Linear model to teach fractions

Let us begin with an example: Find 1/2 of a set or shape

It can be helpful to begin with the linear model as the options for halving are more limited, therefore easier to do. The following steps can be used as a guideline to proceed.

Teacher distributes a range of concrete materials which are suitable for the linear model, for
example, fraction bars, Cuisenaire rods, string/paper clips, folded paper strips. Pupils are asked to
work with the material of their choice.

Pupils are invited to show what a half looks like, for example:

Time is allowed for sharing the various ideas/representations including the inaccurate ones in order to generate discussion.

Pupils are now invited to suggest ways of recording the representations in 2D form. Depending on the material used the pupils might:

Draw/ Trace around the fraction bars/rods

Draw an empty line segment and indicate half way mark using an interval line

Take a photograph of the 2D representation

Paste a folded paper strip into their journal

Displays of concrete and pictorial representations will be useful reference points for pupils, in addition to being a record of pupils’ work.

Using these representations, this is an opportune time for the teacher to introduce formal symbolism. Teacher should add formal symbol of a half to the displays.

All icons are taken from

Close Bitnami banner