Dice Tables

Years 2 - 6

Summary

Easy to state and easy to start, this tactile, visual strategy game includes times tables practice and aspects of probability. One of the main features of the game is choice:
  • choice of the numbers on the playing grid
  • choice of which dice rolls to use
  • choice of where to place a plug
These choices offer the children ownership of the game (hence its mathematics) and are also characteristics that make it suitable for threading.

The game does not have to be played with plugs in a red board, but we know children like the feel of 'plugging in' and the frame does mean that if there is a 'bumping accident' the previous position is easily recovered.

Materials

  • One Poly Plug per pair
    - the red board is shared and players have 12 plugs each in different colours
  • 3 dice per pair
  • 1 Poly Plug Frame per pair

Acknowledgement

This activity was developed with permission from an idea presented by Sandra Knox, Consultant, at Maths for Learning Inclusion, 2009.

Procedure

The aim is to make 4 in a row, column, diagonal or 2x2 square in your colour.
  • Children take turns to select and write numbers in the circles on the playing board. The numbers must be answers to multiplying two dice numbers together, ie: products of two numbers that can be rolled with a dice. Some numbers will have to be repeated, but which ones?
  • The person who writes in the last circle goes second in the next part of the game.
  • Players take turns to roll three dice. They choose any two to make their product, then plug their chosen circle.
  • The game ends if one person makes a four, or if both players use their 12 plugs without making a four.
  

Content

  • likely, less likely and unlikely events
  • mathematical conversation
  • multiplication
  • square numbers
  • times tables
As the children play, underlying questions become more apparent:
  • What are the possible products?
  • Does each possible product have the same chance of coming up?
  • Which number will I repeat and where will I put it?
  • Where will I place my plug to give me the best chance of making 4?
  • Can I place my plug to be good for me and also make it difficult for my opponent?
  • Are some circles more 'powerful' than others?
When appropriate it will be useful to have a class discussion about some of these. For example, if the two dice involved are different colours, say green and black, the 1 on the green dice can be matched with any of the numbers 1 to 6 on the black dice. Similarly for each other green dice number. That means there are 36 possible multiplications, but do they all give different products? The answer is fairly obviously no. The product 4, for example, could be made with a green 1 and black 4, or a green 4 and black 1, or 2 on both dice.

From the Classroom

Josephine Krippner, Year 5/6
St. Michael's Primary School, Kaleen

As part of the six day professional development program, Working Like A Mathematician, organised by the Catholic Education Office, Canberra Goulburn, Jo threaded Dice Tables with her class. She began with two dice and making lines of 4 to win. This PowerPoint shows her class at work and the Investigation Guides she created to extend their thinking.

Children will eventually realise that the 18 possible products have the following chances of occuring: 

Possible Products: 1  2  3  4  5  6  8  9  10  12  15  16  18  20  24  25  30  36

Chance out of 36:  1  2  2  3  2  4  2  1   2   4   2   1   2   2   2   1   2   1
and this knowledge should influence which number(s) they repeat and where to put them.

Variations

  • Play the game using 4 in a row, column, diagonal or the 4 corners only.
  • Play the game on separate boards for each player and stop when one makes a four. This removes the aspect of blocking an opponent, but encourages a broader range of decisions for each player based on probability.
  • Play the game on separate boards using 13 plugs each and when finished score:
    • 5 points for each 5 in a row
    • 4 points for each 4 in a row
    • 3 points for each 4 in a row
    The person with the higher total wins.
  • Go back to the original game and use three 0-9 dice. Now there are more possible products than circles.
    • Which ones will you leave out? Why?
    • Where will you put the ones you use?
  • Many schools have sets of polyhedral dice, that is, regular solid objects other than cubes (6 faces) and icosahedron (10 faces). These open up other What happens if... possiblities for the products. For example the two (or three) dice used don't have to be the same type.
  • If the probability was generated by packs of digit cards from 1-10 instead of dice, every times table product would be possible. Discuss and decide the rules for a modification of the game using this form of random product generator. Investigate the new game.

Extensions

Aspects of this activity can be extended through several Maths300 lessons:
  • Have A Hexagon, Lesson 6, which applies the mathematics of the dice products in a different game situation. If you don't have Maths300 access, explore the Have A Hexagon Task Cameo.
  • Multo, Lesson 52, which practises times tables up to 9 in 4 x 4 grid and explores the question of which numbers to place where.
  • Row Points, Lesson 78, which uses 13 counters on a 5 x 5 grid and the scoring system above to open the door to many investigations. If you don't have Maths300 access, explore the Row Points Task Cameo.


Return to Calculating Changes Activities

Calculating Changes ... is a division of ... Mathematics Centre