Making the most of counting activities

1. Making the most of counting activities This workshop will focus on developing counting activities so that they lead to into exploration of number and algebraic ideas. This workshop is suitable for teachers in middle and senior primary school. Roger.harvey@vuw.ac.nz

2. A Skip counting activity Skip counting is used as a warm up activity in many classrooms. For example counting in 8s 8, 16, 24, 32, . . . . . How can we maximise the learning while skip counting?

3. Let’s count by 19s

4. Let’s count by 19s

5. Let’s count by 19s

6. What patterns have we noticed? Why do the patterns work?

7. Let’s count by 19s

8. Let’s count by 19s

9. Let’s count by 19s

10. What patterns have we noticed? Why do the patterns work?

11. Let’s count by 19s

12. Patterns As we go across we add on 190 because . . . As we go down we take one off the units and add two to the tens because . . . If we go down one row and across one column we add 219 to the number because . . . If we go across two columns we add 360 to the number because. . . .

13. Let’s count by 32

14. Let’s count by 32

15. Counting by 32 As we go across we add on ____ because . . . As we go down we ___________ because . . . If we go down one row and across one column we _______ to the number because . . . If we go across two columns we add_______to the number because. . . .

16. Let’s count by 0.2

17. Let’s count by 0.2

18. Counting by ____ As we go across we add on ____ because . . . As we go down we ___________ because . . . If we go down one row and across one column we _______ to the number because . . . If we go across two columns we add_______to the number because. . . .

19. What were the deliberate teaching actions?

20. Deliberate teacher actions • Layout emphasising the tens structure • Asking how – so that knowledge is shared • Asking participants to notice patterns • Asking why patterns work • Sharing ideas in pairs

21. variations • Change starting number • Use fraction notation • Count backwards • . . . .

22. Using theatre sport techniques • In pairs skip count from any number accompanied by a hand slap • One person take the lead in changing the rhythm, volume, intonation etc • Now take turns as the leader passing the lead from one to another

23. Feedback • How did the theatre sports change things? • Any implications for teaching and learning?

24. Kazemi, E., Franke, M.,Lampert, M. (2009). Developing pedagogies in teacher education to support novice teachers’ ability to enact ambitious instruction. In R. Hunter, B. Bicknell, & T. Burgess (Eds.), Crossing divides: Proceedings of the 32nd annual conference of the Mathematics Education Research Group of Australasia (Vol. 1). PalmerstonNorth, NZ: MERGA. Available from http://www.merga.net.au/node/38?year=2009 Askew, M (2011). Unscripted Maths: Emergence and Improvisation. In J. Clark, B. Kissane, J. Mousley, T. Spencer & S. Thornton (Eds). Proceedings of the AAMT–MERGA conference held in Alice Springs, 3–7 July 2011, incorporating the 23rd biennial conference of The Australian Association of Mathematics Teachers Inc. and the 34th annual conference of the Mathematics Education Research Group of Australasia Inc.

26. Counting • What is so hard about counting (or learning to count)? • What is involved in counting?

27. Hok jet bpeet gaao sip nung soong saam sii haa Numbers in Thai

28. Tahi One Rua Two Toru Three Wha Four Rima Five Ono Six Whitu Seven Waru Eight Iwa Nine Tekau Ten Rau Hundred Mano Thousand Kore Zero

29. one tahi two rua … …. nine iwa ten tekau eleven tekau ma tahi twelve tekau ma rua thirteen tekau ma toru fourteen tekau ma wha fifteen tekau ma rima sixteen tekau ma ono …. twenty rua tekau twenty one rua tekau ma tahi . . . thirty toru tekau forty wha tekau fifty rima tekau sixty ono tekau

30. one two … …. nine ten eleven twelve thirteen fourteen fifteen sixteen …. twenty twenty one . . . thirty forty fifty sixty

31. one one two too … …. nine nine ten ten eleven oneteen twelve tooteen thirteen threeteen fourteen fourteen fifteen fiveteen sixteen sixteen …. nineteen nineteen twenty tooty twenty one tooty one . . . thirty threety forty fourty fifty fivety sixty sixty

32. one one one two too too … …. nine nine nine ten ten ty eleven oneteenonety one twelve tooteen onety too thirteen threeteen onety three fourteen fourteen onety four fifteen fiveteen onety fove sixteen sixteen onety six …. nineteen nineteen onety nine twenty tooty tooty twenty one tooty one tooty one . . . thirty threety threety forty fourty fourty fifty fivety fivety sixty sixty sixty

33. first second third fourth fifth sixth seventh twenty first twenty second

34. first oneth second twoth third threeth fourth fourth fifth fiveth sixth sixth seventh seventh twenty first twenty second

35. Ordinal and fractional numbers first oneth second twoth half third threeth third fourth fourth quarter fifth fiveth fifth sixth sixth sixth seventh seventh seventh twenty first twenty second

36. References • Bramald, R (2000) Helping pre-service teachers to understand just why learning to count is not easy for young children. Teachers and Curriculum vol 4 pp 59 -65 • Fuson, K. (1977) Children’s early counting. • Ginsburg, H. (1977) Children’s Arithmetic. • Kazemi, E. (2009, July). Developing pedagogies in teacher education to support novice teachers’ ability to enact ambitious instruction. Presentation at Crossing divides: Mathematics Education Research Group of Australasia Conference, Wellington. • Maclellan, E. (1997) The importance of counting. In I Thompson (Ed) Teaching and learning early number. Philadelphia: Open University Press. • Young-Loveridge, J (1999). The acquisition of numeracy. SET one, 1999.