Can you guarantee that, for any three numbers you choose, the
product of their differences will always be an even number?
Powers of numbers behave in surprising ways. Take a look at some of these and try to explain why they are true.
Is there an efficient way to work out how many factors a large number has?
Mathematicians are always looking for efficient methods for solving problems. How efficient can you be?
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?
How many more miles must the car travel before the numbers on the milometer and the trip meter contain the same digits in the same order?
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?
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.
Think of two whole numbers under 10, and follow the steps. I can work out both your numbers very quickly. How?
Investigate how you can work out what day of the week your birthday will be on next year, and the year after...
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. . . .
The clues for this Sudoku are the product of the numbers in adjacent squares.
On the graph there are 28 marked points. These points all mark the
vertices (corners) of eight hidden squares. Can you find the eight
What can you say about the child who will be first on the playground tomorrow morning at breaktime in your school?
Explore the effect of reflecting in two parallel mirror lines.
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.
If you move the tiles around, can you make squares with different coloured edges?
Can you describe this route to infinity? Where will the arrows take you next?
Can you find an efficient method to work out how many handshakes
there would be if hundreds of people met?
How many winning lines can you make in a three-dimensional version of noughts and crosses?
Square numbers can be represented as the sum of consecutive odd
numbers. What is the sum of 1 + 3 + ..... + 149 + 151 + 153?
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?
There are four children in a family, two girls, Kate and Sally, and
two boys, Tom and Ben. How old are the children?
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?
How many solutions can you find to this sum? Each of the different letters stands for a different number.
An investigation involving adding and subtracting sets of consecutive numbers. Lots to find out, lots to explore.
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.
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?
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?
The number 2.525252525252.... can be written as a fraction. What is
the sum of the denominator and numerator?
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?
Start with two numbers and generate a sequence where the next number is the mean of the last two numbers...
Can you maximise the area available to a grazing goat?
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?
Explore the effect of combining enlargements.
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?
Can you find rectangles where the value of the area is the same as the value of the perimeter?
An aluminium can contains 330 ml of cola. If the can's diameter is 6 cm what is the can's height?
What size square corners should be cut from a square piece of paper to make a box with the largest possible volume?
Here is a chance to create some attractive images by rotating
shapes through multiples of 90 degrees, or 30 degrees, or 72
If you are given the mean, median and mode of five positive whole numbers, can you find the numbers?
If you have only 40 metres of fencing available, what is the maximum area of land you can fence off?
What is the greatest volume you can get for a rectangular (cuboid)
parcel if the maximum combined length and girth are 2 metres?
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?
A decorator can buy pink paint from two manufacturers. What is the
least number he would need of each type in order to produce
different shades of pink.