How many different symmetrical shapes can you make by shading triangles or squares?
A challenging activity focusing on finding all possible ways of stacking rods.
How many different ways can you find of fitting five hexagons
together? How will you know you have found all the ways?
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.
Use the clues about the symmetrical properties of these letters to
place them on the grid.
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....?
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?
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. . . .
Alice's mum needs to go to each child's house just once and then
back home again. How many different routes are there? Use the
information to find out how long each road is on the route she
If you have only 40 metres of fencing available, what is the maximum area of land you can fence off?
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.
This practical challenge invites you to investigate the different
squares you can make on a square geoboard or pegboard.
Are all the possible combinations of two shapes included in this
set of 27 cards? How do you know?
60 pieces and a challenge. What can you make and how many of the
pieces can you use creating skeleton polyhedra?
How can you put five cereal packets together to make different
shapes if you must put them face-to-face?
Just four procedures were used to produce a design. How was it
done? Can you be systematic and elegant so that someone can follow
Use the differences to find the solution to this Sudoku.
Four small numbers give the clue to the contents of the four
Can you coach your rowing eight to win?
A Sudoku with clues as ratios.
A Sudoku with a twist.
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?
Draw some isosceles triangles with an area of $9$cm$^2$ and a vertex at (20,20). If all the vertices must have whole number coordinates, how many is it possible to draw?
Here you see the front and back views of a dodecahedron. Each
vertex has been numbered so that the numbers around each pentagonal
face add up to 65. Can you find all the missing numbers?
Find out what a "fault-free" rectangle is and try to make some of
This challenge, written for the Young Mathematicians' Award, invites you to explore 'centred squares'.
Can you make dice stairs using the rules stated? How do you know you have all the possible stairs?
Four numbers on an intersection that need to be placed in the
surrounding cells. That is all you need to know to solve this
There were chews for 2p, mini eggs for 3p, Chocko bars for 5p and
lollypops for 7p in the sweet shop. What could each of the children
buy with their money?
You have two egg timers. One takes 4 minutes exactly to empty and
the other takes 7 minutes. What times in whole minutes can you
measure and how?
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?
An investigation that gives you the opportunity to make and justify
Number problems at primary level that require careful consideration.
This Sudoku, based on differences. Using the one clue number can you find the solution?
There is a long tradition of creating mazes throughout history and across the world. This article gives details of mazes you can visit and those that you can tackle on paper.
Two sudokus in one. Challenge yourself to make the necessary
How many different triangles can you make on a circular pegboard that has nine pegs?
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?
This task, written for the National Young Mathematicians' Award 2016, focuses on 'open squares'. What would the next five open squares look like?
Can you find all the different ways of lining up these Cuisenaire
Do you notice anything about the solutions when you add and/or
subtract consecutive negative numbers?
This task, written for the National Young Mathematicians' Award 2016, invites you to explore the different combinations of scores that you might get on these dart boards.
Arrange eight of the numbers between 1 and 9 in the Polo Square
below so that each side adds to the same total.
This pair of linked Sudokus matches letters with numbers and hides a seasonal greeting. Can you find it?
What do the numbers shaded in blue on this hundred square have in common? What do you notice about the pink numbers? How about the shaded numbers in the other squares?
Different combinations of the weights available allow you to make different totals. Which totals can you make?
There are seven pots of plants in a greenhouse. They have lost their labels. Perhaps you can help re-label them.
There are nine teddies in Teddy Town - three red, three blue and three yellow. There are also nine houses, three of each colour. Can you put them on the map of Teddy Town according to the rules?
Ram divided 15 pennies among four small bags. He could then pay any sum of money from 1p to 15p without opening any bag. How many pennies did Ram put in each bag?
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?