Year 11 Conjecturing and generalising

What happens to the area and volume of 2D and 3D shapes when you enlarge them?

In 15 years' time my age will be the square of my age 15 years ago. Can you work out my age, and when I had other special birthdays?

Is there a relationship between the coordinates of the endpoints of a line and the number of grid squares it crosses?

Here are two games you can play. Which offers the better chance of winning?

Charlie likes to go for walks around a square park, while Alison likes to cut across diagonally. Can you find relationships between the vectors they walk along?

Two ladders are propped up against facing walls. At what height do the ladders cross?

An equilateral triangle rotates around regular polygons and produces an outline like a flower. What are the perimeters of the different flowers?

If everyone in your class picked a number from 1 to 225, do you think any two people would pick the same number?

Which is bigger, n+10 or 2n+3? Can you find a good method of answering similar questions?

Can you find the values at the vertices when you know the values on the edges of these multiplication arithmagons?

In this follow-up to the problem Odds and Evens, we invite you to analyse a probability situation in order to find the general solution for a fair game.

What is special about the difference between squares of numbers adjacent to multiples of three?

There are unexpected discoveries to be made about square numbers...