Watch this film carefully. Can you find a general rule for explaining when the dot will be this same distance from the horizontal axis?
These squares have been made from Cuisenaire rods. Can you describe the pattern? What would the next square look like?
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?
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.
Take a counter and surround it by a ring of other counters that MUST touch two others. How many are needed?
Can you see why 2 by 2 could be 5? Can you predict what 2 by 10 will be?
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?
Polygonal numbers are those that are arranged in shapes as they enlarge. Explore the polygonal numbers drawn here.
How many ways can you find to do up all four buttons on my coat? How about if I had five buttons? Six ...?
Can you make dice stairs using the rules stated? How do you know you have all the possible stairs?
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?
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 the interactivity to investigate what kinds of triangles can be drawn on peg boards with different numbers of pegs.
Can you find all the ways to get 15 at the top of this triangle of numbers?
Find out what a "fault-free" rectangle is and try to make some of your own.
Delight your friends with this cunning trick! Can you explain how it works?
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?
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 challenge focuses on finding the sum and difference of pairs of two-digit numbers.
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?
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.
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, written for the Young Mathematicians' Award, invites you to explore 'centred squares'.
Use your addition and subtraction skills, combined with some strategic thinking, to beat your partner at this game.
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.
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.
Can you continue this pattern of triangles and begin to predict how many sticks are used for each new "layer"?
What happens when you round these three-digit numbers to the nearest 100?
What happens when you round these numbers to the nearest whole number?
Find a route from the outside to the inside of this square, stepping on as many tiles as possible.
Strike it Out game for an adult and child. Can you stop your partner from being able to go?
Find the sum of all three-digit numbers each of whose digits is odd.
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?
Nim-7 game for an adult and child. Who will be the one to take the last counter?
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?
Can you work out how to win this game of Nim? Does it matter if you go first or second?
Compare the numbers of particular tiles in one or all of these three designs, inspired by the floor tiles of a church in Cambridge.
Can you explain the strategy for winning this game with any target?
This task follows on from Build it Up and takes the ideas into three dimensions!
What would be the smallest number of moves needed to move a Knight from a chess set from one corner to the opposite corner of a 99 by 99 square board?
It starts quite simple but great opportunities for number discoveries and patterns!
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?
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.
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.
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?
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?