Investigate the family of graphs given by the equation x^3+y^3=3axy for different values of the constant a.
$2\wedge 3\wedge 4$ could be $(2^3)^4$ or $2^{(3^4)}$. Does it make any difference? For both definitions, which is bigger: $r\wedge r\wedge r\wedge r\dots$ where the powers of $r$ go on for ever, or $(r^r)^r$, where $r$ is $\sqrt{2}$?
Investigate how you can work out what day of the week your birthday will be on next year, and the year after...
Arrange the shapes in a line so that you change either colour or shape in the next piece along. Can you find several ways to start with a blue triangle and end with a red circle?
Buzzy Bee was building a honeycomb. She decorated the honeycomb with a pattern using numbers. Can you discover Buzzy's pattern and fill in the empty cells for her?
Explore ways of colouring this set of triangles. Can you make symmetrical patterns?
What is the greatest number of squares you can make by overlapping three squares?
Vincent and Tara are making triangles with the class construction set. They have a pile of strips of different lengths. How many different triangles can they make?
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.
