1. Presentatie titel Calculation up to 100 Okahandja, June 2014
Rotterdam, 00 januari 2007

2. As in calculation <10 and calculation <20, it´s in calculation <100 very important learners learn how to solve problems by making use of structures.
We all know now three phases:
Addition and subtraction by counting (not effective at last)
Addition and subtraction by using models (smart teaching materials)
Addition and subtraction in a formal way.
This last phase is the final phase.

3. 10 frames

4. 10 frames

5. Classroom number line 1 - 100

6. Classroom number snake 1 - 100

7. Number snake 1-100, combined with the empty number line

8. Sun-game

9. Empty number line

11. Strategies calculation up to 100 Intermezzo: How did you do it?
Solve the problems and write down your calculations.
Show the way you find your answer! = = 
85 – 32 = 
72 – 37 =
Solve

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

17. 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:
what about your
strategies?

18. Stepwise addition and subtraction/Stringing
= Joan has read 45 pages in her book. Today she reads 28 pages.
= 65
= 70
= 73

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

20. Stepwise addition and subtraction/Stringing
= 50,
= 70,
= 72
= 67,
= 70,
= 72

21. Stepwise addition and subtraction/Stringing
Teaching materials supporting stepwise addition/subtraction (stringing)
Numberline
Number snake
Sun-game
100-beads/bottle caps string
Empty number line

22. Splitting or Column calculation. This strategy is based on number value.
= 60,
7 + 5 = 12,
= 72

23. Splitting or Column calculation47
25 + 60
12 + 72
= 60,
7 + 5 = 12,
= 72

24. Splitting or Column calculation

25. Splitting or Column calculation
Teaching materials, supporting splitting or column calculation
10-frames

26. Strategie 4: Digit algorithm

27. Smart strategies (a higher level of calculation) The Grandstand problem (in case of addition) =
= 83 3

28. Smart strategies The Scale problem (in case of subtraction)
68 – 29
68 – 29 =
69 – 30 = 39 +1 +1

29. Smart strategies Jumping too far and back (learners think of the nearest decade)=
– 2 =
82 – 37 =
82 – =

30. 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

31. 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’

32. 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

33. The teaching-learning-trajectory
Basic strategies for all learners:
Stepwise addition and subtraction/ Stringing.
The most natural way of addition and subtraction
Splitting/Column calculation.
You need to know if the numbers get bigger ad you want to add and subtract without a calculator
Additional:
Smart calculation

34. Discussion & Exercises= =
76 – 24 =
63 – 28 =
Stepwise (shopkeepers method), Splitting,
Smart calculation

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

36. 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?

37. The 100-caterpillar 100 Just for fun
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!
Just for fun

38. 75-game Just for fun 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!
Just for fun