Welcome to the Numeracy information evening for KS2

AIMS

To update our Parents on how Numeracyis delivered within KS2 (Y3-6)

To understand the importance of Numeracywithin 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

How can we all help?Know what your child is learning in schoolLearning objectives sent home half termly, from Next half term (KS1 now)Passports- started in KS1 (KS2 from September 2014)PrepCommunicate with your child about Numeracy and with their teacherNumeracy diary (flexible/ in line with objectives/targets sent home)Numeracy involved in the ‘real world’Games and FunOwn opinions- positive and encourageKnow why Numeracy is importantOk to make errors as we learn from them- identifies a misconceptionPlease don’t do it for them- support/encourage/listenFeel confident using the strategies that the children are usingWe 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 strategiesAsk your child to explain how they’ve got to the answer

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 perceptionsChild’s perceptions

Our aim, as a school, is to- Improve 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?

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)

• Vocabulary-http://webarchive.nationalarchives.gov.uk/20110202093118/http:/nationalstrategies.standards.dcsf.gov.uk/node/85273

• Resources

• Websites- presentation is on the Parents’ portal (Nottingham)

• Hand out

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. As an individual times table2. As mixed tables3. By switching4. By leaving gaps to fill in?

Know that the 2s, 4’s and 8’s are relatedKnow that 3s, 6s and 12s are relatedKnow that 5s and 10s are relatedPatterns and tricks to help

Year 3 - AdditionMental 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.

Year 3 - AdditionWritten methods

Partitioning into hundreds, tens and ones, then recombining.46 + 38 40 + 30 = 706 + 8 = 14

+30 + 8

46 76 84

Year 3 - AdditionWritten methods

Using place value and number facts to split 1-digit numbers.

176 + 8 = 184 since 176 + 4 = 180 and 8 = 4+4

+4 +4

176 180 184

Year 3 - SubtractionMental 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.

Year 3 - SubtractionWritten methods

Place value subtractions

536 – 30 = 506417 – 7 = 410849 – 800 = 49

Year 3 - SubtractionWritten methods

Find the difference by counting up, using number facts to bridge 100. 123 – 57 = 66

+3 +40 +23

57 60 100 123

Year 3 - Subtraction

Written methodsSubtract 19 or 21, 29 or 31 etc

35 – 19 = 16 +1

15 16 35 -20

Year 4 - AdditionMental 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.

Year 4 - AdditionWritten methods

Using place value and number facts to split numbers.

176 + 8 = 184 since 176 + 4 = 180 and 8 = 4+4

+4 +4

176 180 184

Year 4 - AdditionWritten methods –Partitioning H,T UExpanded Column Addition

634+291 5 (4 + 1) 120 (30 + 90) 800 (600 + 200) 925

600 + 30 + 4 200 + 90 + 1 800 +120+5 = 925

Year 4 - SubtractionMental 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

Year 4 - SubtractionWritten methods

Find the difference by counting up, using number facts to bridge 100. 754 – 86 = 668

+14 +600 +54

86 100 700 754

Year 3 - MultiplicationMental 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.

Year 3 - MultiplicationWritten methods

Repeated addition using a number line

3 x 6 = 18

0 6 12 18

Year 3 - MultiplicationWritten methods

Partitioning to multiply 2-digit numbers by ‘friendly’ single digit numbers. 32 x 3 = 96

x 30 2 3 90 6

Year 3 - DivisionMental 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.

Year 3 - DivisionWritten 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

Year 3 - DivisionWritten methods

Remainders.13 ÷ 3 = 4 r1

+1 0 3 6 9 12

How many 3s make 13? How many left over?

Year 4 - MultiplicationMental 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)

Year 4 - MultiplicationWritten 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

Year 4 - MultiplicationWritten methods – the grid method

Partitioning to multiply 2-digit numbers by ‘friendly’ single digit numbers. 23 x 7 =

x 20 3 7 140 21

Year 4 - DivisionMental 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)

Year 4 - DivisionWritten methodsRemainders

41 ÷ 4 = 10 r1How many 4’s are in 40? How many left over?

10 x 4 +1 0 40 41

10x 4 =40 +1

Year 5 AdditionMental 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’

Year 5 AdditionWritten calculations

• 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+ 2 3 4 5

5 0 95 7 1 7 5

£ 5 4. 2 1 +

£ 1 2. 3 4£ 6 6. 5 5

Partitioning of Th, H,T,U Using column

addition

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

Year 5 AdditionWritten calculations

Year 5 SubtractionMental 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.

Year 5 SubtractionWritten calculations

• Use column subtraction to subtract numbers with up to five digits, including exchanging where necessary.

1 1

1 2 3 4 5 - 6 3 1 1 1 7 1 4

• Use complimentary addition for subtractions where the larger number is a multiple of 1000

Eg. 3000-2387 is done by +3 +10 +600 =613

2387 2390 2400 3000

Year 5 SubtractionWritten 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

• 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

+£00.03 +£00.10 +£6.00 =£6.13

£23.87 £23.90 £24.00 £30.00

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

Year 6 AdditionWritten 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

Partition into Hundreds, Tens, Units and decimal fractions and recombineEither 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 = 43.1OR35 + 7 = 420.8 + 0.3= 1.142 + 1.1= 43.1

35.8 42.8 43.1

+7 +0.3

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 columnsPlace holder 13.860 + 9.481 23.341 1 1 1

Revert to expanded methods if the children experience any difficulty.

Year 6 SubtractionWritten 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)

Year 6 SubtractionWritten calculations

Find a difference by counting up

0.5 - 0.31 =

+ 0.09 +1.0

0.31 0.4 0.5

Reduce the number of steps to make it more efficientCombine

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

Year 6 MultiplicationMental 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)

Year 6 MultiplicationWritten calculations

Partition87 x 6 = 52287 x 6 = (80 x 6) + (7 x 6) = 522

OR

Use the grid method of multiplication ( as Y3 - 5)

Grid method372 x 24 is approximately 400 x 20 = 8000 20 4300 70 2

Extend to decimals with up to two decimal places.

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 1Expanded if not able to understand the method aboveX 10 line will be where errors occurCarrying not added

Year 6 DivisionMental 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

Year 6 DivisionWritten calculations

Sharing, grouping and remainders as Year 5

Chunking977 ÷ 36 is approximately 1000 40 = 25

Partition the dividend into multiples of the divisor:e.g. 977 = 720 + 180 + 77

720 ÷ 36 = 20180 ÷ 36 = 5 77 ÷ 36 = 2r5 20 + 5 + 2r5 = 27r5

OR 977 - 720 36 X 10 (20 groups) 257 - 180 36 x10 /2 ( 5 groups) 77 - 72 36 x 2 ( 2 groups) 5 Answer: 27 5/36

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.

1 6 9 r2

5 83447If 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.

Websites

Maths is fun

Woodlands junior

Topmarks

Bbc bitesize

Ictgames (maths)

Mathszone

Youtube- tutorials/ songs

MATHLETICS

Dictionary