Primary School Parents Meeting on: Progression through Calculations

1. …… Primary School Parents Meeting on:Progression through Calculations

2. Starter (use a calculator!) Think of a number between 1 and 9 Multiply by 2 (x 2) Add 5 (+5) Multiply by 50 (x50) If you have had your birthday this year add 1 760. If not add 1759. Subtract the year of your birth.

3. Aims To look at the ways in which the teaching of mathematics has changed; To look at how children calculate; Try activities to develop calculation strategies; To look at ways in which parents can help their children

4. How has mathematics changed? Daily mathematics lesson; Emphasis on mental calculations; Interactive whole class and group teaching; Enjoyable practical approaches; Mathematics with understanding

5. Calculations Ways to help children to remember… Practice with just one fact a day, or try a ‘fact of the week’ Practice ‘fact families’, e.g. 6+8=14, 8+6+14, 14-6=8, 14-8=6 Work from answers back to facts – how many facts do you know with an answer of 12? Make an addition or multiplication table and cross out all those facts you already know. Now focus on those you need to learn. Encourage children to work out their own ways to remember facts Draw pictures to accompany particular facts. Repeat it and repeat it!

6. Skills of mental calculation Remembering number facts and recalling them without hesitation. Using facts that are known by heart to figure out new facts. Applying understanding of place value and ability to partition numbers into parts Understanding and using the laws of arithmetic and relationships between the four operations to find answers and check results Having a repertoire of mental strategies to do calculations with some thinking time Solving word problems

7. Mental gymnastics Think of a number and keep doubling it. How far can you go? Face the person next to you and alternate! In two’s – one person recites all the numbers from 1 to 100 The other person raises their hand at any number that can be divided by 3 or … Divided by 4 or … Divided by 3 and 4 or … Divided by 5 You can use your number square to help you!

8. Mental calculations Children are encouraged to count in different ways and to calculate mentally. Number lines – Bead bar / number stick / individual number lines / Number ladders

9. Calculations The aim is that children will always be able to recognise when calculations can be done ‘ in their heads’ and choose effective and efficient strategies to work out the answers.

10. Overview Up to Year 3 the emphasis is on: working mentally, calculations recorded in horizontal number sentences some jottings for more challenging numbers Models and Images In Year 3-6 children will be gradually taught more formal written methods of calculation but they will still use mental methods and jottings where appropriate.

11. Developing children’s mental picture of number system DEMONSTRATE on a number line children’s response to a calculation. DISPLAY number lines and washing lines around the room for the children to access. MODEL the use of number lines and tracks to aid calculation from YR and empty number lines from Y2 CONTINUE to demonstrate, display and model use of a number line all the way to Y6!

12. Early Recording

14. So - how can we give children the best foundations for success with written calculations?

15. Laying the foundations for addition and subtraction Partitioning Rounding Compensating Counting on Bridging through 10s, 100s, 1000s boundaries Addition and subtraction facts

16. Laying the foundations for multiplication and division Doubling/ Halving Grouping/ equal groups/ equal jumps Repeated addition/ subtraction Arrays Multiplication and division facts

17. Multiply Slap, clap, click (not as violent as it sounds!) ‘Show me’ – The product of a multiplication A multiple of 2, 3, 5, 10, 4, etc A number that is exactly divisible by 3, 5, 2, 10, 4, etc A common multiple of 2 and 3, 3 and 5, 3 and 10 In groups have a go at ‘Hot Seat’ You can use your number square or calculator to help

18. Common calculation errors! 99 158 +101 + 184 1901 612 4 1 945 1 1 1 - 237 2000 712 - 108 902

20. Dartboard Activity Rules: You have 3 darts. You can hit the same section of the board more than once, but all three must score. Show how you could score each of these totals. Demonstrate the first one Work with a partner Do you always make the totals in the same way? How might you differentiate this game?

21. Addition- Progression Mental calculation supported by: Modelling of method by teacher Jottings Number lines Expanded method using partitioning Compact ‘carrying’ method Demonstrate modelling use of number line Refer to expanded method in frameworkDemonstrate modelling use of number line Refer to expanded method in framework

23. When do children still use jottings/ number lines?? When they can calculate mentally and need a little support. When they are not completely secure with ‘carrying’. When they are dealing with addition of decimals, negative numbers, time, measurement scales, etc.

