You may also like

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 - Upward and Onward

Age 7 to 11
Challenge Level


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 had 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 2D.

 

I'm suggesting we try making something 3D.

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.
Copyright © 1997 - 2021. University of Cambridge. All rights reserved.
NRICH is part of the family of activities in the Millennium Mathematics Project.