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'28 and It's Upward and Onward' printed from http://nrich.maths.org/
Why do this problem?
You may have tried Month Mania
in the past and this activity
takes the action further. This challenge is a great open-ended investigation which has many opportunties for children to explore their own ideas at length. It requires visualisation
and a systematic approach.
You could introduce this activity by sharing the examples of $28$ in the problem and asking if any of them know something special about the number $28$.
Show the group an arrangement of cubes resting on a surface and explain that $28$ small faces are visible. Check that everyone is happy that we're not counting the faces that are resting on the surface. Encourage learners to work in pairs to find other arrangements which have $28$ faces. Depending on your supplies of cubes, you can suggest children keep each arrangement once it is made, or
that they record it in some way. (Isometric paper may be useful.)
Once everyone has found some examples, draw the group together for a few minutes and ask them how they are checking each of their arrangements is different. How can they try to find all the ways? Encourage them to share some different systems, for example sticking with the same number of cubes and looking for ways of changing their arrangement. Other children may find ways to add successive
cubes but keeping the number of visible faces the same.
You may like to keep this challenge as an ongoing 'simmering' activity which children add to over a period of a number of days/weeks.
Tell me about this.
Have you anything to say about this shape that you have made?
How could you change your shape and still have $28$ faces showing?
Children could explore other notable things about $28$, for example it's a hexagonal number
. $28$ is the sum of the first five consecutive primes: $2, 3, 5, 7, 11$. You might like to introduce them to perfect numbers
Plenty of cubes will be needed for this activity. If children are struggling to record their arrangements, digital photographs may be the answer.