Place the numbers 1 to 8 in the circles so that no consecutive
numbers are joined by a line.
Investigate the smallest number of moves it takes to turn these
mats upside-down if you can only turn exactly three at a time.
A game for 2 people. Take turns placing a counter on the star. You win when you have completed a line of 3 in your colour.
Frances and Rishi were given a bag of lollies. They shared them out evenly and had one left over. How many lollies could there have been in the bag?
In this maze of hexagons, you start in the centre at 0. The next
hexagon must be a multiple of 2 and the next a multiple of 5. What
are the possible paths you could take?
Ben and his mum are planting garlic. Use the interactivity to help
you find out how many cloves of garlic they might have had.
First Connect Three game for an adult and child. Use the dice numbers and either addition or subtraction to get three numbers in a straight line.
Arrange the four number cards on the grid, according to the rules,
to make a diagonal, vertical or horizontal line.
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?
Can you find the chosen number from the grid using the clues?
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?
Move from the START to the FINISH by moving across or down to the
next square. Can you find a route to make these totals?
Arrange eight of the numbers between 1 and 9 in the Polo Square
below so that each side adds to the same total.
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....?
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?
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.
I was in my car when I noticed a line of four cars on the lane next
to me with number plates starting and ending with J, K, L and M.
What order were they in?
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?
Using the statements, can you work out how many of each type of
rabbit there are in these pens?
The planet of Vuvv has seven moons. Can you work out how long it is
between each super-eclipse?
Choose four different digits from 1-9 and put one in each box so that the resulting four two-digit numbers add to a total of 100.
Arrange 9 red cubes, 9 blue cubes and 9 yellow cubes into a large 3 by 3 cube. No row or column of cubes must contain two cubes of the same colour.
Only one side of a two-slice toaster is working. What is the
quickest way to toast both sides of three slices of bread?
Use the information to describe these marbles. What colours must be
on marbles that sparkle when rolling but are dark inside?
Exactly 195 digits have been used to number the pages in a book.
How many pages does the book have?
Can you put the numbers from 1 to 15 on the circles so that no
consecutive numbers lie anywhere along a continuous straight line?
This problem is based on the story of the Pied Piper of Hamelin. Investigate the different numbers of people and rats there could have been if you know how many legs there are altogether!
These are the faces of Will, Lil, Bill, Phil and Jill. Use the clues to work out which name goes with each face.
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. . . .
In how many ways could Mrs Beeswax put ten coins into her three
puddings so that each pudding ended up with at least two coins?
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!
There are 4 jugs which hold 9 litres, 7 litres, 4 litres and 2
litres. Find a way to pour 9 litres of drink from one jug to
another until you are left with exactly 3 litres in three of the
Start with three pairs of socks. Now mix them up so that no
mismatched pair is the same as another mismatched pair. Is there
more than one way to do it?
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.
These activities lend themselves to systematic working in the sense that it helps if you have an ordered approach.
These activities focus on finding all possible solutions so if you work in a systematic way, you won't leave any out.
These activities focus on finding all possible solutions so working in a systematic way will ensure none are left out.
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 see who the gold medal winner is? What about the silver medal winner and the bronze medal winner?
Try this matching game which will help you recognise different ways of saying the same time interval.
In this matching game, you have to decide how long different events take.
This task follows on from Build it Up and takes the ideas into three dimensions!
Can you find all the ways to get 15 at the top of this triangle of numbers?
Use the numbers and symbols to make this number sentence correct. How many different ways can you find?
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?
In this calculation, the box represents a missing digit. What could the digit be? What would the solution be in each case?
This challenge focuses on finding the sum and difference of pairs of two-digit numbers.
This tricky challenge asks you to find ways of going across rectangles, going through exactly ten squares.
These activities lend themselves to systematic working in the sense that it helps to have an ordered approach.