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!
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, written for the Young Mathematicians' Award, invites you to explore 'centred squares'.
Can you find all the ways to get 15 at the top of this triangle of numbers?
Strike it Out game for an adult and child. Can you stop your partner from being able to go?
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 and difference between a pair of two-digit numbers. Now find the sum and difference between the sum and difference! What happens?
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.
Use your addition and subtraction skills, combined with some strategic thinking, to beat your partner at this game.
Only one side of a two-slice toaster is working. What is the
quickest way to toast both sides of three slices of bread?
This challenge focuses on finding the sum and difference of pairs of two-digit numbers.
Tom and Ben visited Numberland. Use the maps to work out the number of points each of their routes scores.
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?
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
Can you continue this pattern of triangles and begin to predict how many sticks are used for each new "layer"?
What can you say about these shapes? This problem challenges you to create shapes with different areas and perimeters.
Can you put the numbers 1-5 in the V shape so that both 'arms' have the same total?
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?
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?
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.
Can you see why 2 by 2 could be 5? Can you predict what 2 by 10
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?
An investigation that gives you the opportunity to make and justify
Use the interactivity to investigate what kinds of triangles can be
drawn on peg boards with different numbers of pegs.
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?
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
Use two dice to generate two numbers with one decimal place. What happens when you round these numbers to the nearest whole number?
Got It game for an adult and child. How can you play so that you know you will always win?
Can you make dice stairs using the rules stated? How do you know you have all the possible stairs?
This challenge encourages you to explore dividing a three-digit number by a single-digit number.
Watch this film carefully. Can you find a general rule for
explaining when the dot will be this same distance from the
Nim-7 game for an adult and child. Who will be the one to take the last counter?
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?
What happens when you round these three-digit numbers to the nearest 100?
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?
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?
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?
Compare the numbers of particular tiles in one or all of these
three designs, inspired by the floor tiles of a church in
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.
Here are two kinds of spirals for you to explore. What do you notice?
Are these statements relating to odd and even numbers always true, sometimes true or never true?
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?
Triangle numbers can be represented by a triangular array of squares. What do you notice about the sum of identical triangle numbers?
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.
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.