7 =
KS2 2002 Paper A level 3                              Y4 optional test Paper A level 4

What is thirty multiplied by seven?                   What is the remainder when you divide 53 by 8?
KS2 2004 Mental test level 3                          Y4 optional test 2003 Paper A level 3

Divide ninety by three.                               Write in the missing numbers.
KS2 2003 Mental test level 3                          4 ×  = 200
KS2 2002 Paper A level 3
Calculate 58 × 6.
KS2 1998 Paper A level 4                              Write in the missing number.
 ÷ 5 = 22
Circle each number which has a remainder of 2
KS2 1995 Paper A level 4
when divided by 5.
27    15     26   45      32   24                     Write in the missing digit.
Y5 Optional test 1998 Paper A level 3                  7 × 9 = 333
KS2 1996 Paper A level 4
Calculate 56 ÷ 4.
KS2 2005 Paper A level 3                              Write in the missing digit.
5
Sarah’s cat eats one tin of this cat food each day.
× 8
456
KS2 1995 Paper A level 4

Write in the missing digit.
The answer does not have a remainder.
2 6
3     8

How much does it cost to feed Sarah’s cat for 7       KS2 1995 Paper B level 4 (no calculator)
days?
Y4 optional test 2003 Paper A level 3                 Parveen buys 3 small bags of peanuts. She gives
the shopkeeper £2 and gets 80p change. What is
the cost in pence of one bag of peanuts?
KS2 1999 Paper A level 4
Find fractions of numbers, quantities or shapes, e.g. 5 of 30 plums, 8 of a 6 by 4 rectangle
1                 3
•
Here is a square.                                  What is three-quarters of two hundred?
KS2 2000 Mental test level 4

What fraction of the square is shaded?
4 of them are dog stickers.
1
KS2 2004 Paper A level 3
2 of them are cat stickers.
1

Write the missing number to make this correct.     The rest are rabbit stickers.
1         1
4
of 24 =
2
of                    How many rabbit stickers does she have?
Y4 optional test 2003 Paper A level 3
KS1 2004 level 3
Match each box to the correct number. One has
Which number comes halfway between 330 and         been done for you.
410? Write it in the box.                                                                   45

330                                410                                                 40
1
2
of   30
35

1
3
of   75                      30

KS1 2004 level 3                                                                             25
1
5
of   150
20

15
KS2 2001 level 4
•   Use a calculator to carry out one- and two-step calculations involving all four operations;
recognise negative numbers in the display, correct mistaken entries and interpret the display
correctly in the context of money
Write in the missing number.                          Here are some number cards.
225 –  = 150
4               4           4
KS2 2003 Paper B level 3

Write in the missing number.                                              9               9       9
60 + 99 +  = 340
Use five of the number cards to make this correct.
KS2 2000 Paper B level 3

Write the missing number.
48 ÷  = 4
Y3 Optional test 1998 Paper B level 3                                 +

Apples are sold in packets of 4 at the supermarket.
5       4       8
How many apples are in 72 packs?
Y5 Optional test 1998 Paper B level 3                 KS2 2001 Paper B level 3

Plants are sold in trays of 20.                       Complete this two digit number so that it is a
Ivana buys 7 trays of plants.                         multiple of 6.
How many plants is this?
David wants 240 plants.                                                           7
How many trays does he need to buy?
KS2 2001 Paper B level 3                              Y4 Optional test 1998 Paper B level 3

Pam has £1.37. She wants to buy a box of crayons      Mrs Patel buys 4 milkshakes costing 65p each and
which cost £2.75.                                     3 sandwiches costing £1.70 each.
How much more money does she need?                    Work out the total cost.
Y4 optional test 1998 Paper B level 3                 Y5 optional test 1998 Paper B level 3

