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?
This challenge focuses on finding the sum and difference of pairs of two-digit numbers.
This challenge is about finding the difference between numbers which have the same tens digit.
Can you see why 2 by 2 could be 5? Can you predict what 2 by 10 will be?
How many ways can you find to do up all four buttons on my coat? How about if I had five buttons? Six ...?
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 find all the ways to get 15 at the top of this triangle of numbers?
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?
This task follows on from Build it Up and takes the ideas into three dimensions!
Tom and Ben visited Numberland. Use the maps to work out the number of points each of their routes scores.
Can you make dice stairs using the rules stated? How do you know you have all the possible stairs?
This challenge, written for the Young Mathematicians' Award, invites you to explore 'centred squares'.
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?
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?
Frances and Rishi were given a bag of lollies. They shared them out evenly and had one left over. How many lollies could there have been in the bag?
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?
Got It game for an adult and child. How can you play so that you know you will always win?
Ben and his mum are planting garlic. Use the interactivity to help you find out how many cloves of garlic they might have had.
Investigate the sum of the numbers on the top and bottom faces of a line of three dice. What do you notice?
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?
Find the sum of all three-digit numbers each of whose digits is odd.
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.
Two children made up a game as they walked along the garden paths. Can you find out their scores? Can you find some paths of your own?
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?
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 challenge asks you to imagine a snake coiling on itself.
If there are 3 squares in the ring, can you place three different numbers in them so that their differences are odd? Try with different numbers of squares around the ring. What do you notice?
Here are two kinds of spirals for you to explore. What do you notice?
Polygonal numbers are those that are arranged in shapes as they enlarge. Explore the polygonal numbers drawn here.
What can you say about these shapes? This problem challenges you to create shapes with different areas and perimeters.
This activity focuses on rounding to the nearest 10.
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?
Are these statements relating to odd and even numbers always true, sometimes true or never true?
Stop the Clock game for an adult and child. How can you make sure you always win this game?
Take a counter and surround it by a ring of other counters that MUST touch two others. How many are needed?
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?
Find a route from the outside to the inside of this square, stepping on as many tiles as possible.
This is a game for two players. Can you find out how to be the first to get to 12 o'clock?
Strike it Out game for an adult and child. Can you stop your partner from being able to go?
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?
In this calculation, the box represents a missing digit. What could the digit be? What would the solution be in each case?
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.
This challenge encourages you to explore dividing a three-digit number by a single-digit number.
What happens when you round these three-digit numbers to the nearest 100?
Use two dice to generate two numbers with one decimal place. What happens when you round these numbers to the nearest whole number?
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?
What happens when you round these numbers to the nearest whole number?