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?
Investigate the sum of the numbers on the top and bottom faces of a line of three dice. What do you notice?
Nim-7 game for an adult and child. Who will be the one to take the last counter?
Can you explain the strategy for winning this game with any target?
Sweets are given out to party-goers in a particular way. Investigate the total number of sweets received by people sitting in different positions.
This challenge encourages you to explore dividing a three-digit number by a single-digit number.
How many ways can you find to do up all four buttons on my coat? How about if I had five buttons? Six ...?
Got It game for an adult and child. How can you play so that you know you will always win?
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?
Only one side of a two-slice toaster is working. What is the quickest way to toast both sides of three slices of bread?
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 find all the ways to get 15 at the top of this triangle of numbers?
This task follows on from Build it Up and takes the ideas into three dimensions!
This challenge focuses on finding the sum and difference of pairs of two-digit numbers.
This challenge, written for the Young Mathematicians' Award, invites you to explore 'centred squares'.
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?
This activity involves rounding four-digit numbers to the nearest thousand.
Can you explain how this card trick works?
This challenge asks you to imagine a snake coiling on itself.
Delight your friends with this cunning trick! Can you explain how it works?
Find some examples of pairs of numbers such that their sum is a factor of their product. eg. 4 + 12 = 16 and 4 × 12 = 48 and 16 is a factor of 48.
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?
An investigation that gives you the opportunity to make and justify predictions.
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.
Here are two kinds of spirals for you to explore. What do you notice?
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?
Tom and Ben visited Numberland. Use the maps to work out the number of points each of their routes scores.
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.
Find a route from the outside to the inside of this square, stepping on as many tiles as possible.
Are these statements always true, sometimes true or never true?
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?
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?
Are these statements relating to odd and even numbers always true, sometimes true or never true?
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?
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?
Find the sum of all three-digit numbers each of whose digits is odd.
What can you say about these shapes? This problem challenges you to create shapes with different areas and perimeters.
Can you work out how to win this game of Nim? Does it matter if you go first or second?
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?
List any 3 numbers. It is always possible to find a subset of adjacent numbers that add up to a multiple of 3. Can you explain why and prove it?
Try entering different sets of numbers in the number pyramids. How does the total at the top change?
Find out what a "fault-free" rectangle is and try to make some of your own.
Strike it Out game for an adult and child. Can you stop your partner from being able to go?
Can you put the numbers 1-5 in the V shape so that both 'arms' have the same total?
These squares have been made from Cuisenaire rods. Can you describe the pattern? What would the next square look like?
Use your addition and subtraction skills, combined with some strategic thinking, to beat your partner at this game.
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.
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?
Watch this film carefully. Can you find a general rule for explaining when the dot will be this same distance from the horizontal axis?