INTRODUCTION
The purpose of this booklet is to outline the various calculation methods that children are taught as they progress through the school, many of which look different to the methods that you may have been taught in your primary school days.
During Numeracy lessons, which are blocked into two sessions on alternate days, children will be doing a mixture of counting, talking about numbers, mental calculations and using numbers to solve real life problems. They will begin to record what they’ve done with pictures and numbers.
These recordings will help them to understand what is happening and to show how they’ve worked something out.
As they progress through the school, pupils build up a bank of strategies, from early mental calculation skills to formal written recordings that can be applied when appropriate. Each strategy can be refined or extended to suit the calculation needed these
This booklet shows the range of different methods that we are now teaching. We hope the explanations and examples of strategies will help you to assist your child at home.
Also included in the booklet are various ideas and suggestions for maths activities that you can enjoy doing with your child in the world away from school. It is not an exhaustive list and you will doubtless have many more ideas of your own.
MENTAL CALCULATIONS
It is important to recognise that the ability to calculate mentally lies at the heart of the new 2014
National Curriculum. Mental calculation methods will therefore be taught systematically from
Reception onwards and pupils will be given regular opportunities to develop the necessary skills.
Children are introduced to the processes of calculations through practical, oral and mental activities. Through these activities, they consolidate their understanding of number facts and begin to develop ways of recording to support their thinking and calculation methods. As children progress through the school and are taught more formal written methods, they are still encouraged to think about mental strategies they could use first and only use written methods for those calculations they cannot solve in their heads.
When faced with a calculation problem, encourage your child to ask:

Can I do this in my head?

Could I do this in my head using drawings or jottings to help me?

Do I need to use a written method?

Should I use a calculator?
Also help your child to estimate and then check the answer. Encourage them to ask:

Is the answer sensible?

WHAT BASIC MATHEMATICAL FACTS WILL MY CHILD BE TAUGHT?
Practice is crucial and skills are built on throughout the school right from the foundation years.
Reception

Count forwards and backwards in 1s to and from 20

Place numbers up to 20 in order.

Find one more or one less than a number from 1 to 20

Number bonds and related subtraction facts within 10. E.g. 3 + 7, or what to add to a singledigit number to make 10, e.g. 3 + * = 10

Add and subtract two single-digit numbers and count on or back to find the answer. E.g. 2 +
3, 4 + 5, 6 – 2

Addition doubles for numbers up to 10 E.g. double 4.

Halving numbers: (10, 8) 6, 4, 2 or share into equal groups.
 Combine groups of 2 (5 or 10).
Use words such as more, less, greater, smaller, heavier, lighter to compare things.

Make simple patterns and talk about them.

Name shapes such as a circle, square, triangle, rectangle, cube, cone and sphere.

Use words such as over, under, above, below, on, in, next to, beside to describe where
Year 1 things are.

Count to and across 100, forwards and backwards, beginning with 0 or 1, or from any given number.

Count, read and write numbers to 100 in numerals.
 Read and write numbers from 1 to 20 in numerals and words.

Say the number that is 1 more or less than a given number, and 10 more or less for multiples of 10

Derive and recall all pairs of numbers with a total of 10 and addition facts for totals to at least 5; work out the corresponding subtraction facts.

Derive number bonds and related subtraction facts within 20. E.g. 9 + 7 = 16; 16 - 7 = 9; 7 =
16 – 9, or what to add to a single-digit number to make 20, e.g. 13 + * = 20.

Add and subtract one-digit and two-digit numbers to 20. E.g. 13 + 5; 17 – 9

Count on or back in ones, twos, fives and tens and use this knowledge to derive the multiples of 2, 5 and 10 to the tenth multiple

Addition doubles for all numbers to at least 10 E.g. 8 + 8, double 6.

Recognise odd and even numbers up to 20.

Put numbers in order and use terms like greater/smaller than and =.

Use the words add, sum, total, take away, subtract, difference between…

Record information lists and tables and use practical resources, pictures, block graphs or pictograms to present outcomes.

Compare objects or containers, and say which is longer or shorter, or heavier or lighter, or which holds more.

Name 2-D and 3-D shapes and describe their features and use them to make patterns models and pictures.

Year 2

Count in steps of 2, 3, and 5 from 0, and in tens from any number, forward or backward.

Read and write numbers to at least 100 in numerals and in words.

Compare and order numbers from 0 up to 100; use <, > and = signs.

Recall and use addition and subtraction facts to at least 20 fluently e.g. 9 + 8, 17 – 9, and derive and use related facts up to 100.

Number Bonds to 100 - pairs of multiples of 10 with totals up to 100, e.g. 30 + 70, or 60 + *
= 100

Sums and differences of multiples of 10, e.g. 50 + 80, 120 – 90 and number pairs that total
100

Add and subtract numbers including: a two-digit number and ones; a two-digit number and tens; - two two-digit numbers

What must be added to any two-digit number to make the next multiple of 10? E.g. 52 + * =
60

Addition doubles for all numbers to 20, e.g. 17 + 17 and multiples of 10 to 50, e.g. 40 + 40

Understand that halving is the inverse of doubling and derive and recall doubles of all numbers to 20, and the corresponding halves.

Recall and use multiplication and division facts for the 2, 5 and 10 multiplication tables and corresponding division facts/Recognise multiples of 2, 5and 10

Doubles of all numbers to 20. E.g. double 13, and corresponding halves.

Doubles of multiples of 10 to 50. E.g. double 40, and corresponding halves.

Odd and even numbers to 100.

Understand opposite (inverse) relations E.g. 4 × 5 = 20 and 20 ÷ 5 = 4.

Find ½, ¼ and ¾ of shapes and sets of objects.

