Numeracy workshop KS1 2011

1. Numeracy workshop – KS1(2011) Aims: To share what we believe is fundamental to mathematical understanding To look at progression in the 4 operations To discuss ways to help children at home

2. 3 Ps Pattern Place value Partitioning

3. Progression Concrete (using actual objects) Representation (number lines etc.) Internalised

4. Pattern Counting – underpins everything – do it at any opportunity! in 1s (from 0, then from any number) in 2s (from 0, then from any number) in 10s (from 0, then from any number) forwards and backwards Progression saying number words linking 1-1 to objects associating with written numeral not starting at 0 / 10

5. Place value Early understanding of number - counting actual objects (up to 9) 1-1 correspondence knowing last number said is how many there are recognising small amounts without counting (e.g. dots on dice) beyond that, we’re getting into place value – not completely new numbers! lots of practice counting a set of objects (e.g. 12) then making a group of 10, counting what is left over and seeing the ‘pattern’ 12 = 1 ten + 2 can do at home with 1p and 10p coins until they can do this, not much point in going beyond 20

6. Partitioning idea of number being a continuum, not discrete – dienes help make this visual conservation of number – can move it around and it stays the same 5 objects on table, move them, separate them etc. still the same number early calculations e.g. 4 + 2 = 6 equally important to know that 6 = 4 + 2 lots of time finding different ways of ‘splitting’ e.g. 6 objects (concrete) should begin to see pattern (6+0, 5+1, 4+2 etc.) (representation) when internalised, calculations will be quicker, easier and more accurate time spent on these in KS1 is invaluable

7. Addition use actual objects and physically combine 2 (or more) sets together initially children will count all to find total move on to recognising that first set is still the same number, and just count on the ones you’ve added begin to count on with a number line (or in head, using fingers) lots and lots of practice – to internalise these ‘bonds’ for totals up to 10 (Kumon) If not careful, tendency is to push child on to higher numbers (when they are at counting on stage) and they never get to ‘internalise’

8. Subtraction use actual objects and physically take a group away initially children will count all to find what is left begin to count back with a number line (or in head, using fingers) lots and lots of practice – to internalise these ‘bonds’ for subtraction from numbers up to 10 (Kumon) If not careful, tendency is to push child on to higher numbers (when they are at counting on stage) and they never get to ‘internalise’

9. Bridging 10 needs a basic understanding of place value (i.e. that 10 + 4 = 14) needs children to know pairs of numbers that total 10 (e.g. 8 + 2 = 10) needs children to be able to partition smaller numbers quickly and easily (e.g. 6 = 4 + 2) means that to do 8 + 6, they partition (split) the 6 into 2 and 4, so the calculation becomes 10 + 4, which = 14 because they can do it by counting on (with fingers), we often don’t spend enough time on it with children who don’t get it straight away, but it does underpin calculating at KS2 Again needs to be done with objects first (having a 2 colour, 20 bead string helps, or alternatively a template with 10 spaces to be filled) Then using a number line Eventually, children will be able to do the calculations mentally – they will ‘just know’!

10. Subtraction – bridging 10 similar to addition 15 – 7 = 15 – (5 – 2) = (15 – 5) - 2 10 – 2 = 8

11. 2 digit calculations count on / back in 10s from any number use 100 square notice patterns (which digit changes) think about why? understand partitioning – mathematicians are lazy – with big, scary numbers, split them up into ‘easier to manage chunks’ 25 + 13 = 25 + (10 + 3) = 35 + 3 = 38 32 – 15 = 32 – 10 – 5 22 – 5 = 22 – 2 – 3 = 20 – 3 = 17 Better than partitioning both numbers, as it follows on from counting on in 1s (which they are familiar with) and works for both addition and subtraction

12. Multiplication Concrete – representational – internalisation Linked to ‘story’ e.g. 3 cars, how many wheels? Put out 3 groups of 4 ‘wheels’ and count to find total Begin to make links with addition 4 + 4 + 4 Represent on a number line Will probably understand concept before they can interpret / record with symbols

13. Division Sharing or grouping Sharing is understood first Physically with objects (e.g. 8 sweets shared between 2 children, how many each?) Later can draw representation of problem Grouping – I have 8 sweets, if I give each child 2 sweets, how many children can have some? Physically with objects Then making links with subtraction (8 – 2 – 2 – 2- 2) Working out with a number line