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. . . .
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?
If you have only 40 metres of fencing available, what is the maximum area of land you can fence off?
Can you maximise the area available to a grazing goat?
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?
The diagonals of a trapezium divide it into four parts. Can you
create a trapezium where three of those parts are equal in area?
In a three-dimensional version of noughts and crosses, how many winning lines can you make?
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 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?
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?
Square numbers can be represented as the sum of consecutive odd
numbers. What is the sum of 1 + 3 + ..... + 149 + 151 + 153?
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 an efficient method to work out how many handshakes
there would be if hundreds of people met?
How many different symmetrical shapes can you make by shading triangles or squares?
Start with two numbers. This is the start of a sequence. The next
number is the average of the last two numbers. Continue the
sequence. What will happen if you carry on for ever?
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?
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?
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?
If you are given the mean, median and mode of five positive whole numbers, can you find the numbers?
Have a go at creating these images based on circles. What do you notice about the areas of the different sections?
It is known that the area of the largest equilateral triangular
section of a cube is 140sq cm. What is the side length of the cube?
The distances between the centres of two adjacent faces of. . . .
How many solutions can you find to this sum? Each of the different letters stands for a different number.
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. . . .
Two motorboats travelling up and down a lake at constant speeds
leave opposite ends A and B at the same instant, passing each
other, for the first time 600 metres from A, and on their return,
400. . . .
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?
There are lots of different methods to find out what the shapes are worth - how many can you find?
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.
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...
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?
Do you notice anything about the solutions when you add and/or
subtract consecutive negative numbers?
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.
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.
Here's a chance to work with large numbers...
Sissa cleverly asked the King for a reward that sounded quite modest but turned out to be rather large...
Which has the greatest area, a circle or a square inscribed in an
isosceles, right angle triangle?
Why does this fold create an angle of sixty degrees?
What is the largest number which, when divided into 1905, 2587,
3951, 7020 and 8725 in turn, leaves the same remainder each time?
Can you find the area of a parallelogram defined by two vectors?
Chris is enjoying a swim but needs to get back for lunch. If she can swim at 3 m/s and run at 7m/sec, how far along the bank should she land in order to get back as quickly as possible?
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
Can all unit fractions be written as the sum of two unit fractions?
A napkin is folded so that a corner coincides with the midpoint of
an opposite edge . Investigate the three triangles formed .
An observer is on top of a lighthouse. How far from the foot of the lighthouse is the horizon that the observer can see?
A circle is inscribed in a triangle which has side lengths of 8, 15
and 17 cm. What is the radius of the circle?
A jigsaw where pieces only go together if the fractions are
Explore the effect of combining enlargements.