Fraction patterns

Purpose

The purpose of this multi-level task is to engage students in an investigation that requires them to explore the process of adding fractions and taking reciprocals in order to find a pattern.

Description of Mathematics

This background knowledge presumed for this task is outlined in the diagram below:

The task can be presented with graded expectations to provide appropriate challenge for individual learning needs.

Activity

Task: Investigate the sequence below to find a pattern in the fractions represented by each term.

The arithmetic approach (show more)

  • The student is able to calculate the value of terms and give these as a simplified fraction. The student can find a pattern and use this to predict the next term.

The procedural algebraic approach (show more)

  • The student understands operations on fractions to write each term as a simplified fraction. The student can find a pattern and use this to predict the next term.

The conceptual algebraic approach (show more)

  • The student is able to generalise operations on fractions to write a general term for the sequence.

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