Luke's Fraction Game Years 2 - 6

Summary A game invented by a young child that involves asking others for plugs by using fractions. The board is arranged as an array of gaps and this is the whole which has to be filled. It works well with partners. The game has lots of work on fraction language in context, visualising and naming fractions of a whole, and fractions which add to or subtract from 1. The social interaction in the activity is great too. Try it - extend it - tell us about it. Suitable for threading. Materials One Poly Plug per pair - initially, only the red board

Acknowledgement

Luke, aged around 6, was using Poly Plug in a gifted and talented program when he invented this game. It developed because Sue Davis, the teacher, was discussing fractions with the kids using biscuits sold in trays.

If we eat one biscuit, what fraction of the whole tray has been eaten? What fraction remains?

Luke decided that the red boards could represent trays of biscuits. The other students agreed and the game developed.

Procedure Work with a partner and one Poly Plug set between two. Yellow/blue board is not used. Leave it on table. Push out all the red plugs and store them in your plastic bag. Now everyone has a tray that has fifths and twenty-fifths as its fractions. Everyone walks around with their bag behind one person's back and their board behind the partner's back. When two sets of partners meet one pair gives (and names) a fraction of a tray, eg: Hi, we would like to give you three twenty-fifths of a tray. Then they hand over 3 red plugs.

Content conservation of number fraction calculations fractions as an array fractions as a partition of a whole mathematical conversation visual representation of fractions

The best way to discover the value of an activity is to try it. These Swedish teachers gave it the 'thumbs up' at their workshop.

The plugs given are (secretly) placed in the receivers' board. The receiving partners then make a choice about what they will give, hand over appropriately and both sets of partners move on. A team is finished when they have a complete board and no plugs loose in their bag. You can play the game to find either the first partners to finish, or to make it that as teams finish they stand in a certain place until every team has finished. Everyone started with a full tray of 'biscuits' and no loose ones, so it must be possible to return to that state by sharing. The game might appear a bit chaotic in the beginning - it actually isn't - but it is amazing how it settles down near the end as the number of active partners decreases. See slides of the way the activity was used in Nichola Brandon's Year 4 class in Chapter 2 of the story Fractions in Action.

Extension

• Use one yellow/blue board per team and press out four rows of three. Plugs which remain should be the same colour as their background. In this way the board is 'masked' to make a whole which has 12 parts. Further if we look one way the rows partition the whole into fourths (quarters) and the columns partition the whole into thirds. Contrast plugs with their background when they are put back in and we can ask for 12ths, 4ths or 3rds.

• Use two yellow/blue boards per team and press out four rows of six. (It is possible to hold two boards behind your pack just by gripping either side of where their sides touch.) Plugs which remain should be the same colour as their background. In this way the pair of boards is 'masked' to make a whole which has 24 parts. Further if we look one way the rows partition the whole into fourths (quarters) and the columns partition the whole into sixths. Contrast plugs with their background when they are put back in and we can ask for 24ths, 4ths or 6ths.
  (Some children might even realise that other fractions such as halves, thirds or eighths could be requested - draw the dot diagram and think about it. It's thirds that require a bit of insightful visualisation.)

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