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.
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?
If the answer's 2010, what could the question be?
Place the numbers 1 to 6 in the circles so that each number is the
difference between the two numbers just below 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?
Investigate what happens when you add house numbers along a street
in different ways.
48 is called an abundant number because it is less than the sum of
its factors (without itself). Can you find some more abundant
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?
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.
Find your way through the grid starting at 2 and following these
operations. What number do you end on?
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?
Investigate the different distances of these car journeys and find
out how long they take.
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?
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?
Explore Alex's number plumber. What questions would you like to ask? What do you think is happening to the numbers?
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?
This is an adding game for two players.
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?
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?
These two group activities use mathematical reasoning - one is
numerical, one geometric.
Use your logical-thinking skills to deduce how much Dan's crisps and ice-cream cost altogether.
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?
Look carefully at the numbers. What do you notice? Can you make
another square using the numbers 1 to 16, that displays the same
As you come down the ladders of the Tall Tower you collect useful spells. Which way should you go to collect the most spells?
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?
Twizzle, a female giraffe, needs transporting to another zoo. Which
route will give the fastest journey?
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 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?
Use these head, body and leg pieces to make Robot Monsters which
are different heights.
Arrange eight of the numbers between 1 and 9 in the Polo Square
below so that each side adds to the same total.
A game for 2 people. Use your skills of addition, subtraction, multiplication and division to blast the asteroids.
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?
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?
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?
There were 22 legs creeping across the web. How many flies? How many spiders?
Using the cards 2, 4, 6, 8, +, - and =, what number statements can
Lolla bought a balloon at the circus. She gave the clown six coins
to pay for it. What could Lolla have paid for the balloon?
Arrange the numbers 1 to 6 in each set of circles below. The sum of each side of the triangle should equal the number in its centre.
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?
Vera is shopping at a market with these coins in her purse. Which
things could she give exactly the right amount for?
Sam got into an elevator. He went down five floors, up six floors, down seven floors, then got out on the second floor. On what floor did he get on?
The value of the circle changes in each of the following problems.
Can you discover its value in each problem?
Can you score 100 by throwing rings on this board? Is there more
than way to do it?
Can you substitute numbers for the letters in these sums?
Can you work out how many flowers there will be on the Amazing Splitting Plant after it has been growing for six weeks?
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?
What is happening at each box in these machines?