Instant Recall

And

Deriving facts quickly

A guide to parents who are supporting children with ‘Learning by Heart’ homework.

General hints for parents
Encourage children to talk about their calculation strategies.  Ask questions such as,

‘How did you work that out?’
‘Can you think of any other ways?’
‘What if you started with…….?’

Don’t worry if some methods seem longwinded or unfamiliar to you.  Building confidence in mathematics is crucial so be pleased with their efforts and always encourage with praise.  Make sure these practice sessions are enjoyable!  If your child is really not in the mood it is the wrong time to be practising.

With younger children always have apparatus….toys / small objects / coins etc available so that they can work at a very practical level and check their mental calculations with real materials.  Older children may choose to support their thinking with rough jottings.  Ultimately we are encouraging children to ask themselves ‘Can I do this in my head?’ but they should always work at a level in which they feel secure.  To rush and discourage support materials  would slow down the development of their thinking in the longer term.

The best possible way to develop a real understanding of meaningful calculations with money is to practise with real money and set up mini shopping situations. Involve older children in budgeting projects such as costing the purchase and weekly care cost of a new pet / the petrol costs of a regular shuttle service to the swimming pool / the cost of a season ticket compared to a weekly admission charge/the cost of purchasing a full set of Pokemon cards etc. 

A sensible place to develop an early understanding of capacity is in the bath!  Provide a range of containers and allow children to experiment.  They will soon learn that narrow tall bottles / containers don’t necessarily hold as much water as they thought!  With older children look together at labels on food and drink products.  You will find some interesting facts!  Some ‘liquids’ are measured in grams and millilitres and products such as bark chippings and other garden products are measured in litres!
Comparing different containers and converting litres to millilitres / kilograms to grams and talking about fractions of measurements is an excellent way to provide practical opportunities for your child..

Ask school about purchasing a copy of  ‘Mathematical Vocabulary’.  Children are expected to understand a wide range of vocabulary and to use the full range in their mathematical thinking.  Having a few words of the week displayed at home eg on the fridge door, would be an excellent way to remember to use a range of vocabulary when playing games or discussing work with children.  The book covers all year groups from Reception to Y6

Year 1

Know by heart all pairs of numbers with a total of 10

0	+  10  =  10
1	+  9    =  10
2	+  8    =  10
3	+  7    =  10
4	+  6    =  10
5	+  5    =  10
6	+  4    =  10
7	+  3    =  10
8	+  2    =  10
         9  +  1    =  10
	10  +  0   =  10

Hints for parents

Use objects to consider the additions in a practical way

Look at the patterns with both objects and numbers eg as one number increases the other one decreases

Practise with the numbers in order and chosen randomly

Key vocabulary
Add
Total
How many more to make?
Altogether

Year 1
Know by heart addition facts for all pairs of numbers with a total up to at least 5, and the corresponding subtraction facts

If I know        1  +  0  =  1	
I also know	0  +  1  =  1
1	-  0  =  1
1   -  1  =  0

If I know	2  +  0  =  2
I also know	0  +  2  =  2
2	-  0  =  2
2   -  2  =  0

If I know        2  +  1  =  3
I also know    1  +  2  =  3  
3	-  1  =  2
3	-  2  =  1

If I know 	3  +  0  =  3
I also know	0  +  3  =  3
3	-  0  =  3
3   -  3  =  0

Continue in the same way with the total of 4 and then 5

When children are confident with these pairs to a total of 5 extend the work to
include addition and corresponding subtraction facts for all pairs of numbers with a total up to at least 10.

Hints to parents
The ‘If I know, what else do I know’ rule is a really important one for children to learn in Y1.  It will be with them forever more and will support calculation skills when they begin to work with larger numbers.

Key vocabulary
Minus		Subtract		Take away
Fewer than		less than		difference between

Year 1

Know by heart addition doubles of all numbers to at least 5

1  +  1  =  2	double 1 is / makes / equals  2
2  +  2  =  4	double 2 is / makes / equals  4
3  +  3  =  6	double 3 is…………………..6
4  +  4  =  8	double 4 is…………………..8
5  +  5  =  10	double 5 is…………………..10

Hints to parents.
Doubling is a really important strategy and one which children really enjoy!
When children are confident with these early doubles encourage them to practise the corresponding halves.  When they are confident with the halving operations move on to doubles of numbers to at least 10.

Key vocabulary
Double	two lots of		two times
Twice	times two		pair
Half	halved		divided by 2
Shared between two

Year 2

Know by heart all addition and subtraction facts for each number to at least 10
Eg the number 7
0  +  7  =  7
1	+  6  =  7
2	+  5  =  7
3	+  4  =  7
4	+  3  =  7
5	+  2  =  7
6	+  1  =  7
7	+  0  =  7

Then apply the ‘If I know, I also know’ rule for each of these addition statements.

If I know	3  +  4  =  7
I also know	4  +  3  =  7
	7   -  4  =  3
	7   -  3  =  4

Hints to parents
Give the children a target number and ask ‘how many addition pairs can you find to make that number?’  Children will enjoy finding patterns in the answer to this.  Encourage them to jot their investigations on paper.  For some children the patterns are much clearer when they see them written down.

Enjoy rapid question / answer sessions.

Whenever your child gives you one addition or subtraction statement always ask them to give you another 3 number sentences that they know because of the first one.  Many Y2 children will enjoy practising this skill with much larger numbers.

