Exploring balance and centres of mass can be great fun. The
resulting structures can seem impossible. Here are some images to
encourage you to experiment with non-breakable objects of your own.
Place the numbers 1 to 10 in the circles so that each number is the
difference between the two numbers just below it.
Start by putting one million (1 000 000) into the display of your
calculator. Can you reduce this to 7 using just the 7 key and add,
subtract, multiply, divide and equals as many times as you like?
Use the three triangles to fill these outline shapes. Perhaps you can create some of your own shapes for a friend to fill?
Make one big triangle so the numbers that touch on the small triangles add to 10. You could use the interactivity to help you.
A dog is looking for a good place to bury his bone. Can you work
out where he started and ended in each case? What possible routes
could he have taken?
Can you make the green spot travel through the tube by moving the
yellow spot? Could you draw a tube that both spots would follow?
Use the information about Sally and her brother to find out how many children there are in the Brown family.
This 100 square jigsaw is written in code. It starts with 1 and ends with 100. Can you build it up?
If these balls are put on a line with each ball touching the one in front and the one behind, which arrangement makes the shortest line of balls?
Place the numbers 1 to 6 in the circles so that each number is the
difference between the two numbers just below it.
Can you make a 3x3 cube with these shapes made from small cubes?
There are three versions of this challenge. The idea is to change the colour of all the spots on the grid. Can you do it in fewer throws of the dice?
Can you make a cycle of pairs that add to make a square number
using all the numbers in the box below, once and once only?
Katie had a pack of 20 cards numbered from 1 to 20. She arranged
the cards into 6 unequal piles where each pile added to the same
total. What was the total and how could this be done?
Use the 'double-3 down' dominoes to make a square so that each side has eight dots.
Your challenge is to find the longest way through the network
following this rule. You can start and finish anywhere, and with
any shape, as long as you follow the correct order.
Kate has eight multilink cubes. She has two red ones, two yellow, two green and two blue. She wants to fit them together to make a cube so that each colour shows on each face just once.
You have a set of the digits from 0 – 9. Can you arrange these in the 5 boxes to make two-digit numbers as close to the targets as possible?
A shunting puzzle for 1 person. Swop the positions of the counters at the top and bottom of the board.
This cube has ink on each face which leaves marks on paper as it is rolled. Can you work out what is on each face and the route it has taken?
Using the statements, can you work out how many of each type of
rabbit there are in these pens?
Have a go at this well-known challenge. Can you swap the frogs and toads in as few slides and jumps as possible?
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?
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.
Arrange the digits 1, 1, 2, 2, 3 and 3 so that between the two 1's
there is one digit, between the two 2's there are two digits, and
between the two 3's there are three digits.
Use these four dominoes to make a square that has the same number of dots on each side.
Can you use the information to find out which cards I have used?
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.
Can you make dice stairs using the rules stated? How do you know you have all the possible stairs?
Help the bee to build a stack of blocks far enough to save his
friend trapped in the tower.
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?
We're excited about this new program for drawing beautiful mathematical designs. Can you work out how we made our first few pictures and, even better, share your most elegant solutions with us?
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?
Can you see how these factor-multiple chains work? Find the chain which contains the smallest possible numbers. How about the largest possible numbers?
Pat counts her sweets in different groups and both times she has
some left over. How many sweets could she have had?
As you come down the ladders of the Tall Tower you collect useful spells. Which way should you go to collect the most spells?
What can you say about these shapes? This problem challenges you to create shapes with different areas and perimeters.
Factor track is not a race but a game of skill. The idea is to go round the track in as few moves as possible, keeping to the rules.
Use five steps to count forwards or backwards in 1s or 10s to get to 50. What strategies did you use?
Strike it Out game for an adult and child. Can you stop your partner from being able to go?
Is it possible to draw a 5-pointed star without taking your pencil
off the paper? Is it possible to draw a 6-pointed star in the same
way without taking your pen off?
Use your addition and subtraction skills, combined with some strategic thinking, to beat your partner at this game.
You have two sets of the digits 0 – 9. Can you arrange these in the five boxes to make four-digit numbers as close to the target numbers as possible?
The discs for this game are kept in a flat square box with a square
hole for each disc. Use the information to find out how many discs
of each colour there are in the box.
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
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.
Fill in the missing numbers so that adding each pair of corner
numbers gives you the number between them (in the box).
Work out Tom's number from the answers he gives his friend. He will
only answer 'yes' or 'no'.
Using only six straight cuts, find a way to make as many pieces of
pizza as possible. (The pieces can be different sizes and shapes).