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Katie had a pack of twenty cards numbered from $1$ to $20$.
She arranged the cards into six piles.
The numbers on the cards in each pile added to the same total.
What was the total and how could this be done? Are you curious enough to find out?
This problem is one that can be accessed easily - everyone can make a start - and at the same time it is a great context in which to encourage children to persevere. Finding a full solution requires 'sticking power'! It offers opportunities for learners to practise addition and subtraction, along with some multiplication and division, and requires a systematic approach.
You could start by asking the group to work on the problem in pairs with digit cards numbered from 1 to 20 without saying very much else at this stage. Learners might find it useful to make jottings on mini-whiteboards or paper as they explore the problem.
Learners could find as many completely different solutions to this problem as possible and some children will be able to suggest a way to find them all.
If you want to focus on finding all possibilities, some learners might benefit from using a calculator so they are not held up by the mental arithmetic.
Place four pebbles on the sand in the form of a square. Keep adding as few pebbles as necessary to double the area. How many extra pebbles are added each time?
Investigate the different shaped bracelets you could make from 18 different spherical beads. How do they compare if you use 24 beads?
How many different shaped boxes can you design for 36 sweets in one layer? Can you arrange the sweets so that no sweets of the same colour are next to each other in any direction?