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?
Ben and his mum are planting garlic. Use the interactivity to help
you find out how many cloves of garlic they might have had.
Investigate the smallest number of moves it takes to turn these
mats upside-down if you can only turn exactly three at a time.
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?
Let's suppose that you are going to have a magazine which has 16
pages of A5 size. Can you find some different ways to make these
pages? Investigate the pattern for each if you number the pages.
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?
Arrange the four number cards on the grid, according to the rules,
to make a diagonal, vertical or horizontal line.
How many ways can you find to do up all four buttons on my coat?
How about if I had five buttons? Six ...?
This tricky challenge asks you to find ways of going across rectangles, going through exactly ten squares.
In this problem it is not the squares that jump, you do the jumping! The idea is to go round the track in as few jumps as possible.
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 work out how to balance this equaliser? You can put more
than one weight on a hook.
You have 4 red and 5 blue counters. How many ways can they be
placed on a 3 by 3 grid so that all the rows columns and diagonals
have an even number of red counters?
Only one side of a two-slice toaster is working. What is the
quickest way to toast both sides of three slices of bread?
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?
How many trains can you make which are the same length as Matt's, using rods that are identical?
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.
Exactly 195 digits have been used to number the pages in a book.
How many pages does the book have?
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....?
Find out what a "fault-free" rectangle is and try to make some of
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 find the chosen number from the grid using the clues?
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?
This challenge focuses on finding the sum and difference of pairs of two-digit numbers.
This challenge is about finding the difference between numbers which have the same tens digit.
In this matching game, you have to decide how long different events take.
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?
Try this matching game which will help you recognise different ways of saying the same time interval.
In this calculation, the box represents a missing digit. What could the digit be? What would the solution be in each case?
Place the numbers 1 to 8 in the circles so that no consecutive
numbers are joined by a line.
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.
Look carefully at the numbers. What do you notice? Can you make
another square using the numbers 1 to 16, that displays the same
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?
Can you help the children find the two triangles which have the
lengths of two sides numerically equal to their areas?
Use your logical-thinking skills to deduce how much Dan's crisps and ice-cream cost altogether.
Can you fill in this table square? The numbers 2 -12 were used to generate it with just one number used twice.
A magician took a suit of thirteen cards and held them in his hand
face down. Every card he revealed had the same value as the one he
had just finished spelling. How did this work?
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.
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?
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?
Arrange eight of the numbers between 1 and 9 in the Polo Square
below so that each side adds to the same total.
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 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!
A merchant brings four bars of gold to a jeweller. How can the
jeweller use the scales just twice to identify the lighter, fake
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. . . .
Here are some rods that are different colours. How could I make a dark green rod using yellow and white rods?
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?
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?
Use these head, body and leg pieces to make Robot Monsters which
are different heights.
How many triangles can you make using sticks that are 3cm, 4cm and 5cm long?