problem
Russian cubes
I want some cubes painted with three blue faces and three red faces. How many different cubes can be painted like that?
When you throw two regular, six-faced dice you have more chance of getting one particular result than any other. What result would that be? Why is this?
Triangle ABC has equilateral triangles drawn on its edges. Points P, Q and R are the centres of the equilateral triangles. What can you prove about the triangle PQR?
Can you describe this route to infinity? Where will the arrows take you next?
Can you compare these bars with each other and express their lengths as fractions of the black bar?
Can you use addition and subtraction to answer these questions about real-life distances?