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.
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
Only one side of a two-slice toaster is working. What is the
quickest way to toast both sides of three slices of bread?
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.
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?
Use your addition and subtraction skills, combined with some strategic thinking, to beat your partner at this game.
Tom and Ben visited Numberland. Use the maps to work out the number
of points each of their routes scores.
Got It game for an adult and child. How can you play so that you know you will always win?
Sweets are given out to party-goers in a particular way. Investigate the total number of sweets received by people sitting in different positions.
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?
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?
Strike it Out game for an adult and child. Can you stop your partner from being able to go?
Find the sum of all three-digit numbers each of whose digits is
How many ways can you find to do up all four buttons on my coat?
How about if I had five buttons? Six ...?
Ben’s class were making cutting up number tracks. First they
cut them into twos and added up the numbers on each piece. What
patterns could they see?
What can you say about these shapes? This problem challenges you to
create shapes with different areas and perimeters.
This challenge encourages you to explore dividing a three-digit number by a single-digit number.
An investigation that gives you the opportunity to make and justify
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?
Use two dice to generate two numbers with one decimal place. What happens when you round these numbers to the nearest whole number?
Can you see why 2 by 2 could be 5? Can you predict what 2 by 10
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?
Find out what a "fault-free" rectangle is and try to make some of
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.
What happens when you round these three-digit numbers to the nearest 100?
In each of the pictures the invitation is for you to: Count what you see. Identify how you think the pattern would continue.
Can you continue this pattern of triangles and begin to predict how many sticks are used for each new "layer"?
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?
Polygonal numbers are those that are arranged in shapes as they enlarge. Explore the polygonal numbers drawn here.
Investigate the sum of the numbers on the top and bottom faces of a line of three dice. What do you notice?
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?
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.
What happens when you round these numbers to the nearest whole number?
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?
Nim-7 game for an adult and child. Who will be the one to take the last counter?
Compare the numbers of particular tiles in one or all of these
three designs, inspired by the floor tiles of a church in
For this challenge, you'll need to play Got It! Can you explain the strategy for winning this game with any target?
You can work out the number someone else is thinking of as follows. Ask a friend to think of any natural number less than 100. Then ask them to tell you the remainders when this number is divided by. . . .
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?
Can you work out how to win this game of Nim? Does it matter if you go first or second?
Rectangles are considered different if they vary in size or have different locations. How many different rectangles can be drawn on a chessboard?
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.
A three digit number abc is always divisible by 7 when 2a+3b+c is divisible by 7. Why?
These squares have been made from Cuisenaire rods. Can you describe
the pattern? What would the next square look like?
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?
Find some examples of pairs of numbers such that their sum is a
factor of their product. eg. 4 + 12 = 16 and 4 × 12 = 48 and
16 is a factor of 48.
List any 3 numbers. It is always possible to find a subset of
adjacent numbers that add up to a multiple of 3. Can you explain
why and prove it?
Delight your friends with this cunning trick! Can you explain how