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?
This is a game for two players. Can you find out how to be the first to get to 12 o'clock?
Ben and his mum are planting garlic. Use the interactivity to help you find out how many cloves of garlic they might have had.
Stop the Clock game for an adult and child. How can you make sure you always win this game?
Watch this film carefully. Can you find a general rule for explaining when the dot will be this same distance from the horizontal axis?
How many ways can you find to do up all four buttons on my coat? How about if I had five buttons? Six ...?
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 each of the pictures the invitation is for you to: Count what you see. Identify how you think the pattern would continue.
Can you see why 2 by 2 could be 5? Can you predict what 2 by 10 will be?
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?
These squares have been made from Cuisenaire rods. Can you describe the pattern? What would the next square look like?
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 is about finding the difference between numbers which have the same tens digit.
Take a counter and surround it by a ring of other counters that MUST touch two others. How many are needed?
Can you find all the ways to get 15 at the top of this triangle of numbers? Many opportunities to work in different ways.
Can you make dice stairs using the rules stated? How do you know you have all the possible stairs?
This problem challenges you to find out how many odd numbers there are between pairs of numbers. Can you find a pair of numbers that has four odds between them?
Sweets are given out to party-goers in a particular way. Investigate the total number of sweets received by people sitting in different positions.
Florence, Ethan and Alma have each added together two 'next-door' numbers. What is the same about their answers?
This task follows on from Build it Up and takes the ideas into three dimensions!
This challenge, written for the Young Mathematicians' Award, invites you to explore 'centred squares'.
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?
Use the interactivity to investigate what kinds of triangles can be drawn on peg boards with different numbers of pegs.
Find a route from the outside to the inside of this square, stepping on as many tiles as possible.
In this calculation, the box represents a missing digit. What could the digit be? What would the solution be in each case?
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.
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.
Polygonal numbers are those that are arranged in shapes as they enlarge. Explore the polygonal numbers drawn here.
Strike it Out game for an adult and child. Can you stop your partner from being able to go?
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?
Find out what a "fault-free" rectangle is and try to make some of your own.
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?
Can you find a way of counting the spheres in these arrangements?
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?
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?
Think of a number, square it and subtract your starting number. Is the number you’re left with odd or even? How do the images help to explain this?
What can you say about these shapes? This problem challenges you to create shapes with different areas and perimeters.
Tom and Ben visited Numberland. Use the maps to work out the number of points each of their routes scores.
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?
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?
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?
Can you continue this pattern of triangles and begin to predict how many sticks are used for each new "layer"?
Use two dice to generate two numbers with one decimal place. What happens when you round these numbers to the nearest whole number?
This activity focuses on rounding to the nearest 10.
Use your addition and subtraction skills, combined with some strategic thinking, to beat your partner at this game.
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?