Find the sum of all three-digit numbers each of whose digits is
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?
Only one side of a two-slice toaster is working. What is the
quickest way to toast both sides of three slices of bread?
What happens when you round these three-digit numbers to the nearest 100?
How many ways can you find to do up all four buttons on my coat? How about if I had five buttons? Six ...?
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 activity involves rounding four-digit numbers to the nearest thousand.
Use two dice to generate two numbers with one decimal place. What happens when you round these numbers to the nearest whole number?
Polygonal numbers are those that are arranged in shapes as they enlarge. Explore the polygonal numbers drawn here.
This challenge focuses on finding the sum and difference of pairs of two-digit numbers.
Can you put the numbers 1-5 in the V shape so that both 'arms' have the same total?
Use your addition and subtraction skills, combined with some strategic thinking, to beat your partner at this game.
What happens when you round these numbers to the nearest whole number?
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.
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?
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?
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
This challenge, written for the Young Mathematicians' Award, invites you to explore 'centred squares'.
Are these statements always true, sometimes true or never true?
Tom and Ben visited Numberland. Use the maps to work out the number of points each of their routes scores.
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?
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?
Investigate the sum of the numbers on the top and bottom faces of a line of three dice. What do you notice?
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?
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?
Can you make dice stairs using the rules stated? How do you know you have all the possible stairs?
Do you notice anything about the solutions when you add and/or
subtract consecutive negative numbers?
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 can you say about these shapes? This problem challenges you to create shapes with different areas and perimeters.
Strike it Out game for an adult and child. Can you stop your partner from being able to go?
Choose any 3 digits and make a 6 digit number by repeating the 3
digits in the same order (e.g. 594594). Explain why whatever digits
you choose the number will always be divisible by 7, 11 and 13.
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?
A game for 2 players. Set out 16 counters in rows of 1,3,5 and 7. Players take turns to remove any number of counters from a row. The player left with the last counter looses.
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?
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?
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?
This challenge asks you to imagine a snake coiling on itself.
A three digit number abc is always divisible by 7 when 2a+3b+c is divisible by 7. Why?
Four bags contain a large number of 1s, 3s, 5s and 7s. Pick any ten numbers from the bags above so that their total is 37.
Delight your friends with this cunning trick! Can you explain how
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?
Find out what a "fault-free" rectangle is and try to make some of
Many numbers can be expressed as the sum of two or more consecutive integers. For example, 15=7+8 and 10=1+2+3+4. Can you say which numbers can be expressed in this way?
Are these statements relating to odd and even numbers always true, sometimes true or never true?
Find a route from the outside to the inside of this square, stepping on as many tiles as possible.