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. . . .
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...
Different combinations of the weights available allow you to make different totals. Which totals can you make?
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.
Do you notice anything about the solutions when you add and/or
subtract consecutive negative numbers?
An investigation involving adding and subtracting sets of consecutive numbers. Lots to find out, lots to explore.
On the graph there are 28 marked points. These points all mark the
vertices (corners) of eight hidden squares. Can you find the eight
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?
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.
How many solutions can you find to this sum? Each of the different letters stands for a different number.
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?
How many different symmetrical shapes can you make by shading triangles or squares?
There are lots of different methods to find out what the shapes are worth - how many can you find?
If you have only 40 metres of fencing available, what is the maximum area of land you can fence off?
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?
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.
Given an equilateral triangle inside an isosceles triangle, can you find a relationship between the angles?
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. . . .
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.
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?
If you are given the mean, median and mode of five positive whole numbers, can you find the 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?
What size square corners should be cut from a square piece of paper to make a box with the largest possible volume?
What is the greatest volume you can get for a rectangular (cuboid)
parcel if the maximum combined length and girth are 2 metres?
Have a go at creating these images based on circles. What do you notice about the areas of the different sections?
Can you maximise the area available to a grazing goat?
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?
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. . . .
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 ?
There are four children in a family, two girls, Kate and Sally, and
two boys, Tom and Ben. How old are the children?
Use the differences to find the solution to this Sudoku.
The clues for this Sudoku are the product of the numbers in adjacent squares.
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?
What is the smallest number with exactly 14 divisors?
What is the largest number which, when divided into 1905, 2587,
3951, 7020 and 8725 in turn, leaves the same remainder each time?
Explore the effect of combining enlargements.
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. . . .
A square of area 40 square cms is inscribed in a semicircle. Find
the area of the square that could be inscribed in a circle of the
Explore the effect of reflecting in two parallel mirror lines.
Here is a chance to create some attractive images by rotating
shapes through multiples of 90 degrees, or 30 degrees, or 72
Can you describe this route to infinity? Where will the arrows take you next?
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?
A hexagon, with sides alternately a and b units in length, is inscribed in a circle. How big is the radius of the circle?
What angle is needed for a ball to do a circuit of the billiard
table and then pass through its original position?
A spider is sitting in the middle of one of the smallest walls in a
room and a fly is resting beside the window. What is the shortest
distance the spider would have to crawl to catch the fly?