This challenge asks you to imagine a snake coiling on itself.
Got It game for an adult and child. How can you play so that you know you will always win?
How many ways can you find to do up all four buttons on my coat? How about if I had five buttons? Six ...?
Benâ€™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 challenge focuses on finding the sum and difference of pairs of two-digit numbers.
For this challenge, you'll need to play Got It! Can you explain the strategy for winning this game with any target?
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?
This challenge encourages you to explore dividing a three-digit number by a single-digit number.
This challenge, written for the Young Mathematicians' Award, invites you to explore 'centred squares'.
Investigate the sum of the numbers on the top and bottom faces of a line of three dice. 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?
Can you find all the ways to get 15 at the top of this triangle of numbers?
Only one side of a two-slice toaster is working. What is the
quickest way to toast both sides of three slices of bread?
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.
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?
This task follows on from Build it Up and takes the ideas into three dimensions!
The number of plants in Mr McGregor's magic potting shed increases
overnight. He'd like to put the same number of plants in each of
his gardens, planting one garden each day. How can he do it?
Choose any 3 digits and make a 6 digit number by repeating the 3
digits in the same order (e.g. 594594). Explain why whatever digits
you choose the number will always be divisible by 7, 11 and 13.
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?
Tom and Ben visited Numberland. Use the maps to work out the number of points each of their routes scores.
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.
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.
An investigation that gives you the opportunity to make and justify
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
A three digit number abc is always divisible by 7 when 2a+3b+c is divisible by 7. Why?
Can you see why 2 by 2 could be 5? Can you predict what 2 by 10
Find some examples of pairs of numbers such that their sum is a
factor of their product. eg. 4 + 12 = 16 and 4 × 12 = 48 and
16 is a factor of 48.
Strike it Out game for an adult and child. Can you stop your partner from being able to go?
Nim-7 game for an adult and child. Who will be the one to take the last counter?
Are these statements always true, sometimes true or never true?
Use your addition and subtraction skills, combined with some strategic thinking, to beat your partner at this game.
Here are two kinds of spirals for you to explore. What do you notice?
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?
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?
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 entering different sets of numbers in the number pyramids. How does the total at the top change?
In each of the pictures the invitation is for you to: Count what you see. Identify how you think the pattern would continue.
These squares have been made from Cuisenaire rods. Can you describe
the pattern? What would the next square look like?
Rectangles are considered different if they vary in size or have different locations. How many different rectangles can be drawn on a chessboard?
List any 3 numbers. It is always possible to find a subset of
adjacent numbers that add up to a multiple of 3. Can you explain
why and prove it?
Four bags contain a large number of 1s, 3s, 5s and 7s. Pick any ten numbers from the bags above so that their total is 37.
The sum of the numbers 4 and 1 [1/3] is the same as the product of 4 and 1 [1/3]; that is to say 4 + 1 [1/3] = 4 × 1 [1/3]. What other numbers have the sum equal to the product and can this be so for. . . .
It would be nice to have a strategy for disentangling any tangled
Can you tangle yourself up and reach any fraction?
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 can you say about these shapes? This problem challenges you to create shapes with different areas and perimeters.
The Egyptians expressed all fractions as the sum of different unit
fractions. Here is a chance to explore how they could have written
What happens when you round these three-digit numbers to the nearest 100?
Are these statements relating to odd and even numbers always true, sometimes true or never true?
Find the sum of all three-digit numbers each of whose digits is