Key vocabulary
As for Y1

Year 2
Know by heart all pairs of numbers with a total of 20
0	+  20  =  20
1	+  19  =  20
2	+  18  =  20
3	+  17  =  20
4	+  16  =  20
5	+  15  =  20
6	+  14  =  20
7	+  13  =  20
8	+  12  =  20
9	+  11  =  20
10	 +  10  =  20
11	 +  9  =  20
12  +  8  =  20
13  +  7  =  20
14  +  6  =   20
15	+  5  =  20
16  +  4   =  20
17  +  3  =  20
18  +  2  =  20
19  +  1  =  20
20	+  0  =  20
Hints to parents.
Play number ping pong!
Parent says ‘2’………….child responds rapidly with ‘18’.
Immediately follow with ‘18’………..’2’.
In this way you are reinforcing the fact that addition can be done in any order which encourages children to try turning addition sums around to make them look a bit more friendly.

It would be valuable to discuss points such as;
 ‘If 3  +  7  =  10,  why will 3  +  17  =  20?’  or
 ‘If 3  +  7  =  10,  why will 13  +  7  =  20?’

Children who are enjoying work with larger numbers will soon make the link that 
13  +  17  =  30   but don’t push forwards too soon. It is much more helpful to create fun practice opportunities which allow children to enjoy success.
Work out the missing numbers together eg  ?  +  4  =  20      20  =  ?  +  ?

Key vocabulary
Find pairs ….to make..	how many more to make 20 altogether

Year 2

Know by heart all pairs of multiples of ten with a total of 100.

0  +  100  =  100	100  +  0  =  100

10  +  90  =  100	90  +  10  =  100

20  +  80  =  100	80  +  20  =  100

30  +  70  =  100	70  +  30  =  100

40  +  60  =  100	60  +  40  =  100

50	+  50  =  100

Hints for parents
Again, by considering the ‘matching’ pairs of numbers that total 100 you will be reinforcing one of the key mathematical rules that addition can be done in any order.

Continue to practise the ‘If I know, what else do I know?’ rule eg

If I know that          40   add  60  makes  100
I also know that     60    plus 40  totals   100
That                       100  subtract  40  leaves  60
And that                100 minus 60 equals  40

Using a range of vocabulary in connection with now familiar concepts is an excellent way to extend children’s use of a wider range of vocabulary when articulating their mathematical thinking.

Try the’ ping pong’ approach to practise rapid response of the complements in 100

‘60’………………….’40’
‘80’………….………’20’
        ‘10’………………….’90’   etc

Remember to include 0 (zero) in practice situations.  In years one and two children learn that the effect of adding / subtracting 0 to a number leaves a number unchanged but do not always remember and frequently make errors when faced with zero! 

Year 2

Know by heart multiplication facts for the 2 times table and derive quickly the corresponding division facts.
0  x  2  =      0	2  x  0  =      0
1  x  2  =      2	2  x  1  =      2
2  x  2  =      4	2  x  2  =      4
3  x  2  =      6	2  x  3  =      6
4  x  2  =      8	2  x  4  =      8
5  x  2  =    10	2  x  5  =    10
6  x  2  =    12	2  x  6  =    12
7  x  2  =    14	2  x  7  =    14
8  x  2  =    16	2  x  8  =    16
9  x  2  =    18	2  x  9  =    18
10  x  2  =  20	2  x  10  =  20

Corresponding division facts

2 ÷ 2  =  1	2 ÷ 1  =  2
4 ÷ 2  =  2	4 ÷ 2  =  2
6 ÷ 2  =  3	6 ÷ 3  =  2
8 ÷ 2  =  4	8 ÷ 4  =  2
10 ÷ 2  =  5	10 ÷ 5  =  2
12 ÷ 2  =  6	12 ÷ 6  =  2
14 ÷ 2  =  7	14 ÷ 7  =  2
16 ÷ 2  =  8	16 ÷ 8  =  2
18 ÷ 2  =  9	18 ÷ 9  =  2
20 ÷ 2  =  10	20 ÷ 10  =  2

Hints for parents
It is really important that children are as confident with division facts as they are with multiplication facts.  Division is a much more difficult concept for most children partly because they do not have these facts instantly at their fingertips.
Practise using the ‘If I know, what else do I know? rule eg:
If I know that   2  x  6  =  12                      I also know that     6  x  2  =  12,
 That   12 ÷ 2  =  6       and        that 12 ÷ 6  =  2
Chanting tables/rapid response to questions/playing games and applying knowledge of tables to shopping problems are all good ways of reinforcing children’s understanding.
There are several audio tapes of musical tables / rap tables which help some children to learn.  Many children who insist it is impossible to learn multiplication tables know every word of the latest pop songs in no time at all!
Key vocabulary
Times         multiply          multiple of          lots of groups of      divided by    shared               
Year 2
Know by heart multiplication facts and derive quickly corresponding division facts for the 10 times table
0  x  10  =  0	10  x  0  =  0
1  x  10  =  10	10  x  1  =  10
2  x  10  =  20	10  x  2  =  20
3  x  10  =  30	10  x  3  =  30
4  x  10  =  40	10  x  4  =  40
5  x  10  =  50	10  x  5  =  50
6  x  10  =  60	10  x  6  =  60
7  x  10  =  70	10  x  7  =  70
8  x  10  =  80	10  x  8  =  80
9  x  10  =  90	10  x  9  =  90
10  x  10  =  100	10  x  10  =  100

