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

A Skip counting activity

Skip counting is used as a warm up activity in many classrooms.

For example counting in 8s8, 16, 24, 32, . . . . .

How can we maximise the learning while skip counting?

Let’s count by 19s

Let’s count by 19s19

Let’s count by 19s1938

57

What patterns have we noticed?

Why do the patterns work?

Let’s count by 19s1938

57

76

95

114

133

152

171

190

Let’s count by 19s19 20938 228

57 247

76

95

114

133

152

171

190

Let’s count by 19s19 209 39938 228 418

57 247 437

76 266 456

95 285 475

114 304 494

133 323 513

152 342 532

171 361 551

190 380 570

What patterns have we noticed?

Why do the patterns work?

Let’s count by 19s19 209 399 589 77938 228 418 608 796

57 247 437 627 817

76 266 456 646 836

95 285 475 665 855

114 304 494 684 874

133 323 513 703 893

152 342 532 722 912

171 361 551 741 931

190 380 570 760 950

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. . . .

Let’s count by 3232

Let’s count by 3232 3526496

128

160

192

224

256

288

320

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. . . .

Let’s count by 0.20.20.4

0.6

Let’s count by 0.20.2 2.20.4

0.6

0.8

3.0

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. . . .

What were the deliberate teaching actions?

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

variations

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

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

Feedback

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

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). Palmerston North, NZ: MERGA.

Available from http://www.merga.net.au/node/38?year=2009Askew, 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.

Counting

• What is so hard about counting (or learning to count)?

• What is involved in counting?

Hok jet

bpeet gaao sip

nung

soong

saam

sii

haa

Numbers in Thai

Tahi OneRua TwoToru ThreeWha FourRima FiveOno SixWhitu SevenWaru EightIwa NineTekau Ten

Rau Hundred

Mano Thousand

Kore Zero

one tahitwo rua… ….nine iwaten tekaueleven tekau ma tahitwelve tekau ma ruathirteen tekau ma torufourteen tekau ma whafifteen tekau ma rimasixteen tekau ma ono….twenty rua tekautwenty one rua tekau ma tahi. . . thirty toru tekauforty wha tekaufifty rima tekau

sixty ono tekau

onetwo…….nineteneleventwelve thirteenfourteenfifteensixteen….twentytwenty one. . . thirtyfortyfiftysixty

one onetwo too…….nine nineten teneleven oneteentwelve tooteenthirteen threeteenfourteen fourteenfifteen fiveteensixteen sixteen….nineteen nineteentwenty tootytwenty one tooty one. . . thirty threetyforty fourtyfifty fivetysixty sixty

one one onetwo too too…….nine nine nineten ten tyeleven oneteen onety onetwelve tooteen onety toothirteen threeteen onety threefourteen fourteen onety fourfifteen fiveteen onety fovesixteen sixteen onety six….nineteen nineteen onety ninetwenty tooty tootytwenty one tooty one tooty one. . . thirty threety threetyforty fourty fourtyfifty fivety fivetysixty sixty sixty

firstsecondthirdfourthfifthsixthseventh

twenty firsttwenty second

first onethsecond twoththird threethfourth fourthfifth fivethsixth sixthseventh seventh

twenty firsttwenty second

Ordinal and fractional numbersfirst onethsecond twoth halfthird threeth thirdfourth fourth quarterfifth fiveth fifthsixth sixth sixthseventh seventh seventh

twenty firsttwenty second

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.