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 task follows on from Build it Up and takes the ideas into three dimensions!
Investigate the sum of the numbers on the top and bottom faces of a line of three dice. What do you notice?
This activity involves rounding four-digit numbers to the nearest thousand.
Got It game for an adult and child. How can you play so that you know you will always win?
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 find all the ways to get 15 at the top of this triangle of numbers?
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
Are these statements always true, sometimes true or never true?
This challenge, written for the Young Mathematicians' Award, invites you to explore 'centred squares'.
This challenge focuses on finding the sum and difference of pairs of two-digit numbers.
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?
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.
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.
Can you explain how this card trick works?
A three digit number abc is always divisible by 7 when 2a+3b+c is divisible by 7. Why?
What happens when you round these three-digit numbers to the nearest 100?
Use two dice to generate two numbers with one decimal place. What happens when you round these numbers to the nearest whole number?
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?
Can you see why 2 by 2 could be 5? Can you predict what 2 by 10
An investigation that gives you the opportunity to make and justify
Here are two kinds of spirals for you to explore. What do you notice?
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 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.
Can you explain the strategy for winning this game with any target?
Sweets are given out to party-goers in a particular way. Investigate the total number of sweets received by people sitting in different positions.
Consider all two digit numbers (10, 11, . . . ,99). In writing down
all these numbers, which digits occur least often, and which occur
most often ? What about three digit numbers, four digit numbers. . . .
This challenge asks you to imagine a snake coiling on itself.
Nim-7 game for an adult and child. Who will be the one to take the last counter?
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.
Watch this video to see how to roll the dice. Now it's your turn! What do you notice about the dice numbers you have recorded?
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?
Find a route from the outside to the inside of this square, stepping on as many tiles as possible.
Find the sum of all three-digit numbers each of whose digits is
This challenge encourages you to explore dividing a three-digit number by a single-digit 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?
Strike it Out game for an adult and child. Can you stop your partner from being able to go?
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?
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?
Are these statements relating to odd and even numbers always true, sometimes true or never true?
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?
Try entering different sets of numbers in the number pyramids. How does the total at the top change?
Pick the number of times a week that you eat chocolate. This number must be more than one but less than ten.
Multiply this number by 2. Add 5 (for Sunday). Multiply by 50... Can you explain why it. . . .
Polygonal numbers are those that are arranged in shapes as they enlarge. Explore the polygonal numbers drawn here.
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.
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?
What can you say about these shapes? This problem challenges you to create shapes with different areas and perimeters.
Can you make dice stairs using the rules stated? How do you know you have all the possible stairs?