Corresponding division facts

10 ÷ 1  =  10	10 ÷ 10  =  1
20 ÷ 2  =  10	20 ÷ 10  =  2
30 ÷ 3  =  10	30 ÷ 10  =  3
40 ÷ 4  =  10	40 ÷ 10  =  4
50 ÷ 5  =  10	50 ÷ 10  =  5
60 ÷ 6  =  10	60 ÷ 10  =  6
70 ÷ 7  =  10	70 ÷ 10  =  7
80 ÷ 8  =  10	80 ÷ 10  =  8
90 ÷ 9  =  10	90 ÷ 10  =  9
100 ÷ 10  =  10	100 ÷ 10  =  100

Hints to parents
Children will be beginning to see some patterns in the tables eg when a number is multiplied by itself in the first column it appears in the same way in the opposite column.  Although there is no expectation that they they will understand square numbers at this stage they will be looking out for this pattern as they learn new tables.
Looking at tables on a multiplication grid is a good way to explore patterns and consolidate learning
Fizz Buzz is always fun to play but, take care,  children will often win!
To practise the 2 and 10 times tables together take it in turns to count up in ones (as many people as you like can play).  If a number is in the 2 x table you must say Fizz instead of the number, if it is in the 10x table you must say Buzz if the number is in both tables you must say FIZZ BUZZ!  So……….1, Fizz, 3, Fizz, 5, Fizz, 7, Fizz, 9, FIZZ BUZZ, etc  simplify the game by using only one table at a time and make it more challenging by having another word eg Whizz to say if the number contains the digit 2!

Year 2

Begin to know multiplication facts for the 5 times table

0  x  5  =  0	5  x  0  =  0
1  x  5  =  5	5  x  1  =  5
2  x  5  =  10	5  x  2  =  10
3  x  5  =  15	5  x  3  =  15
4  x  5  =  20	5  x  4  =  20
5  x  5  =  25	5  x  5  =  25
6  x  5  =  30	5  x  6  =  30
7  x  5  =  35	5  x  7  =  35
8  x  5  =  40	5  x  8  =  40
9  x  5  =  45	5  x  9  =  45
10  x  5  =  50	5  x  10  =  50

Hints for parents
Encourage children to talk about the patterns and to notice that all the answers end in either 0 or 5.  

Look at a range of larger numbers together and decide if they would be multiples of 5.

Key vocabulary
Times  
Multiplied by
Lots of
Groups of
Multiple of

Year 2

Know by heart doubles of all numbers to 10 and their corresponding halves

Double  0  =  0
Double  1  =  2	half of  2  =  1
Double  2  =  4	half of  4  =  2
Double  3  =  6	half of  6  =  3
Double  4  =  8	half of  8  =  4
Double  5  =  10	half of  10  =  5
Double  6  =  12	half of  12  =  6
Double  7  =  14	half of  14  =  7
Double  8  =  16	half of  16  =  8
Double  9  =  18	half of  18  =  9
Double  10  =  20	half of  20  =  10

Hints for parents
As well as having instant recall of these doubling and halving facts children need to recognise the opportunities for doubling / halving when questions are presented in a different way.  It would be really supportive if you could practise this work using a range of questioning techniques eg

Double    1 is  2	half of  2  is  1
2  x  2  =  4	4  halved is  2
2 lots of 3 make 6	6  divided by 2 is 3
twice  4  is 8	8p shared between 2 is 4p each
5  multiplied by 2 is the same as 10	10 divided by 2 is 5
6  x  2  =  12	12 ÷ 2  =  6
7  doubled will be 14	14 halved will be 7
double 8 to make 16	halve 16 to make 8
18 is 2 lots of 9	there are 9 lots of 2 in 18
10  x  2  =  20	20 ÷ 2  =  10

When children are working confidently with all these approaches encourage them to solve real life problems by applying their doubling / halving strategies eg 

2 children each spent 40p at the shop how much was spent altogether?
Tom spent half of his 60p pocket money.  How much did he spend?
Two chocolate bars cost £1.00.  How much did one chocolate bar cost?

Year 2

Derive quickly doubles of all numbers to at least 15

Extend earlier work to include the larger numbers up to and including double 15  =  30.

Derive quickly doubles of multiples of 5 to 50

Double    5  =  10
Double  10  =  20
Double  15  =  30
Double  20  =  40
Double  25  =  50
Double  30  =  60
Double  35  =  70
Double  40  =  80
Double  45  =  90
Double  50  =  100

Derive quickly doubles and halves of multiples of 10 to 100

Double  10  =  20	20  halved  =  10
2  x  20  =  40	40 divided by 2  =  20
30 doubled  =  60	half of 60  =  30
40 multiplied by 2  =  80	80  shared between 2  =  40
twice  50  =  100	100  halved  =  50
double  60  =  120	120  divided between 2  =  60
70  2p coins  =  £1 . 40		£1.40 divided between 2 
	people = 70p  each
80 doubled  =  160	there will be 80 bicycles if there are 160 wheels
£90.00 doubled  =  £180.00	180 halved  =  90
100  x  2  =  200	200 stamps shared between 2 equals 
	100 each
Hints to parents
Think of as many real life examples of using doubling and halving to solve problems as
 well as asking for rapid response to questioning.  Practise halving at least as often as
 doubling, this will help children with subtraction at a later date.    
Year 3

Know by heart…..all addition and subtraction facts for each number to 20.
Eg
0	+  7  =  7	7  -  7  =  0
1	+  6  =  7	7  -  6  =  1
2	+  5  =  7	7  -  5  =  2
3	+  4  =  7	7  -  4  =  3
4	+  3  =  7	7  -  3  =  4
5	+  2  =  7	7  -  2  =  5
6	+  1  =  7	7  -  1  =  6
7   +   0  =  7	7  -  0  =  7

