2. AIMS
To update our Parents on how Numeracy
is delivered within KS2 (Y3-6)
To understand the importance of Numeracy
within the curriculum and the wider world
To enhance our children’s learning
To work together as a school and at home
To demonstrate progressive strategies in
the 4 operations of number
To share resources and support ideas
3. How can we all help?
Know what your child is learning in school
Learning objectives sent home half termly, from Next half term (KS1 now)
Passports- started in KS1 (KS2 from September 2014)
Prep
Communicate with your child about Numeracy and with their teacher
Numeracy diary (flexible/ in line with objectives/targets sent home)
Numeracy involved in the ‘real world’
Games and Fun
Own opinions- positive and encourage
Know why Numeracy is important
Ok to make errors as we learn from them- identifies a misconception
Please don’t do it for them- support/encourage/listen
Feel confident using the strategies that the children are using
We didn’t learn it that way when I was at school- I’m not sure how to
do it now?
Use the vocabulary the children understand and the taught strategies
Ask your child to explain how they’ve got to the answer
4. In our recent Tutor Time, we asked the children
‘Why do we learn Numeracy?’
Display board
Positive and important
3 categories
• Helps us/ improve/ get better results/ answer more
quickly
• Jobs and future careers- get a better job, go to a better
University
• Every day life- know what number house my friend
lives, know how many things to box up, cook,
play sport, shop, read the time………………
Parental perceptions
Child’s perceptions
5. Our aim, as a school, is toImprove calculations and be able to do maths in our heads securely
using a variety of strategies for the 4 operations of number and
when the numbers start to get too big, to move onto using paper
and pencil methods, more formal methods and then to use a
calculator.
We want our children to be able to ask themselves….
1. Can I do this in my head?
2. Can I do this in my head using drawings and jottings?
3. Do I need to use a compact/ expanded written
method?
4. Do I need to use a calculator?
6. Addition, Subtraction, Multiplication and Division
( 4 operations of Numeracy)
So how do we teach our children to calculate?
• Estimate/ Round/ work out
• Strategies - Mental and written
• Stages- KS1-KS2 Progressive, able to apply and select an appropriate
method for the question and size of number (TOOLKIT)
• Vocabularyhttp://webarchive.nationalarchives.gov.uk/20110202093118/http:/natio
nalstrategies.standards.dcsf.gov.uk/node/85273
• Resources
• Websites- presentation is on the Parents’ portal (Nottingham)
• Hand out
7. By the end of Year 1: 2x, 5x 10x ~ usually by rote.
By the end of Year 2: 2x, 3x, 4x, 5x & 10x
By the end of Year 3: 2x, 3x, 4x, 5x, 6x, 9x, 10x &
11x
By the end of Year 4: 2x through to 12x tables
STAGES
1.
2.
3.
4.
As
As
By
By
an individual times table
mixed tables
switching
leaving gaps to fill in?
Know that the 2s, 4’s and 8’s are related
Know that 3s, 6s and 12s are related
Know that 5s and 10s are related
Patterns and tricks to help
8. Year 3 - Addition
Mental Calculations
Mental recall of number facts
- Number bonds to 10 and 20
- Pairs to 100 (multiples of 10 and 5)
- Adding multiples and near multiples
of 10 and 100.
- Add two 2–digit numbers by
counting on in tens and ones.
9. Year 3 - Addition
Written methods
Partitioning into hundreds, tens and
ones, then recombining.
46 + 38
40 + 30 = 70
6 + 8 = 14
+30
46
+8
76
84
10. Year 3 - Addition
Written methods
Using place value and number facts to
split 1-digit numbers.
176 + 8 = 184
since 176 + 4 = 180 and 8 = 4+4
+4
176
+4
180
184
11. Year 3 - Subtraction
Mental Calculations
- Number bonds and pairs to 100
- Subtracting multiples and near
multiples of 10
- Subtract a pair of 2-digit
numbers by counting on or
back.
