Can you coach your rowing eight to win?
Move your counters through this snake of cards and see how far you
can go. Are you surprised by where you end up?
Try out the lottery that is played in a far-away land. What is the
chance of winning?
Tim's class collected data about all their pets. Can you put the
animal names under each column in the block graph using the
Roll two red dice and a green dice. Add the two numbers on the red dice and take away the number on the green. What are all the different possibilities that could come up?
If you have only 40 metres of fencing available, what is the maximum area of land you can fence off?
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
Find out about Magic Squares in this article written for students. Why are they magic?!
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.
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?
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?
Use the differences to find the solution to this Sudoku.
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?
Four small numbers give the clue to the contents of the four
A Sudoku with a twist.
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?
Are all the possible combinations of two shapes included in this
set of 27 cards? How do you know?
A Sudoku with clues as ratios.
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.
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. . . .
An investigation that gives you the opportunity to make and justify
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?
Four numbers on an intersection that need to be placed in the
surrounding cells. That is all you need to know to solve this
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?
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?
Can you put the numbers 1-5 in the V shape so that both 'arms' have the same total?
This is a variation of sudoku which contains a set of special clue-numbers. Each set of 4 small digits stands for the numbers in the four cells of the grid adjacent to this set.
An extra constraint means this Sudoku requires you to think in
diagonals as well as horizontal and vertical lines and boxes of
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
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?
Just four procedures were used to produce a design. How was it
done? Can you be systematic and elegant so that someone can follow
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.
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 Sudoku, based on differences. Using the one clue number can you find the solution?
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 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. . . .
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?
What is the date in February 2002 where the 8 digits are
palindromic if the date is written in the British way?
Arrange the four number cards on the grid, according to the rules,
to make a diagonal, vertical or horizontal line.
This multiplication uses each of the digits 0 - 9 once and once only. Using the information given, can you replace the stars in the calculation with figures?
How can you arrange the 5 cubes so that you need the smallest number of Brush Loads of paint to cover them? Try with other numbers of cubes as well.
The Vikings communicated in writing by making simple scratches on
wood or stones called runes. Can you work out how their code works
using the table of the alphabet?
Can you put plus signs in so this is true? 1 2 3 4 5 6 7 8 9 = 99
How many ways can you do it?
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.