Know by heart……all pairs of multiples of 100 with a total of 1000

100	+  900  =  1000	900  +  100  =  1000
200	+  800  =  1000	800  +  200  =  1000
300	+  700  =  1000	700  +  300  =  1000
400	+  600  =  1000	600  +  400  =  1000
500	+  500  =  1000

Derive quickly…..all pairs of multiples of 5 with a total of 100

5  +  95  =  100	95  +  5  =  100
10  +  90  =  100	90  +  10  =  100
15  +  85  =  100	85  +  15  =  100
20  +  80  =  100	80  +  20  =  100
25  +  75  =  100	75  +  25  =  100
30  +  70  =  100	70  +  30  =  100
35  +  65  =  100	65  +  35  =  100
40  +  60  =  100	60  +  40  =  100
45  +  55  =  100	55  +  45  =  100
50	+  50  =  100

Hints to parents
Creating regular, short, opportunities to rapid fire questions where an instant correct answer is required would be better than lengthy practise sessions.
It would be really helpful to link  the pairs that make 100 to money, children do not always readily transfer these skills. Eg  £1.00  =  45p  +  ?      75p  +  ?  =  £1.00       
If I have 65p  how much more money do I need to make it up to £1.00?
If I had £1.00 and spent 20p how much would I have left?
Key vocabulary
How many more to make..?
altogether, make, sum, total, how much more is…than…?…difference between
Year 3
	
Know by heart multiplication facts for the 2 times table and
derive quickly the corresponding division facts.

0  x  2  =      0	2  x  0  =      0
1  x  2  =      2	2  x  1  =      2
2  x  2  =      4	2  x  2  =      4
3  x  2  =      6	2  x  3  =      6
4  x  2  =      8	2  x  4  =      8
5  x  2  =    10	2  x  5  =    10
6  x  2  =    12	2  x  6  =    12
7  x  2  =    14	2  x  7  =    14
8  x  2  =    16	2  x  8  =    16
9  x  2  =    18	2  x  9  =    18
10  x  2  =  20	2  x  10  =  20

Corresponding division facts

2 ÷ 2  =  1	2 ÷ 1  =  2
4 ÷ 2  =  2	4 ÷ 2  =  2
6 ÷ 2  =  3	6 ÷ 3  =  2
8 ÷ 2  =  4	8 ÷ 4  =  2
10 ÷ 2  =  5	10 ÷ 5  =  2
12 ÷ 2  =  6	12 ÷ 6  =  2
14 ÷ 2  =  7	14 ÷ 7  =  2
16 ÷ 2  =  8	16 ÷  8  =  2
18 ÷ 2  =  9	18  ÷ 9  =  2
20 ÷ 2  =  10	20 ÷ 10  =  2

Hints for parents
It is really important that children are as confident with division facts as they are with multiplication facts.  Division is a much more difficult concept for most children partly because they do not have these facts instantly at their fingertips.
Practise using the ‘If I know, what else do I know? rule eg:
If I know that   2  x  6  =  12                      I also know that     6  x  2  =  12,
 That   12÷ 2  =  6       and        that 12÷ 6  =  2
Chanting tables/rapid response to questions/playing games and applying knowledge of tables to shopping problems are all good ways of reinforcing children’s understanding.
There are several audio tapes of musical tables / rap tables which help some children to learn.  Many children who insist it is impossible to learn multiplication tables know every word of the latest pop songs in no time at all!
Key vocabulary	
Times         multiply          multiple of          lots of groups of      divided by    shared         
Year 3

Know by heart multiplication facts for the 5 times table and 
derive quickly corresponding division facts.

0  x  5  =  0	5  x  0  =  0
1  x  5  =  5	5  x  1  =  5
2  x  5  =  10	5  x  2  =  10
3  x  5  =  15	5  x  3  =  15
4  x  5  =  20	5  x  4  =  20
5  x  5  =  25	5  x  5  =  25
6  x  5  =  30	5  x  6  =  30
7  x  5  =  35	5  x  7  =  35
8  x  5  =  40	5  x  8  =  40
9  x  5  =  45	5  x  9  =  45
10  x  5  =  50	5  x  10  =  50

Corresponding division facts

5    ÷  5  =  1	5    ÷  1  =  5
10  ÷  5  =  2	10  ÷  2  =  5
15  ÷  5  =  3	15  ÷  3  =  5
20  ÷  5  =  4	20  ÷  4  =  5
25  ÷  5  =  5
30  ÷  5  =  6	30  ÷  6  =  5
35  ÷  5  =  7	35  ÷  7  =  5
40  ÷  5  =  8	40  ÷  8  =  5
45  ÷  5  =  9	45  ÷  9  =  5
50  ÷  10  =  5	50  ÷  5  =  10

Hints for parents
Encourage children to talk about the patterns and to notice that all the answers end in either 0 or 5.  

Look at a range of larger numbers together and decide if they would be multiples of 5.