Use lists, tables, and diagrams; represent data as block graphs or pictograms.

Measure or weigh using metres, centimetres, kilograms or litres.

Use a ruler to draw and measure lines to the nearest centimetre.

Use symbols +, -, x, ÷ and =, to record work with number sentences.

Tell the time to the half and quarter hour; know seconds, minutes, hours and days and how they relate to one another

Name 2-D and 3-D shapes and describe their features; sort make and describe shapes referring to their properties.

Solve number problems (including pounds, pence, measures etc), and explain how to work them out.
Higher Attaining Pupils in Year 2 will be introduced to objectives from Key Stage 2 – Year 3 .
Year 3

Count from 0 in multiples of 4, 8, 50 and 100.

Count in ones, tens and hundreds.
 Find 10 or 100 more or less than a given number.

Compare and order numbers up to 1000.

Read and write numbers up to 1000 in numerals and in words.

Derive and recall all addition and subtraction facts for each number to 20, sums and differences of multiples of 10 and number pairs that total 100 and 1000 e.g. 300 + 700, or
600 + * = 1000


Number bonds to 100 for multiples of 5. E.g. 45 + * = 100

Pairs of two-digit numbers with a total of 100, e.g. 32 + 68, or 32 + * = 100

Addition doubles for multiples of 10 to 100, e.g. 90 + 90

Add and subtract mentally including: three-digit number and ones; three-digit number and tens; - three-digit number and hundreds

Derive and recall multiplication facts for the 2, 3, 4, 5, 8 and 10 times-tables and the corresponding division facts; recognise multiples of 2, 5 or 10 up to 1000

Multiples of 10 x a single digit. E.g. 30 x 2 = 60, and corresponding division facts.

Doubles of multiples of 10 to 100. E.g. double 90, and corresponding halves.

Use knowledge of number operations and corresponding inverses, including doubling and halving, to estimate and check calculations

Find simple fractions, such as 1/2, 1/3, 1/4, 1/5, 1/10 (up to 7/10 and 9/10 etc), of shapes and numbers. Use pictures to find equivalent fractions.

Read the time on a 12 hour digital clock and tell the time to the nearest 5 minutes on an analogue clock.

Read scales with numbered and unnumbered divisions. Know the relationship between km and m, m and cm, kg and g, l and ml.

Solve simple number problems and explain how to work them out.

Draw and complete shapes with reflective symmetry; draw the reflection of a shape in a mirror.

Use Venn and Carroll diagrams to sort data and objects.

HOW ARE THESE METHODS TAUGHT?
Calculation Guidelines for Foundation Stage (Reception Class)
ADDITION SUBTRACTION MULTIPLICATION DIVISION
Children begin to record in the context of play or practical activities and problems.
Pupils count sets of objects. They then develop ways of recording calculations using dots, pictures, words or symbols of addition activities carried out.
Children use their fingers for counting to 10.
Children learn in a play based environment using mark making resources, visual displays, kinaesthetic displays such as wooden numbers, woven numbers and activities such as singing, role play, stories and PE style games.
They start to use number tracks, to count on. Teachers demonstrate the use of the number track.
Children then begin to use numbered lines independently to count on in ones. They jump forwards along the number line using finger.
Relate subtraction to taking away and counting how many objects are left.
Make a record in pictures, words or symbols of subtraction activities already carried out.
Use of games, songs and practical activities to begin using vocabulary e.g. 10 green bottles, role play, stories, PE style games.
Construct number sentences to go with practical activities
Real life contexts and use of practical equipment to count in repeated groups of the same size:
Count/chant in twos.
Count/chant in tens.
Count/chant in fives.
Double numbers up to 5.
Can find one less to ten.
They use number track, their fingers and practical resources to support calculation. Teachers demonstrate the use of the number track.
Counting backwards along a number line using finger.
Share objects into equal groups.
Activities might include:
• Sharing of milk at break time
• Sharing sweets on a child’s birthday
• Sharing activities in the home corner
• Count in tens/twos
• Separate a given number of objects into two groups (addition and subtraction objective in reception being preliminary to multiplication and division)
Count in twos, tens and fives.
Use related vocabulary:
How many times?
How many are left/left over?
Group
Answer
Right, wrong
What could we try next?
How did you work it out?
Share out
Half, halve
Bead strings or bead bars are used in school to illustrate addition.
Construct number sentences to go with practical activities.
Use of games, songs and practical activities to begin using vocabulary.
Solve simple word problems using their fingers
Can find one more to ten.

Revise adding two sets of numbers by drawing pictures, dots or tally marks.
E.g. At a party, I eat 3 cakes and my friend eats 6. How many cakes did we eat altogether?
+ = signs and missing numbers
Children need to understand the concept of equality before using the ‘=’ sign. Calculations should be written either side of the equality sign so that the sign is not just interpreted as ‘the answer’.
2 = 1 + 1 2 + 3 = 4 + 1 3 = 3 2 + 2 + 2 = 4 + 2
Missing numbers need to be placed in all possible places.
3 + 4 =
 
