You may also like

problem icon

Consecutive Numbers

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

problem icon

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.

problem icon

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: Challenge Level:1

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

the 28
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.
----------
Half a pack of cards with the jokers makes $28$ cards altogether:
cards
----------
The seventh triangular number is also $28$:

tri sq
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?
ex cubes
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.
key
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?
----------
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:
2 on glass
Cubes that click together might make it easier.
----------
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.

The NRICH Project aims to enrich the mathematical experiences of all learners. To support this aim, members of the NRICH team work in a wide range of capacities, including providing professional development for teachers wishing to embed rich mathematical tasks into everyday classroom practice. More information on many of our other activities can be found here.
Copyright © 1997 - 2017. University of Cambridge. All rights reserved.
NRICH is part of the family of activities in the Millennium Mathematics Project.