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?
Find out why these matrices are magic. Can you work out how they were made? Can you make your own Magic Matrix?
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?
What is the sum of all the three digit whole numbers?
Find another number that is one short of a square number and when
you double it and add 1, the result is also a square number.
Look on the back of any modern book and you will find an ISBN code. Take this code and calculate this sum in the way shown. Can you see what the answers always have in common?
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?
Find the sum of all three-digit numbers each of whose digits is
The clockmaker's wife cut up his birthday cake to look like a clock
face. Can you work out who received each piece?
Max and Mandy put their number lines together to make a graph. How
far had each of them moved along and up from 0 to get the counter
to the place marked?
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
Use your logical reasoning to work out how many cows and how many
sheep there are in each field.
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?
Investigate the different distances of these car journeys and find
out how long they take.
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
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?
If the numbers 5, 7 and 4 go into this function machine, what
numbers will come out?
I was looking at the number plate of a car parked outside. Using my special code S208VBJ adds to 65. Can you crack my code and use it to find out what both of these number plates add up to?
Can you score 100 by throwing rings on this board? Is there more
than way to do it?
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?
Where can you draw a line on a clock face so that the numbers on
both sides have the same total?
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?
What is happening at each box in these machines?
Vera is shopping at a market with these coins in her purse. Which
things could she give exactly the right amount for?
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?
The value of the circle changes in each of the following problems. Can you discover its value in each problem?
Mrs Morgan, the class's teacher, pinned numbers onto the backs of
three children. Use the information to find out what the three
Use the information to work out how many gifts there are in each
Number problems at primary level that may require determination.
Put operations signs between the numbers 3 4 5 6 to make the highest possible number and lowest possible number.
Peter, Melanie, Amil and Jack received a total of 38 chocolate
eggs. Use the information to work out how many eggs each person
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?
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?
This is an adding game for two players.
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.
Can you follow the rule to decode the messages?
Investigate the different distances of these car journeys and find out how long they take.
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?
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?
Fill in the missing numbers so that adding each pair of corner
numbers gives you the number between them (in the box).
In this section from a calendar, put a square box around the 1st,
2nd, 8th and 9th. Add all the pairs of numbers. What do you notice
about the answers?
Use 4 four times with simple operations so that you get the answer 12. Can you make 15, 16 and 17 too?
Well now, what would happen if we lost all the nines in our number
system? Have a go at writing the numbers out in this way and have a
look at the multiplications table.
Investigate this balance which is marked in halves. If you had a weight on the left-hand 7, where could you hang two weights on the right to make it balance?
Arrange three 1s, three 2s and three 3s in this square so that
every row, column and diagonal adds to the same total.
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?
This task combines spatial awareness with addition and multiplication.
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.
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?
Rocco ran in a 200 m race for his class. Use the information to
find out how many runners there were in the race and what Rocco's
finishing position was.