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Teaching Mathematics: Foundations to Middle Years

Teaching Mathematics

Written by a group of highly respected and experienced teacher educators, the advice is based on current research and theories and, although written for pre-service teachers, there is much that will appeal to practising teachers.

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Dividing pancakes

Students solve problems about sharing pancakes equally among people. The numbers are selected to match the appropriate fractions for the year level.

'Share three pancakes among four people' is a year 3 example that requires working with quarters.

'Share nine pancakes among 12 people' is a year 6 example that could involve a variety of fractions, including twelfths.

Students use modelling dough to represent pancakes which they cut with plastic knives into (estimated) equal parts.

Three circular 'pancakes' made of modelling dough, each divided into four equal parts.

'Pancakes' divided into quarters.

They record the process through sharing diagrams.

Two circles divided into halves and one circle into quarters surrounded by four stick figures. A colour code shows that each will receive one half and one quarter.

A student’s sharing diagram.

The solution strategies should be displayed and discussed, focussing attention on the equivalence of various forms on the answer. Year 3 students should recognise that \(\frac{1}{2}\) and \(\frac{1}{4}\) together are the same as \(\frac{3}{4}\).

Year 5 and 6 students should be able to find several different solution strategies and gradually recognise the relationship between the division task and the resulting fraction.
For example, 9 ÷ 12 = \(\frac{9}{12}\) which is \(\frac{3}{4}\).

At this point, the physical modelling of the problem should become unnecessary.

More sharing diagrams

Students can physically model problems that require them to cut the items into fractional parts to carry out the sharing process in a variety of ways.