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.
Different combinations of the weights available allow you to make different totals. Which totals can you make?
An investigation involving adding and subtracting sets of consecutive numbers. Lots to find out, lots to explore.
Do you notice anything about the solutions when you add and/or
subtract consecutive negative numbers?
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.
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?
How many different symmetrical shapes can you make by shading triangles or squares?
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 solutions can you find to this sum? Each of the different letters stands for a different number.
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...
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?
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?
On the graph there are 28 marked points. These points all mark the
vertices (corners) of eight hidden squares. Can you find the eight
If you have only 40 metres of fencing available, what is the maximum area of land you can fence off?
All CD Heaven stores were given the same number of a popular CD to
sell for £24. In their two week sale each store reduces the
price of the CD by 25% ... How many CDs did the store sell at. . . .
Substitute -1, -2 or -3, into an algebraic expression and you'll
get three results. Is it possible to tell in advance which of those
three will be the largest ?
Square numbers can be represented as the sum of consecutive odd
numbers. What is the sum of 1 + 3 + ..... + 149 + 151 + 153?
What size square corners should be cut from a square piece of paper to make a box with the largest possible volume?
There are lots of different methods to find out what the shapes are worth - how many can you find?
What is the greatest volume you can get for a rectangular (cuboid)
parcel if the maximum combined length and girth are 2 metres?
An aluminium can contains 330 ml of cola. If the can's diameter is
6 cm what is the can's height?
Many numbers can be expressed as the difference of two perfect squares. What do you notice about the numbers you CANNOT make?
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.
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?
If you are given the mean, median and mode of five positive whole numbers, can you find the numbers?
Can you maximise the area available to a grazing goat?
Why does this fold create an angle of sixty degrees?
A hexagon, with sides alternately a and b units in length, is inscribed in a circle. How big is the radius of the circle?
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. . . .
Have a go at creating these images based on circles. What do you notice about the areas of the different sections?
In a three-dimensional version of noughts and crosses, how many winning lines can you make?
Explore the effect of reflecting in two parallel mirror lines.
Can you find an efficient method to work out how many handshakes
there would be if hundreds of people met?
The diagonals of a trapezium divide it into four parts. Can you
create a trapezium where three of those parts are equal in area?
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?
There are four children in a family, two girls, Kate and Sally, and
two boys, Tom and Ben. How old are the children?
What is the largest number which, when divided into 1905, 2587,
3951, 7020 and 8725 in turn, leaves the same remainder each time?
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 is the smallest number with exactly 14 divisors?
Use the differences to find the solution to this Sudoku.
The clues for this Sudoku are the product of the numbers in adjacent squares.
Here is a chance to create some attractive images by rotating
shapes through multiples of 90 degrees, or 30 degrees, or 72
Sissa cleverly asked the King for a reward that sounded quite modest but turned out to be rather large...
Can you describe this route to infinity? Where will the arrows take you next?
The number 2.525252525252.... can be written as a fraction. What is
the sum of the denominator and numerator?
Explore the effect of combining enlargements.
An observer is on top of a lighthouse. How far from the foot of the lighthouse is the horizon that the observer can see?
Can you work out the dimensions of the three cubes?
A jigsaw where pieces only go together if the fractions are
A 1 metre cube has one face on the ground and one face against a
wall. A 4 metre ladder leans against the wall and just touches the
cube. How high is the top of the ladder above the ground?