Can you put the numbers 1-5 in the V shape so that both 'arms' have the same total?
An investigation that gives you the opportunity to make and justify
Do you notice anything about the solutions when you add and/or
subtract consecutive negative numbers?
What happens when you add three numbers together? Will your answer be odd or even? How do you know?
Find out about Magic Squares in this article written for students. Why are they magic?!
Starting with four different triangles, imagine you have an
unlimited number of each type. How many different tetrahedra can
you make? Convince us you have found them all.
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.
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.
Find a cuboid (with edges of integer values) that has a surface
area of exactly 100 square units. Is there more than one? Can you
find them all?
Bellringers have a special way to write down the patterns they
ring. Learn about these patterns and draw some of your own.
Mr McGregor has a magic potting shed. Overnight, the number of
plants in it doubles. He'd like to put the same number of plants in
each of three gardens, planting one garden each day. Can he do it?
Seven friends went to a fun fair with lots of scary rides. They
decided to pair up for rides until each friend had ridden once with
each of the others. What was the total number rides?
The idea of this game is to add or subtract the two numbers on the dice and cover the result on the grid, trying to get a line of three. Are there some numbers that are good to aim for?
You have been given nine weights, one of which is slightly heavier
than the rest. Can you work out which weight is heavier in just two
weighings of the balance?
Use the clues to work out which cities Mohamed, Sheng, Tanya and
Bharat live in.
Can you find six numbers to go in the Daisy from which you can make all the numbers from 1 to a number bigger than 25?
Only one side of a two-slice toaster is working. What is the
quickest way to toast both sides of three slices of bread?
My two digit number is special because adding the sum of its digits
to the product of its digits gives me my original number. What
could my number be?
Make a pair of cubes that can be moved to show all the days of the
month from the 1st to the 31st.
Can you arrange the numbers 1 to 17 in a row so that each adjacent
pair adds up to a square number?
Sweets are given out to party-goers in a particular way. Investigate the total number of sweets received by people sitting in different positions.
Can you order the digits from 1-6 to make a number which is
divisible by 6 so when the last digit is removed it becomes a
5-figure number divisible by 5, and so on?
Tom and Ben visited Numberland. Use the maps to work out the number
of points each of their routes scores.
How many ways can you find to do up all four buttons on my coat?
How about if I had five buttons? Six ...?
This challenge focuses on finding the sum and difference of pairs of two-digit numbers.
This Sudoku, based on differences. Using the one clue number can you find the solution?
Play the divisibility game to create numbers in which the first two digits make a number divisible by 2, the first three digits make a number divisible by 3...
There is a clock-face where the numbers have become all mixed up. Can you find out where all the numbers have got to from these ten statements?
If these elves wear a different outfit every day for as many days
as possible, how many days can their fun last?
Can you coach your rowing eight to win?
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?
Advent Calendar 2011 - a mathematical activity for each day during the run-up to Christmas.
Investigate the smallest number of moves it takes to turn these
mats upside-down if you can only turn exactly three at a time.
Follow the clues to find the mystery number.
An irregular tetrahedron is composed of four different triangles.
Can such a tetrahedron be constructed where the side lengths are 4,
5, 6, 7, 8 and 9 units of length?
Tim had nine cards each with a different number from 1 to 9 on it.
How could he have put them into three piles so that the total in
each pile was 15?
Ben passed a third of his counters to Jack, Jack passed a quarter
of his counters to Emma and Emma passed a fifth of her counters to
Ben. After this they all had the same number of counters.
Penta people, the Pentominoes, always build their houses from five
square rooms. I wonder how many different Penta homes you can
Is it possible to place 2 counters on the 3 by 3 grid so that there
is an even number of counters in every row and every column? How
about if you have 3 counters or 4 counters or....?
The puzzle can be solved with the help of small clue-numbers which
are either placed on the border lines between selected pairs of
neighbouring squares of the grid or placed after slash marks on. . . .
This practical challenge invites you to investigate the different
squares you can make on a square geoboard or pegboard.
Whenever a monkey has peaches, he always keeps a fraction of them each day, gives the rest away, and then eats one. How long could he make his peaches last for?
Arrange eight of the numbers between 1 and 9 in the Polo Square
below so that each side adds to the same total.
Zumf makes spectacles for the residents of the planet Zargon, who
have either 3 eyes or 4 eyes. How many lenses will Zumf need to
make all the different orders for 9 families?
60 pieces and a challenge. What can you make and how many of the
pieces can you use creating skeleton polyhedra?
Use the differences to find the solution to this Sudoku.
Four small numbers give the clue to the contents of the four
Write the numbers up to 64 in an interesting way so that the shape they make at the end is interesting, different, more exciting ... than just a square.
A package contains a set of resources designed to develop
students’ mathematical thinking. This package places a
particular emphasis on “being systematic” and is
designed to meet. . . .
How many shapes can you build from three red and two green cubes? Can you use what you've found out to predict the number for four red and two green?