A box of four tennis balls costs £2.96.
How much does each ball cost?
Dean and Alex buy 3 boxes of balls between them.
Dean pays £4.50.
How much must Alex pay?
KS2 2002 Paper B level 3                              There are 2 adults and 3 children in a family. How
much does it cost the family to go on the ferry?
KS2 1996 Paper B level 3
Y5 Calculating
•   Extend mental methods for whole-number calculations, e.g. to multiply a two-digit by one-
digit number (e.g. 12 × 9), to multiply by 25 (e.g. 16 × 25), to subtract one near multiple of
1000 from another (e.g. 6070 – 4097)
What number is two less than nine hundred and             What is one thousand minus one hundred and ten?
one?                                                      KS2 2004 Mental test level 3
Y4 optional test 2003 Mental test level 3
What is three thousand subtract ten?
What number is one hundred and ninety-nine more
Y5 optional test 1998 Mental test level 3
than four hundred and twenty-eight.
Y5 optional test 2003 Mental test level 4                 What is the difference between one thousand nine
hundred and ninety-four and four thousand and
One orange costs nineteen pence. How much will            three?
three oranges cost?
Y5 optional test 2003 Mental test level 4
Y4 optional test 2003 Mental test level 3
What is one thousand, two hundred and ninety-nine
One orange costs fifteen pence. How much would            add one?
five oranges cost?                                        Y5 optional test 1999 Mental test level 4
Y4 optional test 1998 Mental test level 4
What is twenty-five multiplied by eight?
An apple costs seventeen pence. How much will             Y4 optional test 1998 Mental test level 4
three cost?
Y4 optional test 1999 Mental test level 4                 What is twelve multiplied by twenty-five?
KS2 2001 Mental test level 4
A fruit pie costs fifty-five pence. What is the cost of
three fruit pies?
KS2 2004 Mental test level 4

4 pineapples cost £3.40.
Calculate the cost of 1 pineapple.
Y4 optional test 2003 Paper A level 4

What is twenty-one multiplied by nine?
KS2 2000 Mental test level 4
•   Use efficient written methods to add and subtract whole numbers and decimals with up to
two places
Calculate 1025 – 336.                                   Write what the two missing digits could be.
KS2 2001 Paper A level 4                                 62 +  95 = 757
KS2 1997 Paper A level 4
Calculate 1202 + 45 + 367.
KS2 2005 Paper A level 4                                Calculate 13.6 – 2.8
KS2 2004 Paper A level 4
Calculate 6247 – 2752.
Y5 optional test 2003 Paper A level 4                   A shop sells sun hats.

Here is the cost of pizzas.
PIZZAS
Small         Medium
Ham                   £4.20         £5.50
Salami                £4.40         £5.75
Mushroom              £4.50         £6.00
Ryan buys some sunglasses for £4.69 and a sun
Cheese                £3.80         £4.95
hat. How much change does he get from £10?
Tuna                  £4.25         £5.40
KS2 2004 Paper A level 4
Extra tomato       50p
Extra cheese       60p

Jill orders one small cheese pizza with extra tomato.
What is the total cost?
Ben buys one small pizza and one medium pizza.
They cost him £10. Which two could they be?
KS2 1996 Paper A level 3
•   Use understanding of place value to multiply and divide whole numbers and decimals by 10,
100 or 1000
Look at these number cards.                               Write in the missing numbers.
A              B              C              D     32.62 ÷ 10 =
730 000         73 000          7 300           730   Y5 optional test Paper A level 4

Write in the missing number.
E               F              G
3400 ÷  = 100
7.3            0.73           0.073
Y4 optional test 2003 Paper B level 3
Write the letter of the card that is                      Write what the four missing digits could be.
ten times as big as 73                      …                ÷ 10 = 3 
one thousand times as big as 73             …             KS2 1997 Paper A level 4
one hundredth of 73                         …
Divide thirty-one point five by ten.
Y7 optional test Paper A level 4
Y5 optional test 2003 Mental test level 5
Multiply thirty-one by ten.
What is seven point five divided by one hundred?
KS3 2003 Mental test level 4
KS2 2004 Mental test level 5
What is four hundred divided by one hundred?
Ten times a number is eighty-six. What is the
Y7 progress test 2005 level 4
number?
What is two thousand divided by ten?                      KS2 2002 Mental test level 5
Y7 optional test Mental test level 4
What is six point two multiplied by one thousand?
How many hundreds are there in one thousand?              KS3 2005 Mental test level 5
Y7 progress test 2004 level 4

How many hundreds are there altogether in two
thousand four hundred?
Y5 optional test 2003 Mental test level 4

Divide nine thousand three hundred by one
hundred.
KS3 2005 Mental test level 4

•   Refine and use efficient written methods to multiply and divide HTU × U, TU × TU, U.t × U,
and HTU ÷ U
Calculate 549 × 6.                                        Calculate 847 ÷ 7.
KS2 1998 Paper A level 4                                  KS2 2001 Paper A level 4

