The Early Years

1. The Early Years 25.11.13

2. What maths have you done today? Money Capacity Rotation Length Temperature Volume Reflection Time Weight Estimating Angles Translation

3. Early Years Foundation Stage handbook: Key aspects of effective learning characteristics include children: • being willing to have a go; • being involved and concentrating; • having their own ideas; • choosing ways to do things; • finding new ways; • enjoying achieving what they set out to do.

4. General statement: Mathematics development involves providing children with opportunities to practise and improve their skills in counting numbers, calculating simple addition and subtraction problems, and to describe shapes, spaces, and measures. This is where you can help at home – practise with your child to help improve their skills!

5. The detail… Number: Children count reliably with numbers from one to 20, place them in order and say which number is one more or one less than a given number. Using quantities and objects, they add and subtract two single-digit numbers and count on or back to find the answer. They solve problems, including doubling, halving and sharing.

6. The detail… Shape, space and measures: Children use everyday language to talk about size, weight, capacity, position, distance, time and money to compare quantities and objects and to solve problems. They recognise, create and describe patterns. They explore characteristics of everyday objects and shapes and use mathematical language to describe them.

7. Where it all begins…… • Counting: • Stable order principle • One to one principle • Cardinal principle • Order irrelevance principle • Abstraction principle • One-ness of one etc. • Place value • Straws • Exchange

8. Counting activities • Fingers • Dice • Dominoes • Numicon • Circle cards • Dot cards • Bead strings • Counters • Digit cards • Links • Games like snakes and ladders

9. 10 green bottles 0 7 8 9 10 6 5 4 3 1 2

10. Issue: Tend to count one set, count the other and then count all. The beginnings of addition Combining two sets of objects (aggregation) 5 7 5 7 12

11. Issue: Requires fluency with counting from any number. Adding on to a set (augmentation) 5 7 10 11 12 6 7 5 8 9

12. Counting on with a bead strings A bead string is a useful bridge from cardinal to ordinal.

13. + 7 10 +2 +5 12 5 0 Counting on with a number line The number line (showing 10s) encourages use of number bonds and place value for added efficiency Counting on with straws + =

14. 1 2 3 2 2 1 0 2 0 + = 1 0 1 0

15. Issue: Relies on ‘counting all’ again. Models for subtraction Removing items from a set (reduction or take-away) 12 - 1 - 2 - 3 - 4 - 5 = 7

16. Issue: Useful when two numbers are ‘close together’, where ‘take-away’ image can be cumbersome Models for subtraction Comparing two sets (comparison or difference) 12 - 1 - 2 - 3 - 4 - 5 = 7 Difference 5 12

17. - 5 5 2 10 -3 -2 7 10 0 12 5 12 0 7 Models for subtraction Number line helps to stop ‘counting all’. Knowledge of place value and number bonds can support more efficient calculating Counting back on a number line Useful when two numbers are ‘close together’, use of number bonds and place value can help. Finding the difference on a number line - 5 =

18. Issue: Helps to see the related calculations; 5+7=12, 7+5=12, 12-7 = 5 and 12-5=7 as all in the same diagram Models for subtraction Seeing one set as partitioned 12 - 1 - 2 - 3 - 4 - 5 = 7 Seeing 12 as made up of 5 and 7

19.  Representing bricks pictographic responses involved an attempt to represent the bricks in some way, as well as representing their actual quantity iconic responses similarly involved one-to-one correspondence. symbolic responses involved the use of conventional symbols such as numerals idiosyncratic responses were those that are not obvious

20. Sharing and making the connection with fractions Sharing 5 apples IESS

21. Here is a picnic that Chris and Michael are going to share equally. Can you tell us what each of them will have?

22. Why do children find telling the time difficult? They don’t need to tell it! • Tips to help… • Give them a reason to tell the time • Mean the time you say! • Focus on minutes past not to: • that will come later • digital time • number lines It uses base 60 not 10 We confuse them!

23. The bar model (Singapore Bar) This has been extremely successful in helping children to make sense of problems in Singapore and Japan. This is increasingly being used in the UK David spent 2/5 of his money on a book. The book cost £10. How much money did he start off with? What if the book cost….. £20? £6? £5?

24. Josie had 7 times as many sweets than Abi. Josie gave Abi some of her sweets. They now each have 20. How many sweets did Josie have before sharing them with Abi?

25. There are 3 footballs in the red basket and 2 footballs in the blue basket. How many footballs are there altogether?

26. Peter has 3 marbles. Harry gives Peter 1 more marble. How many marbles does Peter have now? Concrete Abstract

27. Peter has 5 pencils and 3 erasers. How many more pencils than erasers does he have?

28. Generalisation

29. KS2 2012

30. Peter has 4 books. Harry has five times as many books as Peter. How many books has Harry? 4 There are 32 children in a class. There are 3 times as many boys as girls. How many girls? 4 4 4 4 4

31. Sam had 5 times as many marbles as Tom. If Sam gives 26 marbles to Tom, the two friends will have exactly the same amount. How many marbles do they have altogether? A computer game was reduced in a sale by 20% and it now costs £48. What was the original price? There are 1000 tickets in a raffle at the school fair. 70% of the tickets say ‘Sorry try again’. The rest are prizes: £5 and free holidays. These come in a ratio of 5:1. How many holiday prizes are there?

32. Sophie made some cakes for the school fair. She sold 3/5 of them in the morning and ¼ of what was left in the afternoon. If she sold 200 more cakes in the morning, how many cakes did she make?’ 200 40

33. How can you help at home? • Maths in the kitchen • Maths in the bathroom • Counting games and rhymes - these use counting skills • Use dice - subitising • Look at numbers in the environment • Outside games like catch • Tidying up games • Making up problems • Playing board and card games • All the things we have thought about during this session!