Can you see why 2 by 2 could be 5? Can you predict what 2 by 10
Got It game for an adult and child. How can you play so that you know you will always win?
Watch this film carefully. Can you find a general rule for
explaining when the dot will be this same distance from the
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 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?
Investigate the sum of the numbers on the top and bottom faces of a line of three dice. What do you notice?
How many ways can you find to do up all four buttons on my coat? How about if I had five buttons? Six ...?
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?
Take a counter and surround it by a ring of other counters that
MUST touch two others. How many are needed?
In each of the pictures the invitation is for you to: Count what you see. Identify how you think the pattern would continue.
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?
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?
This challenge focuses on finding the sum and difference of pairs of two-digit numbers.
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.
Only one side of a two-slice toaster is working. What is the
quickest way to toast both sides of three slices of bread?
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?
This task follows on from Build it Up and takes the ideas into three dimensions!
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?
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.
Can you find all the ways to get 15 at the top of this triangle of numbers?
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.
Use the interactivity to investigate what kinds of triangles can be
drawn on peg boards with different numbers of pegs.
These squares have been made from Cuisenaire rods. Can you describe
the pattern? What would the next square look like?
This challenge, written for the Young Mathematicians' Award, invites you to explore 'centred squares'.
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.
This challenge encourages you to explore dividing a three-digit number by a single-digit number.
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 the sum and difference between a pair of two-digit numbers. Now find the sum and difference between the sum and difference! What happens?
Nim-7 game for an adult and child. Who will be the one to take the last counter?
Use your addition and subtraction skills, combined with some strategic thinking, to beat your partner at this game.
The aim of the game is to slide the green square from the top right
hand corner to the bottom left hand corner in the least number of
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?
A three digit number abc is always divisible by 7 when 2a+3b+c is divisible by 7. Why?
Triangle numbers can be represented by a triangular array of squares. What do you notice about the sum of identical triangle numbers?
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?
Rectangles are considered different if they vary in size or have different locations. How many different rectangles can be drawn on a chessboard?
Find out what a "fault-free" rectangle is and try to make some of
An investigation that gives you the opportunity to make and justify
For this challenge, you'll need to play Got It! Can you explain the strategy for winning this game with any target?
Try entering different sets of numbers in the number pyramids. How does the total at the top change?
You can work out the number someone else is thinking of as follows. Ask a friend to think of any natural number less than 100. Then ask them to tell you the remainders when this number is divided by. . . .
Sweets are given out to party-goers in a particular way. Investigate the total number of sweets received by people sitting in different positions.
Can you make dice stairs using the rules stated? How do you know you have all the possible stairs?
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?
Are these statements relating to odd and even numbers always true, sometimes true or never true?
Strike it Out game for an adult and child. Can you stop your partner from being able to go?
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.
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?
Can you continue this pattern of triangles and begin to predict how many sticks are used for each new "layer"?