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.
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?
How many winning lines can you make in a three-dimensional version of noughts and crosses?
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. . . .
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?
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?
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?
How many solutions can you find to this sum? Each of the different letters stands for a different number.
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?
The clues for this Sudoku are the product of the numbers in adjacent squares.
If you have only 40 metres of fencing available, what is the maximum area of land you can fence off?
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...
Square numbers can be represented as the sum of consecutive odd numbers. What is the sum of 1 + 3 + ..... + 149 + 151 + 153?
An aluminium can contains 330 ml of cola. If the can's diameter is 6 cm what is the can's height?
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 ?
Given an equilateral triangle inside an isosceles triangle, can you find a relationship between the angles?
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.
Many numbers can be expressed as the difference of two perfect squares. What do you notice about the numbers you CANNOT make?
Some people offer advice on how to win at games of chance, or how to influence probability in your favour. Can you decide whether advice is good or not?
What is the greatest volume you can get for a rectangular (cuboid) parcel if the maximum combined length and girth are 2 metres?
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.
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?
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?
Can you describe this route to infinity? Where will the arrows take you next?
The diagonals of a trapezium divide it into four parts. Can you create a trapezium where three of those parts are equal in area?
Can you find an efficient method to work out how many handshakes there would be if hundreds of people met?
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 move the tiles around, can you make squares with different coloured edges?
If you are given the mean, median and mode of five positive whole numbers, can you find the numbers?
What size square corners should be cut from a square piece of paper to make a box with the largest possible volume?
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.
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?
Is there an efficient way to work out how many factors a large number has?
What does this number mean ? Which order of 1, 2, 3 and 4 makes the highest value ? Which makes the lowest ?
A hexagon, with sides alternately a and b units in length, is inscribed in a circle. How big is the radius of the circle?
An observer is on top of a lighthouse. How far from the foot of the lighthouse is the horizon that the observer can see?
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 degrees or...
Sissa cleverly asked the King for a reward that sounded quite modest but turned out to be rather large...
Explore the effect of reflecting in two parallel mirror lines.
What angle is needed for a ball to do a circuit of the billiard table and then pass through its original position?
Can you work out the dimensions of the three cubes?
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?