Are these statements always true, sometimes true or never true?
Find out about Magic Squares in this article written for students. Why are they magic?!
Four bags contain a large number of 1s, 3s, 5s and 7s. Pick any ten numbers from the bags above so that their total is 37.
There were 22 legs creeping across the web. How many flies? How many spiders?
This article gives you a few ideas for understanding the Got It! game and how you might find a winning strategy.
There are three baskets, a brown one, a red one and a pink one, holding a total of 10 eggs. Can you use the information given to find out how many eggs are in each basket?
Claire thinks she has the most sports cards in her album. "I have
12 pages with 2 cards on each page", says Claire. Ross counts his
cards. "No! I have 3 cards on each of my pages and there are. . . .
Arrange the numbers 1 to 6 in each set of circles below. The sum of each side of the triangle should equal the number in its centre.
Woof is a big dog. Yap is a little dog.
Emma has 16 dog biscuits to give to the two dogs.
She gave Woof 4 more biscuits than Yap.
How many biscuits did each dog get?
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?
As you come down the ladders of the Tall Tower you collect useful spells. Which way should you go to collect the most spells?
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 ways to get 15 at the top of this triangle of numbers?
A game for 2 people using a pack of cards Turn over 2 cards and try
to make an odd number or a multiple of 3.
Put operations signs between the numbers 3 4 5 6 to make the highest possible number and lowest possible number.
There are 78 prisoners in a square cell block of twelve cells. The
clever prison warder arranged them so there were 25 along each wall
of the prison block. How did he do it?
What happens when you add three numbers together? Will your answer be odd or even? How do you know?
In this calculation, the box represents a missing digit. What could the digit be? What would the solution be in each case?
Twizzle, a female giraffe, needs transporting to another zoo. Which
route will give the fastest journey?
On Planet Plex, there are only 6 hours in the day. Can you answer
these questions about how Arog the Alien spends his day?
Arrange eight of the numbers between 1 and 9 in the Polo Square
below so that each side adds to the same total.
In this game for two players, the idea is to take it in turns to choose 1, 3, 5 or 7. The winner is the first to make the total 37.
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?
Can you draw a continuous line through 16 numbers on this grid so
that the total of the numbers you pass through is as high as
This big box adds something to any number that goes into it. If you know the numbers that come out, what addition might be going on in the box?
Winifred Wytsh bought a box each of jelly babies, milk jelly bears,
yellow jelly bees and jelly belly beans. In how many different ways
could she make a jolly jelly feast with 32 legs?
We start with one yellow cube and build around it to make a 3x3x3 cube with red cubes. Then we build around that red cube with blue cubes and so on. How many cubes of each colour have we used?
Can you each work out the number on your card? What do you notice?
How could you sort the cards?
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 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?
Skippy and Anna are locked in a room in a large castle. The key to that room, and all the other rooms, is a number. The numbers are locked away in a problem. Can you help them to get out?
Here is a chance to play a version of the classic Countdown Game.
The clockmaker's wife cut up his birthday cake to look like a clock
face. Can you work out who received each piece?
Ben’s class were cutting up number tracks. First they cut them into twos and added up the numbers on each piece. What patterns could they see?
There are 44 people coming to a dinner party. There are 15 square
tables that seat 4 people. Find a way to seat the 44 people using
all 15 tables, with no empty places.
Fill in the numbers to make the sum of each row, column and
diagonal equal to 15.
Fill in the numbers to make the sum of each row, column and
diagonal equal to 34. For an extra challenge try the huge American
Flag magic square.
You have 5 darts and your target score is 44. How many different
ways could you score 44?
Fill in the missing numbers so that adding each pair of corner
numbers gives you the number between them (in the box).
Find a great variety of ways of asking questions which make 8.
This task follows on from Build it Up and takes the ideas into three dimensions!
Are these statements relating to calculation and properties of shapes always true, sometimes true or never true?
Cherri, Saxon, Mel and Paul are friends. They are all different
ages. Can you find out the age of each friend using the
How have the numbers been placed in this Carroll diagram? Which labels would you put on each row and column?
Can you find 2 butterflies to go on each flower so that the numbers
on each pair of butterflies adds to the same number as the one on
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.
Using the statements, can you work out how many of each type of
rabbit there are in these pens?
Use the interactivities to fill in these Carroll diagrams. How do you know where to place the numbers?
Sam got into an elevator. He went down five floors, up six floors, down seven floors, then got out on the second floor. On what floor did he get on?
This challenge combines addition, multiplication, perseverance and even proof.