Try entering different sets of numbers in the number pyramids. How does the total at the top change?
Do you notice anything about the solutions when you add and/or
subtract consecutive negative numbers?
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?
The NRICH team are always looking for new ways to engage teachers
and pupils in problem solving. Here we explain the thinking behind
Charlie and Abi put a counter on 42. They wondered if they could visit all the other numbers on their 1-100 board, moving the counter using just these two operations: x2 and -5. What do you think?
Strike it Out game for an adult and child. Can you stop your partner from being able to go?
Find the sum of all three-digit numbers each of whose digits is
Got It game for an adult and child. How can you play so that you know you will always win?
Nim-7 game for an adult and child. Who will be the one to take the last counter?
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
Can you explain the strategy for winning this game with any target?
Use your addition and subtraction skills, combined with some strategic thinking, to beat your partner at this game.
Can you see why 2 by 2 could be 5? Can you predict what 2 by 10
This activity involves rounding four-digit numbers to the nearest thousand.
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?
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?
What happens when you round these three-digit numbers to the nearest 100?
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.
Use two dice to generate two numbers with one decimal place. What happens when you round these numbers to the nearest whole number?
Imagine we have four bags containing numbers from a sequence. What numbers can we make now?
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 challenge asks you to imagine a snake coiling on itself.
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.
How many ways can you find to do up all four buttons on my coat? How about if I had five buttons? Six ...?
Triangle numbers can be represented by a triangular array of squares. What do you notice about the sum of identical triangle numbers?
Find out what a "fault-free" rectangle is and try to make some of
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?
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?
This challenge, written for the Young Mathematicians' Award, invites you to explore 'centred squares'.
When number pyramids have a sequence on the bottom layer, some interesting patterns emerge...
A country has decided to have just two different coins, 3z and 5z
coins. Which totals can be made? Is there a largest total that
cannot be made? How do you know?
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?
Sweets are given out to party-goers in a particular way. Investigate the total number of sweets received by people sitting in different positions.
What can you say about these shapes? This problem challenges you to create shapes with different areas and perimeters.
Investigate the sum of the numbers on the top and bottom faces of a line of three dice. What do you notice?
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?
Can you put the numbers 1-5 in the V shape so that both 'arms' have the same total?
Tom and Ben visited Numberland. Use the maps to work out the number of points each of their routes scores.
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.
Are these statements always true, sometimes true or never true?
Can you find all the ways to get 15 at the top of this triangle of numbers?
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 challenge encourages you to explore dividing a three-digit number by a single-digit number.
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?
This task follows on from Build it Up and takes the ideas into three dimensions!
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?
Can you make dice stairs using the rules stated? How do you know you have all the possible stairs?
Find a route from the outside to the inside of this square, stepping on as many tiles as possible.