problem
Favourite
Two and Two
Age
7 to 16
Challenge level
How many solutions can you find to this sum? Each of the different letters stands for a different number.
problem
Favourite
Consecutive Numbers
Age
7 to 14
Challenge level
An investigation involving adding and subtracting sets of consecutive numbers. Lots to find out, lots to explore.
problem
Favourite
Missing Multipliers
Age
7 to 14
Challenge level
What is the smallest number of answers you need to reveal in order to work out the missing headers?
problem
Favourite
Dozens
Age
7 to 14
Challenge level
Can you select the missing digit(s) to find the largest multiple?
problem
Favourite
Fruity Totals
Age
7 to 16
Challenge level
In this interactivity each fruit has a hidden value. Can you deduce what each one is worth?
problem
Favourite
The Number Jumbler
Age
7 to 14
Challenge level
The Number Jumbler can always work out your chosen symbol. Can you work out how?
problem
Favourite
5 by 5 Mathdokus
Age
7 to 16
Challenge level
Can you use the clues to complete these 5 by 5 Mathematical Sudokus?
problem
Favourite
Charlie's delightful machine
Age
11 to 16
Challenge level
Here is a machine with four coloured lights. Can you develop a strategy to work out the rules controlling each light?
problem
Favourite
Guess my Quad
Age
11 to 14
Challenge level
How many questions do you need to identify my quadrilateral?
problem
Favourite
Ben's Game
Age
11 to 16
Challenge level
Ben, Jack and Emma passed counters to each other and ended with the same number of counters. How many did they start with?
problem
Favourite
Sociable Cards
Age
11 to 14
Challenge level
Move your counters through this snake of cards and see how far you can go. Are you surprised by where you end up?
problem
Favourite
Number Daisy
Age
11 to 14
Challenge level
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?
problem
Favourite
Growing Surprises
Age
11 to 14
Challenge level
Can you find the connections between linear and quadratic patterns?
problem
Favourite
Cuboids
Age
11 to 14
Challenge level
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?
problem
Favourite
Consecutive negative numbers
Age
11 to 14
Challenge level
Do you notice anything about the solutions when you add and/or subtract consecutive negative numbers?
problem
Favourite
American Billions
Age
11 to 14
Challenge level
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...
problem
Favourite
Completing Quadrilaterals
Age
11 to 14
Challenge level
We started drawing some quadrilaterals - can you complete them?
problem
Favourite
Square It
Age
11 to 16
Challenge level
Players take it in turns to choose a dot on the grid. The winner is the first to have four dots that can be joined to form a square.
problem
Favourite
Weights
Age
11 to 14
Challenge level
Different combinations of the weights available allow you to make different totals. Which totals can you make?
problem
Favourite
Days and Dates
Age
11 to 14
Challenge level
Investigate how you can work out what day of the week your birthday will be on next year, and the year after...
problem
Favourite
An Equilateral Triangular Problem
Age
11 to 14
Challenge level
Take an equilateral triangle and cut it into smaller pieces. What can you do with them?
problem
Favourite
Consecutive Seven
Age
11 to 14
Challenge level
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?
problem
Favourite
Opposite vertices
Age
11 to 14
Challenge level
Can you recreate squares and rhombuses if you are only given a side or a diagonal?
problem
Favourite
1 Step 2 Step
Age
11 to 14
Challenge level
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?
problem
Favourite
Gabriel's Problem
Age
11 to 14
Challenge level
Gabriel multiplied together some numbers and then erased them. Can you figure out where each number was?
problem
Favourite
Fence it
Age
11 to 14
Challenge level
If you have only 40 metres of fencing available, what is the maximum area of land you can fence off?
problem
Favourite
M, M and M
Age
11 to 14
Challenge level
If you are given the mean, median and mode of five positive whole numbers, can you find the numbers?
problem
Favourite
Counting Factors
Age
11 to 14
Challenge level
Is there an efficient way to work out how many factors a large number has?
problem
Favourite
What's it worth?
Age
11 to 16
Challenge level
There are lots of different methods to find out what the shapes are worth - how many can you find?
problem
Favourite
Can you Make 100?
