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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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Happy Numbers

Take any whole number between 1 and 999, add the squares of the digits to get a new number. Make some conjectures about what happens in general.

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Intersecting Circles

Three circles have a maximum of six intersections with each other. What is the maximum number of intersections that a hundred circles could have?

Seven Squares

Stage: 3 Challenge Level: Challenge Level:2 Challenge Level:2

How did Phoebe group the matchsticks that she drew?
How did the others, Alice and Luke, group their matchsticks?


In the follow-up activities draw them out for yourself and notice how YOUR drawings develop. Always begin with simple cases and try to PREDICT what will happen.


Look for patterns.
How can you describe the lines? Horizontal? Vertical?
Try to understand why the patterns develop in the ways that they do.