= 3 + 4 3 +

+ 4 = 7 7 = 3 +
 
+


= 7 7 =
= 7 7 =

+ 4

+

The Number Line
Children use a numbered line to count on in ones.
7 + 4
+ = signs and missing numbers
Continue using a range of equations as in Y1 but with appropriate, larger numbers. E.g. Extend to 14 + 5 = 10 +  and 32 +  +  = 100
35 = 1 +  + 5
Count on using a number line in tens and ones (rather than jump in ones along the whole line, jump on a whole ten, then jump in ones).
E.g. 23 + 12 = 23 jump on 10/+ 10 = 33 then jump on 2/+ 2 = 35
+10
+2
23 33 35
The Number Line: bridging through 10.
The steps in addition often bridge through a multiple of 10 e.g. Children should be able to partition the 7 to relate adding the 2 and then the 5.
8 + 7 = 15
8 10 15
0 1 2 3 4 5 6 7 8 9 10 11 12
Recording by:
- drawing jumps on prepared lines
- constructing own lines
Extend to word problems using a number line. E.g. 7 people are on the bus. 4 more get on at the next stop. How many are on the bus now. (See above)
Extend to adding one-digit and two-digit numbers to 20 using the number line. E.g. 12 + 5 (start counting on from 12 on the number line, and move 5 places/jumps to land on 17).
Add 9 or 11 by adding 10 and adjusting by 1
35 + 9 = 44 +10
35 44 45
-1
Calculations methods for more able pupils can be extended to:
Partition into tens and ones for larger numbers
Partition both numbers and recombine.
Partition into tens and ones Partition both numbers and recombine. (In the example below, 23 is split into 10, 10 and 3).
Count on by partitioning the second number only e.g.
36 + 53 = 53 + 30 + 6 = 83 + 6 = 89
48 + 36 = 84
48
53
+30
+30
+2
78 80
+4
83
84
+6
89
Count on from the largest number irrespective of the order of the calculation e.g. 38 + 86 = 124
Add a near multiple of 10 to a two-digit number
Secure mental methods by using a number line to model the method.
Continue as in Year 2 but with appropriate numbers e.g. 35 + 19 is the

Count on by partitioning the second number only e.g.
36 + 53 = 53 + 30 + 6
= 83 + 6
= 89
+30
+6 same as 35 + 20 – 1.
Pencil and paper procedures (partitioning = break the number up into its tens and units)
67 + 24 = 80 (60 + 20) + 11 (7 + 4) = 91
53 83 89
Partition into tens and ones and recombine using informal jottings rather than a number line
Partition means to break the tens and units digit up into 2 separate numbers.
E.g. 12 can be broken up into 10 + 2 (12); 23 can be broken up into 20 + 3 (23)
E.g. 12 + 23
Group the tens numbers and add them = 10 + 20 (30)
Group the units numbers and add them = 2 + 3 (5)
Add both sets of numbers together = 30 + 5
Get the answer = 35
E.g. 16 + 35 = 10 + 30 = 40 ; 6 + 5 = 11 = 40 + 11 = 51
Partition into tens and units using the diamond method
E.g. 37 + 15
30 7 10 5
40 + 12
=52
267 + 85 = 200 + 140 (60 + 80) + 12 (7 + 5) = 352
Add numbers with up to 3 digits, using formal written methods.
Using similar methods, children will:
 add several numbers with different numbers of digits;
 begin to add two or more three-digit sums of money, with or without adjustment from the pence to the pounds;
 know that the decimal points should line up under each other, particularly when adding or subtracting mixed amounts, e.g.
£3.59 + 78p.
 solve word problems. E.g My sunflower is 123cm tall in May. By
June it has grown another 56cm. How tall is the sunflower now?

- = signs and missing numbers
7 - 3 =   = 7 – 3 7 -  = 4 4 =  - 3

- 3 = 4 4 = 7 -
 
-

= 4 4 =

-

Understand subtraction as 'take away'
E.g. 5-2. I had five balloons. Two burst. How many did I have left? take away = 3 left
Understand how to ‘find the difference’ by counting on/up …
I have saved 5p. The socks that I want to buy cost 11p. How much more do I need in order to buy the socks?
+ 6
- = signs and missing numbers
Continue using a range of equations as in Year 1 but with appropriate numbers. Extend to 14 + 5 = 20 - 
Find a small difference by counting on in units. E.g. 42 – 39 = 3
+ 1
+ 2
39 40
Find a difference by counting on
42
Find a small difference by counting up - Continue as in Y2 but with appropriate numbers e.g. 102 – 97 = 5 (count on from 97 up to 102)
Subtract mentally a ‘near multiple of 10’ to or from a two-digit number - Continue as in Year 2 but with appropriate numbers e.g.
78 – 49 is the same as 78 – 50 + 1
Use known number facts and place value to subtract
Continue as in Y2 but with appropriate numbers e.g. 97 – 15 = 82
(count on from the lower number up to the larger number OR back from the larger number to the smaller).
0 1 2 3 4 5 6 7 8 9 10 11 12
E.g. A teddy bear costs £5 and a doll costs £2. How much more does the bear cost? (Count on/up from the £2 to £5)
Find a 'difference' by counting back
I have 11 toy cars. There are 5 cars too many to fit in the garage. How many cars fit in the garage?
-5 11
Extend to subtracting one-digit and two-digit numbers to 20 using the number line. E.g. 13 – 6; 19 – 8; 17-11; 19-14 etc.
Find a difference by subtracting the units in one jump.
Counting back method
Extension methods:
Subtracting the tens in one jump and the units in one jump.
Counting back method
Finding the difference or ‘counting on using the number line’ for 3 digit number e.g. 234-157
+3 +70 + 4 = 77
157 160 230 234
Subtract numbers with up to 3 digits, using formal written/column methods.
567
- 341
226

Use known number facts and place value to subtract (partition second number only)
37 – 12 = 37 – 10 – 2
= 27 – 2
= 25
25 27 37
Subtract 9 or 11. Begin to add/subtract 19 or 21
35 – 9 = 26
+1
25
26
35
-10
Bridge through 10 where necessary 32 - 17
15 20 22
-5 -2
-10
32

