These two group activities use mathematical reasoning - one is numerical, one geometric.
An investigation involving adding and subtracting sets of consecutive numbers. Lots to find out, lots to explore.
EWWNP means Exploring Wild and Wonderful Number Patterns Created by Yourself! Investigate what happens if we create number patterns using some simple rules.
This well explained solution comes from Gemma who goes to Foxford School and Community College, Coventry.
Remember: the jugs hold $9$, $7$, $4$ and $2$ litres, and you can't guess any amounts.
9 0 0 0 From the $9$ litre bottle take $4$ litres to $4$ litre bottle. 5 0 4 0 $4$ litres from $4$ litre bottle to $7$ litre bottle. 5 4 0 0 Take $4$ litres from the $9$ litre bottle to the $4$ litre bottle. 1 4 4 0 $3$ litres from the $4$ litre bottle to $7$ litre bottle. 1 7 1 0 $2$ litres from $7$ litre bottle to $2$ litre bottle. 1 5 1 2 $2$ litres from the $2$ litre bottle to $9$ litre bottle. 3 5 1 0 $2$ litres from $7$ litre bottle to $2$ litre bottle. 3 3 1 2 $2$ litres from $2$ litre bottle into $4$ litre bottle. 3 3 3 0
9 0 0 0
5 0 4 0
5 4 0 0
1 4 4 0
1 7 1 0
1 5 1 2
3 5 1 0
3 3 1 2
3 3 3 0
Syed also from Foxford School and Community College, Coventry has found a different solution, and presented it in a table.
Here's a third solution from Thomas at Tattingstone Primary, UK.
9 0 0 0 2 7 0 0 2 5 0 2 4 5 0 0 4 3 0 2 6 3 0 0 6 1 0 2 8 1 0 0 8 0 1 0 1 7 1 0 1 5 1 2 3 5 1 0 3 3 1 2 3 3 3 0