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…… Primary School Parents Meeting on: Progression through Calculations

Do I need jottings ?. Shall I use a pencil and paper method?. Can I do it in my head?. …… Primary School Parents Meeting on: Progression through Calculations. Do I need to use a calculator?. Starter (use a calculator!). Think of a number between 1 and 9 Multiply by 2 (x 2) Add 5 (+5)

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…… Primary School Parents Meeting on: Progression through Calculations

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  1. Do I need jottings ? Shall I use a pencil and paper method? Can I do it in my head? …… Primary SchoolParents Meeting on:Progression through Calculations Do I need to use a calculator?

  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

  13. So - how can we give children the best foundations for success with written calculations? • We need to encourage children to use • mental calculation strategies for • smaller/ simpler numbers. • We need to encourage children to • ask the question “Can I do it in my • head?” or “Can I do it in my head with • jottings/ a number line?”

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

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

  16. 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

  17. Common calculation errors! 99 158 +101+ 184 1901612 4 1 945 1 1 1 - 237 2000 712 - 108 902

  18. 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?

  19. Addition- Progression • Mental calculation supported by: Modelling of method by teacher Jottings Number lines • Expanded method using partitioning • Compact ‘carrying’ method

  20. Jottings

  21. 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.

  22. 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 + 76110 13 13110 123 123

  23. Subtraction - Progression • Mental calculations supported by: Modelling of method by teacher Jottings Number line • Expanded decomposition using partitioning • Compact decomposition

  24. 78 – 12? How do you work out…. 74 – 57?

  25. 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

  26. 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’.

  27. Stage 1: Mental method using partitioning. • 76 – 32 = (70 – 30) + (6– 2) = 44 • Stage 2: Expanded vertical layout • Stage 3: Compact decomposition Ongoing methods: mental methods andsubtraction using a number line

  28. 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 Multiplication facts ITP

  29. Multiplication Facts ITP

  30. Using a number line

  31. Grid method of multiplication 3 10 60 18 60 + 18 = 78 6 so 6 x 13 = 78 Grid ITP

  32. 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

  33. This child has used a strategy of grouping tallies to find the answer. This child has used a strategy of counting equal groups to find the answer.

  34. Table Trios and Multiplication Clocks!

  35. 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

  36. Stage 1: Short division. i.e. TU ÷ U, HTU ÷ U • Known as the ‘chunking’ method. • 6 72 • - 60 x 10 • 12 • - 6x 1 • 6 • - 6x 1 • 0 • Answer = 12 • 9 97 • - 90 x 10 • 7 • Answer = 10 r 7

  37. Stage 3 Long division (HTU ÷ TU) 15 43215432 - 150 x 10- 300 x 20 282132 - 150 x 10- 120 x 8 13212 - 60 x 4 72 Answer = 28 r 12 - 60 x 4 12 Answer = 28 r 12

  38. How to help your child with mathematics!

  39. Visual maths • Number lines • Noticing numbers 1 6 2 5 3 4 23

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

  41. Sorting • Socks • Cars • Shoes

  42. 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;

  43. Rectangle

  44. Spot the Shape 1 and 2

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