This month: Stage 1&2 Stage 2&3 Stage 3&4 Stage 5

28 and It's Upward and Onward

Stage: 2 Challenge Level:

You may like to have a go at the problem So It's $28$ before trying this challenge.

We are about to explore the number $28$.

In $2010$ the month of February will have four weeks of $7$ days making $28$ days altogether.

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Half a pack of cards with the jokers makes $28$ cards altogether:

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The seventh triangular number is also $28$:

But all these examples of $28$ are just flat - or you might call them $2$D.

I'm suggesting we try making something $3$D.

How about if we put some small cubes together and count the faces which are visible. Can we arrange the cubes so that there are exactly $28$ faces?

In the pictures above, we're not counting faces that are 'on the table'. I've coloured the cubes (according to how many faces are showing) to make the counting a little easier.

It would probably be good to make one of these shapes and do your own counting.

Can you arrange some cubes so that $28$ of their faces are visible?

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You might want to try another way with a new shape resting on a glass table (you could just pretend!) so you can count the faces underneath too. Here are two shapes:

Cubes that click together might make it easier.

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So this is your challenge: make a shape that has $28$ little square faces visible.

Now try on a pretend glass table and see how many you can make then. Any surprises?