Work out 32 × 21.                                         Calculate 942 ÷ 6
Y7 progress test 2003 Paper A level 4                     Y5 optional test 2003 Paper A level 4

Calculate 47 × 32.                                        Write in the missing digits to make this correct.
Y5 optional test 2003 Paper A level 4
4
There are 12 pencils in a box. A school buys 24
boxes. How many pencils does the school buy?                             ×                       6
KS2 1997 Paper A level 4
2      0       5        2
KS2 2001 Paper A level 4
Find fractions using division, e.g. 100 of 5 kg, and percentages of numbers and quantities,
1
•
e.g. 10%, 5% and 15% of £80
What is one-fifth of twenty-five?                  What is fifty per cent of ten?
Y4 optional test 2003 Mental test level 3          KS3 2004 Mental test level 4

Match each box to the correct number. One has      What is ten per cent of ninety metres?
been done for you.                                 Y4 optional test 1998 Mental test level 4
45
What is fifty per cent of twenty pounds?
40     KS3 2003 Mental test level 4
1
2
of   30
35     What is fifty percent of forty?
Y5 optional test 1998 Mental test level 4
1
3
of   75                          30

25
1
5
of   150
20

15
KS2 2001 Paper B level 4
Y6 Calculating
•   Calculate mentally with integers and decimals: U.t ± U.t, TU × U, TU ÷ U, U.t × U, U.t ÷ U
What is the sum of eight point five and eight point   What number is halfway between thirty and eighty?
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
Circle two numbers which add to make 0.12.
and nought point six.
0.1      0.5      0.05        0.7     0.07    0.2
KS2 2005 Mental test level 4
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
In a café I buy two cups of coffee and a sandwich.    KS2 1999 Paper A level 5
Altogether I pay three pounds.
The first two numbers in this sequence are 2.1 and
The sandwich costs one pound sixty.
2.2. The sequence then follows the rule ‘to get the
What is the cost of one cup of coffee?
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.                    2.1      2.2       4.3     6.5            
Josh buys three packets. How much change does         KS2 2003 Paper A level 4
he get from one pound?
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
•   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- 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
Write in the missing digit.
number.
 7 × 9 = 333
KS2 1996 Paper A level 4                                             2.46     8.61     7.38

Write in the missing digit.                                          11.07             1.23
5  × 8 = 456
4.92     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.                          Calculate 123 ÷ 5.
The trays are packed in boxes.
Each box contains 180 eggs.                           Calculate 16.5 ÷ 3.
How many trays are in each box?
KS2 1999 Paper A level 4                              Calculate 27.6 ÷ 8.

Some children go camping.                             Shenaz buys a pack of 24 cans of cola for £6.00
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?
There are 70 children.
Each tent takes up to 6 children.
What is the least number of tents they will need?
KS2 1998 Paper A level 4                              What is the cost of each can?
KS2 1998 Paper A level 5
Relate fractions to multiplication and division, e.g. 6 ÷ 2 = 2 of 6 = 6 × 2; express a quotient
1                1
•
as a fraction or decimal, e.g. 67 ÷ 5 = 13.4 or 13 5; find fractions and percentages of whole-
2

number quantities, e.g. 8 of 96, 65% of £260
5

One third of a number is twelve. What is the         Calculate 60% of 765.
number?                                              KS2 2000 Paper B level 4
KS2 1997 Mental test level 4
In a sale, there is fifty per cent off all prices.
What is three-quarters of two hundred?               A chair costs forty-five pounds in the sale.
KS2 2000 Mental test level 4                         How much was it before the sale?
KS2 1999 Mental test level 4
What is three-fifths of forty pounds?
John had £5. He gave 25% of it to charity. How
KS3 2003 Mental test level 5
much did he give?
Joe has some pocket money. He spends three-          Y4 optional test Paper B level 4
quarters of it. He has fifty pence left. How much
pocket money did he have?                            Sophie poured some water out of a litre jug. Look
how much is left in the jug. Estimate how many
Y5 optional test 2003 Mental test level 4
millilitres of water are left.
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
•   Use a calculator to solve problems involving multi-step calculations
Three pupils answered different questions. This is     Emma saves £3.50 each week. How much has she
what each pupil’s calculator showed:                   saved after 16 weeks?
Y5 optional test Paper B level 4

