fractions1

# fractions1 - The Cuisenaire product Paul Stephenson...

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The Cuisenaire product Paul Stephenson Kfarlcrs dt'liyhtcd by the siniplit it\ of the mctlnxl ot multiplication shown in MT203 (Foster, 2007) may be interested In a (iattcgno-inspired variant. Each set of intersections in the repre- sentation Colin Foster describes corre- sponds to a S\-indow' pane in the metliod known by tliat or similar names ('lattice'/ 'gelosia'/. ..). This may be as old as place value itself and, if so, goes back to the Ancient Hindus. In 'line multiplication' eat h individual product is modelled as a rectangle t)l points, whereas in tbe lattice mctliod. as it has come down to us \ia the Arabs am! later European texts, each [)roduct is shown as a written number. However, in both cases the position of tbe number in tbe 'lattice' dictates its place value. Wbat Gattegno does is to use the multiplication square as a 'readv reckoner' aiul todc the place value of each individual product by its colour. Tbe colour arises from tbe overlap oi tinted acetates — the process of colour sublraction (using that word to mean the pbysical, not the lTiatbcmatical, operation, of course). The picture to the right shows tbe Cuisenaire Product Finder set to multiply 973 bv682. Paul Stephenson is operations director of The Magic Mathworks Travelling Circus. www. m a g i cm ath works. o rg Reference Foster, C. (2007) Line Multiplication, ^MriOJ, Jdy, 29. Notes 1 lor an animated version of Colin's piece, visit: litt|>://nridi. maths. nrg,''pul>lii'/vu-\\ or. php?c»|)j_i(! = 5ii|2, where it appears as the problem •MultipKnngwitli IJnrs' in llic NRiCH list tor May 2007. 2 The hodua Finder wa.s issued by The Cuisenaire Company oi America, !nc, in 198). It is no longer in their catalogue but an internet search may turn up second-hand copies. An alternative is lor you — or, bt-ttcr still, your pupils — to make them. The tint.s need not correspond to those of the original atetates but should be chosen to produce distinct colours when

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fractions1 - The Cuisenaire product Paul Stephenson...

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