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?
This activity involves rounding four-digit numbers to the nearest thousand.
Are these statements always true, sometimes true or never true?
Nim-7 game for an adult and child. Who will be the one to take the last counter?
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
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?
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?
Investigate the sum of the numbers on the top and bottom faces of a line of three dice. What do you notice?
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?
Can you explain how this card trick works?
Are these statements relating to odd and even numbers always true, sometimes true or never true?
This challenge asks you to imagine a snake coiling on itself.
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
Here are two kinds of spirals for you to explore. What do you notice?
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?
Find a route from the outside to the inside of this square, stepping on as many tiles as possible.
Do you notice anything about the solutions when you add and/or
subtract consecutive negative numbers?
What happens when you round these three-digit numbers to the nearest 100?
Polygonal numbers are those that are arranged in shapes as they enlarge. Explore the polygonal numbers drawn here.
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?
This challenge focuses on finding the sum and difference of pairs of two-digit numbers.
Use two dice to generate two numbers with one decimal place. What happens when you round these numbers to the nearest whole number?
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?
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.
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.
A three digit number abc is always divisible by 7 when 2a+3b+c is divisible by 7. Why?
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?
An investigation that gives you the opportunity to make and justify
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?
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. . . .
What happens when you round these numbers to the nearest whole number?
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.
Delight your friends with this cunning trick! Can you explain how
Got It game for an adult and child. How can you play so that you know you will always win?
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?
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.
How many pairs of numbers can you find that add up to a multiple of 11? Do you notice anything interesting about your results?
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, written for the Young Mathematicians' Award, invites you to explore 'centred squares'.
How many centimetres of rope will I need to make another mat just
like the one I have here?
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. . . .
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?
This task follows on from Build it Up and takes the ideas into three dimensions!
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?
Tom and Ben visited Numberland. Use the maps to work out the number of points each of their routes scores.
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?
The NRICH team are always looking for new ways to engage teachers
and pupils in problem solving. Here we explain the thinking behind