Explaining, convincing and proving

problem

Counting Stick Conjectures

Age

5 to 11

Challenge level

How many rectangles can you see? Are they all the same size? Can you predict how many rectangles there will be in counting sticks of different lengths?
problem

Making Pathways

Age

7 to 11

Challenge level

Can you find different ways of creating paths using these paving slabs?
game

Online

Age

7 to 11

Challenge level

Can you end up with all the occurrences of the same letter in this two-player game?
problem

Cows and Sheep

Age

7 to 11

Challenge level

Use your logical reasoning to work out how many cows and how many sheep there are in each field.
problem

True or False?

Age

7 to 11

Challenge level

Without doing lots of calculations, can you decide which of these number sentences are true? How do you know?
problem

Unravelling Sequences

Age

7 to 11

Challenge level

Can you describe what is happening as this program runs? Can you unpick the steps in the process?
problem

Mathdoku

Age

7 to 11

Challenge level

Complete the Mathdoku grid using the clues. Can you convince us that the number you have chosen for each square has to be correct?
problem

Triangle in a Square

Age

7 to 11

Challenge level

Do you agree with Badger's statements? Is Badger's reasoning watertight? Why or why not?
problem

Add 3 Dice

Age

7 to 11

Challenge level

Three dice are placed in a row. Find a way to turn each one so that the three numbers on top of the dice total the same as the three numbers on the front of the dice. Can you find all the ways to do this?
problem

Open Squares

Age

7 to 11

Challenge level

This task, written for the National Young Mathematicians' Award 2016, focuses on 'open squares'. What would the next five open squares look like?