Equivalent Fractions

This activity sheet is written to support the Australian Curriculum V7.5 F – 10 Curriculum, Mathematics / Year 7 / Number and Algebra / Real Numbers / ACMNA152. The content descriptor for ACMNA152 states:
“Compare fractions using equivalence.”
The activity sheet requires students to practise the mathematical skill of identifying and comparing equivalent fractions. It starts with a pedagogical model (diagram) of a circle divided into sectors and shows how different fractions can be represented by the shading of these sectors. The students work through several questions where they write or shade the equivalent fractions given either the diagram or the fraction. It then moves onto numeric techniques where the numerator or the denominator of the equivalent fractions are written solely from the given fraction.

The final question of the sheet (question 7) is designed as an extension activity leading into a class discussion. It attempts to further develop the ideas that equivalent fractions can have many different values, fractions can be simplified (this would be developed further at a later time) and that equivalent fractions can be written in patterns, which is an important foundation concept for algebra.

This activity sheet is aimed at year 7 students of high ability, although students of lower ability should have success with most of the questions but may find some questions challenging and not get a lot out of the final question.