Fractions, Plugs & a Calculator

Years 3 - 6

Summary

Students explore a straight forward fraction such as one half but do so with various wholes. The focus of the activity expands to realise that all whole rectangular arrays can be partitioned into fractions by the rows, the columns and the separate cells (plugs in this case). The activity continues to make links between fraction and decimal representation of these partitions. Suitable for threading.

Materials

  • One Poly Plug per pair (at least)
  • Straws
  • One calculator per pair (at least)
The straws partition the whole array into quarters (fourths).

Special Note

Whenever using Poly Plug avoid using the terms 'hole or holes' to refer to the gaps or spaces created in a board by removing plugs. This will avoid any language confusion with the word 'whole' when using the boards to explore fractions.

Procedure

This activity is written as a whole class lesson, but can be easily adapted to groups.
Remove plugs from your red board to make a equal rows of spaces. It doesn't matter what size, but the rows should be side by side. Fill the gaps with yellow plugs.

Now change half of the plugs to blue.

How do you know this is half?

I always ask this question when anything about fractions comes up because I want to keep focusing attention on:

  • identifying the whole
  • checking that is divided into parts
  • checking that the parts are equal in some way.
  

Content

Listed alphabetically.
Primary content in bold.
  • decimal representation of a fraction
  • division
  • fractions as an array
  • fractions as a partition of a whole
  • visual representation of fractions
Another device I use in this context to generate discussion is:
Hang on here. I said half ... but your half has more plugs than her half. How come?

True, the kids think I am nuts sometimes, but it makes them tell me the three conditions (above) to look for which are the basis of using fraction language.

Then we get into a discussion of how we write 'one half' (in words first like this) and what the symbols mean. When they are happy with that (and even in Grade 2 there are kids who are happy with that), I ask:

But how does the calculator show one half?

Why does it show it as 0·5?

We have a thorough discussion of the buttons to press on a calculator to show ONE WHOLE rectangle DIVIDED into TWO. Then I ask groups to:

  • choose an array to make one quarter, one tenth, one fifth and one eighth
  • predict and check the calculator's way of writing one quarter, one tenth, one fifth and one eighth
Later the groups go off exploring their own fractions. After a day or so they have to make me a poster showing:

  • some of the fractions they explored with the Poly Plug
  • the calculator and 'normal' ways of writing these
  • an explanation of why the calculator writes them as it does.
I suppose it is a bit back to front from the old way, but this is one of the main components in my introduction to decimals program.
My whole is made of twelfths
and the rows tell me three quarters of it is blue.

It soon becomes a natural step to look at more 'untidy' decimals such as one third. This can lead to quite a discussion.

See slides of the way the activity was used in Nichola Brandon's Year 4 class in Chapter 4 of the story Fractions in Action.


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