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Halving a rectangle

The part-whole concept is one of the big ideas in fractions. The part-whole construct is often represented with an area model, such as a shape partitioned into equal parts.

Below is an example of a year 5 student's reasoning about the number of ways any rectangle can be divided in half.

The student started with one example, but started to think deductively when she realised that the relevant angles would be equal 'wherever the cuts were made'.

The student will be able to use more formal deductive reasoning and prove her hypothesis in secondary school after she has learnt the rules applying to parallel lines and pairs of angles.

Rectangles with central points marked and straight lines drawn through the centres to divide them into halves, with corresponding sides and alternate interior angles marked as being equal.

Halving a rectangle.

Curriculum links

Year 1: Recognise and describe one-half as one of two equal parts of a whole

Year 2: Recognise and interpret common uses of halves, quarters and eighths of shapes and collections

Year 5: Describe translations, reflections and rotations of two-dimensional shapes. Identify line and rotational symmetries

Year 6: Investigate combinations of translations, reflections and rotations, with and without the use of digital technologies