How many different symmetrical shapes can you make by shading triangles or squares?
Systematically explore the range of symmetric designs that can be
created by shading parts of the motif below. Use normal square
lattice paper to record your results.
A challenging activity focusing on finding all possible ways of stacking rods.
Use the clues about the symmetrical properties of these letters to
place them on the grid.
How many different ways can you find of fitting five hexagons
together? How will you know you have found all the ways?
In how many ways can you fit two of these yellow triangles
together? Can you predict the number of ways two blue triangles can
be fitted together?
In how many ways can you stack these rods, following the rules?
Can you use your powers of logic and deduction to work out the missing information in these sporty situations?
Follow the clues to find the mystery number.
Four small numbers give the clue to the contents of the four
Using different numbers of sticks, how many different triangles are
you able to make? Can you make any rules about the numbers of
sticks that make the most triangles?
Find the smallest whole number which, when mutiplied by 7, gives a
product consisting entirely of ones.
Can you find which shapes you need to put into the grid to make the
totals at the end of each row and the bottom of each column?
A student in a maths class was trying to get some information from
her teacher. She was given some clues and then the teacher ended by
saying, "Well, how old are they?"
A particular technique for solving Sudoku puzzles, known as "naked pair", is explained in this easy-to-read article.
How many rectangles can you find in this shape? Which ones are
differently sized and which are 'similar'?
Look carefully at the numbers. What do you notice? Can you make
another square using the numbers 1 to 16, that displays the same
A Latin square of order n is an array of n symbols in which each symbol occurs exactly once in each row and exactly once in each column.
Hover your mouse over the counters to see which ones will be
removed. Click to remover them. The winner is the last one to
remove a counter. How you can make sure you win?
A dog is looking for a good place to bury his bone. Can you work
out where he started and ended in each case? What possible routes
could he have taken?
How many different shaped boxes can you design for 36 sweets in one
layer? Can you arrange the sweets so that no sweets of the same
colour are next to each other in any direction?
This pair of linked Sudokus matches letters with numbers and hides a seasonal greeting. Can you find it?
Can you help the children find the two triangles which have the
lengths of two sides numerically equal to their areas?
Can you draw a square in which the perimeter is numerically equal
to the area?
Use the clues to find out who's who in the family, to fill in the family tree and to find out which of the family members are mathematicians and which are not.
An activity making various patterns with 2 x 1 rectangular tiles.
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...
Use your logical-thinking skills to deduce how much Dan's crisps and ice-cream cost altogether.
This magic square has operations written in it, to make it into a
maze. Start wherever you like, go through every cell and go out a
total of 15!
Can you fill in this table square? The numbers 2 -12 were used to generate it with just one number used twice.
George and Jim want to buy a chocolate bar. George needs 2p more
and Jim need 50p more to buy it. How much is the chocolate bar?
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?
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. . . .
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?
This package contains a collection of problems from the NRICH
website that could be suitable for students who have a good
understanding of Factors and Multiples and who feel ready to take
on some. . . .
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. . . .
A merchant brings four bars of gold to a jeweller. How can the
jeweller use the scales just twice to identify the lighter, fake
How many different triangles can you make on a circular pegboard that has nine pegs?
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.
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?
60 pieces and a challenge. What can you make and how many of the
pieces can you use creating skeleton polyhedra?
Arrange eight of the numbers between 1 and 9 in the Polo Square
below so that each side adds to the same total.
Use the differences to find the solution to this Sudoku.
The letters of the word ABACUS have been arranged in the shape of a
triangle. How many different ways can you find to read the word
ABACUS from this triangular pattern?
A Sudoku with clues as ratios.
Rather than using the numbers 1-9, this sudoku uses the nine
different letters used to make the words "Advent Calendar".
When you throw two regular, six-faced dice you have more chance of getting one particular result than any other. What result would that be? Why is this?
Tim's class collected data about all their pets. Can you put the
animal names under each column in the block graph using the
What do the digits in the number fifteen add up to? How many other
numbers have digits with the same total but no zeros?
The clues for this Sudoku are the product of the numbers in adjacent squares.