Find out what a "fault-free" rectangle is and try to make some of your own.
Find the sum of all three-digit numbers each of whose digits is odd.
This challenge, written for the Young Mathematicians' Award, invites you to explore 'centred squares'.
How many ways can you find to do up all four buttons on my coat? How about if I had five buttons? Six ...?
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.
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?
This challenge focuses on finding the sum and difference of pairs of two-digit numbers.
This task follows on from Build it Up and takes the ideas into three dimensions!
Strike it Out game for an adult and child. Can you stop your partner from being able to go?
Only one side of a two-slice toaster is working. What is the quickest way to toast both sides of three slices of bread?
Sweets are given out to party-goers in a particular way. Investigate the total number of sweets received by people sitting in different positions.
Use your addition and subtraction skills, combined with some strategic thinking, to beat your partner at this game.
Can you find all the ways to get 15 at the top of this triangle of numbers?
Use two dice to generate two numbers with one decimal place. What happens when you round these numbers to the nearest whole number?
What happens when you round these three-digit numbers to the nearest 100?
Try entering different sets of numbers in the number pyramids. How does the total at the top change?
Tom and Ben visited Numberland. Use the maps to work out the number of points each of their routes scores.
These squares have been made from Cuisenaire rods. Can you describe the pattern? What would the next square look like?
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?
Can you continue this pattern of triangles and begin to predict how many sticks are used for each new "layer"?
What happens when you round these numbers to the nearest whole number?
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.
Can you explain the strategy for winning this game with any target?
Polygonal numbers are those that are arranged in shapes as they enlarge. Explore the polygonal numbers drawn here.
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?
Can you see why 2 by 2 could be 5? Can you predict what 2 by 10 will be?
What can you say about these shapes? This problem challenges you to create shapes with different areas and perimeters.
Can you put the numbers 1-5 in the V shape so that both 'arms' have the same total?
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?
Use the interactivity to investigate what kinds of triangles can be drawn on peg boards with different numbers of pegs.
An investigation that gives you the opportunity to make and justify predictions.
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?
This challenge encourages you to explore dividing a three-digit number by a single-digit number.
Got It game for an adult and child. How can you play so that you know you will always win?
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?
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?
Compare the numbers of particular tiles in one or all of these three designs, inspired by the floor tiles of a church in Cambridge.
The number of plants in Mr McGregor's magic potting shed increases overnight. He'd like to put the same number of plants in each of his gardens, planting one garden each day. How can he do it?
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?
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?
Watch this film carefully. Can you find a general rule for explaining when the dot will be this same distance from the horizontal axis?
Nim-7 game for an adult and child. Who will be the one to take the last counter?
Can you make dice stairs using the rules stated? How do you know you have all the possible stairs?
Investigate the sum of the numbers on the top and bottom faces of a line of three dice. What do you notice?
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?
How many centimetres of rope will I need to make another mat just like the one I have here?
Here are two kinds of spirals for you to explore. What do you notice?
One block is needed to make an up-and-down staircase, with one step up and one step down. How many blocks would be needed to build an up-and-down staircase with 5 steps up and 5 steps down?
The aim of the game is to slide the green square from the top right hand corner to the bottom left hand corner in the least number of moves.
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.