Key vocabulary
Times  
Multiplied by
Lots of
Groups of
Multiple of

Year 3

Know by heart multiplication facts and derive quickly corresponding division facts for the 10 times table

0  x  10  =  0	10  x  0  =  0
1  x  10  =  10	10  x  1  =  10
2  x  10  =  20	10  x  2  =  20
3  x  10  =  30	10  x  3  =  30
4  x  10  =  40	10  x  4  =  40
5  x  10  =  50	10  x  5  =  50
6  x  10  =  60	10  x  6  =  60
7  x  10  =  70	10  x  7  =  70
8  x  10  =  80	10  x  8  =  80
9  x  10  =  90	10  x  9  =  90
10  x  10  =  100	10  x  10  =  100

Corresponding division facts

10 ÷ 1  =  10	10 ÷ 10  =  1
20 ÷ 2  =  10	20 ÷ 10  =  2
30 ÷ 3  =  10	30 ÷ 10  =  3
40 ÷ 4  =  10	40 ÷ 10  =  4
50 ÷ 5  =  10	50 ÷ 10  =  5
60 ÷ 6  =  10	60 ÷ 10  =  6
70 ÷ 7  =  10	70 ÷ 10  =  7
80 ÷ 8  =  10	80 ÷ 10  =  8
90 ÷ 9  =  10	90 ÷ 10  =  9
100 ÷ 10  =  10	100 ÷ 10  =  100

Hints to parents
Children will be beginning to see some patterns in the tables eg when a number is multiplied by itself in the first column it appears in the same way in the opposite column.  Although there is no expectation that they they will understand square numbers at this stage they will be looking out for this pattern as they learn new tables.

Looking at tables on a multiplication grid is a good way to explore patterns and consolidate learning

Fizz Buzz is always fun to play but, take care,  children will often win!
To practise the 2 and 10 times tables together take it in turns to count up in ones (as many people as      you like can play).  If a number is in the 2 x table you must say Fizz instead of the number, if it is in the 10x table you must say Buzz if the number is in both tables you must say FIZZ BUZZ!  So……….1, Fizz, 3, Fizz, 5, Fizz, 7, Fizz, 9, FIZZ BUZZ, etc  simplify the game by using only one table at a time and make it more challenging by having another word eg Whizz to say if the number
      contains the digit 2!
Year 3
Begin to know the 3 and 4 times tables

0	x  3  =  0	3  x  0  =  0
1	x  3  =  3	3  x  1  =  3
2	x  3  =  6	3  x  2  =  6
3	x  3  =  9	3  x  3  =  9
4	x  3  =  12	3  x  4  =  12
5	x  3  =  15	3  x  5  =  15
6	x  3  =  18	3  x  6  =  18
7	x  3  =  21	3  x  7  =  21
8	x  3  =  24	3  x  8  =  24
9	x  3  =  27	3  x  9  =  27
10	x  3  =  30	3  x  10 =  30

     0  x  4  =  0	4  x  0  =  0
     1  x  4  =  4	4  x  1  =  4
     2  x  4  =  8	4  x  2  =  8
     3  x  4  =  12	4  x  3  =  12
     4  x  4  =  16	4  x  4  =  16
     5  x  4  =  20	4  x  5  =  20
     6  x  4  =  24	4  x  6  =  24
     7  x  4  =  28	4  x  7  =  28
     8  x  4  =  32	4  x  8  =  32
     9  x  4  =  36	4  x  9  =  36
     10 x 4  =  40	4  x 10 =  40

Hints to parents

Some children find listening to musical tables on tapes etc really helpful………..also a good way to keep children occupied on a journey!   Tapes are available for about 99p from Toys R Us,  WH Smiths, Early Learning Centres and other similar retailers.

Frequent short practices would really help children to consolidate their learning………….it’s worth it, they will have these skills for life.

Key Vocabulary
Lots of
groups of
times
product
multiply
multiplied by
multiple of
Year 3

Derive quickly doubles of all whole numbers to at least 20 and all the corresponding halves

1	+  1  =  2	half of 2 is 1
2	x  2  =  4	4 halved is 2
3	doubled  is  6	6  ÷  2  =  3
double 4  is  8	8 shared between 2 is 4 each
2 lots of  5 are 10	10  ÷  2  =  5
6   +  6  =  12	12  -  6  =  6
2	x  7  =  14	14  halved  makes  7
double  8  is 16	half  of  16  is  8
2	lots  of  9  are  18	18  halved  is  9
      10 doubled  is  20	20  ÷  2  =  10
11	times  2  is  22	22 shared equally between 2 is 11 each	
12	multiplied by  2  is  24	half of 24 is 12
13	doubled  is 26	26 halved makes 13
14	x  2  =  28	28  -  14  =  14
twice 15  is  30	half of 30  is 15
16	+  16  makes  32	32 split into 2 makes 16 twice
17	times  2  is  34	34 halved is 17
2	x  18  =  36	18 is half of 36
19	doubled  is  38	38  ÷  2  =  19
double  20  is 40	half  of  40  is  20

Year 3

Derive quickly doubles of multiples of 5 to 100 and all the corresponding halves

Double 5 is 10	double 10 is 20
Double 15 is 30	double 20 is 40
Double 25 is 50	double 30 is 60
Double 35 is 70	double 40 is 80
Double 45 is 90	double 50 is 100
Double 55 is 110	double 60 is 120
Double 65 is 130	double 70 is 140
Double 75 is 150	double 80 is 160
Double 85 is 170	double 90 is 180
Double 95 is 190	double 100 is 200

10   ÷   2  =  5	20    halved  is  10
30   ÷   2  =  15	40    halved  is  20
50   ÷   2  =  25	60    halved  is  30
70   ÷   2  =  35	80    halved  is  40
90   ÷   2  =  45	100  halved  is  50
110  ÷  2  =  55	120  halved  is  60
130  ÷  2  =  65	140  halved  is  70
150  ÷  2  =  75	160  halved  is  80
170  ÷  2  =  85	180  halved  is  90
190  ÷  2  =  95	200  halved  is  100

Hints for parents  It is really important to use the full range of vocabulary when practising with children so that they more readily link their skills to a wider range of situations.  Also try to create problem solving situations with eg money in which they can use doubling and halving strategies to calculate answers.

