Start Cube Drilling

Imagine a 3 by 3 by 3 cube. If you and a friend drill holes in some of the small cubes in the ways described, how many will have holes drilled through them?
Exploring and noticing Working systematically Conjecturing and generalising Visualising and representing Reasoning, convincing and proving
Being curious Being resourceful Being resilient Being collaborative

Problem



This activity is all about imagining, like you might when you listen to a story or poem.


There is no need to write or draw anything


BUT talking about it could be good!


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Start Cube Drilling


Imagine a 3 by 3 by 3 cube hanging in front of you with just the front face facing you.

The cube is made up of 3 x 3 x 3, that is 27, small cubes.

You drill a hole through the four corner cubes, that are facing you, all the way through to the back.

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Start Cube Drilling


A friend looks down on the cube, from above, and they also drill four holes through their four corner cubes all the way through to the bottom.

You and your friend examine all the 27 small cubes.

QUESTION
How many small cubes will then have holes drilled in them?


If you'd like more of a challenge, try Cube Drilling .