Multiplication is related to doubling, counting groups of the same size and repeated ‘addition’.
Looking at columns Looking at rows
2 + 2 + 2 3 + 3
3 groups of 2 2 groups of 3
x = signs and missing numbers
7 x 2 =
 
= 2 x 7 7 x

= 14 14 =

x 7

x 2 = 14 14 = 2 x
 
x

= 14 14 =

x

Arrays
    4 x 2 or 4 + 4
   
2 x 4 or 2 + 2 + 2 + 2
Repeated addition
Counting using a variety of practical resources
Counting in 2s e.g. counting socks, shoes, animal’s legs…
Counting in 5s e.g. counting fingers, fingers in gloves, toes…
Counting in 10s e.g. fingers, toes…
Pictures / marks
There are 3 sweets in a bag. How many sweets are there in 5 bags?
Introduce arrays and repeated addition
    4 x 2 or 4 + 4
   
2 x 4 or 2 + 2 + 2 + 2
OR
Doubling multiples of 5 up to 50 using partitioning
15 x 2 = 30
Children need to be secure with partitioning numbers into
10s and 1s and partitioning in different ways: 6 = 5 + 1 so e.g. Double 6 is the same as double five add double one.
AND double 15
10 + 5
20 + 10 = 30
X 10 5
2 20 10 = 30
x = signs and missing numbers and arrays and repeated addition - as in Year 2 but with appropriate numbers.
Use known facts and place value to carry out multiplications using the grid method
To calculate 13 x 7 using the grid method, the numbers are partitioned into parts
(10’s and 1’s) and each of these is multiplied by 7. The two answers are then added together.
Partition 32 x 3 = 96 x 30 2
3 90 6
=96
Using an informal jotting using partitioning
30 x 5 = (30 x 5) + (8 x 5) = 150 + 40 = 190
Expanded Column Multiplication – teacher modelled
Children should describe what they do by referring to the actual values of the digits in the columns. E.g., the first step in
38 × 7 is ‘30 multiplied by 7’, not ‘3 times 7’, although the relationship 3 × 7 should be stressed.
30 + 8 38
x 7 x 7
56 (8 x 7 = 56) 56
210 (30 x 7 = 210) 210
266 266
Short Column Multiplication
38
x 7
266
5

Sharing - Requires secure counting skills. Develop importance of one-to-one correspondence.
Sharing – 6 sweets are shared between 2 people. How many do they have each?
 
     
Grouping - Sorting objects into 2s / 3s/ 4s etc. How many pairs of socks are there?
Grouping in 4s:
÷ = signs and missing numbers
6 ÷ 2 =

 
= 6 ÷ 2 6 ÷
÷ 2 = 3 3 =

÷ 2

÷

= 3 3 = 6 ÷


= 3 3 =

÷

Understand division as sharing and grouping
6  2 can be modelled as: There are 6 strawberries.
How many people can have 2 each? How many 2s make 6?
6

2 can be modelled as:
18 ÷ 3 can be modelled as:
0 1 2 3 4 5 6
Sharing – 18 shared between 3 (see Year 1 diagram)
Grouping - How many 3’s make 18?
+3 +3 +3 +3 +3 +3
0 3 6 9 12 15 18
30 ÷ 5 extended to a word problem …
Grouping in 3s: There are 12 crocus bulbs. Plant 3 in each pot. How many pots are there?
Grouping - How many 3’s make 18? (Draw jumps of 3 along a number line.
This shows that you need 6 jumps of 3 to reach 18).
+3 +3 +3 +3 +3 +3
0 3 6 9 12 15 18
We do not use repeated subtraction.
Fractions - Link to counting, understanding number and simple fractions e.g. find ½, ¼, ¾ of shapes and sets of objects. E.g. ¼ of 20
= 20 ÷ 4 = 5
In the context of money count forwards and backwards using 2p, 5p and 10p coins
We do not use repeated subtraction.
÷ = signs and missing numbers
26 ÷ 2 =  24 ÷

= 12
Sharing and Grouping
30 ÷ 6 can be modelled as:
 ÷ 10 = 8
Grouping – groups of 6 placed on no. line and the number of groups counted e.g.
+6 +6 +6 +6 +6
0 6 12 18 24 30
Sharing – sharing among 6, the number given to each person
Remainders:
16 ÷ 3 = 5 r1 How many 3’s make 16, how many left over?
0 3 6 9 12 15 16
Extension for more able Y3s:E.g 84 ÷ 6
It would take a long time to jump in 6s to 84 so children can jump in bigger ‘chunks’. A jump of 10 groups of 6 takes you to 60. Then you need another 4 lots of 6 to reach 84.
Altogether, that is 14 jumps of 6

Recognising Numbers

Choose a number for the week, e.g. 2. Encourage your child to look out for this number all the time. Can your child see the number 2 anywhere? At home - in the kitchen; On pages in a book; In the street - on doors, on car number plates, on buses; While out shopping - on the shop till, on shelves, in shop windows

Find two apples, toys, spoons, straws, sweets, etc. Make patterns, such as two knives, two forks, two spoons, two knives, two forks, two spoons… Practise writing the number 2. Choose a different number each week.
 Dice game Use a ‘dotted’ dice and write the numbers 1 to 6 on a sheet of paper (or use the numbered animals). Throw the dice. Can your child guess how many dots there are? Check by counting. Ask your child which number on the paper matches the dots on the dice.

Stick numbers on the fridge - can you find number 8? 12? 17?

Practise writing numbers on paper, in sand, with paint, in shaving foam etc.

Hide numbers around the house and challenge them to find them then put them in order.
Counting ideas and putting numbers in order

Practise chanting the number names. Encourage your child to join in with you. When they are confident, try starting from different numbers – e.g. 4,5,6 Also try counting backwards.

