Powers of numbers behave in surprising ways. Take a look at some of these and try to explain why they are true.
Can you guarantee that, for any three numbers you choose, the
product of their differences will always be an even number?
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?
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?
How many pairs of numbers can you find that add up to a multiple of 11? Do you notice anything interesting about your results?
Mathematicians are always looking for efficient methods for solving problems. How efficient can you be?
The clues for this Sudoku are the product of the numbers in adjacent squares.
Find at least one way to put in some operation signs (+ - x ÷)
to make these digits come to 100.
Do you know a quick way to check if a number is a multiple of two? How about three, four or six?
What is the smallest number with exactly 14 divisors?
Think of two whole numbers under 10, and follow the steps. I can work out both your numbers very quickly. How?
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?
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.
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?
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...
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. . . .
Can you maximise the area available to a grazing goat?
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?
Five children went into the sweet shop after school. There were
choco bars, chews, mini eggs and lollypops, all costing under 50p.
Suggest a way in which Nathan could spend all his money.
Explore the effect of reflecting in two parallel mirror lines.
What can you say about the child who will be first on the playground tomorrow morning at breaktime in your school?
There are four children in a family, two girls, Kate and Sally, and
two boys, Tom and Ben. How old are the children?
Explore the effect of combining enlargements.
There are lots of different methods to find out what the shapes are worth - how many can you find?
Can you find an efficient method to work out how many handshakes
there would be if hundreds of people met?
On the graph there are 28 marked points. These points all mark the
vertices (corners) of eight hidden squares. Can you find the eight
In a three-dimensional version of noughts and crosses, how many winning lines can you make?
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?
A 2 by 3 rectangle contains 8 squares and a 3 by 4 rectangle
contains 20 squares. What size rectangle(s) contain(s) exactly 100
squares? Can you find them all?
There is a particular value of x, and a value of y to go with it,
which make all five expressions equal in value, can you find that
x, y pair ?
Square numbers can be represented as the sum of consecutive odd
numbers. What is the sum of 1 + 3 + ..... + 149 + 151 + 153?
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?
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 to. . . .
Do you notice anything about the solutions when you add and/or
subtract consecutive negative numbers?
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?
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.
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?
What size square corners should be cut from a square piece of paper to make a box with the largest possible volume?
The number 2.525252525252.... can be written as a fraction. What is
the sum of the denominator and numerator?
Use the differences to find the solution to this Sudoku.
A country has decided to have just two different coins, 3z and 5z
coins. Which totals can be made? Is there a largest total that
cannot be made? How do you know?
Can you arrange these numbers into 7 subsets, each of three
numbers, so that when the numbers in each are added together, they
make seven consecutive numbers?
An investigation involving adding and subtracting sets of consecutive numbers. Lots to find out, lots to explore.
Can you describe this route to infinity? Where will the arrows take you next?
Start with two numbers and generate a sequence where the next number is the mean of the last two numbers...
How many solutions can you find to this sum? Each of the different letters stands for a different number.
Which set of numbers that add to 10 have the largest product?
Can all unit fractions be written as the sum of two unit fractions?
Here is a chance to create some attractive images by rotating
shapes through multiples of 90 degrees, or 30 degrees, or 72
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?