Use the interactivity to investigate what kinds of triangles can be
drawn on peg boards with different numbers of pegs.
Ben and his mum are planting garlic. Use the interactivity to help
you find out how many cloves of garlic they might have had.
Can you continue this pattern of triangles and begin to predict how many sticks are used for each new "layer"?
How many centimetres of rope will I need to make another mat just
like the one I have here?
Only one side of a two-slice toaster is working. What is the
quickest way to toast both sides of three slices of bread?
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 see why 2 by 2 could be 5? Can you predict what 2 by 10
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?
These squares have been made from Cuisenaire rods. Can you describe
the pattern? What would the next square look like?
In each of the pictures the invitation is for you to: Count what you see. Identify how you think the pattern would continue.
Watch this film carefully. Can you find a general rule for
explaining when the dot will be this same distance from the
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?
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?
Compare the numbers of particular tiles in one or all of these
three designs, inspired by the floor tiles of a church in
Stop the Clock game for an adult and child. How can you make sure you always win this game?
Polygonal numbers are those that are arranged in shapes as they enlarge. Explore the polygonal numbers drawn here.
This is a game for two players. Can you find out how to be the first to get to 12 o'clock?
Take a counter and surround it by a ring of other counters that
MUST touch two others. How many are needed?
An investigation that gives you the opportunity to make and justify
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
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?
Find out what a "fault-free" rectangle is and try to make some of
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?
Sweets are given out to party-goers in a particular way. Investigate the total number of sweets received by people sitting in different positions.
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?
What can you say about these shapes? This problem challenges you to
create shapes with different areas and perimeters.
This challenge asks you to imagine a snake coiling on itself.
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?
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
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?
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?
For this challenge, you'll need to play Got It! Can you explain the strategy for winning this game with any target?
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 work out how to win this game of Nim? Does it matter if you go first or second?
Find the sum of all three-digit numbers each of whose digits is
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.
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?
Nim-7 game for an adult and child. Who will be the one to take the last counter?
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.
This challenge is about finding the difference between numbers which have the same tens digit.
This challenge focuses on finding the sum and difference of pairs of two-digit numbers.
Strike it Out game for an adult and child. Can you stop your partner from being able to go?
Got It game for an adult and child. How can you play so that you know you will always win?
It starts quite simple but great opportunities for number discoveries and patterns!
This challenge encourages you to explore dividing a three-digit number by a single-digit number.
What happens when you round these three-digit numbers to the nearest 100?
Use two dice to generate two numbers with one decimal place. What happens when you round these numbers to the nearest whole number?
This activity focuses on rounding to the nearest 10.
What happens when you round these numbers to the nearest whole number?