Give your child the opportunity to count objects (coins, pasta, shapes, buttons etc.)
Encourage them to move each object as they count them.

Count things you cannot touch – window panes, jumps, claps, oranges in a bag.

Play games that involve counting – eg snakes and ladders, dice games.

Make mistakes when chanting, counting or ordering numbers. Can your child spot what you have done wrong?

Chose a ‘number of the week’ e.g. 5. Practice counting in 5’s, up to 5, on from 5,collect groups of 5 items.

Cut out pictures of animals, or anything else your child is interested in. Label the animals 1 to
5. Shuffle the animals. Put them in order from 1 to 5 (or 1-10 or 1-20 etc.) Remove one animal.
Ask your child which number is missing. Repeat with other numbers and more than one missing number. Ask your child to say what number comes before or after a number you choose; which number comes 2 before, 3 after etc.

One more, one less For this game you need a dice, a coin and some building blocks or Lego bricks. Take turns to roll the dice. Build a tower with that number of blocks or bricks. Then toss the coin. Heads means take one brick off. Tails means add one on. If you can guess how many bricks there will be after this, you keep them. The first to collect 20 bricks or more wins.
In the street

Recognising bus numbers

Number plate hunt. Who can find a 7? Add the numbers up.

Comparing door numbers

Doing the washing

Counting in 2s – matching shoes

Sorting by colour and size.

Matching/pairing up socks.

Find four shoes that are different sizes. Can you put them in order.
Time

What day is it yesterday, today, tomorrow?

Use timers, phones and clocks to measure short periods of time e.g. time two minutes for brushing teeth.

Count down 10/ 20 seconds to get to the table/ into bed etc.

Recognising numbers on the clock. If you cover a number, what number was missing?
Food

Can you cut your toast into 4 pieces? Can you cut it into triangles?

Setting the table. Counting the right number of plates etc. How many more do we need?

Can you make shapes/ patterns out of the knives and forks?

Helping with the cooking by measuring and counting ingredients.

Setting the timer.

Positional language at dinner time: what is on the rice, where are the carrots etc?
Going shopping

Reading price tags

Counting items into the basket

Finding and counting coins

Comparing weights – which is heavier?
Measuring

Are you taller than a …?

Marking height on the wall.
 Cut hand shapes out of paper. How many hands long is the sofa? How long is the table?
Who has the biggest hands in our family?

How many steps from the gate to the front door?

Let the children pour from one container to another so that they can understand that the
Shapes volume of liquid does not change, unless some is added or taken away, even though it may change its shape.

Cut a potato into shapes (circles, triangle etc). Use with paint to make pictures and patterns.

Cut out shapes from coloured paper/ newspaper and arrange into pictures.

Shape hunt: Can you find a square in your house (windows etc), a circle …
 Roll a shape - Cut out 12 shapes. Make 3 triangles, 3 squares, 3 rectangles and 3 circles.

Take turns to roll a dice and collect a shape that has that number of sides, e.g. roll a 4, collect asquare. The first to have four different shapes wins. If you can name each shape you go first next time!

Give the names for the two and three dimensional shapes they see around them: the square tiles in the kitchen floor, the spherical tennis ball and the oblong sides of the food containers
Games from the supermarket.

Putting cards into piles

Jigsaws (you can make your own by cutting up a magazine picture)

Snap (matching pairs) or Happy Families (collect 4 of a kind)

Snakes and ladders or other simple dice games.

Adding numbers on two dice.

Bingo, with numbers or shapes

Hopscotch
Number rhymes and songs
Eg: 5 little monkeys jumping on the bed
One fell off and bumped his head
Mummy called the doctor and the doctor said
“No more monkeys jumping on the bed!”
4 little monkeys jumping on the bed …
Your child can teach you lots more or try this website which has the words and sings it for you: http://www.nurseryrhymes4u.com/NURSERY_RHYMES/COUNTING.html

- Counting forms an important part of the calculation children have to do every day. With good counting skills, children can add, subtract, multiply and divide.

Counting on or back in 1s, 10s and 100s from any number

Going Up and Down Your Stairs - Pick a number for the bottom step. Then count in tens or hundreds going up. Counting in hundreds can be done in grams and millimetres as well. Pick a bigger number for the top step and count backwards as you go down the stairs. (For some, this can be done using decimals or even move into negative numbers).

Counting in regular steps going up or down stairs can help with times tables. What number will we be on when we reach the 6th step? What number is at the top/bottom step? How many steps to reach 28 if we count in 4s? If we count in 200g steps, when will we reach 1kg?

Car Journeys - Choose the colour of a car. Each time you see a car of your colour, look at the number plate. The person who has seen the largest/smallest number on a number plate is the winner. What is the number on the plate? What is this to the nearest 10 or 100 or 1000? How many more would you need to reach the next multiple of 10, 100 or 1000?

Disco numbers - Hundreds = Touch your head; Tens = Touch your shoulders; Ones/units = Clap your hands/stamp your feet. So, for 326…Touch your head 3 times, touch your shoulders twice and clap/stamp 6 times.

Secret numbers - Write the numbers 0 to 20 on a sheet of paper. Ask your child secretly to choose a number on the paper. Then ask him / her some questions to find out what the secret number is, e.g. Is it less than 10? Is it between 10 and 20? Does it have a 5 in it?
He / she may answer only yes or no. Once you have guessed the number, it is your turn to choose a number. Your child asks the questions. For an easier game, use numbers up to 10. For a harder game, use only 5 questions, or use bigger numbers.

