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Sharing as division

Sharing as division

The meaning of fractions as division becomes apparent in practical tasks where the number of items to be shared is less than the number of groups that must be made.

Students model problems that require them to cut the items into fractional parts to carry out the sharing process.

For example, share two loaves equally between three people. Each person receives two-thirds of a loaf: 2 ÷ 3 = \(\frac{2}{3}\).

Sharing problems build the foundation for understanding fractions as an expression of division, as in \(\frac{2}{3}\) = 2 ÷ 3.

Sharing problems also provide the important opportunity for students to experience the process of re-unitising. Re-unitising occurs when the size of the fraction being used is changed to suit the needs of the problem.

For example, in the problem of three loaves shared equally between four people, the first step could be to halve the loaves. This gives each person one half of a loaf and uses two of the loaves.

The third loaf can then be cut into four equal parts and the sharing continued. So each person gets one half and one quarter, making three quarters of a loaf each. Watch the video The Sharing Process.

 

You can download The Sharing Process video transcript.

 

Sharing diagrams such as the one illustrated above should feature in student recording of their solution strategies.

Yes

Yes

Name Class Section
Document Dividing pancakes Folder 17
Document Year 3: Model and represent unit fractions including 1/2, 1/4, 1/3, 1/5 and their multiples to a complete whole Infobox 3
Document Year 6: Find a simple fraction of a quantity where the result is a whole number, with and without digital technologies Infobox 3
Document Source Infobox 3