1. Presentatie titel Calculation up to 100 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

5. Teaching materials
3 Classroom number line

6. Teaching materials
4 Classroom number snake

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! = = 
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:
In grade 5:

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
= Joan has read 45 pages in her book. Today she reads 28 pages.
= 65
= 70
= 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
get from 50p?
36p + ____p = 50p
Counting on using a number line is particularly useful in calculating change.
‘Shopkeepers strategy’

24. Strategie 2: Stepwise addition and subtraction/Stringing
= 50,
= 70,
= 72
= 67,
= 70,
= 72

25. Strategie 2: Stepwise addition and subtraction/Stringing
Teaching materials
Numberline
Number snake
Sun-game
100-beads/bottle caps string
Empty number line

26. Strategie 3: Splitting or Column calculation
= 60,
7 + 5 = 12,
= 72

27. Strategie 3: Splitting or Column calculation47
25 + 60
12 + 72
= 60,
7 + 5 = 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 =
= 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=
– 2 =
82 – 37 =
82 – =

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 – – – 8 – 9 – 10 – 11 – 12 - ….- 33 – 34 – 35 – 36 – 37 – 38 – 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= =
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,10 15 20 25 30 35 40 45
Player 1
Player 2
Rules of the game:
Take a turn to a number,
Choose from 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!