Calculation up to 100: teaching-learning trajectory and teaching materials.

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
5 100-beads/bottle caps string

7. Teaching materials
7 Empty number line

9. Teaching materials
6 Sun-game

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

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

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

14. 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 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

17. Strategie 1: Counting one-by-one
Counting or calculating?

18. Strategie 1: Counting one-by-one
Teaching materials

All kind of counting materials

19. 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

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

21. 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’

22. Strategie 2: Stepwise addition and
subtraction/Stringing
47
47
50
70
+
+
+
+
25
3 = 50,
20 = 70,
2 = 72
47
47
67
70
+
+
+
+
25
20 = 67,
3 = 70,
2 = 72
47 + 25
47 + 20 = 67,
67 + 5 = 72

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

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

25. Strategie 3: Splitting or Column calculation
44
25 +
60
9+
69
44 + 25
40 + 20 = 60,
4 + 5 = 9,
60 + 9 = 69

26. Strategie 3: Splitting or Column calculation
def(icit)

27. Strategie 3: Splitting or Column calculation
Teaching materials


10-frames
bundles of sticks

28. Strategie 4: Digit algorithm

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

30. 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’

31. 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

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

33. Exercises
46
58
76
63
Stepwise
+ 23 =
+ 36 =
– 24 =
– 28 =
stinging (shopkeepers method),
Stepwise splitting,

34. Discussion
What materials are you using now in
computation up to 100?
What strategies do you teach in computation up
to 100?
Do you see a relationship between computation
up to 20 and computation up to 100? Please,
explain.

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. Please, make the materials yourself
Use the materials and discover the possibilities to
teach mathematics with these ‘easy to make’ teaching
materials!
Jaap Griffioen – j.griffioen@hr.nl
 Jaap de Waard – j.de.waard@hr.nl


38. 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!

39. 75-game
5
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!