How many centimetres of rope will I need to make another mat just
like the one I have here?
What can you say about these shapes? This problem challenges you to
create shapes with different areas and perimeters.
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 continue this pattern of triangles and begin to predict how many sticks are used for each new "layer"?
An investigation that gives you the opportunity to make and justify
Polygonal numbers are those that are arranged in shapes as they enlarge. Explore the polygonal numbers drawn here.
Compare the numbers of particular tiles in one or all of these
three designs, inspired by the floor tiles of a church in
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?
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?
Only one side of a two-slice toaster is working. What is the
quickest way to toast both sides of three slices of bread?
Tom and Ben visited Numberland. Use the maps to work out the number
of points each of their routes scores.
Use two dice to generate two numbers with one decimal place. What happens when you round these numbers to the nearest whole number?
In how many different ways can you break up a stick of 7 interlocking cubes? Now try with a stick of 8 cubes and a stick of 6 cubes.
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
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?
Sweets are given out to party-goers in a particular way. Investigate the total number of sweets received by people sitting in different positions.
This challenge focuses on finding the sum and difference of pairs of two-digit numbers.
How many different journeys could you make if you were going to visit four stations in this network? How about if there were five stations? Can you predict the number of journeys for seven stations?
What happens when you round these numbers to the nearest whole number?
Find out what a "fault-free" rectangle is and try to make some of
Can you make dice stairs using the rules stated? How do you know you have all the possible stairs?
This challenge, written for the Young Mathematicians' Award, invites you to explore 'centred squares'.
This task follows on from Build it Up and takes the ideas into three dimensions!
Can you find all the ways to get 15 at the top of this triangle of numbers?
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?
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 put the numbers 1-5 in the V shape so that both 'arms' have the same total?
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?
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.
Find the sum of all three-digit numbers each of whose digits is
Polygons drawn on square dotty paper have dots on their perimeter
(p) and often internal (i) ones as well. Find a relationship
between p, i and the area of the polygons.
This challenge asks you to imagine a snake coiling on itself.
Use your addition and subtraction skills, combined with some strategic thinking, to beat your partner at this game.
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?
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?
Can you see why 2 by 2 could be 5? Can you predict what 2 by 10
Use the interactivity to investigate what kinds of triangles can be
drawn on peg boards with different numbers of pegs.
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?
Do you notice anything about the solutions when you add and/or
subtract consecutive negative numbers?
It's easy to work out the areas of most squares that we meet, but
what if they were tilted?
Here are two kinds of spirals for you to explore. What do you notice?
Investigate the sum of the numbers on the top and bottom faces of a line of three dice. What do you notice?
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?
How could Penny, Tom and Matthew work out how many chocolates there
are in different sized boxes?
These squares have been made from Cuisenaire rods. Can you describe
the pattern? What would the next square look like?
Try entering different sets of numbers in the number pyramids. How does the total at the top change?
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?
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?