Year 3

Derive quickly doubles of multiples of 50 to 500 and all the corresponding halves.

50    x  2  =  100	100   ÷   2  =  50
100  x  2  =  200	200   ÷   2  =  100
150  x  2  =  300	300   ÷   2  =  150
200  x  2  =  400	400   ÷   2  =  200
250  x  2  =  500	500   ÷   2  =  250
300  x  2  =  600	600   ÷   2  =  300
350  x  2  =  700	700   ÷   2  =  350
400  x  2  =  800	800   ÷   2  =  400
450  x  2  =  900	900   ÷   2  =  450
500  x  2  =  1000	1000  ÷  2  =  500

Hints to parents

Practise instant recall of these facts in order at first, looking out for any patterns that arise.  When children are secure practise the facts out of order, mixing doubling with halving.
Ask the children to think of these multiples of 50 as multiples of 50p pieces and to convert all the totals to amounts of money as you go on.  They could also describe the coins and notes that would be needed to make the amounts of money.

Key vocabulary

Double
Halve
Share equally
Two each
Grouped in pairs
Equal groups of
Halved multiplied by 2
Divided by 2
Twice
Split into 2
Shared between 2
Divided equally

Year 4

Consolidate knowing by heart addition and subtraction facts for all numbers to 20

Eg
0	 +  7  =  7	7  -  7  =  0
1	 +  6  =  7	7  -  6  =  1
2	+  5  =  7	7  -  5  =  2
3	+  4  =  7	7  -  4  =  3
4	+  3  =  7	7  -  3  =  4
5	+  2  =  7	7  -  2  =  5
6	+  1  =  7	7  -  1  =  6
7   +   0  =  7	7  -  0  =  7

Derive quickly all number pairs that total 100

Eg
62	+  38
75	+  25
40	+  60

     Derive quickly
All pairs of multiples of 50 with a total of 1000

50    +  950	100  +  900
150  +  850	200  +  800
250  +  750	300  +  700
350  +  650	400  +  600
450  +  550	500  +  500
550  +  450	600  +  400
650  +  350	700  +  300
750  +  250	800  +  200
850  +  150	900  +  100
950	+  50	

      Hints for parents
Remind children that if they know 

                                                          4  +  6  =  10      then they also know that 

                                                     40  +  60  =  100   and they also know that
                                               
                                                 400  +  600  =  1000
Year 4

Know by heart multiplication facts for the 2, 3, 4, 5 and 10 times tables and derive quickly the corresponding division facts.

2 times table

0  x  2  =      0		2  x  0  =      0
1  x  2  =      2	2  x  1  =      2
2  x  2  =      4	2  x  2  =      4
3  x  2  =      6	2  x  3  =      6
4  x  2  =      8	2  x  4  =      8
5  x  2  =    10	2  x  5  =    10
6  x  2  =    12	2  x  6  =    12
7  x  2  =    14	2  x  7  =    14
8  x  2  =    16	2  x  8  =    16
9  x  2  =    18	2  x  9  =    18
10  x  2  =  20	2  x  10  =  20

Corresponding division facts

2 ÷ 2  =  1	2 ÷ 1  =  2
4 ÷ 2  =  2	4 ÷ 2  =  2
6 ÷ 2  =  3	6 ÷ 3  =  2
8 ÷ 2  =  4	8 ÷ 4  =  2
10 ÷ 2  =  5	10 ÷ 5  =  2
12 ÷ 2  =  6	12 ÷ 6  =  2
14 ÷ 2  =  7	14 ÷ 7  =  2
16 ÷ 2  =  8	16 ÷  8  =  2
18 ÷ 2  =  9	18  ÷ 9  =  2
      20 ÷ 2  =  10	20 ÷ 10  =  2

Year 4

5 times table 

0  x  5  =  0	5  x  0  =  0
1  x  5  =  5	5  x  1  =  5
2  x  5  =  10	5  x  2  =  10
3  x  5  =  15	5  x  3  =  15
4  x  5  =  20	5  x  4  =  20
5  x  5  =  25	5  x  5  =  25
6  x  5  =  30	5  x  6  =  30
7  x  5  =  35	5  x  7  =  35
8  x  5  =  40	5  x  8  =  40
9  x  5  =  45	5  x  9  =  45
10  x  5  =  50	5  x  10  =  50

Corresponding division facts

5    ÷  5  =  1	5    ÷  1  =  5
10  ÷  5  =  2	10  ÷  2  =  5
15  ÷  5  =  3	15  ÷  3  =  5
20  ÷  5  =  4	20  ÷  4  =  5
25  ÷  5  =  5
30  ÷  5  =  6	30  ÷  6  =  5
35  ÷  5  =  7	35  ÷  7  =  5
40  ÷  5  =  8	40  ÷  8  =  5
45  ÷  5  =  9	45  ÷  9  =  5
50  ÷  10  =  5	50  ÷  5  =  10

Year 4

10 times table

0  x  10  =  0	10  x  0  =  0
1  x  10  =  10	10  x  1  =  10
2  x  10  =  20	10  x  2  =  20
3  x  10  =  30	10  x  3  =  30
4  x  10  =  40	10  x  4  =  40
5  x  10  =  50	10  x  5  =  50
6  x  10  =  60	10  x  6  =  60
7  x  10  =  70	10  x  7  =  70
8  x  10  =  80	10  x  8  =  80
9  x  10  =  90	10  x  9  =  90
10  x  10  =  100	10  x  10  =  100

