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?
Find the sum of all three-digit numbers each of whose digits is
Use your addition and subtraction skills, combined with some strategic thinking, to beat your partner at this game.
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?
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.
Only one side of a two-slice toaster is working. What is the
quickest way to toast both sides of three slices of bread?
Can you put the numbers 1-5 in the V shape so that both 'arms' have the same total?
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
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?
An investigation that gives you the opportunity to make and justify
How many ways can you find to do up all four buttons on my coat?
How about if I had five buttons? Six ...?
Tom and Ben visited Numberland. Use the maps to work out the number
of points each of their routes scores.
This challenge focuses on finding the sum and difference of pairs of two-digit 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?
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?
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?
Strike it Out game for an adult and child. Can you stop your partner from being able to go?
What happens when you round these numbers to the nearest whole number?
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 activity involves rounding four-digit numbers to the nearest thousand.
This article for teachers describes several games, found on the
site, all of which have a related structure that can be used to
develop the skills of strategic planning.
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.
A three digit number abc is always divisible by 7 when 2a+3b+c is divisible by 7. Why?
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?
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.
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.
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?
Investigate the sum of the numbers on the top and bottom faces of a line of three dice. What do you notice?
Polygonal numbers are those that are arranged in shapes as they enlarge. Explore the polygonal numbers drawn here.
Got It game for an adult and child. How can you play so that you know you will always win?
Can you explain how this card trick works?
Find out what a "fault-free" rectangle is and try to make some of
Can you see why 2 by 2 could be 5? Can you predict what 2 by 10
Do you notice anything about the solutions when you add and/or
subtract consecutive negative 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?
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?
Delight your friends with this cunning trick! Can you explain how
The NRICH team are always looking for new ways to engage teachers
and pupils in problem solving. Here we explain the thinking behind
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?
For this challenge, you'll need to play Got It! Can you explain the strategy for winning this game with any target?
Can you continue this pattern of triangles and begin to predict how many sticks are used for each new "layer"?
Compare the numbers of particular tiles in one or all of these
three designs, inspired by the floor tiles of a church in
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.
Problem solving is at the heart of the NRICH site. All the problems
give learners opportunities to learn, develop or use mathematical
concepts and skills. Read here for more information.
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?
In how many ways can you arrange three dice side by side on a
surface so that the sum of the numbers on each of the four faces
(top, bottom, front and back) is equal?
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.