1. Primary Maths Week
Mrs Bhabra
Mr John

2. Sums and Things for Parents
I think of a number and add 6.
My answer is negative 7, what number did I start with?
Sums and Things for Parents
This presentation is intended to explain the mental and written calculation process to parents, drawing on the mental skills and strategies children use and the recording used to support their thinking. It will enable parents to help their children. It is based on the LEA recommendations for Pencil and Paper procedures published November 2002 that is available on this website. It covers Y1-9.
There is associated guidance, including a booklet for parents and ‘Homework Helps’ to support this work.
It is vital that schools have agreed their policy on recording calculation in order to establish continuity and progression.
Title slide
Explain that you hope the presentation will enable parents to find out about the mathematics their children are doing, particularly the way they calculate and record calculations and also enable them to help their children at home.
Include a ‘fun’ mental/oral starter here so that the parents get to ‘do some maths’ straightaway. Try one where they can work with a partner and talk, perhaps using mini-whiteboards.

3. Sums and Things for Parents
Negative 13
Well done.
How did you think that through?
Sums and Things for Parents

4. Using three darts can you make 50?20 22 12 33 25 18

5. The story so far ……….
children’s recall of number facts has become more accurate and faster
children are more aware of the strategies they use to calculate
they use vocabulary correctly
they are more confident about maths
maths is more fun!
The story so far.
Since the implementation of the National Numeracy Strategy in 1999, these are some of the developments that have been made. Add anything relevant to your school.

6. What can a numerate child do?
By the age of 11 they should :
have a sense of the size of number and where it fits into the number system
know by heart addition and subtraction facts to 20, multiplication and division facts to 10x10, doubles and halves, complements to 100, multiply and divide by 10, 100 and 1000
use what they know to figure out answers mentally
What can a numerate child do?
Outline expectations for a numerate child by the age of 11.
§         have a sense of the size of number and where it fits into the number system – this is why counting is so important, not just at KS1 but throughout both Key stages and with increasingly difficult numbers.
§         know by heart addition and subtraction facts to 20, multiplication and division facts to 10x10, doubles and halves, complements to 100, multiply and divide by 10 and 100 – explain terminology if necessary
§         use what they know to figure out answers mentally – if they know 3x4=12, then they can figure out 30x4, 30x40, 0.3x4, etc.

7. The aim
The aim is for children to do mathematics in their heads, and if the numbers are too large, to use pencil and paper to avoid losing track. To do this children need to learn quick and efficient methods, including appropriate written methods.
This is a very important idea and often challenges received ideas - recording calculations assists children’s thinking and is not an end in itself. This recording will take a variety of forms and styles.

8. We want children to ask themselves:
Can I do this in my head?
Can I do this in my head using drawings or jottings?
Do I need to use an expanded/compact written method?
We want children to ask themselves
Children are encouraged to approach every calculation in this way. They use their ‘number sense’ in order to decide the best way of tackling each calculation. There are posters up in the classrooms (available from Mathsweb) in order to remind children of this. This is the list for Y5/6, the first three apply at Y3/4 and the first two at Y1/2

9. How do you add and subtract?
– 5600
83 – – 4996
How do you add and subtract?
Ask the parents to decide how they would tackle each calculation. Use individual whiteboards and pens. Tell them they can work with a partner and encourage talk. Take feedback.
All the calculations can be tackled mentally using a variety of strategies apart from (for most people), which lends itself to a written method. Outline some of the strategies that may be used. Emphasize looking at the numbers and then deciding, not just automatically doing ‘sums’. If parents are puzzled by the last example get them to think about it in the context of money and ‘counting on’. Tell the parents have just been using the problem-solving approach to calculation – making decisions after looking at the numbers.
Possible strategies (there are more!):
– 5600
count on 40 then 5 add 50 to 78, then add 6, replace zeros
vertical algorithm add 4000, then adjust
83 – – 4996
count on 2, to 70 then add 13 count on 4, then 2
subtract 300, then adjust double 26, adjust place value, then add 14
double 2.5, then add 0.2 ‘money’ – count on from 2.78 to 5.10

10. 16 - 9 Mistakes children make: 1 (Animated slide)
- 9
(Animated slide)
This slide shows children choosing to use an algorithm (method) without due consideration.
16 – 9,
is written vertically – because they've just been taught how to do it. SO
6 subtract 9, can’t do it
exchange a ten
so now we’ve got 16 – 9 ………..
SO the method didn’t get us anywhere.

