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
The Scot, John Napier, invented these strips about 400 years ago to
help calculate multiplication and division. Can you work out how to
use Napier's bones to find the answer to these multiplications?
Use 4 four times with simple operations so that you get the answer 12. Can you make 15, 16 and 17 too?
Find out what a Deca Tree is and then work out how many leaves
there will be after the woodcutter has cut off a trunk, a branch, a
twig and a leaf.
Find the sum of all three-digit numbers each of whose digits is
What is the sum of all the three digit whole numbers?
There are over sixty different ways of making 24 by adding,
subtracting, multiplying and dividing all four numbers 4, 6, 6 and
8 (using each number only once). How many can you find?
Put operations signs between the numbers 3 4 5 6 to make the highest possible number and lowest possible number.
The clockmaker's wife cut up his birthday cake to look like a clock
face. Can you work out who received each piece?
There are three buckets each of which holds a maximum of 5 litres.
Use the clues to work out how much liquid there is in each bucket.
Sweets are given out to party-goers in a particular way. Investigate the total number of sweets received by people sitting in different positions.
Fill in the missing numbers so that adding each pair of corner
numbers gives you the number between them (in the box).
A lady has a steel rod and a wooden pole and she knows the length
of each. How can she measure out an 8 unit piece of pole?
Use your addition and subtraction skills, combined with some strategic thinking, to beat your partner at this game.
Here are the prices for 1st and 2nd class mail within the UK. You have an unlimited number of each of these stamps. Which stamps would you need to post a parcel weighing 825g?
Can you follow the rule to decode the messages?
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.
Mrs Morgan, the class's teacher, pinned numbers onto the backs of
three children. Use the information to find out what the three
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.
Where can you draw a line on a clock face so that the numbers on
both sides have the same total?
Complete these two jigsaws then put one on top of the other. What
happens when you add the 'touching' numbers? What happens when you
change the position of the jigsaws?
Susie took cherries out of a bowl by following a certain pattern.
How many cherries had there been in the bowl to start with if she
was left with 14 single ones?
Place this "worm" on the 100 square and find the total of the four
squares it covers. Keeping its head in the same place, what other
totals can you make?
Can you score 100 by throwing rings on this board? Is there more
than way to do it?
The value of the circle changes in each of the following problems.
Can you discover its value in each problem?
Put the numbers 1, 2, 3, 4, 5, 6 into the squares so that the
numbers on each circle add up to the same amount. Can you find the
rule for giving another set of six numbers?
Tell your friends that you have a strange calculator that turns
numbers backwards. What secret number do you have to enter to make
141 414 turn around?
Can you substitute numbers for the letters in these sums?
Vera is shopping at a market with these coins in her purse. Which
things could she give exactly the right amount for?
In this problem you have to place four by four magic squares on the
faces of a cube so that along each edge of the cube the numbers
What do the digits in the number fifteen add up to? How many other
numbers have digits with the same total but no zeros?
What is happening at each box in these machines?
This group activity will encourage you to share calculation
strategies and to think about which strategy might be the most
On a calculator, make 15 by using only the 2 key and any of the
four operations keys. How many ways can you find to do it?
Using 3 rods of integer lengths, none longer than 10 units and not
using any rod more than once, you can measure all the lengths in
whole units from 1 to 10 units. How many ways can you do this?
Use the information to work out how many gifts there are in each
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
Put a number at the top of the machine and collect a number at the
bottom. What do you get? Which numbers get back to themselves?
In sheep talk the only letters used are B and A. A sequence of
words is formed by following certain rules. What do you notice when
you count the letters in each word?
These alphabet bricks are painted in a special way. A is on one
brick, B on two bricks, and so on. How many bricks will be painted
by the time they have got to other letters of the alphabet?
Peter, Melanie, Amil and Jack received a total of 38 chocolate
eggs. Use the information to work out how many eggs each person
On the planet Vuv there are two sorts of creatures. The Zios have 3 legs and the Zepts have 7 legs. The great planetary explorer Nico counted 52 legs. How many Zios and how many Zepts were there?
Cassandra, David and Lachlan are brothers and sisters. They range
in age between 1 year and 14 years. Can you figure out their exact
ages from the clues?
If the numbers 5, 7 and 4 go into this function machine, what
numbers will come out?
Strike it Out game for an adult and child. Can you stop your partner from being able to go?
Arrange three 1s, three 2s and three 3s in this square so that
every row, column and diagonal adds to the same total.
Use your logical reasoning to work out how many cows and how many
sheep there are in each field.
Start with four numbers at the corners of a square and put the
total of two corners in the middle of that side. Keep going... Can
you estimate what the size of the last four numbers will be?
Investigate the different distances of these car journeys and find
out how long they take.
Annie cut this numbered cake into 3 pieces with 3 cuts so that the
numbers on each piece added to the same total. Where were the cuts
and what fraction of the whole cake was each piece?