Download Game Boards

You will see that we have given three versions of the game and a blank for you to innovate on in any way that you see fit. The first version uses dots in typical dice arrays and is meant for the younger students. The version with whole numbers is a degree or two more difficult and the one with fractions  much more challenging. Finally there is a blank form for you to create variations that match your range of learners. The point here is that a simple game can be adapted to allow for multiple entry points. A whole class could play different variants of it but participate equally well in a reflection on possible strategies at its conclusion.

Preparation: Game boards can be laminated so that students can mark them with coloured pens or cover the spaces with coloured see-through counters.

Rules

Competitive Form: Before playing the total aimed for is decided. This could include the highest or the lowest total or the one nearest to a specified reasonable total.
The first player decides where on the board to begin.
From then on counters can be placed on any square next to an already occupied one until the board is covered. The player who meets the identified goal is the winner for that round.
Note: Players need to plan ahead to be able to win this game. This involves keeping totals and comparing the effects of different moves. It is interesting to leave it to the students themselves to decide how they will handle finding the total. Some will keep a running tally, some will simply add all the scores at the end and others will compute mentally as they go along. At the end of the game it is important to reflect on the strategies used as well as on the methods for computing. The idea in the competitive form is to learn how to win as well as how to keep score.

Cooperative Form: In this version of the game both players win if they end with the same score or both lose if they do not. The point here is to work together and to plan to help each other to achieve that goal. This game is equally challenging and requires the same level of adaptive reasoning as the earlier form.

Inclusive Form: This version of the game is designed to enable all students to play. A child who can only subitize one or two dots or the numbers 1 and 2 for instance plays to cover as many of those two numbers or arrays as possible in their round. The other player needs to plan to make that happen as often as possible. What this means is that both players are engaged at a level that allows some challenge for them.

Reflection

Engage the students in a reflection of the strategies used in planning moves as well as in methods of scoring. For some students the planning ahead and predicting moves will be an obvious part of paly, for others though some scaffolding will be needed before they begin to plan effectively. This is all part of mathematical thinking and the focus is on adaptive reasoning.