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?
The nth term of a sequence is given by the formula n^3 + 11n . Find
the first four terms of the sequence given by this formula and the
first term of the sequence which is bigger than one million. Prove
that all terms of the sequence are divisible by 6.
Consider numbers of the form un = 1! + 2! + 3! +...+n!. How many such numbers are perfect squares?
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.