11. …….and more: 6 10 13
643
+ 274
8117
803
526
187
Incorrect transfer
Mistakes children make
643
Explain the misconception relating to place value.
803
-526
 187
Explain how the child ‘exchanged’ a hundred from the eight and put it in the units. Then exchanged a further hundred from the remaining seven hundreds and put it in the tens. Demonstrating a partial recall of the decomposition process but not fully understanding it.
These are common mistakes; you could add further examples of your own.
Incorrect digit placement
Tour of Mathematics in Practice.

12. EYFS
The Early Years Foundation Stage Mathematics programme is split into two areas:
Numbers and Shape
Space and Measure

13. Linking into Early Learning Goals at the end of the year…
Say which number is one more or less than a given number
Using quantities and objects, they add and subtract two single digit numbers and count on and back to find the answer
They solve problems involving doubling, halving and sharing.

14. Counting on in Ones and Tens

15. Addition = 86
+10 96
+10
106
+10
116
+10
123 +7 76
116 76
+ 40
123
+ 7
Now say you are going to demonstrate the recording methods used for each of the operations in turn.
(animated slide)
Addition
The number line models the counting on that children may be doing in their heads. It supports their thinking.
You will see this type of recording in children’s books from KS1 onwards.
The second example illustrates moving towards a more efficient method. Something that the parents may have done in their calculations earlier.
To fit in with your school’s policy you need to chose one of the next 2 slides and delete the other:
Addition using the vertical expansion
Addition using the horizontal expansion

16. Addition
Moving on to… =
= 110
= 13
123

17. Addition =
358
+ 473
358
+ 473
831 1
700
120
(Animated slide)
Addition using the vertical expansion
Stress the importance of the correct vocabulary..eight add three, fifty add seventy…3 hundred add 4 hundred
Here the least significant digits are added first.
If your policy uses the intermediate step of adding the most significant digits first you will need to amend this slide. 11
831

18. Subtraction – KS1
Imran has 43 conkers; he gives 24 away to his friends. How many does he have left?
43 – 24 = 43 -1 19 20 -3 23
-10 33
-10
(Animated slide)
This slide demonstrates to parents the process of using an empty number line to support children’s thinking in subtraction.
It might well be how they (the parents) would work this mentally using an imaginary number line.
Children will experience this type of recording from Y2. The jumps are below the line to show ‘counting back’.
19 conkers

19. Subtraction
Sam has saved 93p, Amy has 55p. How much more money does Sam have than Amy?
93 – 55 = 60 +5 90
+30 93 +3 55
(Animated slide)
Another subtraction calculation, this time involving difference.
Here the child has counted on from 55 to 93, recording the jumps on a number line. Having a visual image like this supports the child with what is going on in their head. The big jump of 30 may initially be made with three jumps of 10.
38p more

20. Subtraction
8.23 – 4.55 =
3.68
+0.23
+0.45 +3
The same method but using decimals. Counting on or complementary addition is used.
This is one of the reasons that children work on complements, as mentioned earlier.
Putting one number underneath the other would result in many children giving an answer of 4.12.
4.55
5.00
8.00
8.23

21. Subtraction
A sports stadium holds 9010 spectators people attend a football match. How many empty seats are there?
+ 57
+300
+3010
5643
5700
6000
9010
3010
300 57
3367
(animated slide)
The same method but using large numbers. Counting on or complementary addition is used again.
Some children may begin to record the jumps vertically without using a line.
If you have time let the parents have a go.
3367 empty seats

