Different combinations of the weights available allow you to make different totals. Which totals can you make?
How many solutions can you find to this sum? Each of the different letters stands for a different number.
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.
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?
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?
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?
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.
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?
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 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?
How many different symmetrical shapes can you make by shading triangles or squares?
If you have only 40 metres of fencing available, what is the maximum area of land you can fence off?
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?
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. . . .
How many winning lines can you make in a three-dimensional version of noughts and crosses?
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 describe this route to infinity? Where will the arrows take you next?
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.
If you move the tiles around, can you make squares with different coloured edges?
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...
Can you find an efficient method to work out how many handshakes there would be if hundreds of people met?
Square numbers can be represented as the sum of consecutive odd numbers. What is the sum of 1 + 3 + ..... + 149 + 151 + 153?
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. . . .
Can you work out the dimensions of the three cubes?
Explore the effect of reflecting in two parallel mirror lines.
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?
Can you maximise the area available to a grazing goat?
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?
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?
The diagonals of a trapezium divide it into four parts. Can you create a trapezium where three of those parts are equal in area?
An aluminium can contains 330 ml of cola. If the can's diameter is 6 cm what is the can's height?
What is the greatest volume you can get for a rectangular (cuboid) parcel if the maximum combined length and girth are 2 metres?
Investigate how you can work out what day of the week your birthday will be on next year, and the year after...
Show that is it impossible to have a tetrahedron whose six edges have lengths 10, 20, 30, 40, 50 and 60 units...
Is there an efficient way to work out how many factors a large number has?
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?
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?
Explore the effect of combining enlargements.
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?
Start with two numbers and generate a sequence where the next number is the mean of the last two numbers...
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 same radius.
Explore when it is possible to construct a circle which just touches all four sides of a quadrilateral.
How many more miles must the car travel before the numbers on the milometer and the trip meter contain the same digits in the same order?
If it takes four men one day to build a wall, how long does it take 60,000 men to build a similar wall?