12. Year 3 - Subtraction
Written methods
Place value subtractions
536 – 30 = 506
417 – 7 = 410
849 – 800 = 49
13. Year 3 - Subtraction
Written methods
Find the difference by counting up,
using number facts to bridge 100.
123 – 57 = 66
+3
57
+40
60
+23
100
123
14. Year 3 - Subtraction
Written methods
Subtract 19 or 21, 29 or 31 etc
35 – 19 = 16
+1
15
16
35
-20
15. Year 4 - Addition
Mental Calculations
Mental recall of number facts
- Number bonds to 20 (13+7)
- Quickly recall pairs to 100 and £1
(53p+47p)
- Adding multiples and near multiples
of 10, 100 and 1000 (640+1300)
- Add any two 2–digit numbers by
counting on in tens and ones.
16. Year 4 - Addition
Written methods
Using place value and number facts to
split numbers.
176 + 8 = 184
since 176 + 4 = 180 and 8 = 4+4
+4
176
+4
180
184
18. Year 4 - Subtraction
Mental Calculations
- Quickly recall number bonds and pairs
to 100
- Subtracting multiples and near
multiples of 10, 100 (192 - 40)
- Subtract a pair of 2-digit numbers by
counting on or back.
- Find change from £10, £20 and £50
19. Year 4 - Subtraction
Written methods
Find the difference by counting up,
using number facts to bridge 100.
754 – 86 = 668
+14
86
+600
100
+54
700
754
20. Year 3 - Multiplication
Mental Calculations
- Multiplication facts in 2x, 3x,
4x, 5x, 9x 10x table.
- Understand that multiplication
is commutative. 5 x 8 = 8 x 5
- Double numbers up to 50
- Multiply whole numbers by 10
and 100.
21. Year 3 - Multiplication
Written methods
Repeated addition using a number line
3 x 6 = 18
0
6
12
18
22. Year 3 - Multiplication
Written methods
Partitioning to multiply 2-digit numbers
by ‘friendly’ single digit numbers.
32 x 3 = 96
x
3
30
90
2
6
23. Year 3 - Division
Mental Calculations
- Use grouping/fingers to divide
in 2x, 3x, 4x, 5x, 10x table.
- Understand that division is
related to multiplication.
- Halve even numbers to 100.
- Divide whole numbers by 10 or
100.
24. Year 3 - Division
Written methods
Grouping using a number line.
I have 24 biscuits and there are six
people in my family. How many do they get
each?
24 ÷ 6 = 4
0
6
12
18
24
25. Year 3 - Division
Written methods
Remainders.
13 ÷ 3 = 4 r1
+1
0
3
6
9
12
How many 3s make 13? How many left over?
26. Year 4 - Multiplication
Mental Calculations
- Multiplication facts up to 12 x 12
- Double and halve numbers up to 100
- Multiply whole numbers by 10, 100 and
1000 (300 x 6 or 4000 x 8)
27. Year 4 - Multiplication
Written method - Partition
Partitioning to multiply 2-digit numbers
by ‘friendly’ single digit numbers.
23 x 4 = 92
23 x 4 = (20 x 4) + (3 x 4)
80 + 12
= 92
28. Year 4 - Multiplication
Written methods – the grid method
Partitioning to multiply 2-digit numbers
by ‘friendly’ single digit numbers.
23 x 7 =
x
7
20
140
3
21
29. Year 4 - Division
Mental Calculations
- Know division facts for times tables
up to 12 (144 ÷12 = 12)
- Halve even numbers to 200
(half of 152 = 76)
- Divide whole numbers by 10 or 100.
(3200 ÷ 8 = 400)
30. Year 4 - Division
Written methods
Remainders
41 ÷ 4 = 10 r1
How many 4’s are in 40? How many left over?
0
10 x 4
10x 4 =40 +1
40
+1
41
31. Year 5 Addition
Mental calculations
• Mental recall of number bonds to 1 and the
next whole number
• Adding numbers with two significant digits
only
• Adding one or two digit multiples of 10,
100, 1000, 10,000 and 100,000
• Adding decimal numbers which are near
multiples of 1 or 10 including money
• Using place value and number facts to add
two or more ‘friendly numbers’
32. Year 5 Addition
Written calculations
Partitioning of Th, H,T,U
Using column addition
• To add two or more
whole numbers with up
to 5 digits
• To add any pair of 2
place decimal numbers
including money.
