Exploring and noticing

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 parallelogram.

The number in the square is the mean of the four numbers surrounding it. Can you find the missing numbers? 

How did the the rotation robot make these patterns?

How many winning lines can you make in a three-dimensional version of noughts and crosses?

If you can copy a network without lifting your pen off the paper and without drawing any line twice, then it is traversable. Decide which of these diagrams are traversable.

Mr McGregor has a magic potting shed. Overnight, the number of plants in it doubles. He'd like to put the same number of plants in each of three gardens, planting one garden each day. Can he do it?

Jo has three numbers which she adds together in pairs. When she does this she has three different totals: 11, 17 and 22 What are the three numbers Jo had to start with?”

In this game the winner is the first to complete a row of three. Are some squares easier to land on than others?

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?

Can you do a little mathematical detective work to figure out which number has been wiped out?