Ben’s class were making cutting up number tracks. First they
cut them into twos and added up the numbers on each piece. What
patterns could they see?
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 challenge encourages you to explore dividing a three-digit number by a single-digit number.
Got It game for an adult and child. How can you play so that you know you will always win?
Can you continue this pattern of triangles and begin to predict how many sticks are used for each new "layer"?
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?
An investigation that gives you the opportunity to make and justify
This challenge focuses on finding the sum and difference of pairs of two-digit numbers.
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?
Ben and his mum are planting garlic. Use the interactivity to help
you find out how many cloves of garlic they might have had.
Only one side of a two-slice toaster is working. What is the
quickest way to toast both sides of three slices of bread?
Polygonal numbers are those that are arranged in shapes as they enlarge. Explore the polygonal numbers drawn here.
Frances and Rishi were given a bag of lollies. They shared them out evenly and had one left over. How many lollies could there have been in the bag?
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.
This problem challenges you to find out how many odd numbers there
are between pairs of numbers. Can you find a pair of numbers that
has four odds between them?
Tom and Ben visited Numberland. Use the maps to work out the number
of points each of their routes scores.
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?
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 activity involves rounding four-digit numbers to the nearest thousand.
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.
This challenge asks you to imagine a snake coiling on itself.
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?
Find out what a "fault-free" rectangle is and try to make some of
How many centimetres of rope will I need to make another mat just
like the one I have here?
What can you say about these shapes? This problem challenges you to
create shapes with different areas and perimeters.
Two children made up a game as they walked along the garden paths.
Can you find out their scores? Can you find some paths of your own?
Sweets are given out to party-goers in a particular way. Investigate the total number of sweets received by people sitting in different positions.
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?
Use your addition and subtraction skills, combined with some strategic thinking, to beat your partner at this game.
Can you put the numbers 1-5 in the V shape so that both 'arms' have the same total?
In this calculation, the box represents a missing digit. What could the digit be? What would the solution be in each case?
Strike it Out game for an adult and child. Can you stop your partner from being able to go?
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?
Nim-7 game for an adult and child. Who will be the one to take the last counter?
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?
Compare the numbers of particular tiles in one or all of these
three designs, inspired by the floor tiles of a church in
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?
Find a route from the outside to the inside of this square, stepping on as many tiles as possible.
A game for two people, or play online. Given a target number, say 23, and a range of numbers to choose from, say 1-4, players take it in turns to add to the running total to hit their target.
For this challenge, you'll need to play Got It! Can you explain the strategy for winning this game with any target?
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 happens when you round these three-digit numbers to the nearest 100?
This activity focuses on rounding to the nearest 10.
The NRICH team are always looking for new ways to engage teachers
and pupils in problem solving. Here we explain the thinking behind
Use two dice to generate two numbers with one decimal place. What happens when you round these numbers to the nearest whole number?
In each of the pictures the invitation is for you to: Count what you see. Identify how you think the pattern would continue.
This challenge is about finding the difference between numbers which have the same tens digit.