Can you put the numbers 1 to 8 into the circles so that the four
calculations are correct?
Place the numbers 1 to 6 in the circles so that each number is the
difference between the two numbers just below it.
Starting with the number 180, take away 9 again and again, joining up the dots as you go. Watch out - don't join all the dots!
Place the numbers 1 to 10 in the circles so that each number is the
difference between the two numbers just below it.
Find your way through the grid starting at 2 and following these
operations. What number do you end on?
Use the information about Sally and her brother to find out how many children there are in the Brown family.
A group of children are using measuring cylinders but they lose the
labels. Can you help relabel them?
Can you see why 2 by 2 could be 5? Can you predict what 2 by 10
Place six toy ladybirds into the box so that there are two ladybirds in every column and every row.
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?
Using the statements, can you work out how many of each type of
rabbit there are in these pens?
Add the sum of the squares of four numbers between 10 and 20 to the
sum of the squares of three numbers less than 6 to make the square
of another, larger, number.
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?
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!
Make your own double-sided magic square. But can you complete both
sides once you've made the pieces?
If you have only four weights, where could you place them in order
to balance this equaliser?
In a square in which the houses are evenly spaced, numbers 3 and 10
are opposite each other. What is the smallest and what is the
largest possible number of houses in the square?
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?
Can you make a train the same length as Laura's but using three differently coloured rods? Is there only one way of doing it?
How could you put eight beanbags in the hoops so that there are
four in the blue hoop, five in the red and six in the yellow? Can
you find all the ways of doing this?
You have 5 darts and your target score is 44. How many different
ways could you score 44?
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?
Choose four of the numbers from 1 to 9 to put in the squares so that the differences between joined squares are odd.
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?
A game for 2 people. Use your skills of addition, subtraction, multiplication and division to blast the asteroids.
Look carefully at the numbers. What do you notice? Can you make
another square using the numbers 1 to 16, that displays the same
Use your logical-thinking skills to deduce how much Dan's crisps and ice-cream cost altogether.
This is an adding game for two players.
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.
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?
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!
Exactly 195 digits have been used to number the pages in a book.
How many pages does the book have?
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?
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?
Arrange eight of the numbers between 1 and 9 in the Polo Square
below so that each side adds to the same total.
In your bank, you have three types of coins. The number of spots shows how much they are worth. Can you choose coins to exchange with the groups given to make the same total?
Try adding together the dates of all the days in one week. Now
multiply the first date by 7 and add 21. Can you explain what
What do you notice about the date 03.06.09? Or 08.01.09? This
challenge invites you to investigate some interesting dates
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
This challenge focuses on finding the sum and difference of pairs of two-digit numbers.
This challenging activity involves finding different ways to distribute fifteen items among four sets, when the sets must include three, four, five and six items.
Can you arrange 5 different digits (from 0 - 9) in the cross in the
This challenge extends the Plants investigation so now four or more children are involved.
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 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 a Magic Square all the rows, columns and diagonals add to the 'Magic Constant'. How would you change the magic constant of this square?
There are to be 6 homes built on a new development site. They could
be semi-detached, detached or terraced houses. How many different
combinations of these can you find?
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?
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?
This dice train has been made using specific rules. How many different trains can you make?