# 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.

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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 8s 8, 16, 24, 32,..... How can we maximise the learning while skip counting?

Let’s count by 19s

19

Let’s count by 19s 19 38 57

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

Let’s count by 19s 19 38 57 76 95 114 133 152 171 190

Let’s count by 19s 19209 38228 57247 76 95 114 133 152 171 190

Let’s count by 19s 19209399 38228418 57247437 76266456 95285475 114304494 133323513 152342532 171361551 190380570

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

Let’s count by 19s 19209399589779 38228418608796 57247437627817 76266456646836 95285475665855 114304494684874 133323513703893 152342532722912 171361551741931 190380570760950

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 32 32

Let’s count by 32 32352 64 96 128 160 192 224 256 288 320

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 0.2 0.2 0.4 0.6

Let’s count by 0.2 0.22.2 0.4 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=2009 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.

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

TahiOne Rua Two ToruThree WhaFour RimaFive OnoSix WhituSeven WaruEight IwaNine TekauTen RauHundred ManoThousand KoreZero

onetahi tworua ……. nineiwa tentekau eleventekau ma tahi twelve tekau ma rua thirteentekau ma toru fourteentekau ma wha fifteentekau ma rima sixteentekau ma ono …. twentyrua tekau twenty onerua tekau ma tahi... thirtytoru tekau fortywha tekau fiftyrima tekau sixtyono tekau

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

one twotoo … ….nineten elevenoneteen twelve tooteen thirteenthreeteenfourteen fifteenfiveteensixteen ….nineteen twentytooty twenty onetooty one... thirtythreety fortyfourty fiftyfivetysixty

oneoneone twotootoo … …. nineninenine tententy elevenoneteenonety one twelve tooteenonety too thirteenthreeteenonety three fourteenfourteenonety four fifteenfiveteenonety fove sixteensixteenonety six …. nineteennineteenonety nine twentytootytooty twenty onetooty onetooty one... thirtythreetythreety fortyfourtyfourty fiftyfivetyfivety sixtysixtysixty

first second third fourth fifth sixth seventh twenty first twenty second

firstoneth secondtwoth thirdthreethfourth fifthfivethsixthseventh twenty first twenty second

Ordinal and fractional numbers firstoneth secondtwothhalf thirdthreeththird fourthfourthquarter fifthfivethfifth sixthsixthsixth seventhseventhseventh twenty first twenty 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.

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