Times tables: teaching-learning trajectory and teaching materials

1. Times tables
Presentatie titel
Okahandja, October 2013
Rotterdam, 00 januari 2007

3. The concept of multiplication:
counting-based repeated addition

4. Times tables
repeated addition

5. Times tables – repeated addition

6. The concept of multiplication:
structuring-based multiplication

7. Structuring-based multiplication

8. Times tables –
the strategies of structured multiplication
Strategy: ‘one-times-more’
Strategy: ‘changing’

9. Times tables
the strategies of structured multiplication
Strategy: ‘one-times-less’
Strategy: ‘doubling’

10. Times tables
the strategies of structured multiplication
Strategy: ‘halving’

11. The concept of multiplication:
formal multiplication
How to construct a times table by using the strategies?
1x7
known
2x7
double 7 + 7 or changing
3x7
one times more: 2 x 7 + 7 or changing
4x7
doubling 2 x 7: 14 + 14, or one times
less
5x7
halving 10 x 7 or changing
6x7
7x7
8x7
x7
9x7
one times more: 5 x 7 + 7
via 5 x 7 + 2 x 7 (distribution)
doubling 4 x 7: 28 + 28 or via 5 x 7 + 3
one times less: 10 x 7 – 7

12. Formal multiplication;
anchor points and strategies

13. Formal multiplication;
anchor points and strategies

14. Teaching materials times tables
Step 1: repeated addition
Times tables containers,
Buttons, bottle tops, beans, …. all kind of counting
materials
Step 2: structured multiplication
Tiles
Times table square
Step 3: formal multiplication
Relation schemes

15. Memorization
Say the times table and lay the tiles
Times table snakes
Times table memory games
Times table bingo
Relation schemes
Times tables ‘award’
Exercises

16. 1
Times tables containers 1 - 10
1
2
3
4
5
times
times
times
times
times
6 times
7 times
8 times
9 times
10 times

17. 1
Times tables containers 1 - 10
Say the times table and lay the objects
Make drawings of 2 x 3, 5 x 4, 3 x 6, …….
Make a ‘times tables exhibition’ in the classroom
Make your ‘times tables posters’

18. 2
Buttons, bottletops, beans, strings,
sticks, stones, all kind of counting
materials

19. 2
Buttons, bottletops, beans, strings,
sticks, stones, all kind of counting
materials
Make groups and say the times table
Make groups and write the times table
Make drawings of 2 x 3, 5 x 4, 3 x 6, …….

20. 3
Tiles

21. 3
Tiles
Lay the 2-times table in two columns, lay the 3-times
table in two columns, …..
Lay 5 times 4. Add one row of 4 tiles. How do you
know 6 x 4 =?
Lay 5 times 6. Take away one row of 6 tiles. Which
sum did you make? …..
Take 12 tiles and make different ‘floors’. Write your
calculations.
Take 13 tiles and make different ‘floors’. Write your
calculations.
Take 20 tiles and make different ‘floors’. Write your
calculations……
Etc.,

22. 4
Times tables memory game
2x5
6x8
4x3
3x4

23. 4
Times tables memory game
10
2x5
12
48
6x8
4x3

24. 5
Times table snakes
12/ 8 x 3
2x3
15/ 9 x 3
30/ 5 x 3
6/4x3
3/ 3 x 3
18/ 7 x 3
24/10 x 3
9
21/ 1 x 3
27/ 6 x 3

25. 6
Relation sheets
….x 3 = ….
….x 3 = ….
1-time more
1-time less
4 x 3 = 12
….x 3 = ….
….x 3 = ….
halving
doubling

26. 7
x
1
2
3
4
5
Times table square
1
2
3
4
5

27. 7
x
1
2
3
4
5
Times table square
1
2
3
4
5

28. 7
Times table square
Lay the 4 times table with bottle tops, say and write
the 4 times table.
Lay 10 bottle tops in different ways and write the
sums.
Lay 24 bottle tops in different ways and write the
sums.
Etc.,

29. Make and collect the materials
Practise the materials yourself and discover the
possibilities to teach mathematics in your class with
these ‘easy to make’ teaching materials!
Jaap Griffioen – j.griffioen@hr.nl
 Jaap de Waard – j.de.waard@hr.nl


30. How do you know the times tables?
Discussion
Excersises with teaching materials, multiplication
problems, games (24-game)
Speedtest