Year 7 Being resourceful

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

Players take it in turns to choose a dot on the grid. The winner is the first to have four dots that can be joined to form a square.

Here is a chance to play a fractions version of the classic Countdown Game.

Can you decide whether these short statistical statements are always, sometimes or never true?

If you have a large supply of 3kg and 8kg weights, how many of each would you need for the average (mean) of the weights to be 6kg?