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How many solutions can you find to this sum? Each of the different letters stands for a different number.
15 = 7 + 8 and 10 = 1 + 2 + 3 + 4. Can you say which numbers can be expressed as the sum of two or more consecutive integers?
Draw some isosceles triangles with an area of $9$cm$^2$ and a vertex at (20,20). If all the vertices must have whole number coordinates, how many is it possible to draw?
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...
If you are given the mean, median and mode of five positive whole numbers, can you find the numbers?
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?
Can you find rectangles where the value of the area is the same as the value of the perimeter?
Polygons drawn on square dotty paper have dots on their perimeter (p) and often internal (i) ones as well. Find a relationship between p, i and the area of the polygons.
Can you arrange the numbers 1 to 17 in a row so that each adjacent pair adds up to a square number?
How many different symmetrical shapes can you make by shading triangles or squares?
Can you find a way to identify times tables after they have been shifted up or down?
A monkey with peaches, keeps a fraction of them each day, gives the rest away, and then eats one. How long can his peaches last?
Here is a machine with four coloured lights. Can you develop a strategy to work out the rules controlling each light?
Can you use small coloured cubes to make a 3 by 3 by 3 cube so that each face of the bigger cube contains one of each colour?
Many numbers can be expressed as the difference of two perfect squares. What do you notice about the numbers you CANNOT make?
What is the smallest number of answers you need to reveal in order to work out the missing headers?
An investigation involving adding and subtracting sets of consecutive numbers. Lots to find out, lots to explore.
Play this game and see if you can figure out the computer's chosen number.
In this interactivity each fruit has a hidden value. Can you deduce what each one is worth?
Can you use the clues to complete these 5 by 5 Mathematical Sudokus?
If you have only 40 metres of fencing available, what is the maximum area of land you can fence off?
Each clue in this Sudoku is the product of the two numbers in adjacent cells.
By selecting digits for an addition grid, what targets can you make?
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?
Do you notice anything about the solutions when you add and/or subtract consecutive negative numbers?
Can all unit fractions be written as the sum of two unit fractions?
What happens when you add a three digit number to its reverse?
There are lots of ideas to explore in these sequences of ordered fractions.
Can you work out what step size to take to ensure you visit all the dots on the circle?
Different combinations of the weights available allow you to make different totals. Which totals can you make?
Can you find ways to put numbers in the overlaps so the rings have equal totals?
Try entering different sets of numbers in the number pyramids. How does the total at the top change?
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?
Mathematicians are always looking for efficient methods for solving problems. How efficient can you be?
Is there an efficient way to work out how many factors a large number has?
Charlie and Abi put a counter on 42. They wondered if they could visit all the other numbers on their 1-100 board, moving the counter using just these two operations: x2 and -5. What do you think?
Charlie has made a Magic V. Can you use his example to make some more? And how about Magic Ls, Ns and Ws?
Gabriel multiplied together some numbers and then erased them. Can you figure out where each number was?
Imagine you have an unlimited number of four types of triangle. How many different tetrahedra can you make?
How many ways can you find to put in operation signs (+, −, ×, ÷) to make 100?
A cinema has 100 seats. Show how it is possible to sell exactly 100 tickets and take exactly £100 if the prices are £10 for adults, 50p for pensioners and 10p for children.
Can you find a cuboid that has a surface area of exactly 100 square units. Is there more than one? Can you find them all?
Using your knowledge of the properties of numbers, can you fill all the squares on the board?
Powers of numbers behave in surprising ways. Take a look at some of these and try to explain why they are true.
Move your counters through this snake of cards and see how far you can go. Are you surprised by where you end up?
Nine squares are fitted together to form a rectangle. Can you find its dimensions?
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?
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?
Choose some fractions and add them together. Can you get close to 1?
Using the digits 1 to 9, the number 4396 can be written as the product of two numbers. Can you find the factors?
There are lots of different methods to find out what the shapes are worth - how many can you find?
The items in the shopping basket add and multiply to give the same amount. What could their prices be?
Ben, Jack and Emma passed counters to each other and ended with the same number of counters. How many did they start with?
The clues for this Sudoku are the product of the numbers in adjacent squares.
Can you do a little mathematical detective work to figure out which number has been wiped out?
There is nothing half so much worth doing as simply messing about in boats...
Use the differences to find the solution to this Sudoku.
The heptathlon is an athletics competition consisting of 7 events. Can you make sense of the scoring system in order to advise a heptathlete on the best way to reach her target?
A mother wants to share a sum of money by giving each of her children in turn a lump sum plus a fraction of the remainder. How can she do this in order to share the money out equally?
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 each price?
Can you find the hidden factors which multiply together to produce each quadratic expression?
Can you create a Latin Square from multiples of a six digit number?
Here is a Sudoku with a difference! Use information about lowest common multiples to help you solve it.
Andy wants to cycle from Land's End to John o'Groats. Will he be able to eat enough to keep him going?
How have "Warmsnug" arrived at the prices shown on their windows? Which window has been given an incorrect price?
What is the largest number which, when divided into 1905, 2587, 3951, 7020 and 8725 in turn, leaves the same remainder each time?
There is a particular value of x, and a value of y to go with it, which make all five expressions equal in value, can you find that x, y pair ?
When I park my car in Mathstown, there are two car parks to choose from. Can you help me to decide which one to use?
Five equations and five unknowns. Is there an easy way to find the unknown values?