Investigate the sum of the numbers on the top and bottom faces of a line of three dice. What do you notice?
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?
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 explain the strategy for winning this game with any target?
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?
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, written for the Young Mathematicians' Award, invites you to explore 'centred squares'.
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 encourages you to explore dividing a three-digit number by a single-digit number.
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?
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.
Are these statements always true, sometimes true or never true?
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 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!
This challenge focuses on finding the sum and difference of pairs of two-digit 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.
Use your addition and subtraction skills, combined with some strategic thinking, to beat your partner at this game.
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
This activity involves rounding four-digit numbers to the nearest thousand.
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.
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.
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?
Sweets are given out to party-goers in a particular way. Investigate the total number of sweets received by people sitting in different positions.
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.
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?
Strike it Out game for an adult and child. Can you stop your partner from being able to go?
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?
Are these statements relating to odd and even numbers always true, sometimes true or never true?
Find a route from the outside to the inside of this square, stepping on as many tiles as possible.
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?
Here are two kinds of spirals for you to explore. What do you notice?
An investigation that gives you the opportunity to make and justify
Nim-7 game for an adult and child. Who will be the one to take the last counter?
Put the numbers 1, 2, 3, 4, 5, 6 into the squares so that the
numbers on each circle add up to the same amount. Can you find the
rule for giving another set of six numbers?
Can you see why 2 by 2 could be 5? Can you predict what 2 by 10
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. . . .
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?
Find out what a "fault-free" rectangle is and try to make some of
A three digit number abc is always divisible by 7 when 2a+3b+c is divisible by 7. Why?
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?
It would be nice to have a strategy for disentangling any tangled
What can you say about these shapes? This problem challenges you to create shapes with different areas and perimeters.
Can you tangle yourself up and reach any fraction?
These squares have been made from Cuisenaire rods. Can you describe
the pattern? What would the next square look like?
Can you put the numbers 1-5 in the V shape so that both 'arms' have the same total?
How many pairs of numbers can you find that add up to a multiple of 11? Do you notice anything interesting about your results?
Rectangles are considered different if they vary in size or have different locations. How many different rectangles can be drawn on a chessboard?