**Introduction**

The Singapore
mathematics syllabuses are very well designed, especially the primary school
syllabus. Fundamental concepts and
skills are introduced before going on to complex calculations and problem
solving. At primary 1, pupils learn the
idea of multiplication and division of small numbers by grouping (or partitioning). They are not made to recite the times tables
meaninglessly.

Division is easy if the number of things in each group is known. You just keep on circling the known number of
objects until everything is circled.
However, if the number of groups is required but the number of things in
each group is not given, and if the objects are not arranged in a convenient
way, the task can be a bit more challenging.
Remember: they have not memorised the multiplication tables yet.

**Problem / Question**

**Solution (Suggested)**

One way to solve this problem is to label the fish 1, 2, 3, 1, 2, 3, ...
in a cyclic fashion, assigning fish to each of the three friends one at a time,
thereby ensuring that each person gets the same number of fish. Start with “1” somewhere on the left, “3” on
the right and “2” somewhere in the middle.
Assign the next “1” close to the previous “1”, the next “2” close to the
previous “2” and the next “3” close to the previous “3”. So all the 1s are close together, the 2s are close
together and the 3s are close together.
After all the fish have been labelled, the partitioning (or grouping)
becomes obvious.

H02. Use a
diagram / model

H04. Look for
pattern(s)

H09. Restate
the problem in another way

**Suitable Levels**

*****Primary School / Elementary School Mathematics

* any precocious or independent learner who is
interested