Mathematics Developmental Continuum P-10

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Students' Solutions to a 'Division' Problem

Amy is at the lowest developmental level. She uses her common sense and real world experience but she does not engage mathematically with the problem.

Amy student work sample

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Ellen has identified only that 3 times 20 is required. The word times in the instruction may have prompted her to multiply.

Ellen student work sample

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Daniel uses repeated addition of 60, until he gets to 300.

Daniel student work sample
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Elisha uses repeated subtraction of 60, until all the medicine is gone.

Elisha student work sample

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Ben knows that multiplication is involved, and uses repeated addition to show that there are 15 doses in 300ml of medicine. Ben may not know division is useful here.

Ben student work sample

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Bob reasons multiplicatively, building up from his known fact that there are five 20ml doses in 100ml to find that there are 15 doses in 300 ml. Bob may not know division is useful here.

Bob student work sample

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Con identifies that division is appropriate, and carries it out efficiently.

Con student work sample

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