1. Cardinal Road Infant and Nursery School Calculation Evening, January 2016

2. Objectives for the evening: To share how we teach maths at Cardinal Road. To give an understanding of progression in maths.

3. The Four Rules Understanding Mental calculations Rapid recall Efficient written methods Models, images & concrete materials Stories / rhymes Problem solving and role play Use of ICT

4. Foundation Stage Children need to leave the Foundation Stage (the end of Reception) with a solid understanding of numbers and their value. This is the first stage in being able to calculate – if you cannot count you cannot progress.

5. Foundation Stage 22-36 months (pre Nursery) Children begin to be aware of numbers in the environment. They can say a few numbers in order and experiment using them in their everyday play. They are able to ‘give me one’ ‘give me two’ Children begin to be aware that if you add another object to a group it will become more and if you take away from a group it will become less.

6. Foundation Stage 30-50 months (Nursery) Children will learn number names through songs and rhymes. They will learn to recite numbers to 10 and beyond in order. They will recognise numbers of personal significance. They will begin to link the abstract numeral to the quantity. Children will have a short carpet time focusing on Maths and will be provided with plenty of opportunity to experiment with number and counting throughout the nursery environment during play.

7. Foundation Stage 40-60 months (Reception) Children now explicitly make the link that numbers identify how many objects are in a set and match numeral to quantity. Children use their fingers, marks on paper or pictures to show numbers. Children compare two groups of objects, saying when they have more and less and the same number. They separate groups of three or four objects in different ways, beginning to recognise that the total is still the same. Shows an interest in representing numbers. Realise that not only objects, but anything can be counted, including steps, claps or jumps.

8. Foundation Stage Early Learning Goal (ELG) End of Reception Expectation Children count reliably with numbers from 1 to 20. They can count backwards and forwards from any given number from 1-20. They can place them in order and say which number is one more or one less than a given number. Children understand that as you move forwards the number value increases and decreases when I move backwards Using quantities and objects, they add and subtract two single- digit numbers by counting on or back to find the answer. They solve problems, including doubling, halving and sharing.

9. ADDITION AND SUBTRACTION

10. PROGRESSION FOR ADDITION AND SUBTRACTION Counting One more / less Addition as combining two groups, then counting on Subtraction as take away or difference (eg how many more is … than …?) Ten more/less Recall of addition/subtraction facts to 10, 20 and beyond Understand that subtraction and addition are inverses

11. ADDITION

12. Year 1 A 2 digit and a 1 digit number 10 + 3 = I buy 10 cakes and my friend buys 3 cakes. How many cakes did we buy altogether? Addition

13. An understanding of place Value 8 25 47 So that in Year 2……

14. 74 + 48 Addition by partitioning 70 + 40 = 110 4 + 8 = 12 122 Year 2

15. 374 + 248 Addition by partitioning 70 + 40 = 110 4 + 8 = 12 300 + 200 = 500 622 300 + 70 + 4 200 + 40 + 8 500 + 110 + 12

16. 1 COLUMN ADDITION Extended to: 1247 + 367 £2.36 + £6.48 3.5 + 4.8 7.48 + 2.6 12.5 km + 6.08 km 1 + 248 374 622 MORE TRADITIONAL METHODS ARE STILL USED!

17. SUBTRACTION

18. Earlier work involves taking away objects from groups, counting back on a number line or using number beads. Counting on fingers etc

19. Year 1 (2 digit and 1 digit number) Taking away – jumps of 1 (modelled using bead strings) 13 – 5 = 8 8 9 10 11 12 13 -1 -1 -1 -1 -1

20. 74 4850 54 − 2 − 4 − 20 Number lines - taking away 74 – 26 = 48 Year 2

21. MULTIPLICATION AND DIVISION

22. Counting Doubling and halving Multiplication as repeated addition and describing an array Division as grouping and sharing Understand that multiplication and division are inverses (Year 2) Recall of multiplication and division facts Multiply two / three-digit numbers by 10 / 100 Progression for multiplication and division context

23. COUNTING IN CONTEXT How many 10p coins are here? How much money is that? How many toes are there on 2 feet? How many gloves in 3 pairs? If Sarah counts in 2s and Nigel counts in 5s, when will they reach the same number? How many lengths of 10m can you cut from 80m of rope?

24. DOUBLING AND HALVING IN CONTEXT There are 8 raisins. Take half of them. How many have you taken? One snake is 20cm long. Another snake is double that length. How long is the longer snake? I double a number and then double the answer. I now have the number 32. What number did I start with?

25. 2 x 3 or 3 x 2 3 plates, 2 cakes on each plate (Children could draw a picture to help them work out the answer) 2 x 3 or 3 x 2 3 plates, 2 cakes on each plate (Children could use dots or tally marks to represent objects – quicker than drawing a picture) Multiplication pictures symbols

26. Number tracks and number lines (modelled using bead strings) 2 x 3 or 3 x 2 [two, three times] or [three groups of two]

27. Arrays 5 x 3 or 3 x 5 14 x 2 = 28 x 104 2208 Array creator

28. 43 x 6 258 1 40 x 6 = 240 3 x 6 = 18 X403 624018 43 x 6 Arrays then can lead into what we call grid multiplication- partitioning numbers for multiplication

29. DIVISION

30. 6 ÷ 2 6 cakes shared between 2 6 cakes put into groups of 2 (Children could draw a picture to help them work out the answer) pictures Division

31. 6 ÷ 2 6 cakes shared between 2 6 cakes put into groups of 2 (Children could use dots or tally marks to represent objects – quicker than drawing a picture) symbols

32. Number tracks and number lines - grouping (modelled using bead strings) 8 ÷ 2 = 4 6 ÷ 2 = 3 0 2 4 6

33. Number lines / Arrays 15 ÷ 5 = 3 0 5 10 15

34. Sharing equally 8 sweets are shared between 2 people. How many do they each receive?

35. GROUPING OR REPEATED SUBTRACTION- ASKING IN A DIFFERENT WAY! There are 8 sweets. How many people can have two sweets each?

36. As children progress in division, they will continue to use: repeated subtraction using a number line. They may use an empty number line or a hand drawn jumping line. e.g. 24 ÷ 4 = 6 - children will start at 0 and jump forwards in 4’s to find how many 4’s go into 24 or they may do a multiplication (repeated addition from earlier) Children will also move onto remainders e.g. 13 ÷ 4 = 3 r 1

37. 0 4 812 16 2024 24 ÷ 4 = 6

38. Transum http://www.transum.org/Software/ - provides a mathematics challenge for every day of the year!http://www.transum.org/Software/ Nrich http://nrich.maths.org/public/ - thousands of FREE mathematics enrichment materials for ages 5 to 19 years. The resources are designed to develop problem-solving and mathematical thinking skills.http://nrich.maths.org/public/ Woodlands http://resources.woodlands-junior.kent.sch.uk/maths/http://resources.woodlands-junior.kent.sch.uk/maths/ - interactive maths games and activities for both KS1 and 2 I Love Maths Games – games, puzzles and investigations http://www.ilovemathsgames.com/ http://www.ilovemathsgames.com/ Professor Kageyama’s maths training for DS consoles Useful websites and resources

39. Maths for mums and dads – Rob Eastaway Rob EastawayRob Eastaway has been Director of Maths Inspiration since it began in 2004. He is an author whose books on everyday maths include the bestselling Why Do Buses Come In Threes? and The Hidden Maths of Sport. He appears regularly on BBC Radio 4 and 5 Live to talk about the maths of everyday life and has given maths talks across the world to audiences of all ages http://www.bbc.co.uk/news/11260872