Human Moves Monster

Task 124 ... Years 2 - 8

Summary

Using the equivalent of a knight move in chess students are asked to capture all the monsters in the least number of moves. There are two levels of challenge and more than one solution is possible. The task can be difficult and perhaps that makes it all the more satisfying when solved. It is essential that students find a way of recording their trials so that they don't waste time exploring sequences that have already been unsuccessful.

Materials

playing board and nine 'monsters'

Content

spatial awareness including symmetry
problem solving skills

Iceberg

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

Students are most likely to use a Trial, Record & Improve strategy with this task. However, the more they explore it the more likely it is that they might see some 'symmetries' in the board and monster placement. These imply that starting in one place and following a movement pattern would be the same result as starting in an equivalent place and following the same pattern. Finding these and keeping good records cuts down the effort involved in solutions.

One solution for the 'black dots' part of the task is 10 moves:

Begin on P
P --> M (capture
M--> T (no capture)
T --> I (capture)
I --> L (capture)
L --> S (capture)
S --> H (capture)
H --> Q (capture)
Q --> N (capture)
N --> G (capture)
G --> R (capture)

One solution for the 'white triangles' part of the task is 11 moves:

Begin on I
I --> L (capture)
L --> S (capture)
S --> H (capture)
H --> Q (capture)
Q --> N (capture)
N --> G (capture)
G --> R (capture)
R --> I (no capture)
I --> T (capture)
T --> I (no capture)
I --> B (capture)

The task card starts with one arrangement of nine monsters and then offers another problem by changing the starting arrangement of the monsters. The implied mathematician's question is:

What happens if ... we change the starting arrangement of the monsters?

Perhaps students can find a new challenge by changing the arrangement again. Or by asking:

What happens if ... we change the number of monsters?
What happens if ... we change the capture rule?

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.

This challenge works well as a whole class lesson if you take your 'little monsters' outside (or to the multi-purpose room) to start the lesson. If you have a Maths Mat, you can fold it to make the 5x5 grid. If not, then you will need to mark out the grid in advance with chalk or tape. It won't be hard to find nine volunteer monsters. Ask them to sit in the appropriate cells of the grid. Make teams of four out of the remaining class members, explain how the human moves and challenge teams to find a way to capture all the monsters. Teams take it in turns to demonstrate their attempts.

Given that these are not easy problems, the monsters will get bored if they sit and wait too long. Therefore have some cards marked Monster 1 - 9 to use as place markers and let the monsters become temporary members of the teams. When it is time for a demonstration, the monsters can soon be recalled for capture.

Learning from physical involvement such as this is reinforced and enhanced if the students build a table top version of the problem when they return to the classroom. Then they solve it personally and make a record. Poly Plug is a great tool for this part of Human Moves Monster. Remove the plugs from the red board to make the 5 x 5 grid. Place blue plugs in the monster positions and use one yellow plug as the human. The iceberg above suggests several directions you can take the lesson, but the overall reason for using it is to model the Working Mathematically Process - learning to work like a mathematician.

At this stage, Human Moves Monster does not have a matching lesson on Maths300.

You can learn more about using Poly Plug for this task in Human Moves Monster in Menu Maths Pack B. If you like the idea of using Poly Plug for strategy games, then you could also investigate Poly Plug Game Pack

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.
The Human Moves Monster task is an integral part of:

MWA Space & Logic Years 7 & 8

Follow this link to Task Centre Home page.