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Division as sharing and measuring

A division equation can refer to two different actions.

For example, 21 ÷ 7 = 3 can determine the result of 21 objects shared equally among 7 parties. This is called partitive division.

21 ÷ 7 = 3 may also be used to find how many measures of 7 objects can be made from a set of 21 objects. This is called quotitive division.

Watch the Different Divisions video.


You can download the Different Divisions video transcript.


In the early stages of multiplicative thinking, students generally share objects equally in ones, or build up collected counts in measurement problems. More advanced strategies allow students to anticipate the result of sharing without actually doing it.

Students must recognise that giving one object to each party creates a measure in sharing situations where they find it difficult to anticipate the result.

For example: Kylie has 32 lollies to share equally among her 4 friends. Each time Kylie gives 1 lolly to each friend, she uses 4 lollies. So the division problem can be solved as: How many fours are in 32?