Exploring and noticing

A game for two people, or play online. Given a target number, say 23, and a range of numbers to choose from, say 1-4, players take it in turns to add to the running total to hit their target.

How many moves does it take to swap over some red and blue frogs? Do you have a method?

Think of two whole numbers under 10, and follow the steps. I can work out both your numbers very quickly. How?

How many balls of modelling clay and how many straws does it take to make these skeleton shapes?

Can you make a cycle of pairs that add to make a square number using all the numbers in the box below, once and once only?

Can you make square numbers by adding two prime numbers together?

Here are the six faces of a cube - in no particular order. Here are three views of the cube. Can you deduce where the faces are in relation to each other and record them on the net of this cube?

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

Can you work out the arrangement of the digits in the square so that the given products are correct? The numbers 1 - 9 may be used once and once only.