Corresponding division facts

10 ÷ 1  =  10	10 ÷ 10  =  1
20 ÷ 2  =  10	20 ÷ 10  =  2
30 ÷ 3  =  10	30 ÷ 10  =  3
40 ÷ 4  =  10	40 ÷ 10  =  4
50 ÷ 5  =  10	50 ÷ 10  =  5
60 ÷ 6  =  10	60 ÷ 10  =  6
70 ÷ 7  =  10	70 ÷ 10  =  7
80 ÷ 8  =  10	80 ÷ 10  =  8
90 ÷ 9  =  10	90 ÷ 10  =  9
100 ÷ 10  =  10	100 ÷ 10  =  100

Year 4

3	times table

0	x  3  =  0	3  x  0  =  0
1	x  3  =  3	3  x  1  =  3
2	x  3  =  6	3  x  2  =  6
3	x  3  =  9	3  x  3  =  9
4	x  3  =  12	3  x  4  =  12
5	x  3  =  15	3  x  5  =  15
6	x  3  =  18	3  x  6  =  18
7	x  3  =  21	3  x  7  =  21
8	x  3  =  24	3  x  8  =  24
9	x  3  =  27	3  x  9  =  27
10	x  3  =  30	3  x  10 =  30

 Corresponding division facts

3    ÷  1  =  3	3    ÷  3  =  1
6    ÷  2  =  3	6    ÷  3  =  2
9    ÷  3  =  3	
12  ÷  4  =  3	12  ÷  3  =  4
      15  ÷  5  =  3	15  ÷  3  =  5
18  ÷  6  =  3	18  ÷  3  =  6
 21  ÷  7  =  3	21  ÷  3  =  7
24  ÷  8  =  3	24  ÷  3  =  8
27  ÷  9  =  3	27  ÷  3  =  9
30  ÷  10 = 3	30  ÷  3  =  10

Year 4

4	times table

     0  x  4  =  0	4  x  0  =  0
     1  x  4  =  4	4  x  1  =  4
     2  x  4  =  8	4  x  2  =  8
     3  x  4  =  12	4  x  3  =  12
     4  x  4  =  16	4  x  4  =  16
     5  x  4  =  20	4  x  5  =  20
     6  x  4  =  24	4  x  6  =  24
     7  x  4  =  28	4  x  7  =  28
     8  x  4  =  32	4  x  8  =  32
     9  x  4  =  36	4  x  9  =  36
     10 x 4  =  40	4  x 10 =  40

Corresponding division facts

4    ÷  1  =  4	4    ÷  4  =  1
8    ÷  2  =  4	8    ÷  4  =  2
12  ÷  3  =  4	12  ÷  4  =  3
     16  ÷  4  =  4	
20  ÷  5  =  4	20  ÷  4  =  5
24  ÷  6  =  4	24  ÷  4  =  6
28  ÷  7  =  4	28  ÷  4  =  7
32  ÷  8  =  4	32  ÷  4  =  8
36  ÷  9  =  4	36  ÷  4  =  9
40  ÷  10  =  4	40  ÷  4  =  10

Year 4

Begin to know multiplication facts for the 6 times tables.

0  x  6  =  0	6  x  0  =  0
1  x  6  =  6	6  x  1  =  6
2  x  6  =  12	6  x  2  =  12
3  x  6  =  18	6  x  3  =  18
4  x  6  =  24	6  x  4  =  24
5  x  6  =  30	6  x  5  =  30
6  x  6  =  36
7  x  6  =  42	6  x  7  =  42
8  x  6  =  48	6  x  8  =  48
9  x  6  =  54	6  x  9  =  54
10 x 6  =  60	6  x  10 = 60

Begin to know multiplication facts for the 7 times table

0  x  7  =  0	7  x  0  =  0
1  x  7  =  7	7  x  1  =  7
2  x  7  =  14	7  x  2  =  14
3  x  7  =  21	7  x  3  =  21
4  x  7  =  28	7  x  4  =  28
5  x  7  =  35	7  x  5  =  35
6  x  7  =  42	7  x  6  =  42
7  x  7  =  49	
8  x  7  =  56	7  x  8  =  56
9  x  7  =  63	7  x  9  =  63
10 x 7  =  70	7  x  10 = 70

Hints for parents

If children struggle with some of these facts encourage them to use their favourite tables to calculate these more difficult ones.
They could recall the 5 times facts and add one more to work out the 6 times table and use the 5 times combined with doubles to calculate the 7 times tables.
Some children would enjoy doubling and doubling again to work out 4 times and then add a double to calculate 6 times.  
This sort of approach enables some children to calculate tables facts at great speed and is fun!

Year 4

Begin to know multiplication facts for the 8 times table

0  x  8  =  0	8  x  0  =  0
1  x  8  =  8	8  x  1  =  8
2  x  8  =  16	8  x  2  =  16
3  x  8  =  24	8  x  3  =  24
4  x  8  =  32	8  x  4  =  32
5  x  8  =  40	8  x  5  =  40
6  x  8  =  48	8  x  6  =  48
7  x  8  =  56	8  x  7  =  56
8  x  8  =  64
9  x  8  =  72	8  x  9  =  72
10 x 8  =  80	8  x  10 = 80

Begin to know multiplication facts for the 9 times table

0  x  9  =  0	9  x  0  =  0
1  x  9  =  9	9  x  1  =  9
2  x  9  =  18	9  x  2  =  18
3  x  9  =  27	9  x  3  =  27
4  x  9  =  36	9  x  4  =  36
5  x  9  =  45	9  x  5  =  45
6  x  9  =  54	9  x  6  =  54
7  x  9  =  63	9  x  7  =  63
8  x  9  =  72	9  x  8  =  72

Hints for parents
Encourage children to use doubling to work out their 8 times tables if they are      experiencing difficulty
Learning the straight tables facts.
Double and double again gives the 4 times table and if you double again then you have the 8 times table.
	
