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Math with Manipulatives
Open-ended investigation has allowed my children to make a number of observations for themselves over the years. For example they learnt (and showed their siblings) that 1 litre of water has a mass of 1kg, so water can be used in a balance to establish the mass of other items, and discovered the commutative property of multiplication by playing with Cuisenaire rods.
A box or shelf of maths manipulatives is a good investment. Many simple, cheap items such as measuring jugs, playing cards, counters and a selection of dice can be used in so many different ways, and by all ages. Other items are more expensive, but are worthwhile for their long life. A decent balance, Cuisenaire rods and fraction blocks have been used by every child in our family well into high school. Other items not pictured that we have owned or borrowed include a metre stick, a maths number balance, trundle wheel, a geared clock, an abacus, a tangram set, and 2D wooden geometric shapes.
One item can be used in many ways, for example fraction blocks can be used as weights, and platonic solids can be measured.
Many of the items we own have been used in ways that were not expected by us or intended by the manufacturer, which is part of the appeal. Play- based learning is all about exploration.
Many of these items have also been useful for activities I’ve chosen to do with the children or to provide a concrete way to understand maths questions. We have used them to explain concepts, depict simple algebraic equations, measure our garden to create a site map, and understand the link between fractions, decimals and percentages.
But often it’s after an item has been used for its intended purpose, that another child comes along, starts to build or fiddle and makes, what for them, is a significant cognitive leap.
Otherways 173 (Aug 2022)