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Add these numbers…

Add these numbers…. 1000 20 30 1000 1030 1000 20. … and how do you think it has changed for your children?. What was your experience of maths lessons like when you were at school?. Maths. Maths. Play. The aim.

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Add these numbers…

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  1. Add these numbers… • 1000 • 20 • 30 • 1000 • 1030 • 1000 • 20

  2. … and how do you think it has changed for your children? What was your experience of maths lessons like when you were at school?

  3. Maths

  4. Maths Play

  5. The aim Some calculations are too difficult for most people to do mentally. They do not justify the use of a calculator since they can be done quickly using a pencil-and-paper method. These calculations usually involve three- and four-digit numbers. The aim For each of the four operations, as many children as possible can, by the age of 11, carry out a compact written method.

  6. 10 13 6 Mistakes children make: 643 + 274 8117 • 803 • 526 • 187

  7. Ma & Pa’s standard written method..

  8. Every number has a place

  9. Addition 75 + 21 35 + 19 62 + 28 57 + 35 68 + 761 + 45 5735 + 3657 523 + 399

  10. The first stage in written addition There is a large emphasis on counting and knowing what numbers look like, for example knowing that two counters is the value ‘two’. Children are encouraged to develop a mental picture of the number system in their heads to use for calculation. They develop ways of recording calculations using pictures, etc.

  11. Addition • Work out the answers to: • E + B • C + B • E + A • E + C • D + B • G + D When did you count all, and when did you count on? Why?

  12. A less than F A less than J A less than H I subtract B K subtract B J subtract C Subtraction

  13. Using the beaded line… E J O T O E J T How does this compare with using a line with all the letters marked on?

  14. The number system, building towards the ENL: 0 to 20 Real bead strings Empty 0-20 line

  15. Count all – a child doing 3 + 5 counts out three counters and then five counters and then finds the total by counting all the counters.

  16. '3' Count on from the first number – a child finding 3 + 5 counts on from the first number: ‘four, five, six, seven, eight’.

  17. '5' Count on from the larger number : 3 + 5 a child chooses the larger number, even when it is not the first number, and counts on from there: 'six, seven, eight' As well as children using their fingers to add on small amounts, a number line will be introduced.

  18. 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 Children then begin to use numbered lines to support their own calculations using a numbered line to count on in ones. 8 + 5 = 13 +1 +1 +1 +1 +1

  19. Adding numbers using the number line. 25 47 So how do we do this using the number line?

  20. Use the counting up method!! 25 + 47 = +20 +5 47 67 72 So we start at the biggest number…47 Andcount up 25 places What number do we end on??? So…. 25 + 47 = 72

  21. +10 +10 +10 +10 +7 76 96 106 116 123 86 + 40 + 7 116 123 76 Addition • 76 + 47 =

  22. 300 50 8 + 400 70 3 700 120 11 358 + 473 831 1 1 Expanded addition… 358 + 473 =

  23. Vocabulary Add, adding, addition Number sentence Calculation Sum (only to be used for addition calculations, not subtraction) Total Altogether Counting up Partitioning Number line Number bonds Rounding

  24. 780 – 560 83 – 68 5002 – 4996 Subtraction 53 – 19 86 – 22 82 – 79 82 – 5 76 - 48

  25. 9 - 3

  26. 9 - 3

  27. 9 - 3

  28. Counting back – taking away There were five frogs. Two jumped into the pond. How many were left? 1 less than 10

  29. 10 and 4 less Counting on – finding a difference Max has 5 cubes. Milly has 2 cubes. How many more cubes does Max have? How many less/fewer cubes does Milly have? What is the difference between?

  30. Subtraction Take away OR find the difference? 72 – 46 How would you tackle this number sentence? Can you explain your method?

  31. 19 23 33 43 -4 -10 -10 Subtraction – Counting back Imran has 43 conkers; he gives 24 away to his friends. How many does he have left? 43 – 24 = 19 conkers

  32. +5 +30 +3 93 90 55 60 Finding the difference Sam has saved 93p, Amy has 55p. How much more money does Sam have than Amy? 93 – 55 = 38p more

  33. 624 – 381 = 6.24 – 3.81 = +0.19 +19 +200 +2.00 +0.24 +24 6.24 624 381 3.81 400 4.00 6.00 600 Number lines with more complex calculations

  34. 83 - 26

  35. 83 – 26 70 80 1 3  - 20 6  50 7  = 57

  36. 83 – 26 1 7 8 3 - 2 6 7 5

  37. 94 – 57 80 90 1 4  - 50 7  30 7  = 37

  38. 94 - 57 1 8 9 4 - 5 7 3 7

  39. Vocabulary Subtract, subtracting, subtraction Number sentence Calculation Take away difference Counting on, counting back Partitioning Number line Number bonds

  40. 67 x 54 268 335 603 76 x 8 5648 101 r 5 7 847

  41. Multiplication 57 x 2 43 x 10 36 x 25

  42. What is multiplication? How would you illustrate this multiplication to a child? What would you draw and what language would you use? 4 x 5 = 20

  43. 5 x 4 or 4 x 5? Vocabulary

  44. Other good images – number lines 2 + 2 + 2 + 2 + 2 0 2 4 6 8 10 This image can be expressed as 2 multiplied by 5, two five times, 5 groups of 2, 5 lots of 2 and 5 hops of 2 on a number line.

  45. 10p + 10p + 10p + 10p + 10p 0 10 20 30 40 50 10p x 5 10 multiplied by 5 5 hops of 10 5 lots of 10p

  46. Multiplication as repeated addition 2 + 2 + 2 + 2 = 8 4 pairs of socks is 8 socks 4 groups of 2 is 8 (4 × 2 = 8) Or show as 4 hops of 2 on a number line 2 multiplied by 4 is 8 (2 × 4 = 8) 0 1 2 3 4 5 6 7 8

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