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Building with Rods

Stage: 2 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

Building with Rods


We have three rods that are each $2$ units long.

The different colours are used to make the diagrams clearer and they always remain in the same place i.e the blue as the bottom layer, the green as the top layer and the red as the middle layer. 

The challenge is to find how many different ways you can stack these rods.

The rule is that a small cube must sit squarely on top of another small cube.

It does not matter if they are likely to topple over.

Both these two arrangements fit the rule.

However, these two arrangements do not fit the rule as the rods have to be lined up squarely and each little cube must sit on top of one other cube and not overlap two cubes. 

How can you convince someone that you have found all the possibilities?

 

Why do this problem?

This activity acts as a further extension to Two on Five. It's an activity that is intended for high-attaining pupils to give them opportunities to explore a spatial context using their intuition and flair.  It also provides an opportunity to create a system for solving such problems.

Possible approach

As this activity is intended to challenge the 'best' problem solvers in the class, it might be presented as on the website or in a one-to-one situation, encouraging discussion between adult and pupil. The pupils may need access to a computer program for drawing solutions.
 

Key questions

Tell me about what you have found.
Can you describe the ways that you arrived at these shape arrangements?
How did you construct these on the computer?

Possible extension

For those who are successful they should be encouraged to try Building with Longer Rods.

Possible support

It will probably be helpful to have interlocking cubes available and different kinds of squared paper.