Challenge Level

While we were sorting some papers we found 3 strange sheets which seemed to come from small books but there were page numbers at the foot of each page. Did the pages come from the same book?

Challenge Level

Polygonal numbers are those that are arranged in shapes as they enlarge. Explore the polygonal numbers drawn here.

Challenge Level

Can you continue this pattern of triangles and begin to predict how many sticks are used for each new "layer"?

Challenge Level

Surprise your friends with this magic square trick.

Challenge Level

This challenge, written for the Young Mathematicians' Award, invites you to explore 'centred squares'.

Challenge Level

These squares have been made from Cuisenaire rods. Can you describe the pattern? What would the next square look like?

Challenge Level

Tom and Ben visited Numberland. Use the maps to work out the number of points each of their routes scores.

Challenge Level

How can you arrange these 10 matches in four piles so that when you move one match from three of the piles into the fourth, you end up with the same arrangement?

Challenge Level

Try adding together the dates of all the days in one week. Now multiply the first date by 7 and add 21. Can you explain what happens?

Challenge Level

In each of the pictures the invitation is for you to: Count what you see. Identify how you think the pattern would continue.

Challenge Level

We can arrange dots in a similar way to the 5 on a dice and they usually sit quite well into a rectangular shape. How many altogether in this 3 by 5? What happens for other sizes?

Challenge Level

Find the sum and difference between a pair of two-digit numbers. Now find the sum and difference between the sum and difference! What happens?

Challenge Level

This challenge focuses on finding the sum and difference of pairs of two-digit numbers.

Challenge Level

Take a counter and surround it by a ring of other counters that MUST touch two others. How many are needed?

Challenge Level

An investigation that gives you the opportunity to make and justify predictions.

Challenge Level

Only one side of a two-slice toaster is working. What is the quickest way to toast both sides of three slices of bread?

Challenge Level

How many ways can you find to do up all four buttons on my coat? How about if I had five buttons? Six ...?

Challenge Level

Sweets are given out to party-goers in a particular way. Investigate the total number of sweets received by people sitting in different positions.

Challenge Level

Can you make dice stairs using the rules stated? How do you know you have all the possible stairs?

Challenge Level

This challenge encourages you to explore dividing a three-digit number by a single-digit number.

Challenge Level

Can you find all the ways to get 15 at the top of this triangle of numbers? Many opportunities to work in different ways.

Challenge Level

This task follows on from Build it Up and takes the ideas into three dimensions!

Challenge Level

Compare the numbers of particular tiles in one or all of these three designs, inspired by the floor tiles of a church in Cambridge.

Challenge Level

What happens if you join every second point on this circle? How about every third point? Try with different steps and see if you can predict what will happen.

Challenge Level

In a Magic Square all the rows, columns and diagonals add to the 'Magic Constant'. How would you change the magic constant of this square?

Challenge Level

Can you dissect an equilateral triangle into 6 smaller ones? What number of smaller equilateral triangles is it NOT possible to dissect a larger equilateral triangle into?

Challenge Level

Watch this animation. What do you notice? What happens when you try more or fewer cubes in a bundle?

Challenge Level

Think of a number, square it and subtract your starting number. Is the number you’re left with odd or even? How do the images help to explain this?

Challenge Level

In how many different ways can you break up a stick of 7 interlocking cubes? Now try with a stick of 8 cubes and a stick of 6 cubes.

Challenge Level

What happens when you round these three-digit numbers to the nearest 100?

Challenge Level

What can you say about these shapes? This problem challenges you to create shapes with different areas and perimeters.

Challenge Level

Place the numbers from 1 to 9 in the squares below so that the difference between joined squares is odd. How many different ways can you do this?

Challenge Level

In this problem we are looking at sets of parallel sticks that cross each other. What is the least number of crossings you can make? And the greatest?

Challenge Level

It starts quite simple but great opportunities for number discoveries and patterns!

Challenge Level

How many different journeys could you make if you were going to visit four stations in this network? How about if there were five stations? Can you predict the number of journeys for seven stations?

Challenge Level

Does this 'trick' for calculating multiples of 11 always work? Why or why not?

Challenge Level

Can you put the numbers 1-5 in the V shape so that both 'arms' have the same total?

Challenge Level

Ben’s class were cutting up number tracks. First they cut them into twos and added up the numbers on each piece. What patterns could they see?

Challenge Level

Put the numbers 1, 2, 3, 4, 5, 6 into the squares so that the numbers on each circle add up to the same amount. Can you find the rule for giving another set of six numbers?

Challenge Level

15 = 7 + 8 and 10 = 1 + 2 + 3 + 4. Can you say which numbers can be expressed as the sum of two or more consecutive integers?

Challenge Level

Watch this animation. What do you see? Can you explain why this happens?

Challenge Level

Delight your friends with this cunning trick! Can you explain how it works?

Challenge Level

Use two dice to generate two numbers with one decimal place. What happens when you round these numbers to the nearest whole number?

Challenge Level

Find the sum of all three-digit numbers each of whose digits is odd.

An article for teachers and pupils that encourages you to look at the mathematical properties of similar games.

Challenge Level

What happens when you round these numbers to the nearest whole number?

Challenge Level

In this game for two players, the idea is to take it in turns to choose 1, 3, 5 or 7. The winner is the first to make the total 37.

Challenge Level

Find a route from the outside to the inside of this square, stepping on as many tiles as possible.

Challenge Level

Here are some arrangements of circles. How many circles would I need to make the next size up for each? Can you create your own arrangement and investigate the number of circles it needs?