Investigate the sum of the numbers on the top and bottom faces of a line of three dice. What do you notice?
Try out this number trick. What happens with different starting numbers? What do you notice?
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?
Find the sum of all three-digit numbers each of whose digits is odd.
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?
Watch this video to see how to roll the dice. Now it's your turn! What do you notice about the dice numbers you have recorded?
Here are two kinds of spirals for you to explore. What do you notice?
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?
Can you see why 2 by 2 could be 5? Can you predict what 2 by 10 will be?
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?
An investigation that gives you the opportunity to make and justify predictions.
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?
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?
This challenge encourages you to explore dividing a three-digit number by a single-digit number.
This challenge focuses on finding the sum and difference of pairs of two-digit numbers.
Can you put the numbers 1-5 in the V shape so that both 'arms' have the same total?
Watch this animation. What do you notice? What happens when you try more or fewer cubes in a bundle?
Are these statements always true, sometimes true or never true?
Can you make dice stairs using the rules stated? How do you know you have all the possible stairs?
This task follows on from Build it Up and takes the ideas into three dimensions!
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?
Polygonal numbers are those that are arranged in shapes as they enlarge. Explore the polygonal numbers drawn here.
Only one side of a two-slice toaster is working. What is the quickest way to toast both sides of three slices of bread?
Use your addition and subtraction skills, combined with some strategic thinking, to beat your partner at this game.
Does this 'trick' for calculating multiples of 11 always work? Why or why not?
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?
Sweets are given out to party-goers in a particular way. Investigate the total number of sweets received by people sitting in different positions.
What can you say about these shapes? This problem challenges you to create shapes with different areas and perimeters.
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.
How many ways can you find to do up all four buttons on my coat? How about if I had five buttons? Six ...?
This challenge, written for the Young Mathematicians' Award, invites you to explore 'centred squares'.
Strike it Out game for an adult and child. Can you stop your partner from being able to go?
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. . . .
Investigate the different ways that fifteen schools could have given money in a charity fundraiser.
Can you find all the ways to get 15 at the top of this triangle of numbers? Many opportunities to work in different ways.
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.
This activity involves rounding four-digit numbers to the nearest thousand.
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?
Find a route from the outside to the inside of this square, stepping on as many tiles as possible.
These tasks give learners chance to generalise, which involves identifying an underlying structure.
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?
Are these statements relating to odd and even numbers always true, sometimes true or never true?
This challenge asks you to imagine a snake coiling on itself.
Do you notice anything about the solutions when you add and/or subtract consecutive negative numbers?
Spotting patterns can be an important first step - explaining why it is appropriate to generalise is the next step, and often the most interesting and important.
Try entering different sets of numbers in the number pyramids. How does the total at the top change?
An article for teachers and pupils that encourages you to look at the mathematical properties of similar games.
These squares have been made from Cuisenaire rods. Can you describe the pattern? What would the next square look like?
Can you find an efficient method to work out how many handshakes there would be if hundreds of people met?