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?
Tom and Ben visited Numberland. Use the maps to work out the number of points each of their routes scores.
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?
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!
Only one side of a two-slice toaster is working. What is the quickest way to toast both sides of three slices of bread?
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?
Try out this number trick. What happens with different starting numbers? What do you notice?
How many ways can you find to do up all four buttons on my coat? How about if I had five buttons? Six ...?
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?
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?
Find the sum of all three-digit numbers each of whose digits is odd.
Can you find all the ways to get 15 at the top of this triangle of numbers? Many opportunities to work in different ways.
Sweets are given out to party-goers in a particular way. Investigate the total number of sweets received by people sitting in different positions.
Strike it Out game for an adult and child. Can you stop your partner from being able to go?
What can you say about these shapes? This problem challenges you to create shapes with different areas and perimeters.
Use your addition and subtraction skills, combined with some strategic thinking, to beat your partner at this game.
Polygonal numbers are those that are arranged in shapes as they enlarge. Explore the polygonal numbers drawn here.
What happens when you round these three-digit numbers to the nearest 100?
Can you put the numbers 1-5 in the V shape so that both 'arms' have the same total?
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?
An investigation that gives you the opportunity to make and justify predictions.
This challenge, written for the Young Mathematicians' Award, invites you to explore 'centred squares'.
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?
Investigate the different ways that fifteen schools could have given money in a charity fundraiser.
Watch this animation. What do you notice? What happens when you try more or fewer cubes in a bundle?
Can you make dice stairs using the rules stated? How do you know you have all the possible stairs?
Surprise your friends with this magic square trick.
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?
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.
Can you continue this pattern of triangles and begin to predict how many sticks are used for each new "layer"?
Choose any 3 digits and make a 6 digit number by repeating the 3 digits in the same order (e.g. 594594). Explain why whatever digits you choose the number will always be divisible by 7, 11 and 13.
Try entering different sets of numbers in the number pyramids. How does the total at the top change?
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.
Does this 'trick' for calculating multiples of 11 always work? Why or why not?
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?
What happens when you round these numbers to the nearest whole number?
Use two dice to generate two numbers with one decimal place. What happens when you round these numbers to the nearest whole number?
This challenge encourages you to explore dividing a three-digit number by a single-digit number.
This article for teachers describes several games, found on the site, all of which have a related structure that can be used to develop the skills of strategic planning.
Pick the number of times a week that you eat chocolate. This number must be more than one but less than ten. Multiply this number by 2. Add 5 (for Sunday). Multiply by 50... Can you explain why it. . . .
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?
You can work out the number someone else is thinking of as follows. Ask a friend to think of any natural number less than 100. Then ask them to tell you the remainders when this number is divided by. . . .
Watch this film carefully. Can you find a general rule for explaining when the dot will be this same distance from the horizontal axis?
Are these statements always true, sometimes true or never true?
Investigate the sum of the numbers on the top and bottom faces of a line of three dice. What do you notice?
An article for teachers and pupils that encourages you to look at the mathematical properties of similar games.
Take a look at the video of this trick. Can you perform it yourself? Why is this maths and not magic?
Jo has three numbers which she adds together in pairs. When she does this she has three different totals: 11, 17 and 22 What are the three numbers Jo had to start with?”