22. Subtraction continued…
500 30 3
100 80 7 +
500 20 13
100 80 7 +
400
120 13
100 80 7 +
533
-187 = = = =
346 H T U

23. How do you multiply and divide?
57 x ÷ 2
43 x ÷ 2
36 x ÷ 4
18 x  10
8 x ÷ 5
34 x 7
How do you multiply and divide?
As before ask the parents to decide how they would tackle each calculation. Use individual whiteboards and pens. Tell them they can work with a partner and encourage talk. Take feedback.
All the calculations can be tackled mentally using a variety of strategies. Outline some of the strategies that may be used. Emphasize looking at the numbers and then deciding, not just automatically doing ‘sums’. Tell the parents they were using the problem-solving approach to calculation.
Possible strategies (there are more!):
57 x ÷ 2
Partition, double 50, double 7, recombine partition, halve 70, halve 8, recombine
43 x ÷ 2
X100, then halve partition, halve 700, halve 42, recombine
36 x ÷ 4
X100, then 4 halve, and then halve again
18 x  10
18x10, halve answer, then move digits one place to right, (NOT decimal point to left)
Add 18x10 to 18x5 use this opportunity to explain how to x and ÷ by 10, 100
8 x ÷ 5
8x20 then subtract ÷ 10, then double
34 x ÷ 6
Partition, 30x7, add 4x7 tables facts, 6x9=54

24. Arrays
3 x 3 = 9
3+3+3=9
4 x 5 = 20
5 x 15 = 75
7 x 5 = 35

25. Multiplication
47 x 8 = x
37 x 46 = x
1702
Children are now taught to use the grid method for multiplication.
The numbers are partitioned, multiplied and then recombined.
If you have time let the parents have a go.
Children have experienced great success with this method of recording.
It has also helped enormously when they move into KS3 with algebra.
If you have worked with your High School or other primaries on a recording policy it is important to mention this to parents.
All High Schools and Upper Schools have been informed about the policy by KS3 consultants and are being encouraged to adopt it.

26. Mistakes children make:67
x 54
268
335
603 76
x 8
5648
Incorrect placement of digits
(animated slide)
Common mistakes children make:
Misconception related to place value.
2. Place value again. Here the child multiplied by 5 not 50. Parents probably remembered ‘putting down a zero’. What exactly did that mean! Also the answer makes no sense, it’s far too small.
3. The ‘guzinter’ or ‘bus shelter’ method.
How many times 7 guzinter 8: one remainder 1.
How many times 7 guzinter 4: none remainder 4.
How many times 7 guzinter 7: one.
Remainder 1 and remainder 4, so that’s remainder 5.
It would be lovely if it worked!
This is a very difficult method to teach, it relies on remembering a ‘rigmarole’ rather than on any understanding. It also requires false ideas because of the language used e.g. ‘7 into 4 won’t go’ is untrue because the 4 is actually 40 which is divisible by 7!
101 r 5
7 847
Incorrect multiplying
Incorrect carrying

27. ……… leading to algebra at KS3
(a + b)2
= (a + b) x (a + b)
x a b
a a2 ab a2 + ab
b ab b ab + b2
a2 + 2ab + b2
(animated slide)
Remember these!
The expansion of brackets. Here the grid method demonstrates this quite clearly, rather than ‘eyebrows’ and ‘smiley faces’.
(a + b)2 = a2 + 2ab + b2

28. 18 ÷ 3 = 6
We look carefully at the divisor and jump to the target number on a number line. Then count how many jumps.
____

29. 47  8 8 47 375  43 43 375 Division (animated slide)
8 47
(animated slide)
These are examples of the ‘gozinter’ method that show how it doesn’t really get you anywhere. Try them!
375  43

30. Depth and breadth
New national curriculum is now focusing on how to ‘move children on’ in different ways.
No longer simply giving them the next year’s work, as they need to have a greater understanding of their current mathematical knowledge.

31. Examples of working beyond age expected.
Year 2 : combine finding a fraction of a number AND more than/less than to achieve greater understanding of number.
Use < = > in between these fractions..
½ of ¼ of 40
¼ of /3 of 30

32. How we will enforce this:
Weekly practical lessons on a Friday for children to explore number and challenge themselves to question statements and what they already know.
For some children, this time can be used to focus on their mental arithmetic and speed of recall.

33. Make sure maths is fun! How can you help? Use school methods
Talk about how you do maths
Be positive
Ask your child to explain
Give praise and encouragement
(Animated slide)
Final slide and how parents can help at home.
Encourage parents to talk to the teachers.
LEA publications:
Sums and things for parents
Helping your child with maths
Useful websites for parents:
Make sure maths is fun!

34. Thank you for your support
Any Questions?
Thank you for your support