How many pairs of numbers can you find that add up to a multiple of 11? Do you notice anything interesting about your results?
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.
This activity involves rounding four-digit numbers to the nearest thousand.
Take any two digit number, for example 58. What do you have to do to reverse the order of the digits? Can you find a rule for reversing the order of digits for any two digit 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?
For this challenge, you'll need to play Got It! Can you explain the strategy for winning this game with any target?
A three digit number abc is always divisible by 7 when 2a+3b+c is divisible by 7. Why?
Caroline and James pick sets of five numbers. Charlie chooses three of them that add together to make a multiple of three. Can they stop him?
Are these statements always true, sometimes true or never true?
Investigate the sum of the numbers on the top and bottom faces of a line of three dice. What do you notice?
Imagine we have four bags containing a large number of 1s, 4s, 7s and 10s. What numbers can we make?
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?
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 a route from the outside to the inside of this square, stepping on as many tiles as possible.
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 relating to odd and even numbers always true, sometimes true or never true?
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?
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.
Got It game for an adult and child. How can you play so that you know you will always win?
This challenge asks you to imagine a snake coiling on itself.
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?
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?
How many ways can you find to do up all four buttons on my coat? How about if I had five buttons? Six ...?
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 encourages you to explore dividing a three-digit number by a single-digit number.
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.
Imagine we have four bags containing numbers from a sequence. What numbers can we make now?
Here are two kinds of spirals for you to explore. What do you notice?
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. . . .
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 the sum of all three-digit numbers each of whose digits is
Nim-7 game for an adult and child. Who will be the one to take the last counter?
Only one side of a two-slice toaster is working. What is the
quickest way to toast both sides of three slices of bread?
How could Penny, Tom and Matthew work out how many chocolates there
are in different sized boxes?
This challenge, written for the Young Mathematicians' Award, invites you to explore 'centred squares'.
Charlie has made a Magic V. Can you use his example to make some more? And how about Magic Ls, Ns and Ws?
An investigation that gives you the opportunity to make and justify
Pick a square within a multiplication square and add the numbers on
each diagonal. What do you notice?
Use two dice to generate two numbers with one decimal place. What happens when you round these numbers to the nearest whole number?
Imagine starting with one yellow cube and covering it all over with
a single layer of red cubes, and then covering that cube with a
layer of blue cubes. How many red and blue cubes would you need?
Use the animation to help you work out how many lines are needed to draw mystic roses of different sizes.
This challenge focuses on finding the sum and difference of pairs of two-digit numbers.
If you can copy a network without lifting your pen off the paper and without drawing any line twice, then it is traversable.
Decide which of these diagrams are traversable.
What happens when you round these three-digit numbers to the nearest 100?
Tom and Ben visited Numberland. Use the maps to work out the number of points each of their routes scores.
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?
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?
Can you explain how this card trick works?
This task follows on from Build it Up and takes the ideas into three dimensions!