# Tactical

### Task 21 ... Years 2 - 10

#### Summary

A logic game with clear rules and a spatial dimension. The aim is to force your opponent to take the last counter.

#### Materials

• Sixteen counters and a playing board arranged in 4 rows of 4

#### Content

• 2D spatial perception
• logical reasoning, in particular 'if...then' reasoning and working backwards

#### Iceberg

A task is the tip of a learning iceberg. There is always more to a task than is recorded on the card.

• This is a game situation and students are most likely to 'just play it' for a while. To encourage deeper thought you might use techniques such as:
A student once said to me...
The best thing is to get rid of all of a row or column whenever you can. Then there's not so much to look at and you can think better.
What do you think of that approach?
• Ask students if they have any strategies of their own. List them on a chart as they are developed and encourage others to test them out.
• Ask students to explore positions which are one move before the situation where the opponent has to take the last counter. These might be called 'end games'.
Design an arrangement of counters which would force your opponent to lose on his/her next move.
Make displays of these arrangements so that students have something to aim for.
• What happens if the rules change so that the person who takes the last counter is the winner?
• Task 120, Nim, is related to Tactical and students might find it simpler because it operates in only one dimension at a time.

#### Whole Class Investigation

Tasks are an invitation for two students to work like a mathematician. Tasks can also be modified to become whole class investigations which model how a mathematician works.

Use circular margarine lids (or other suitable discs) to play the game on the floor where everyone can see. Perhaps the teacher can challenge one or two students to start things off. Children love to return to this game, so perhaps the large version can remain on the floor for a while as a focus for conversation.

Following the introduction, supply each pair of students with a grid and counters so they can play the game at their tables. If you have Poly Plug it is easy to set up a table top version of the game. Students could be encouraged to try out strategies on the table top version then demonstrate and discuss them around the floorboard version.

At this stage, Tactical does not have a matching lesson on Maths300.

Visit Tactical on Poly Plug & Tasks.

#### Is it in Maths With Attitude?

Maths With Attitude is a set of hands-on learning kits available from Years 3-10 which structure the use of tasks and whole class investigations into a week by week planner.

Tactical is not in any MWA kit. However it can be used to enrich the Space & Logic kit at Years 5/6 and Years 9/10.

Also Task 120, Nim, has similarities and Nim is an integral part of:

• MWA Number & Computation Years 3 & 4

The Nim lesson is an integral part of:

• MWA Space & Logic Years 5 & 6
• MWA Space & Logic Years 7 & 8
This task is also included in the Task Centre Kit for Aboriginal Students.