Find a route from the outside to the inside of this square, stepping on as many tiles as possible.
Can you explain the strategy for winning this game with any target?
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.
Find out what a "fault-free" rectangle is and try to make some of your own.
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?
Can you see why 2 by 2 could be 5? Can you predict what 2 by 10 will be?
Here are two kinds of spirals for you to explore. What do you notice?
Got It game for an adult and child. How can you play so that you know you will always win?
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?
Only one side of a two-slice toaster is working. What is the quickest way to toast both sides of three slices of bread?
Watch this film carefully. Can you find a general rule for explaining when the dot will be this same distance from the horizontal axis?
A game for 2 players. Set out 16 counters in rows of 1,3,5 and 7. Players take turns to remove any number of counters from a row. The player left with the last counter looses.
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'.
Can you work out how to win this game of Nim? Does it matter if you go first or second?
Sweets are given out to party-goers in a particular way. Investigate the total number of sweets received by people sitting in different positions.
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 challenge asks you to imagine a snake coiling on itself.
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?
How many ways can you find to do up all four buttons on my coat? How about if I had five buttons? Six ...?
Use your addition and subtraction skills, combined with some strategic thinking, to beat your partner at this game.
This task follows on from Build it Up and takes the ideas into three dimensions!
Can you find all the ways to get 15 at the top of this triangle of numbers?
Nim-7 game for an adult and child. Who will be the one to take the last counter?
Are these statements relating to odd and even numbers always true, sometimes true or never true?
What happens when you round these three-digit numbers to the nearest 100?
Do you notice anything about the solutions when you add and/or subtract consecutive negative numbers?
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?
This activity involves rounding four-digit numbers to the nearest thousand.
What happens when you round these numbers to the nearest whole number?
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.
Try entering different sets of numbers in the number pyramids. How does the total at the top change?
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?
Tom and Ben visited Numberland. Use the maps to work out the number of points each of their routes scores.
Use the interactivity to investigate what kinds of triangles can be drawn on peg boards with different numbers of pegs.
Triangular numbers can be represented by a triangular array of squares. What do you notice about the sum of identical triangle numbers?
In each of the pictures the invitation is for you to: Count what you see. Identify how you think the pattern would continue.
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?
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.
What can you say about these shapes? This problem challenges you to create shapes with different areas and perimeters.
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.
An investigation that gives you the opportunity to make and justify predictions.
Find the sum of all three-digit numbers each of whose digits is odd.
Strike it Out game for an adult and child. Can you stop your partner from being able to go?
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?
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.
How could Penny, Tom and Matthew work out how many chocolates there are in different sized boxes?
Can you make dice stairs using the rules stated? How do you know you have all the possible stairs?
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?