How many different triangles can you draw on the dotty grid which each have one dot in the middle?

The computer has made a rectangle and will tell you the number of spots it uses in total. Can you find out where the rectangle is?

My coat has three buttons. How many ways can you find to do up all the buttons?

Place the numbers 1 to 6 in the circles so that each number is the difference between the two numbers just below it.

Three children are going to buy some plants for their birthdays. They will plant them within circular paths. How could they do this?

Use the lines on this figure to show how the square can be divided into 2 halves, 3 thirds, 6 sixths and 9 ninths.

These eleven shapes each stand for a different number. Can you use the multiplication sums to work out what they are?

How can you arrange the 5 cubes so that you need the smallest number of Brush Loads of paint to cover them? Try with other numbers of cubes as well.

Find out what a Deca Tree is and then work out how many leaves there will be after the woodcutter has cut off a trunk, a branch, a twig and a leaf.

Each of the nets of nine solid shapes has been cut into two pieces. Can you see which pieces go together?

Can you draw a square in which the perimeter is numerically equal to the area?

How many different triangles can you make on a circular pegboard that has nine pegs?

Can you go through this maze so that the numbers you pass add to exactly 100?

These points all mark the vertices (corners) of ten hidden squares. Can you find the 10 hidden squares?

This dice train has been made using specific rules. How many different trains can you make?

Arrange the four number cards on the grid, according to the rules, to make a diagonal, vertical or horizontal line.

Take turns to place a decimal number on the spiral. Can you get three consecutive numbers?

On the graph there are 28 marked points. These points all mark the vertices (corners) of eight hidden squares. Can you find the eight hidden squares?

This challenge extends the Plants investigation so now four or more children are involved.

Can you find a reliable strategy for choosing coordinates that will locate the robber in the minimum number of guesses?

A game in which players take it in turns to choose a number. Can you block your opponent?

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

How many solutions can you find to this sum? Each of the different letters stands for a different number.