If you are given the mean, median and mode of five positive whole numbers, can you find the numbers?
How many solutions can you find to this sum? Each of the different letters stands for a different number.
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?
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 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. . . .
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 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?
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. . . .
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 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?
Start with two numbers and generate a sequence where the next number is the mean of the last two numbers...
Do you know a quick way to check if a number is a multiple of two? How about three, four or six?
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?
In 15 years' time my age will be the square of my age 15 years ago. Can you work out my age, and when I had other special birthdays?
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.
Think of two whole numbers under 10, and follow the steps. I can work out both your numbers very quickly. How?
Different combinations of the weights available allow you to make different totals. Which totals can you 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.
How many pairs of numbers can you find that add up to a multiple of 11? Do you notice anything interesting about your results?
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?
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?
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. . . .
What is the greatest volume you can get for a rectangular (cuboid)
parcel if the maximum combined length and girth are 2 metres?
There are four children in a family, two girls, Kate and Sally, and
two boys, Tom and Ben. How old are the children?
An investigation involving adding and subtracting sets of consecutive numbers. Lots to find out, lots to explore.
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?
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.
Is there an efficient way to work out how many factors a large number has?
Use the differences to find the solution to this Sudoku.
The clues for this Sudoku are the product of the numbers in adjacent squares.
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?
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.
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?
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.
The number 2.525252525252.... can be written as a fraction. What is
the sum of the denominator and numerator?
A hexagon, with sides alternately a and b units in length, is inscribed in a circle. How big is the radius of the circle?
Can you maximise the area available to a grazing goat?
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?
Water freezes at 0°Celsius (32°Fahrenheit) and boils at 100°C (212°Fahrenheit). Is there a temperature at which Celsius and Fahrenheit readings are the same?
There are lots of different methods to find out what the shapes are worth - how many can you find?
Explore the effect of combining enlargements.
Here is a chance to create some attractive images by rotating
shapes through multiples of 90 degrees, or 30 degrees, or 72
A jigsaw where pieces only go together if the fractions are
Can you find an efficient method to work out how many handshakes
there would be if hundreds of people met?
Have a go at creating these images based on circles. What do you notice about the areas of the different sections?
Square numbers can be represented as the sum of consecutive odd
numbers. What is the sum of 1 + 3 + ..... + 149 + 151 + 153?