Explaining, convincing and proving

Imagine we have four bags containing numbers from a sequence. What numbers can we make now?

Use properties of numbers to work out whether you can satisfy all these statements at the same time.

Can you guarantee that, for any three numbers you choose, the product of their differences will always be an even number?

Can you find a cuboid that has a surface area of exactly 100 square units. Is there more than one? Can you find them all?

Start with two numbers and generate a sequence where the next number is the mean of the last two numbers...

Do you notice anything about the solutions when you add and/or subtract consecutive negative numbers?

The Egyptians expressed all fractions as the sum of different unit fractions. The Greedy Algorithm might provide us with an efficient way of doing this.

Interior angles can help us to work out which polygons will tessellate. Can we use similar ideas to predict which polygons combine to create semi-regular solids?

Can you find the values at the vertices when you know the values on the edges?

Semi-regular tessellations combine two or more different regular polygons to fill the plane. Can you find all the semi-regular tessellations?