Dice game - You need a 1–6 dice, paper and pencil. Take turns. Choose a number between 1 and 10 and write it down. Throw the dice and say the dice number. Work out the difference between the chosen number and the dice number, e.g. if you wrote down a 2 and the dice shows 5, the difference is 3. You could also draw a number line to help your child to see the difference between the two numbers.

How old? Start with your child’s age. Ask your child: How old will you be when you are 1 year older? How old were you last year? How old will you be 10 years from now? and so on.
 During a week, look outside for ‘thirties’ numbers, such as 34 or 38, on house doors, number plates, bus stops, etc. How many can you spot? What is the biggest one you can find? Next week, look for ‘fifties’ numbers, or ‘sixties’…

Its important children learn number bonds to 10 e.g. 4 + 6 = 10; 3 + 7 = 10 and number bonds to 20 e.g. 14+6 = 20; 12 + 8 = 20 by heart.

Play ‘ping pong’ to practice components with your child. You say a number and they reply with how much more is needed to make 10, 20, 100 or 1000. Encourage your child to answer quickly without counting or using fingers. E.g. make 100 you shout 40 they shout 60.

Throw two dice. Ask your child to find the total of the numbers (+), the difference between them (-) or the product (x).


Use a set of playing cards (without the picture cards). Turn over two cards and ask your child to add or multiply the numbers. If they answer correctly, they keep the cards. How any cards can they collect in two minutes?

Play 24 with a pack of playing cards using all of them. You need 4 players each puts a card down and first one to make 24 using any or all of the 4 operations and using all or some of the cards. First one to make number keeps all the cards. E.g. you put down a Jack , 2 hearts, 7 spades and 2 clubs. You could say
2x Jack add 2 hearts.

Play Bingo. Each player chooses five answers (e.g. numbers to 10 to practice simple addition, multiples of 5 to practice the five times table etc). Ask a question and if a player has the answer, they can cross it off. The winner is the first player to cross off all their answers.

Give your child an answer. Ask them to write as many number sentences as they can with this answer. You could just ask for addition sentences or any type of calculation.

Give your child a number fact – e.g. 5 + 8 = 13. Ask them what else they can find out from this fact – 50 + 80 = 130, 8 + 5 = 13, 13 – 8 = 5, 130 – 50 = 80 etc.

Make up rhymes together to help your child remember tricky times tables.

Rehearse times tables by counting in ‘steps’ of 2, 5 and 10. Count using silly voices e.g. robot.

Adding circles - For this game, you need a dice and pencil and paper. Each of you should draw four circles on your piece of paper. Write a different number between 2 and 12 in each circle.
Roll the dice twice. Add the two numbers. If the total is one of the numbers in your circles then you may cross it out. The first person to cross out all four circles wins.

Dicey coins - For this game you need a dice and about twenty 10p coins. Take turns to roll the dice and take that number of 10p coins. Guess how much money this is. Then count aloud in tens to check, e.g. saying ten, twenty, thirty, forty… If you do this correctly you keep one of the
10p pieces. First person to collect £1 wins.

Speedy pairs to 10 - Make a set of 12 cards showing the numbers 0 to 10, but with two 5s.
If you wish, you could use playing cards. Shuffle the cards and give them to your child. Time how long it takes to find all the pairs to 10. Repeat later in the week. See if your child can beat his / her time.

Circle trios - Draw four circles each on your piece of paper. Write four numbers between 3 and
18, one in each circle. Take turns to roll a dice three times and add the three numbers. If the total is one of the numbers in your circles then you may cross it out. The first to cross out all four circles wins.

Choose a shape of the week e.g. a square. Look for this shape in the environment. How many of these shapes can your child spot during the week, at home and when you are out? Ask your child to describe the shape to you.

At home, or when you are out, look at the surface of shapes. Ask your child – what shape is this plate, this mirror, the bath mat, the tea towel, the window, the door, the red traffic light, and so on.

Play ‘guess my shape’. You think of shape. Your child asks questions to try to identify it but you can only answer ‘yes’ or ‘no’.

Hunt for right angles around your home. Can your child spot angles that are bigger or smaller than a right angle?


Look for symmetrical objects. Help your child to paint or draw symmetrical pictures/patterns.

Make a model using different boxes/containers of different sizes. Ask your child to describe their model to you.

Practise measuring the lengths and heights of objects in metric measurements.
Help your child use different rulers or tape measures correctly. Encourage them to estimate before measuring. Compare measurements in metric and imperial.

Let your child help with the cooking. Help them to measure ingredients accurately. Talk about what each division on a scale represents.

Choose some food items out of the cupboard. Try to put the objects in order of weight by feel alone. Then check by looking at the weights on the packets.

Practise telling the time with your child. Use both digital and analogue clocks. Ask your child to be a ‘timekeeper’ – e.g. tell me when it is half past four because we are going swimming.

Use a stop clock to time how long it takes to do everyday tasks –e.g. how long does it take to get dressed. Encourage your child to estimate first.

Use a TV guide. Ask your child to work out the length of their favourite programmes. Can they calculate how long they spend watching TV each day/week?

Using Recipes - Recipes often suggest how many people you can feed or how many items you can make. If the recipe is for 8 people, can you make it for 4? If the recipe is for 8 biscuits, have we got enough ingredients to make 16? Will there be any biscuits/cakes left for you to give to your teacher?

Go shopping with your child to buy two or three items. Ask them to work out the total amount spent and how much change you will get.
Any opportunity to find value for money gives children experience of money and solving problems. When out and about, getting children to handle money and pay at the counter helps children to count in different ways and make totals in a variety of ways. Things you might ask:
How much will we save if we buy 3 for 2? Is it better to buy 2 individual apples or a bag? How much do 2 of these cost? How special is a special offer? Do we save much? For small shopping lists, how much have we spent so far? How much change from £5/£10? How many weeks will it take to save your pocket money if you want to buy that? How many 10p coins do you need to pay for that?

