It starts quite simple but great opportunities for number discoveries and patterns!
Compare the numbers of particular tiles in one or all of these
three designs, inspired by the floor tiles of a church in
This challenge, written for the Young Mathematicians' Award, invites you to explore 'centred squares'.
How many ways can you find to do up all four buttons on my coat? How about if I had five buttons? Six ...?
Find the sum of all three-digit numbers each of whose digits is
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?
Only one side of a two-slice toaster is working. What is the
quickest way to toast both sides of three slices of bread?
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?
Use the interactivity to investigate what kinds of triangles can be
drawn on peg boards with different numbers of pegs.
Imagine starting with one yellow cube and covering it all over with
a single layer of red cubes, and then covering that cube with a
layer of blue cubes. How many red and blue cubes would you need?
Can you put the numbers 1-5 in the V shape so that both 'arms' have the same total?
An investigation that gives you the opportunity to make and justify
Here are two kinds of spirals for you to explore. What do you notice?
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
This task follows on from Build it Up and takes the ideas into three dimensions!
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?
Are these statements relating to odd and even numbers always true, sometimes true or never true?
Triangle numbers can be represented by a triangular array of squares. What do you notice about the sum of identical triangle numbers?
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.
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. . . .
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?
Spotting patterns can be an important first step - explaining why it is appropriate to generalise is the next step, and often the most interesting and important.
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?
How many centimetres of rope will I need to make another mat just
like the one I have here?
Can you find all the ways to get 15 at the top of this triangle of numbers?
If you can copy a network without lifting your pen off the paper and without drawing any line twice, then it is traversable.
Decide which of these diagrams are traversable.
When number pyramids have a sequence on the bottom layer, some interesting patterns emerge...
Find a route from the outside to the inside of this square, stepping on as many tiles as possible.
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 focuses on finding the sum and difference of pairs of two-digit numbers.
Use two dice to generate two numbers with one decimal place. What happens when you round these numbers to the nearest whole number?
What happens when you round these three-digit numbers to the nearest 100?
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?
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?
Got It game for an adult and child. How can you play so that you know you will always win?
What happens when you round these numbers to the nearest whole number?
This activity involves rounding four-digit numbers to the nearest thousand.
Sweets are given out to party-goers in a particular way. Investigate the total number of sweets received by people sitting in different positions.
How could Penny, Tom and Matthew work out how many chocolates there
are in different sized boxes?
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.
What can you say about these shapes? This problem challenges you to create shapes with different areas and perimeters.
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.
This challenge asks you to imagine a snake coiling on itself.
Polygonal numbers are those that are arranged in shapes as they enlarge. Explore the polygonal numbers drawn here.
Can you make dice stairs using the rules stated? How do you know you have all the possible stairs?