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?
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 focuses on finding the sum and difference of pairs of two-digit numbers.
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?
Tom and Ben visited Numberland. Use the maps to work out the number
of points each of their routes scores.
Sweets are given out to party-goers in a particular way. Investigate the total number of sweets received by people sitting in different positions.
Use your addition and subtraction skills, combined with some strategic thinking, to beat your partner at this game.
How many ways can you find to do up all four buttons on my coat?
How about if I had five buttons? Six ...?
Only one side of a two-slice toaster is working. What is the
quickest way to toast both sides of three slices of bread?
Find the sum of all three-digit numbers each of whose digits is
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.
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?
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?
An investigation that gives you the opportunity to make and justify
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.
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?
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?
Can you see why 2 by 2 could be 5? Can you predict what 2 by 10
Find out what a "fault-free" rectangle is and try to make some of
What happens when you round these three-digit numbers to the nearest 100?
Can you put the numbers 1-5 in the V shape so that both 'arms' have the same total?
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 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.
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
Can you continue this pattern of triangles and begin to predict how
many sticks are used for each new "layer"?
Take a counter and surround it by a ring of other counters that
MUST touch two others. How many are needed?
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?
Polygonal numbers are those that are arranged in shapes as they enlarge. Explore the polygonal numbers drawn here.
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?
What happens when you round these numbers to the nearest whole 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?
Compare the numbers of particular tiles in one or all of these
three designs, inspired by the floor tiles of a church in
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?
Investigate the sum of the numbers on the top and bottom faces of a line of three dice. What do you notice?
For this challenge, you'll need to play Got It! Can you explain the
strategy for winning this game with any target?
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?
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. . . .
A three digit number abc is always divisible by 7 when 2a+3b+c is divisible by 7. Why?
Try entering different sets of numbers in the number pyramids. How does the total at the top change?
Imagine we have four bags containing a large number of 1s, 4s, 7s and 10s. What numbers can we make?
This activity involves rounding four-digit numbers to the nearest thousand.
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.
These squares have been made from Cuisenaire rods. Can you describe
the pattern? What would the next square look like?
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.
This challenge asks you to imagine a snake coiling on itself.
In each of the pictures the invitation is for you to: Count what you see. Identify how you think the pattern would continue.
Delight your friends with this cunning trick! Can you explain how