5 4 3 2 1+
2345
509
57175
£ 5 4. 2 1 +
£ 1 2. 3 4
£ 6 6. 5 5
33. Year 5 Addition
Written calculations
Begin to add related fractions using
equivalences.
1/2 + 1/6 =
Can be solved by converting ½ in to sixths
Eg. 3/6 + 1/6
34. Year 5 Subtraction
Mental calculations
• Subtract numbers with two significant digits
only
• Subtract one or two digit multiples of 100,
1000, 10,000 and 100,000
• Subtract one or two digit near multiples of 100,
1000, 10,000 and 100,000 from other numbers
• Subtract decimal numbers which are near
multiples of 1 or 10 including money
• Use counting up and number bonds to perform
mental subtraction
• Recognise fraction complements to 1 and the
next whole number.
35. Year 5 Subtraction
Written calculations
1 1
• Use column subtraction to
12345subtract numbers with up
631
to five digits, including
11714
exchanging where
necessary.
• Use complimentary addition for
subtractions where the larger number is
a multiple of 1000
Eg. 3000-2387 is done by
+3
2387
+10
2390
+600
2400
=613
3000
36. Year 5 Subtraction
Written calculations
• Use complementary addition for subtractions of
decimals with up to two places including amounts
of money eg. £30.00- £23.87 could be solved by
+£00.03 +£00.10
£23.87
£23.90
+£6.00
£24.00
=£6.13
£30.00
• Begin to subtract related fractions using
equivalences.
E.g. ½ - 1/6 =
Can be solved by converting ½ to 3/6 so 3/6-1/6=
2/6
37. Year 6 Addition
Mental Calculations
• Know number bonds to 100,1000 and
derive related facts- decimals
• (3.46 + 0.54)
• Add multiples and near multiples of power
10 (6345 + 199)
• Add negative numbers in context
(temperature)
• Add 1 and 2 place decimal numbers less
than 1
• ( 4.5 + 6.3 or 0.74 + 0.33)
• Add positive to negative numbers
38. Year 6 Addition
Written Calculations
+ = signs and missing numbers
• Continue using a range of strategies as in Year 1-5
but with appropriate numbers, more digits and decimals.
• Use column addition to add numbers up to 5 digits
• Use column addition to add decimals numbers up to 3
decimal places
• Add mixed number and fractions with different
denominators
39. Partition into Hundreds, Tens, Units and decimal fractions and recombine
Either partition both numbers and recombine or
partition the second number only e.g.
35.8 + 7.3 = 35.8 + 7 + 0.3
= 42.8 + 0.3
= 43.1
OR
35 + 7 = 42
0.8 + 0.3= 1.1
42 + 1.1= 43.1
+7
35.8
+0.3
42.8
43.1
40. Column addition for numbers up to 5 digits
Extend to numbers with any number of digits and decimals
with 1, 2 and/or 3 decimal places.
13.86 + 9.481 = 23.341
NOTE The decimal doesn’t move.
Line up in columns
Place holder
13.860
+ 9.481
23.341
1 1 1
Revert to expanded methods if the children experience any
difficulty.
