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?
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?
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?
Find the next number in this pattern: 3, 7, 19, 55 ...
Place the numbers 1 to 6 in the circles so that each number is the
difference between the two numbers just below it.
Place the numbers 1 to 10 in the circles so that each number is the
difference between the two numbers just below it.
At the beginning of May Tom put his tomato plant outside. On the
same day he sowed a bean in another pot. When will the two be the
Find your way through the grid starting at 2 and following these
operations. What number do you end on?
Can you put the numbers 1 to 8 into the circles so that the four
calculations are correct?
If the answer's 2010, what could the question be?
This activity is best done with a whole class or in a large group. Can you match the cards? What happens when you add pairs of the numbers together?
What happens when you add the digits of a number then multiply the
result by 2 and you keep doing this? You could try for different
numbers and different rules.
Explore Alex's number plumber. What questions would you like to ask? What do you think is happening to the numbers?
These two group activities use mathematical reasoning - one is
numerical, one geometric.
Investigate what happens when you add house numbers along a street
in different ways.
Ahmed is making rods using different numbers of cubes. Which rod is twice the length of his first rod?
These caterpillars have 16 parts. What different shapes do they make if each part lies in the small squares of a 4 by 4 square?
Suppose there is a train with 24 carriages which are going to be put together to make up some new trains. Can you find all the ways that this can be done?
48 is called an abundant number because it is less than the sum of
its factors (without itself). Can you find some more abundant
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?
EWWNP means Exploring Wild and Wonderful Number Patterns Created by Yourself! Investigate what happens if we create number patterns using some simple rules.
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?
If the numbers 5, 7 and 4 go into this function machine, what
numbers will come out?
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?
These sixteen children are standing in four lines of four, one
behind the other. They are each holding a card with a number on it.
Can you work out the missing numbers?
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?
In this investigation, you are challenged to make mobile phone
numbers which are easy to remember. What happens if you make a
sequence adding 2 each time?
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?
A game for 2 people. Use your skills of addition, subtraction, multiplication and division to blast the asteroids.
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?
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
Choose four of the numbers from 1 to 9 to put in the squares so that the differences between joined squares are odd.
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?
Arrange eight of the numbers between 1 and 9 in the Polo Square
below so that each side adds to the same total.
As you come down the ladders of the Tall Tower you collect useful spells. Which way should you go to collect the most spells?
Twizzle, a female giraffe, needs transporting to another zoo. Which
route will give the fastest journey?
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?
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?
Go through the maze, collecting and losing your money as you go.
Which route gives you the highest return? And the lowest?
Use these head, body and leg pieces to make Robot Monsters which
are different heights.
Use your logical-thinking skills to deduce how much Dan's crisps and ice-cream cost altogether.
You have 5 darts and your target score is 44. How many different
ways could you score 44?
What is happening at each box in these machines?
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?
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?
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 is a clock-face where the numbers have become all mixed up. Can you find out where all the numbers have got to from these ten statements?
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?
Using the cards 2, 4, 6, 8, +, - and =, what number statements can
Vera is shopping at a market with these coins in her purse. Which
things could she give exactly the right amount for?