Shopping gives children the opportunity to spot and name shapes, especially 3-D shapes (e.g. cubes, cylinders, cuboids, spheres, prisms, cones, pyramids etc.).

Plan an outing during the holidays. Ask your child to think about what time you will need to set off and how much money you will need to take.

Use a bus or train timetable. Ask your child to work out how long a journey between two places should take. Go on the journey. Do you arrive earlier/later than expected? By how much?

Help your child to scale a recipe up or down to feed the right amount of people.
Getting children involved in real situations where they are using mathematical skills is motivating and stimulating.

Reading Numbers - Children need to be able to read and write whole numbers going into thousands.
They also have to round numbers to the nearest 10, 100 or decimal place. Children also have to be able to read and interpret tables and charts. Newspaper and BBC Sport web pages are a good source of tables and charts. There is also plenty of sport on the telly.

How many people watched Forest play Leicester?

Where was the biggest crowd in League 1?

How many goals were scored in the premiership altogether/before half time/in the second half?

Wales beat England at rugby 42 – 17(honest). How many tries do you think were scored?

For cricket fans, how many runs did the top 3 run scorers score? How much did the rest score?

In darts, a player has 116 left. How will he score this to win with 3 darts?

Snooker has a whole set of possibilities. After a break of 50, guess how many balls were potted? What is the most or least it could have been?

In athletics/motor racing/skiing you have to read time to the decimal places. Good for ordering numbers!

At the Olympics or at the athletics, how much higher and further did someone throw/jump than their nearest rival?
Playing Cards - There are many ways to use playing cards to help children to use their maths skills.
 Ordinary Playing Cards - Take out the picture cards. Play snap but you only have a snap if the total of the cards is 10. For older children, the number on the cards stands for how many tens there are in the number. Play snap but you only have a snap if the total of the cards is 100.

You can also play a points game. When 2 cards of the same suit are put down, multiply/add the cards together (depending on their age). If you are correct, you score the number of points in the answer you gave. Choose a target e.g. 100 points. The first past the total is the winner.
(This also involves addition and subtraction. How many more do we need to win? Which cards do you think would help?)
Top Trumps - These are great games on their own and can support reading from a chart. They usually have a range of large and small numbers and a range of areas of interest.

Which superhero is the tallest/strongest etc? Which car/bike/plane in the fastest/costs the most? Who is the oldest? Which do you think is the best card?

Uno – good game for recognising and matching numbers

Dominoes – supports counting and associating patterns with numbers

Snakes and Ladders – counting numbers up to 100/

Scrabble – adding, multiplying (doubling, trebling) and good for vocabulary development and spelling.

Monopoly – good for handling money, paying using notes, giving change.

Yahtzee – a good game for adding, multiplying and probability.

 www.mathszone.co.uk
 http://www.bbc.co.uk/bitesize/ks1/maths/
 http://www.familylearning.org.uk/online_math_games.html
 www.sesamestreet.org

Written numbers and digits Yr 2/3 – http://www.sums.co.uk/playground/n2a/playground.htm

Grid References Yr 2/3 - http://www.sums.co.uk/playground/ss3/playground.htm
 Dividing - http://www.sums.co.uk/playground/c3a/playground.htm

Subtraction Yr 1/2 - http://www.sums.co.uk/playground/c1a/playground.htm
 http://www.crickweb.co.uk/Early-Years.html
 http://www.crickweb.co.uk/ks1numeracy.html

Woodlands Junior - This website has lots of games and activities across all areas of Maths and is one of the sites we use the most. The interactive times tables section is particularly good for rapid recall of facts and has a competitive element where you can race against others. Many of the activities take you to other websites (some of which we have signposted in the section).
 http://www.woodlands-junior.kent.sch.uk/maths/
 http://www.woodlands-junior.kent.sch.uk/maths/timestable/interactive.htm
 PBS Kids - This site has a range of educational games for children of all ages and has plenty for younger children.
 http://pbskids.org/games/alltopics.html

BBC - The BBC website provides a range of Maths activities for children across the primary range. On the page that appears when using the link below, you will find a number of different sites some of which have useful parent support information.
 http://www.bbc.co.uk/schools/websites/4_11/site/numeracy.shtml

Ambleside Primary School - http://www.amblesideprimary.com/ambleweb/numeracy.htm

TopMarks Education Resources - http://www.topmarks.co.uk/

Loders primary Schools – Maths Problem Solving
 http://www.loders.dorset.sch.uk/HomeSchool/witches/problemsolv.htm

CoolMath4kids (US Site) - http://www.coolmath4kids.com/

Rain Forest Maths - http://www.rainforestmaths.com/

The next two sections show some of the key assessment criteria for level 2 and 3 in the area of
‘ number ’, along with examples of questions your child may be expected to answer in this area when they sit their ‘SATs’ in May. You could discuss the questions with your child at home, and help them to understand and practise similar questions in any areas where they have difficulty. However, we would stress the following points:

Children develop at different speeds. Making steady progress is more important than achieving a particular level by a certain age.

This is only a sample of the skills children are assessed on.

