Powers of numbers behave in surprising ways. Take a look at some of
these and try to explain why they are true.
Mathematicians are always looking for efficient methods for solving problems. How efficient can you be?
Play the divisibility game to create numbers in which the first two digits make a number divisible by 2, the first three digits make a number divisible by 3...
Find at least one way to put in some operation signs (+ - x ÷)
to make these digits come to 100.
What is the smallest number with exactly 14 divisors?
Do you know a quick way to check if a number is a multiple of two?
How about three, four or six?
Ben passed a third of his counters to Jack, Jack passed a quarter
of his counters to Emma and Emma passed a fifth of her counters to
Ben. After this they all had the same number of counters.
Take any four digit number. Move the first digit to the 'back of
the queue' and move the rest along. Now add your two numbers. What
properties do your answers always have?
My two digit number is special because adding the sum of its digits
to the product of its digits gives me my original number. What
could my number be?
An investigation involving adding and subtracting sets of consecutive numbers. Lots to find out, lots to explore.
How many solutions can you find to this sum? Each of the different letters stands for a different number.
A car's milometer reads 4631 miles and the trip meter has 173.3 on
it. How many more miles must the car travel before the two numbers
contain the same digits in the same order?
Can you find six numbers to go in the Daisy from which you can make
all the numbers from 1 to a number bigger than 25?
How many pairs of numbers can you find that add up to a multiple of
11? Do you notice anything interesting about your results?
The number 2.525252525252.... can be written as a fraction. What is
the sum of the denominator and numerator?
Some 4 digit numbers can be written as the product of a 3 digit
number and a 2 digit number using the digits 1 to 9 each once and
only once. The number 4396 can be written as just such a product.
Can. . . .
There are four children in a family, two girls, Kate and Sally, and
two boys, Tom and Ben. How old are the children?
Caroline and James pick sets of five numbers. Charlie chooses three of them that add together to make a multiple of three. Can they stop him?
Do you notice anything about the solutions when you add and/or
subtract consecutive negative numbers?
Liam's house has a staircase with 12 steps. He can go down the steps one at a time or two at time. In how many different ways can Liam go down the 12 steps?
Find a cuboid (with edges of integer values) that has a surface
area of exactly 100 square units. Is there more than one? Can you
find them all?
Different combinations of the weights available allow you to make different totals. Which totals can you make?
Many numbers can be expressed as the sum of two or more consecutive integers. For example, 15=7+8 and 10=1+2+3+4. Can you say which numbers can be expressed in this way?
The clues for this Sudoku are the product of the numbers in
Can you see how to build a harmonic triangle? Can you work out the
next two rows?
Four bags contain a large number of 1s, 3s, 5s and 7s. Pick any ten
numbers from the bags above so that their total is 37.
What can you say about the child who will be first on the playground tomorrow morning at breaktime in your school?
Can you guarantee that, for any three numbers you choose, the
product of their differences will always be an even number?
According to an old Indian myth, Sissa ben Dahir was a courtier for
a king. The king decided to reward Sissa for his dedication and
Sissa asked for one grain of rice to be put on the first square. . . .
Here is a chance to create some attractive images by rotating
shapes through multiples of 90 degrees, or 30 degrees, or 72
Here are four tiles. They can be arranged in a 2 by 2 square so
that this large square has a green edge. If the tiles are moved
around, we can make a 2 by 2 square with a blue edge... Now try. . . .
Explore the effect of combining enlargements.
On the graph there are 28 marked points. These points all mark the
vertices (corners) of eight hidden squares. Can you find the eight
A game for 2 or more people, based on the traditional card game
Rummy. Players aim to make two `tricks', where each trick has to
consist of a picture of a shape, a name that describes that shape,
and. . . .
How many different symmetrical shapes can you make by shading triangles or squares?
If you have only 40 metres of fencing available, what is the maximum area of land you can fence off?
Explore the effect of reflecting in two parallel mirror lines.
Can you describe this route to infinity? Where will the arrows take you next?
Start with two numbers. This is the start of a sequence. The next
number is the average of the last two numbers. Continue the
sequence. What will happen if you carry on for ever?
What size square corners should be cut from a square piece of paper to make a box with the largest possible volume?
What is the greatest volume you can get for a rectangular (cuboid)
parcel if the maximum combined length and girth are 2 metres?
Chris and Jo put two red and four blue ribbons in a box. They each
pick a ribbon from the box without looking. Jo wins if the two
ribbons are the same colour. Is the game fair?
Some people offer advice on how to win at games of chance, or how
to influence probability in your favour. Can you decide whether
advice is good or not?
Imagine a large cube made from small red cubes being dropped into a
pot of yellow paint. How many of the small cubes will have yellow
paint on their faces?
The area of a square inscribed in a circle with a unit radius is,
satisfyingly, 2. What is the area of a regular hexagon inscribed in
a circle with a unit radius?
Can you maximise the area available to a grazing goat?
If you are given the mean, median and mode of five positive whole
numbers, can you find the numbers?
Imagine you have a large supply of 3kg and 8kg weights. How many of
each weight would you need for the average (mean) of the weights to
be 6kg? What other averages could you have?
Each of the following shapes is made from arcs of a circle of
radius r. What is the perimeter of a shape with 3, 4, 5 and n
Can you find rectangles where the value of the area is the same as the value of the perimeter?