### Consecutive Numbers

An investigation involving adding and subtracting sets of consecutive numbers. Lots to find out, lots to explore.

### Tea Cups

Place the 16 different combinations of cup/saucer in this 4 by 4 arrangement so that no row or column contains more than one cup or saucer of the same colour.

### Exploring Wild & Wonderful Number Patterns

EWWNP means Exploring Wild and Wonderful Number Patterns Created by Yourself! Investigate what happens if we create number patterns using some simple rules.

# 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?
You may like to take photos of them.
Please send in any thoughts, ideas or pictures relating to your explorations.