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?
Think of two whole numbers under 10, and follow the steps. I can work out both your numbers very quickly. How?
There are four children in a family, two girls, Kate and Sally, and
two boys, Tom and Ben. How old are the children?
If: A + C = A; F x D = F; B - G = G; A + H = E; B / H = G; E - G =
F and A-H represent the numbers from 0 to 7 Find the values of A,
B, C, D, E, F and H.
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.
There are lots of different methods to find out what the shapes are worth - how many can you find?
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 ?
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?
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?
Which set of numbers that add to 10 have the largest product?
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?
What size square corners should be cut from a square piece of paper to make a box with the largest possible volume?
Can all unit fractions be written as the sum of two unit fractions?
Start with two numbers and generate a sequence where the next number is the mean of the last two 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?
Square numbers can be represented as the sum of consecutive odd
numbers. What is the sum of 1 + 3 + ..... + 149 + 151 + 153?
Can you find an efficient method to work out how many handshakes
there would be if hundreds of people met?
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?
Explore the effect of combining enlargements.
Explore the effect of reflecting in two parallel mirror lines.
In a three-dimensional version of noughts and crosses, how many winning lines can you make?
Can you see how to build a harmonic triangle? Can you work out the next two rows?
Do you notice anything about the solutions when you add and/or
subtract consecutive negative numbers?
What is the smallest number with exactly 14 divisors?
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.
Can you guarantee that, for any three numbers you choose, the
product of their differences will always be an even number?
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?
Powers of numbers behave in surprising ways. Take a look at some of these and try to explain why they are true.
On the graph there are 28 marked points. These points all mark the
vertices (corners) of eight hidden squares. Can you find the eight
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 describe this route to infinity? Where will the arrows take you next?
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?
An investigation involving adding and subtracting sets of consecutive numbers. Lots to find out, lots to explore.
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 know a quick way to check if a number is a multiple of two? How about three, four or six?
Different combinations of the weights available allow you to make different totals. Which totals can you make?
What is the greatest volume you can get for a rectangular (cuboid)
parcel if the maximum combined length and girth are 2 metres?
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
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?
Use the differences to find the solution to this Sudoku.
Can you find rectangles where the value of the area is the same as the value of the perimeter?
Can you maximise the area available to a grazing goat?
Here is a chance to create some attractive images by rotating
shapes through multiples of 90 degrees, or 30 degrees, or 72
How many pairs of numbers can you find that add up to a multiple of 11? Do you notice anything interesting about your results?
If it takes four men one day to build a wall, how long does it take
60,000 men to build a similar wall?
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?
The Egyptians expressed all fractions as the sum of different unit
fractions. The Greedy Algorithm might provide us with an efficient
way of doing this.
The clues for this Sudoku are the product of the numbers in adjacent squares.
Mathematicians are always looking for efficient methods for solving problems. How efficient can you be?
Is it always possible to combine two paints made up in the ratios
1:x and 1:y and turn them into paint made up in the ratio a:b ? Can
you find an efficent way of doing this?