Exploring and noticing
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Discuss and choose
This activity challenges you to decide on the 'best' number to use in each statement. You may need to do some estimating, some calculating and some research.
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Pebbles
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?
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Round and round the circle
What happens if you join every second point on this circle? How about every third point? Try with different steps and see if you can predict what will happen.
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Differences
Can you guarantee that, for any three numbers you choose, the product of their differences will always be an even number?
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Prison cells
There are 78 prisoners in a square cell block of twelve cells. The
clever prison warder arranged them so there were 25 along each wall
of the prison block. How did he do it?
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Numerically equal
Can you draw a square in which the perimeter is numerically equal to the area?
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Shopping basket
The items in the shopping basket add and multiply to give the same amount. What could their prices be?
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Pick's theorem
Polygons drawn on square dotty paper have dots on their perimeter (p) and often internal (i) ones as well. Find a relationship between p, i and the area of the polygons.
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Special numbers
My two digit number is special because adding the sum of its digits to the product of its digits gives me my original number. What could my number be?