In each of the pictures the invitation is for you to: Count what you see. Identify how you think the pattern would continue.
Take a counter and surround it by a ring of other counters that
MUST touch two others. How many are needed?
These squares have been made from Cuisenaire rods. Can you describe
the pattern? What would the next square look like?
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?
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?
How many ways can you find to do up all four buttons on my coat?
How about if I had five buttons? Six ...?
Use the interactivity to investigate what kinds of triangles can be
drawn on peg boards with different numbers of pegs.
Can you see why 2 by 2 could be 5? Can you predict what 2 by 10
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?
Only one side of a two-slice toaster is working. What is the
quickest way to toast both sides of three slices of bread?
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?
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?
Find out what a "fault-free" rectangle is and try to make some of
Delight your friends with this cunning trick! Can you explain how
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 challenge asks you to imagine a snake coiling on itself.
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 the sum and difference between a pair of two-digit numbers. Now find the sum and difference between the sum and difference! What happens?
Square numbers can be represented as the sum of consecutive odd
numbers. What is the sum of 1 + 3 + ..... + 149 + 151 + 153?
Triangle numbers can be represented by a triangular array of
squares. What do you notice about the sum of identical triangle
Compare the numbers of particular tiles in one or all of these
three designs, inspired by the floor tiles of a church in
Imagine a large cube made from small red cubes being dropped into a
pot of yellow paint. How many of the small cubes will have yellow
paint on their faces?
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.
How many moves does it take to swap over some red and blue frogs? Do you have a method?
This challenge focuses on finding the sum and difference of pairs of two-digit numbers.
Can you continue this pattern of triangles and begin to predict how
many sticks are used for each new "layer"?
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?
How could Penny, Tom and Matthew work out how many chocolates there
are in different sized boxes?
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?
Use the animation to help you work out how many lines are needed to draw mystic roses of different sizes.
A 2 by 3 rectangle contains 8 squares and a 3 by 4 rectangle
contains 20 squares. What size rectangle(s) contain(s) exactly 100
squares? Can you find them all?
Polygonal numbers are those that are arranged in shapes as they enlarge. Explore the polygonal numbers drawn here.
Find the sum of all three-digit numbers each of whose digits is
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 find the values at the vertices when you know the values on
Can you tangle yourself up and reach any fraction?
It would be nice to have a strategy for disentangling any tangled
Tom and Ben visited Numberland. Use the maps to work out the number
of points each of their routes scores.
It starts quite simple but great opportunities for number discoveries and patterns!
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 encourages you to explore dividing a three-digit number by a single-digit number.
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.
Try entering different sets of numbers in the number pyramids. How does the total at the top change?
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?
How many centimetres of rope will I need to make another mat just
like the one I have here?
What size square corners should be cut from a square piece of paper to make a box with the largest possible volume?
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