Presentatie titel

1. Calculation up to 100 Presentatie titel Okahandja, October 2013 Rotterdam, 00 januari 2007

2. Teaching materials 1 All kind of counting materials

3. Teaching materials 2 10-frames

4. Teaching materials 2 10-frames 1 1 1 2 1 3

5. Teaching materials 3 Classroom number line 1 - 100

6. Teaching materials 4 Classroom number snake 1 - 100

8. Teaching materials 5 100-beads/bottle caps string Foto van voorbeeld met doppen

9. Teaching materials 6 Sun-game

10. Teaching materials 7 Empty number line

12. Strategies calculation up to 100 Solve the problems and write down your calculations. Show the way you find your answer! • 43 + 35 = • 58 + 26 =  • 85 – 32 =  • 72 – 37 = • Solve

13. The calculations of the learners of Elim Primary School in Windhoek

15. The calculations of the learners of Elim Primary School in Windhoek

16. The calculations of the learners of Elim Primary School in Windhoek

17. The calculations of the learners of Elim Primary School in Windhoek

18. The strategies used by the learners of Elim Primary School in Windhoek • In grade 3: Counting one-by-one, Stepwise addition and subtraction/ Stringing, Splitting, Digit algorithm • In grade 4: Stepwise addition and subtraction/ Stringing, Splitting, Digit algorithm • In grade 5: Digit algorithm

19. Strategie 1: Counting one-by-one • Counting or calculating?

20. Strategie 1: Counting one-by-one • Teaching materials • All kinds of counting materials

21. Strategie 2: Stepwise addition and subtraction/Stringing 45 + 28 = Joan has read 45 pages in her book. Today she reads 28 pages. • 45 + 20 = 65 65 + 25 = 70 70 + 23 = 73

22. Strategie 2: Stepwise addition and subtraction/Stringing 84 – 27 = I cut 27cm off a ribbon measuring 84 cm. How much is left?

23. Strategie 2: Stepwise addition and subtraction/Stringing 50 – 36 = I spent 36p in a shop. How much change did I getfrom 50p? 36p + ____p = 50p Counting on using a number line is particularly useful in calculating change. ‘Shopkeepers strategy’

24. Strategie 2: Stepwiseaddition and subtraction/Stringing • 47 + 25 47 + 3 = 50, 50 + 20 = 70, 70 + 2 = 72 • 47 + 25 47 + 20 = 67, 67 + 3 = 70, 70 + 2 = 72 • 47 + 25 47 + 20 = 67, 67 + 5 = 72

25. Strategie 2: Stepwise addition and subtraction/Stringing • Teaching materials • Numberline • Numbersnake • Sun-game • 100-beads/bottle caps string • Emptynumberline

26. Strategie 3: Splitting or Column calculation • 47 + 25 40 + 20 = 60, 7 + 5 = 12, 60 + 12 = 72

27. Strategie 3: Splitting or Column calculation 47 25 + 60 12 + 72 47 + 25 40 + 20 = 60, 7 + 5 = 12, 60 + 12 = 72

28. Strategie 3: Splitting or Column calculation

29. Strategie 3: Splitting or Column calculation • Teaching materials • 10-frames

30. Strategie 4: Digit algorithm

31. Strategie 5: Smart strategies 5.1: The Grandstand problem • 56 + 27 • 56 + 27 = 53 + 30 = 83 3

32. Strategie 5: Smart strategies 5.2: The Scale problem • 68 – 29 • 68 – 29 = 69 – 30 = 39 +1 +1

33. Strategie 5: Smart strategies 5.3: Jumping too far and back • 45 + 28 = 45 + 30 – 2 = • 82 – 37 = 82 – 40 + 3 =

34. Which strategie do you choose? A book with 84 pages. You are reading at the bottom of page 37. How many pages still to read? The black t-shirt costs N$ 92 and the grey t-shirt costs N$ 69. How much more expensive is the black t-shirt? N$ 92 N$ 69

35. The basic strategies: 1 Stepwise addition and subtraction/ Stringing • Starts with flexible counting • The ‘large number line’: 10 – 20 – 30 – 40 – 50 – 60 – 70 – 80 – 90 – 100 • The ‘small number line’: 1 – 2 – 3 – 4 - 5 – 6 - 7 – 8 – 9 – 10 – 11 – 12 - ….- 33 – 34 – 35 – 36 – 37 – 38 – 39 - 40- etc • Use of the empty number line as a ‘notation scheme’ and ‘paradigm’

36. The basic strategies: 2 Splitting/ column calculation • Starts with place value • Use of the 10-frames as a ‘paradigm’ • Use of the ‘column notation scheme’ emphasises the place value

37. The teaching-learning-trajectory Basic strategies for all learners: • Stepwise addition and subtraction/ Stringing • Splitting/Column calculation Additional: • Smart calculation

38. Discussion & Exercises • Discussion • Exercises 46 + 23 = 58 + 36 = 76 – 24 = 63 – 28 = • Stepwise (shopkeepers method), Splitting, Smart calculation

39. Studies • Teaching-learning trajectory ‘stepwise addition and subtraction, • Teaching-learning trajectory splitting • Teaching-learning trajectory smart calculation

40. Studies • How does it start? • Which steps for the learners to make in the learning trajectory? • Which teaching materials are usefull in the teaching trajectory? • Which notation schemes do the learners use? • What are the learning outcomes in this teaching learning trajectory?

41. Make the materials yourself • Use the materials and discover the possibilities to teach mathematics with these ‘easy to make’ teaching materials.

42. The 100-caterpillar 100 • Choose two different numbers between 0 en 100, • Put these numbers in order in the first and the second part of the caterpillar, • Make the number in the next part by adding the two previous numbers, • The number in the fifth part must be 100!

43. 75-game • Rules of the game: • Take a turn to a number, • Choosefrom the numbers 5, 10, 15, 20, 25, 30, 35, • 40, 45, • Each number can be chosen only once! • Do you have three numbers which together have 75? • You are the winner!