24. Example of when child insecure with vertical methodExample of when child insecure with vertical method

25. Stage 1: Mental method using partitioning:   47 + 76 = (40 + 70) + (7 + 6) = 110 + 13 = 123 Stage 2/3: Use an expanded layout 47 47 + 76 + 76 110 13 13 110 123 123  

26. Subtraction - Progression Mental calculations supported by: Modelling of method by teacher Jottings Number line Expanded decomposition using partitioning Compact decomposition Refer to expanded method in framework, demo this using Base 10 apparatus/ arrow cardsRefer to expanded method in framework, demo this using Base 10 apparatus/ arrow cards

28. Using a Number line for Subtraction Counting Back 78 – 12 -10 -2 66 68 78 Counting on to find the Difference 74 – 57 +10 +3 +4 57 67 70 74

29. When do children still use jottings/ number lines?? When they can calculate mentally and need a little support. When they are calculating the difference between two numbers relatively close together. When not completely secure with decomposition When calculating with decimals. When decomposition is made difficult by ‘trapped zeroes’. Demo difference ITP for differenceDemo difference ITP for difference

31. Example of when number lines still important in Y6/Y7Example of when number lines still important in Y6/Y7

33. Multiplication - Progression Mental calculation supported by: Jottings Number lines Modelling of method by teacher Understanding of multiplication as: an array repeated addition scaling Grid method Demo use of number lines with equal jumps to support in mental and oral and develop understanding Arrays on egg boxes, bun tins etc. ITP Demo grid method, have a go, discuss when introduced for policy. Discuss do ch move onto traditional compact method, stress benefits of grid method for long multiplication and the fact that ch can continue with this into Y7Demo use of number lines with equal jumps to support in mental and oral and develop understanding Arrays on egg boxes, bun tins etc. ITP Demo grid method, have a go, discuss when introduced for policy. Discuss do ch move onto traditional compact method, stress benefits of grid method for long multiplication and the fact that ch can continue with this into Y7

37. Division - Progression Mental calculations supported by: Jottings Number lines Modelling of method by teacher Understanding division as sharing and grouping. Visualising division using: arrays repeated subtraction Demo ITPs, Demo ITPs,

40. Table Trios and Multiplication Clocks!

41. Division - Progression Chunking Step 1: Demonstrate practically by repeatedly subtracting groups of objects and keeping count Step 2: Model on a number line Step 3: Model vertical method Demo each stage and the importance of building on children’s understandingDemo each stage and the importance of building on children’s understanding

44. How to help your child with mathematics!

45. Visual maths Number lines Noticing numbers

46. Rhymes/songs 5 little speckled frogs; 10 huge dinosaurs (bottles); 1, 2, 3, 4, 5 once I caught a fish alive;

47. Sorting Socks Cars Shoes

48. Measures Keep a record of your child's growth; Scales and balances e.g. see-saws Capacity – different containers to play with in the sink or bath;

49. Rectangle

50. Spot the Shape 1 and 2

51. Shape and space Recognising shapes around them e.g. doors, windows, cans, boxes etc Construction sets, Lego, Shapes of cakes, biscuits, sandwiches.

52. How can parents help? Count with their child Play number games Involve children in shopping activities Involve children when taking measurements or weighing items Take note of numbers in real life e.g. telephone numbers, bus numbers, lottery numbers etc Give children opportunities to use money to shop, check change etc Talking about the mathematics in football e.g.. How many points does your favourite team need to catch the next team in the division? When helping their children calculate use the method that they have been taught.

53. Key Messages To develop written calculation strategies, children need: Secure mental strategies from YR. A solid understanding of the number system. Practical, hands on experience including counters and base 10 apparatus. Visual images including number lines and arrays. Experience of expanded methods to develop understanding and avoid rote learning. Secure understanding of each stage before moving onto the next. The questions at the forefront of their minds: ‘Can I do it in my head? If not which method will help me?’