There are some interesting patterns in the 9 times table. Look at the answers to the multiplications in the 9 times table.   The digit sum is always 9 eg  36……3  +  6  =  9
                                                                                    72……7  +  2  =  9

The tens digit increases by 1 each time whilst the unit digit decreases by 1
Some children enjoy multiplying by 10 and then subtracting one multiple.
Year 4

Derive quickly doubles of all whole numbers up to and including 50 and the corresponding halves.

Eg        38  +  38  =  76	29  doubled is  58

            84    ÷  2   =  42	half  of  96  is  48

Derive quickly doubles of multiples of 10 to 500 and the corresponding halves.

Eg       460  x  2  =  920	270  doubled  makes  540     
    
            870  ÷  2  =  435	520  halved will be  260

Derive quickly doubles of multiples of 100 to 5000 and the corresponding halves.

Eg        3400  x  2  =  6800	2900  doubled  is  5800

             7500  ÷  2  =  3750	half  of  £4600.00 is  £2300.00

Hints to parents

Children really enjoy these doubling strategies especially when it enables them to work confidently with large numbers.  

If they start to struggle, encourage them to partition the numbers into friendlier chunks. 

Eg    3400  x  2  is  (3000  x  2)  plus  (400  x  2)

4600	 ÷  2  is  the same as (4000  ÷  2)  +  (600  ÷  2)

Some children may find it helpful to make jottings to support their thinking when they first work with these larger numbers so make sure they have pencil and paper available.  As their confidence grows they will rely less and less on these jottings but it is important that they never feel over faced. 

Year 5

Derive quickly pairs of decimals that total 1

0.1  +  0.9  =  1	0.9  +  0.1  =  1
0.2  +  0.8  =  1	0.8  +  0.2  =  1
0.3  +  0.7  =  1	0.7  +  0.3  =  1
0.4  +  0.6  =  1	0.6  +  0.4  =  1
0.5	+  0.5  =  1

    Derive quickly pairs of decimals that total 10
    Eg

6.2  +  3.8  =  10	4.9  +  5.1  =  10
3.7  +  6.3  =  10	1.5  +  8.5  =  10

Derive quickly all 2 digit pairs that total 100
Eg

43  +  57  =  100	69  +  31  =  100

Derive quickly all pairs of multiples of 50 with a total of 1000
Eg

350  +  650  =  1000	750  +  250  =  1000

Hints to parents
Ask children to make lists of these pairs.  They can vary the way in which they set the list out to try and complete all the options more quickly.  For example if they know that 350 + 650 = 1000 then they immediately know that 650 + 350 = 1000 .  By recording that opposite their first statement they will complete all options in half the thinking time.  As they become more confident challenge them to ‘beat the clock’ as they record the patterns.

Rapid fire questions in short practice situations are a good way to practise and whenever possible make up problems involving money or measures in which children can apply their skills.
Eg…………if I have 27p how much more do I need to make £1.00?
If I start with £1.00 and spend 56p how much will I have left?
If I roll out 85cm of string how much more do I need to roll out to have a full metre?

Year 5

Know by heart all multiplication facts for all tables up to and including the 10  x  10

Derive quickly all the corresponding division facts for these tables  (see Y4 examples).

Year 5

Derive quickly doubles of all whole numbers  1  to  100  and the corresponding halves

Eg  78  x  2  =  156	double  93  is  186
       
      156  ÷  2  =  78	186  halved  is  93

Derive quickly doubles of multiples of 10 to 1000 and the corresponding halves

Eg  670  x   2  =  1340	560  doubled  is  1120

     1340  ÷  2  =  670	1120  halved  is  560

Derive quickly doubles of multiples of 100 10000 and the corresponding halves

Eg  6500  x  2  =  13000	8500  doubled  makes  17000

    13000  ÷  2  =  6500	half of 17000  is  8500

Hints to parents
When children are confident with halving and doubling to this level make as many links as possible to measures.
Eg  13000g  is  13 kg  so  half of 13kg will be 6500g or 6.5kg or 6kg 500g.

Children need as much practice as possible to see how they can use skills they have learned in the context of number to aspects of measure.

Remember 
1kg    =  1000g
1km   =  1000m
1l       =  1000ml

Year 6

Consolidate knowing by heart all multiplication facts for all tables 
up to and including 10 x 10

Derive quickly the corresponding division facts for the same tables.

Derive quickly squares of multiples of 10 to 100

10  x  10  =  100	20  x  20  =  400
30  x  30  =  900	40  x  40  =  1600
50  x  50  =  2500	60  x  60  =  3600
70  x  70  =  4900	80  x  80  =  6400
90  x  90  =  8100	100  x  100  =  10000

Derive quickly doubles of all 2 digit numbers including decimals and the corresponding halves

Eg  3.8  x  2  =  7.6	0.76  x  2  =  1.52
       7.6  ÷  2  =  3.8	half of 1.52  is  0 76

Derive quickly doubles of multiples of 10 to 1000 and the corresponding halves

Eg  670  x  2  =  1340	1340  halved  is  670

Derive quickly doubles of multiples of 100 to 10000 and the corresponding halves.

Eg  6500  x  2  =  1300	1300  ÷  2  =  6500