Sima thinks of a number.
Asim’s question was about money. Complete the          She divides it by 12. Her answer is 26.
sentence:                                              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
3.5 means 3 hours and …… minutes.                      each and a spade at £9.65. How much money does
Charlie’s question was about length. Complete the      she have left?
sentence:                                              Seeds are £1.45 for a packet. Steffan has £10 to
3.5 means 3 metres and …… centimetres.                 spend on seeds. What is the greatest number of
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
Y6 progression to Y7 Calculating
•    Understand how the commutative, associative and distributive laws, and the relationships
between operations, including inverse operations, can be used to calculate more efficiently;
use the order of operations, including brackets
Write the correct sign >, < or = in each of the                  Leila knows that
following.                                                       65 × 3 = 195
(10 + 5) – 9               (10 + 9) – 5              Explain how she can use this information to find the
3 × (4 + 5)               (3 × 4) + 5               answer to this multiplication:
165 × 3
(10 × 4) ÷ 2               10 × (4 ÷ 2)
KS2 2000 Paper A level 5
KS2 2005 Paper A level 4
Kim knows that
Calculate 900 ÷ (45 × 4).
137 × 28 = 3836
KS2 2004 Paper A level 5
Explain how she can use this information to work
Put a tick () in the correct box for each calculation.          out this multiplication.
Use a calculator.                                                138 × 28
less than   equal to      more than   KS2 1997 Paper A level 5
1000       1000           1000

8.9 × 9.9 × 11.9                                             Liam thinks of a number. He multiplies the number
by 5 and then subtracts 60 from the result.
(786 – 387) ÷ 0.41
His answer equals the number he started with.
95.4 + (91 × 9.95)                                           What was the number Liam started with?
12.5 × (21.1 + 58.9)                                         KS2 2004 Paper A level 5

KS2 2000 Paper B level 5
•   Consolidate and extend mental methods of calculation to include decimals, fractions and
percentages
What is fifteen multiplied by eleven?                 What is one point three multiplied by four?
KS2 2003 Mental test level 4                          KS2 2004 Mental test level 5

What is eighteen multiplied by nine?                  Multiply eight point seven by two.
KS3 2005 Mental test level 5                          KS3 2004 Mental test level 5

Multiply thirty-nine by seven.                        Divide thirty-one point five by ten.
KS2 2005 Mental test level 5                          Y5 optional test 2003 Mental test level 5

What is twenty-five multiplied by two hundred?        What is seven point five divided by one hundred?
KS2 2002 Mental test level 5                          KS2 2004 Mental test level 5

A rectangle measures eleven centimetres by twenty     Ten times a number is eighty-six. What is the
centimetres. What is its area?                        number?
KS2 2004 Mental test level 5                          KS2 2002 Mental test level 5

Calculate ten minus four point three five.            What is nought point two six divided by ten?
KS2 2001 Mental test level 5                          KS2 2001 Mental test level 5

Subtract nought point seven five from six.            A tile is nought point two metres long.
KS3 2003 Mental test level 4                          One hundred tiles are placed end to end in a row.
How long is the row?
What is one and a half added to four and a half?      Y5 optional test 1998 Mental test level 5
KS2 2000 Mental test level 3
What is half of six point three?
What is one-half added to three-quarters?             KS3 2001 Mental test level 5
KS2 2003 Mental test level 4
What is three point nine divided by two?
What is two thirds of sixty-six?                      KS3 2003 Mental test level 6
KS2 2004 Mental test level 5                          What is fifty per cent of twenty pounds?
KS3 2003 Mental test level 4
What is three-quarters of five hundred?
KS2 2003 Mental test level 5                          What is two percent of three hundred?
KS2 2000 Mental test level 5
Three-quarters of a number is 48. What is the
number?                                               What is ninety-nine per cent of two hundred?
KS2 2003 Mental test level 5                          KS2 2002 Mental test level 5

What is three-fifths of forty pounds?                 What is twenty per cent of sixty pounds?
KS3 2003 Mental test level 5                          KS3 2005 Mental test level 5

Tariq won one hundred pounds in a maths               Increase one pound fifty by fifty per cent.
competition. He gave two-fifths of his prize money    KS3 2004 Mental test level 5
to charity. How much of his prize money, in pounds,
did he have left?
KS3 2004 Mental test level 5
•   Use standard column procedures to add and subtract integers and decimals, and to multiply
two- and three-digit integers by a one- or two-digit integer; extend division to dividing three-
digit integers by a two-digit integer
Calculate 417 × 20.                                 Write in the missing number.
KS2 2002 Paper A level 4                                                  50 ÷  = 2.5
KS2 2003 Paper A level 5
Calculate 143 × 37.
KS2 2005 Paper A level 5                            Calculate 4.65 × 9.

