The purpose of this activity is to engage students in finding many ways to form one (whole) with fractional units. In doing so they will use simple equivalence and learn to recognise non-unit fractions as iteration of unit fractions.
This activity assumes the students have experience in the following areas:
The problem is sufficiently open ended to allow the students freedom of choice in their approach. It may be scaffolded with guidance that leads to a solution, and/or the students might be given the opportunity to solve the problem independently.
The example responses at the end of the resource give an indication of the kind of response to expect from students who approach the problem in particular ways.
Here are three ways to make one (whole) with halves, thirds, quarters and sixths of a circle.
How might these ways to make one be recorded as equations or expressions?
What other ways to make one can you find just using halves, thirds, quarters and sixths?
Can you prove you have found all the possible ways?
The following prompts illustrate how this activity can be structured around the phases of the Mathematics Investigation Cycle.
Introduce the problem. Allow students time to read it and discuss in pairs or small groups.
Discuss ideas about how to solve the problem. Emphasise that, in the planning phase, you want students to say how they would solve the problem, not to actually solve it.
Allow students time to work through their strategy and find a solution to the problem.
Allow students time to check their answers and then either have them pair share with other groups or ask for volunteers to share their solution with the class.
The student uses trial and error approaches to find other ways to make one.
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An improvement is to name iterations of unit fractions as non-unit fractions, like this:
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The student uses a systematic strategy to find all the possible ways to make one and uses expressions or equations to record the ways.
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Some students may consider order relevant in establishing unique names for one. That assumption will increase the number of possible ways they find.
Printed from https://meaningfulmaths.nt.edu.au/mmws/nz/resource/fraction-circles-1 at 8:51pm on the 26th February 2024