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?
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.
If the answer's 2010, what could the question be?
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 what happens when you add house numbers along a street
in different ways.
Find the next number in this pattern: 3, 7, 19, 55 ...
Can you design a new shape for the twenty-eight squares and arrange
the numbers in a logical way? What patterns do you notice?
Sweets are given out to party-goers in a particular way. Investigate the total number of sweets received by people sitting in different positions.
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?
If you have ten counters numbered 1 to 10, how many can you put into pairs that add to 10? Which ones do you have to leave out? Why?
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?
Can you each work out the number on your card? What do you notice?
How could you sort the cards?
How would you count the number of fingers in these pictures?
Explore Alex's number plumber. What questions would you like to ask? What do you think is happening to the numbers?
Exactly 195 digits have been used to number the pages in a book.
How many pages does the book have?
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.
Noah saw 12 legs walk by into the Ark. How many creatures did he see?
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 how many ways could Mrs Beeswax put ten coins into her three
puddings so that each pudding ended up with at least two coins?
Find your way through the grid starting at 2 and following these
operations. What number do you end on?
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
Dotty Six is a simple dice game that you can adapt in many ways.
If the numbers 5, 7 and 4 go into this function machine, what
numbers will come out?
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?
48 is called an abundant number because it is less than the sum of
its factors (without itself). Can you find some more abundant
Place the numbers 1 to 6 in the circles so that each number is the
difference between the two numbers just below it.
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?
Dotty Six game for an adult and child. Will you be the first to have three sixes in a straight line?
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?
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?
Can you follow the rule to decode the messages?
Use five steps to count forwards or backwards in 1s or 10s to get to 50. What strategies did you use?
EWWNP means Exploring Wild and Wonderful Number Patterns Created by Yourself! Investigate what happens if we create number patterns using some simple rules.
Jack's mum bought some candles to use on his birthday cakes and when his sister was born, she used them on her cakes too. Can you use the information to find out when Kate was born?
Use your logical-thinking skills to deduce how much Dan's crisps and ice-cream cost altogether.
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.
Leah and Tom each have a number line. Can you work out where their counters will land? What are the secret jumps they make with their counters?
These two group activities use mathematical reasoning - one is
numerical, one geometric.
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?
I throw three dice and get 5, 3 and 2. Add the scores on the three
dice. What do you get? Now multiply the scores. What do you notice?
This challenge combines addition, multiplication, perseverance and even proof.
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?
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.
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?
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
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
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?