Calculate 509 × 24.                                 Calculate 13.6 × 8.
KS2 2001 Paper A level 5
Calculate 157 ÷ 5.
Calculate 268 × 53.
Calculate 1.75 ÷ 5.
KS21999 Paper A level 5

Calculate 431 × 23.                                 Calculate 37.2 ÷ 8.
KS2 1998 Paper A level 5                            Write in the missing digit.
 92 ÷ 14 = 28
Calculate 924 ÷ 22.
KS2 1995 Paper A level 5
KS2 2002 Paper A level 5
Write in the missing digits.
Write in the missing digit. The answer does not
have a remainder.                                                    323 ×  7 = 1518 
2 6                         KS2 1995 Paper A level 5
3   8

KS2 1995 Paper A level 5
•   Calculate percentage increases or decreases and fractions of quantities and measurements
Calculate 5 of 325.
1
Calculate 5% of £3600.
Y5 optional test Paper B 2003 level 5                  KS2 2004 Paper A level 5

Calculate 8 of 980.
3
Calculate 15% of 460.
KS2 2003 Paper B level 5                               KS2 2001 Paper A level 5

Calculate 12 of 378.
5
Calculate 24% of 525.
KS2 2001 Paper B level 5                               KS2 1998 Paper B level 5

Calculate 8 of 5000.
7
Write in the missing numbers.
KS2 1999 Paper B level 5                                        30% of 60 is      
30% of         is 60
Three-quarters of a number is 48.
KS2 2005 Paper B level 5
What is the number?
KS2 2003 Paper A level 5                               A larger bottle of juice will hold 30% more than this
bottle. How much will the larger bottle hold?
There are 24 coloured cubes in a box. Three-
quarters of the cubes are red, four of the cubes are
blue and the rest are green.

How many green cubes are in the box?
One more blue cube is put into the box. What           Y5 optional test 1998 Paper B level 4
fraction of the cubes in the box are blue now?
KS2 2002 Paper B level 5                               The population of the world is approximately 6200
million people.
It is increasing by approximately 93 million people
each year.
Use this information to calculate the percentage
increase in the population over a year.
KS2 2001 Paper C level 6
•   Use bracket keys and the memory of a calculator to carry out calculations with more than
one step; use the square root key
Write in what the missing numbers could be.            Write in the missing number.
170 +  = 220 –                                       32.45 ×  = 253.11
KS2 2002 Paper B level 5                               KS2 2002 Paper B level 5

Write the missing number.                              Write in the missing number.
10 233 ÷  = 379                                       404.09 ÷  = 8.5
KS2 1997 Paper B level 5                               KS2 2001 Paper B level 5

2753 people go to a sports event. Each person          Write in the missing number.
pays £2.30 for a ticket. What is the total amount of    ÷ 21.7 = 37.5
ticket money collected?
KS2 2004 Paper B level 5
Programmes cost 65p each. The total money from
programme sales is £612.95. How many                   Write the answer..
programmes are sold?
100 – (22.75 + 19.08) =
KS2 1998 Paper B level 5
KS2 2004 Paper B level 5
A shop sells sheets of sticky labels.
Use a calculator to work out
On each sheet there are 36 rows and 18 columns of
labels.                                                49.3 × (2.06 + 8.5)
KS2 2002 Paper B level 5

Here is a rectangle with a width of 15.7 centimetres.

The perimeter of this rectangle is 85 centimetres.
Calculate the length of the rectangle.
KS2 2005 Paper B level 5
How many labels are there altogether on
45 sheets?
Every day a machine makes 100 000 paper clips
KS2 1999 Paper B level 5                               which go into boxes. A full box has 120 paper clips.
How many full boxes can be made from 100 000
Here is a flag.                                        paper clips?
125 cm                       Each paper clip is made from 9.2 centimetres of
wire. What is the greatest number of paper clips that
can be made from 10 metres of wire?
60 cm
KS2 1998 Paper B level 5

Write three decimals, each greater than zero, which
What is the area of this flag?                         add together to make a total of 0.01
20% of the flag is blue. What area of the flag is       +  +  = 0.01
blue?
KS2 1999 Paper C level 6
KS2 1995 Paper B level 5

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