Visualising and representing

In this interactivity each fruit has a hidden value. Can you deduce what each one is worth?

We usually use squares to measure area, but what if we use triangles instead?

Investigate how you can work out what day of the week your birthday will be on next year, and the year after...

Identical squares of side one unit contain some circles shaded blue. In which of the four examples is the shaded area greatest?

How many moves does it take to swap over some red and blue frogs? Do you have a method?

In how many ways can you fit all three pieces together to make shapes with line symmetry?

How many different symmetrical shapes can you make by shading triangles or squares?

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?

What do you notice about the sum of two identical triangular numbers?

Square numbers can be represented as the sum of consecutive odd numbers. What is the sum of 1 + 3 + ..... + 149 + 151 + 153?