We want children to enjoy maths. Practising regularly for short periods may be better than one long session. Often maths skills can be developed effectively through games, or involvement in real life situations like shopping.
Level 2 Maths
Skill
I know that addition and subtraction are opposites (inverses)
I understand the place value of digits in numbers to 100 and can use this to order numbers to 100.
I can work out halves of even numbers to 20 and begin to remember them.
I can remember and use the addition and subtraction facts to
10.
Examples of how the skill may be assessed
Here are three numbers: 12, 17 and 5. Use these three numbers to make 4 number sentences
Put these numbers in order, starting with the smallest
43 12 20 78 21
What is half of 18? Half of 16? Half of 10? I think of a number and double it. The answer is 18. What was my number?
What are the missing numbers?
_ + 6 = 15 8 + _ = 11 20 – 15 = _
Can you find all the addition pairs to 19?
Give any two numbers with a difference of 3 (e.g. 15 and 18)
I can decide if I should add or subtract when solving problems.
I can use repeated addition to solve multiplication problems
I can recognise number sequences, including odd and even numbers.
Decide what calculation is needed to solve problems like:
23 slugs entered the slug race. 7 got lost. How many slugs were left?
Aabid has 20p and Claudia has 41p. How much do they have altogether?
Sana had 50p. She spent 24p. How much did she have left?
Pavan’s cat weighs 18kg. Olivia’s dog weighs 32kg. How much heavier is Olivia’s dog?
6 football teams enter a five-a-side tournament. How many players are in the tournament?
A regular hexagon has sides of 2cm each. What is the distance all the way around?
Write the missing numbers in these sequences.
2, 4, 6, __, 10, 12, __, __
21, 19, 17, __, 13, 11, __
__, 10, 15, 20, __, 30
Can you make up a number sequence that increases in steps of 3?
Or of 10?
Answers/Tips
12 + 5 = 17 5 + 12 = 17
17 – 5 = 12 17 – 12 = 5
12 20 21 43 78
Remind the children that doubling and halving are opposites.
Encourage children to use their knowledge of inverses to solve missing number questions.
Encourage systematic working.
E.g.
0 + 19 = 19 1 + 18 = 19
2 + 17 = 19 3 + 16 = 19 … etc
23 – 7
20 + 41
50 – 24
32 – 18
6 x 5 =
5 + 5 + 5 + 5 + 5 + 5 = 30
6 x 2cm =
2 + 2 + 2 + 2 + 2 + 2 = 12cm
Encourage children to ask themselves whether the sequence is going up or down.
Then see whether they can identify the size of each step.
Use vocabulary such as
‘increases’, ‘less than’ and ‘more than’.
78 50 92 100 I can write the numbers to 100 accurately
I can count sets of objects reliably
I can solve number problems involving money or measures.
Write these numbers in figures: Seventy eight
Fifty Ninety two One hundred
Count in twos, fives or tens, from 0 to 100.
George had 56p. He spent 9p. How much did he have left?
Praveen saves 44p. Then her friend gives her 21p. How much does she have now?
Graham the grub travels 27cm. Lily the ladybird crawls 34cm. How much further does Lily travel than George?
Children could be encouraged to draw pictures to help them think about word problems, or to represent the problem on a blank number line.

Skill
I understand the place value of digits in numbers to 1000.
I can order decimals with one decimal place.
I can compare numbers to 1000 e.g. < less than, > greater than
I can add and subtract two-digit numbers mentally
Level 3 Maths
Examples of how the skill may be assessed
Fill in the missing numbers:
200 + __ + 7 = 267 488 = __ + 80 + 8
How many tens are there in 530?
Put these decimal numbers in order, starting with the smallest:
3.8 1.8 1.4 0.9 4.7
Use the correct symbol in each place: < , > or =
343 __ 434 980 __ 899
50 + 60 __ 110 3 x 99 __ 250
45 + 34 = 56 + 27 =
93 – 88 = 68 – 21 =
Answers/Tips
200 + 60 + 7 = 267
488 = 400 + 80 + 8
There are 53 tens in 530.
0.9 1.4 1.8 3.8 4.7
343 < 434 980 > 899
50 + 60 = 110 3 x 99 > 250
Children should use the most appropriate mental strategy. For example, for 93 – 88 they may add on to find the difference, as the numbers are close together.
For 68 – 21 it is more appropriate to subtract 20 and then 1.
I can add and subtract three digit numbers using written methods
783 + 142
I know the multiplication facts and use them to work out division facts.
I can find missing whole numbers using inverses.
I can solve whole number multiplication and division problems.
I can solve whole number division problems involving remainders, rounding up or down depending on the context.
I can continue whole number sequences forwards or backwards.
Learn the 2x, 3x, 4x, 5x and 10x tables.
What is 32 divided by 4
Fill in the missing numbers:
__ - 2 = 6 9 = 36 - __ 3 x __ = 21
Matthew is thinking of a number. He divides it by 10 and gets 7.
What was his number?
If I multiply a number by 4 and then divide the answer by 4, what happens?
One length of the swimming pool is 25 metres.
Jane swims 5 lengths of the pool. How far does Jane swim altogether?
Paul swims 225 metres in the pool. How many lengths does he swim?
Mr Bloggs the baker packs cakes in boxes of 4. He bakes 35 cakes.
How many boxes can he fill? Or, how many boxes does he need to pack all the cakes?
Fill in the gaps in these sequences.
3, 6, 9, 12, __, __,
202, 192, 182, 172, __, __,
__, 9, 14, 19, 24, 29, 34, __, __
I know that 4 x 8 = 32, so I also know that 32 divided by 4 is 8.
12 – 2 = 6
9 = 36 – 4
3 x 7 = 21
Matthew was thinking of 70.
Encourage discussion about how the problems could be solved.
Does it help to draw a picture or use a blank number line?
Notice that the answer is 8 boxes or 9 boxes, depending on which question you are answering. This rounding up or down depending on the context is a skill children need to develop.
3 , 6, 9, 12, 15, 18
202, 192, 182, 172, 162, 152
4 , 9, 14, 19, 24, 29, 34, 39, 44
F.Shields 1/2014