41. Year 6 Subtraction
Written calculations
• Use number bonds to 100 of any pair of integers by
complementary addition
( 1000 - 654 = as 46 + 300 = 346)
• Use number bonds to 1 and 10 to subtract any pair of one
or two place decimal number using complementary
addition including money
( 10 – 3.65 as 0.35 + 6 = 6.35)
(£50 - £34.29 as 71p + £15 = £15.71)
• Use number facts and place value to subtract larger
numbers or decimals up to two decimal places
( 467 900 – 3005 = as - 3000 + 5 = 464 905)
( 4.63 – 1.02 = as count on or if the number to take away
is smaller , partition and combine)
42. Year 6 Subtraction
Written calculations
Find a difference by counting up
0.5 - 0.31 =
+ 0.09
0.31
+1.0
0.4
0.5
Reduce the number of steps to make it more efficient
Combine
Complementary Addition as in Y5
Decomposition with exchanging where needed
• Larger number on top
• Start with units
• 0 is where problems arise
• Not borrowing- it is exchanging
43. Year 6 Multiplication
Mental calculations
•
•
•
•
•
•
•
•
•
Know all tables facts up to 12 x 12 (rapid recall)
X integers by 10,100,100 ( numbers move not just put a 0 on end)
Identify factors, multiples, square numbers and prime numbers
Use place value and number facts
( 40 000 x 6 = 4 x 6 x 10000 = 240 000)
Use doubling and halving
(x100, x50, x25 ~ x2, x4, x8 etc)
( 28 x 25 as 28 x 100 = 2800, ½ 1400 and ½ again 700)
Use near multiple rounding
(34 x19 as 34 x 20 – 34)
(34 x21 as 34 x 20 + 34)
X 1 and 2 place decimals by partitioning and place value
( 3.6 x 4 as 3 x 4 + 0.6 x 4 = 12 + 2.4 = 14.4)
Double decimal numbers up to 2 decimal places using partitioning
( Double 36.73 as 36 (72) + 0.73 (1.46) = 73.46)
44. Year 6 Multiplication
Written calculations
Partition
87 x 6 = 522
87 x 6 = (80 x 6) + (7 x 6) = 522
OR
Use the grid method of multiplication ( as Y3 - 5)
Grid method
372 x 24 is approximately 400 x 20 = 8000
20 4
300
70
2
Extend to decimals with up to two decimal places.
45. Short Column Multiplication
The recording is reduced further, with carry digits recorded below/ above
the line.
38
x 7
266
5
Children who are already secure with multiplication for TU × U and TU ×
TU should have little difficulty in using the same method for HTU × TU or
applying decimals.
286
x 29
2574 (9 x 286 = 2574)
5720 (20 x 286 = 5720)
8294
1
Expanded if not able to understand the method above
X 10 line will be where errors occur
Carrying not added
46. Year 6 Division
Mental calculations
• Know by heart all division facts to 144
12
• Divide integers by power of 10 to give answers up to 3
decimal places
• Identify common factors, multiples, square roots and
prime numbers
• Use tests of divisibility
• Use doubling and halving
• Divide 1 and 2 place decimals up to 10 using place value
( 2.4
6 = 0.4)
• Halve decimals up to 2 places by partitioning
( ½ 0f 36.86 as ½ 36( 18)+½ 0.86(0.43)= 18+0.43=18.43 )
• Know and use equivalence between fractions, decimals
and per cent
• Recognise ratio and reduce into simplest form
47. Year 6 Division
Written calculations
Sharing, grouping and remainders as Year 5
Chunking
977 ÷ 36 is approximately 1000 = 25
40
Partition the dividend into multiples of the divisor:
e.g.
977 = 720 + 180 + 77
720 ÷ 36 = 20
180 ÷ 36 = 5
77 ÷ 36 = 2r5 + 5 + 2r5 = 27r5
20
OR
977
-
Answer: 27
5/36
720 36 X 10
(20 groups)
257
180
36 x10 /2 ( 5 groups)
77
72
36 x 2
( 2 groups)
5
48. Short Division Method
Write down how many times your divisor goes into the first number of the
dividend. If there is a remainder, that's okay (The remainder can be as a
fraction or a number left over).
Write down your remainder to the left of the next digit in the dividend.
Continue. Repeat steps 1-3 until you are done.
5
1 6 9 r2
83447
If you are dividing by 2 digit number you may need to use
chunking
Both methods above are necessary at this stage, to deal with the
wide range of problems experienced at Year Six.
49. Websites
Maths is fun
Woodlands junior
Topmarks
Bbc bitesize
Ictgames (maths)
Mathszone
Youtube- tutorials/ songs
MATHLETICS
Dictionary
