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?
Ben and his mum are planting garlic. Use the interactivity to help you find out how many cloves of garlic they might have had.
Are these statements relating to odd and even numbers always true, sometimes true or never true?
Are these statements relating to calculation and properties of shapes always true, sometimes true or never true?
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.
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?
This activity involves rounding four-digit numbers to the nearest thousand.
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?
What happens when you round these numbers to the nearest whole number?
This activity focuses on rounding to the nearest 10.
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?
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.
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?
Tom and Ben visited Numberland. Use the maps to work out the number of points each of their routes scores.
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?
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?
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 two dice to generate two numbers with one decimal place. What happens when you round these numbers to the nearest whole number?
Here are two kinds of spirals for you to explore. What do you notice?
What happens when you round these three-digit numbers to the nearest 100?
Got It game for an adult and child. How can you play so that you know you will always win?
Find a route from the outside to the inside of this square, stepping on as many tiles as possible.
Nim-7 game for an adult and child. Who will be the one to take the last counter?
Find the sum of all three-digit numbers each of whose digits is odd.
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?
This challenge encourages you to explore dividing a three-digit number by a single-digit 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?
This challenge is about finding the difference between numbers which have the same tens digit.
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?
Can you make dice stairs using the rules stated? How do you know you have all the possible stairs?
Investigate the sum of the numbers on the top and bottom faces of a line of three dice. What do you notice?
What can you say about these shapes? This problem challenges you to create shapes with different areas and perimeters.
Are these statements always true, sometimes true or never true?
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!
Polygonal numbers are those that are arranged in shapes as they enlarge. Explore the polygonal numbers drawn here.
This challenge focuses on finding the sum and difference of pairs of two-digit numbers.
In this calculation, the box represents a missing digit. What could the digit be? What would the solution be in each case?
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?
Strike it Out game for an adult and child. Can you stop your partner from being able to go?
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.
Stop the Clock game for an adult and child. How can you make sure you always win this game?
Find out what a "fault-free" rectangle is and try to make some of your own.
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.
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?
In each of the pictures the invitation is for you to: Count what you see. Identify how you think the pattern would continue.
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.