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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?
On the graph there are 28 marked points. These points all mark the vertices (corners) of eight hidden squares. Can you find the eight hidden 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. . . .
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?
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.
Can all unit fractions be written as the sum of two unit fractions?
How many solutions can you find to this sum? Each of the different letters stands for a different number.
Square numbers can be represented as the sum of consecutive odd numbers. What is the sum of 1 + 3 + ..... + 149 + 151 + 153?
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?
Can you find an efficient method to work out how many handshakes there would be if hundreds of people met?
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. . . .
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.
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?
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?
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...
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?
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?
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?
Can you maximise the area available to a grazing goat?
If you have only 40 metres of fencing available, what is the maximum area of land you can fence off?
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.
Can you find the area of a parallelogram defined by two vectors?
Triangle ABC is isosceles while triangle DEF is equilateral. Find one angle in terms of the other two.
What size square corners should be cut from a square piece of paper to make a box with the largest possible volume?
The diagonals of a trapezium divide it into four parts. Can you create a trapezium where three of those parts are equal in area?
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?
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. . . .
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?
Why does this fold create an angle of sixty degrees?
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.
A hexagon, with sides alternately a and b units in length, is inscribed in a circle. How big is the radius of the circle?
Explore the effect of combining enlargements.
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. . . .
What is the greatest volume you can get for a rectangular (cuboid) parcel if the maximum combined length and girth are 2 metres?
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?
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.
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?
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 "nodes".
There are lots of different methods to find out what the shapes are worth - how many can you find?
A jigsaw where pieces only go together if the fractions are equivalent.
According to an old Indian myth, Sissa ben Dahir was a courtier for a king. The king decided to reward Sissa for his dedication and Sissa asked for one grain of rice to be put on the first square. . . .