Exploring and noticing

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?

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?

Can you find and prove the relationship between the area of a trapezium and the area of a triangle constructed within it?

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 rhombus.

The items in the shopping basket add and multiply to give the same amount. What could their prices be?

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?

Choose four consecutive whole numbers. Multiply the first and last numbers together. Multiply the middle pair together. What do you notice?

How have "Warmsnug" arrived at the prices shown on their windows? Which window has been given an incorrect price?