Year 11 Exploring and noticing

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?

In this twist on the well-known Countdown numbers game, use your knowledge of Powers and Roots to make a target.

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?

Can you find out what is special about the dimensions of rectangles you can make with squares, sticks and units?

Chris is enjoying a swim but needs to get back for lunch. How far along the bank should she land?

There is a particular value of x, and a value of y to go with it, which make all five expressions equal in value, can you find that x, y pair ?

Your school has been left a million pounds in the will of an ex- pupil. What model of investment and spending would you use in order to ensure the best return on the money?

Jo made a cube from some smaller cubes, painted some of the faces of the large cube, and then took it apart again. 45 small cubes had no paint on them at all. How many small cubes did Jo use?

The heptathlon is an athletics competition consisting of 7 events. Can you make sense of the scoring system in order to advise a heptathlete on the best way to reach her target?

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...

If a sum invested gains 10% each year how long before it has doubled its value?