Age
11 to 14
Challenge level
How many ways can you find to put in operation signs (+, −, ×, ÷) to make 100?
problem
Favourite
Isosceles Triangles
Age
11 to 14
Challenge level
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?
problem
Favourite
Elevenses
Age
11 to 14
Challenge level
How many pairs of numbers can you find that add up to a multiple of 11? Do you notice anything interesting about your results?
problem
Favourite
Summing Consecutive Numbers
Age
11 to 14
Challenge level
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?
problem
Favourite
Shopping Basket
Age
11 to 16
Challenge level
The items in the shopping basket add and multiply to give the same amount. What could their prices be?
problem
Favourite
Alison's quilt
Age
11 to 14
Challenge level
Nine squares are fitted together to form a rectangle. Can you find its dimensions?
problem
Favourite
Stars
Age
11 to 14
Challenge level
Can you work out what step size to take to ensure you visit all the dots on the circle?
problem
Favourite
Can they be equal?
Age
11 to 14
Challenge level
Can you find rectangles where the value of the area is the same as the value of the perimeter?
problem
Favourite
Triangles to Tetrahedra
Age
11 to 14
Challenge level
Imagine you have an unlimited number of four types of triangle. How many different tetrahedra can you make?
problem
Favourite
Almost One
Age
11 to 14
Challenge level
Choose some fractions and add them together. Can you get close to 1?
problem
Favourite
Shapely pairs
Age
11 to 14
Challenge level
A game in which players take it in turns to turn up two cards. If they can draw a triangle which satisfies both properties they win the pair of cards. And a few challenging questions to follow...
problem
Favourite
Power mad!
Age
11 to 14
Challenge level
Powers of numbers behave in surprising ways. Take a look at some of these and try to explain why they are true.
problem
Favourite
Magic Letters
Age
11 to 14
Challenge level
Charlie has made a Magic V. Can you use his example to make some more? And how about Magic Ls, Ns and Ws?
problem
Favourite
Cinema Problem
Age
11 to 14
Challenge level
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.
problem
Favourite
Pocket money
Age
11 to 14
Challenge level
Which of these pocket money systems would you rather have?
problem
Favourite
How far does it move?
Age
11 to 14
Challenge level
Experiment with the interactivity of "rolling" regular polygons, and explore how the different positions of the dot affects the distance it travels at each stage.
problem
Favourite
Multiples Sudoku
Age
11 to 14
Challenge level
Each clue in this Sudoku is the product of the two numbers in adjacent cells.
problem
Favourite
Wipeout
Age
11 to 16
Challenge level
Can you do a little mathematical detective work to figure out which number has been wiped out?
problem
Favourite
Speeding up, slowing down
Age
11 to 14
Challenge level
Experiment with the interactivity of "rolling" regular polygons, and explore how the different positions of the dot affects its speed at each stage.
problem
Favourite
Keep it simple
Age
11 to 14
Challenge level
Can all unit fractions be written as the sum of two unit fractions?
problem
Favourite
Making a difference
Age
11 to 14
Challenge level
How many different differences can you make?
problem
Favourite
Shady Symmetry
Age
11 to 14
Challenge level
How many different symmetrical shapes can you make by shading triangles or squares?
problem
Favourite
Up and across
Age
11 to 14
Challenge level
Experiment with the interactivity of "rolling" regular polygons, and explore how the different positions of the dot affects its vertical and horizontal movement at each stage.
problem
Favourite
Sticky Numbers
Age
11 to 14
Challenge level
Can you arrange the numbers 1 to 17 in a row so that each adjacent pair adds up to a square number?
problem
Favourite
Funny Factorisation
Age
11 to 16
Challenge level
Using the digits 1 to 9, the number 4396 can be written as the product of two numbers. Can you find the factors?
problem
Favourite
How Many Miles To Go?
Age
11 to 14
Challenge level
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?
problem
Favourite
Squares in rectangles
Age
11 to 14
Challenge level
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?
problem
Favourite
How steep is the slope?
Age
11 to 14
Challenge level
On the grid provided, we can draw lines with different gradients. How many different gradients can you find? Can you arrange them in order of steepness?
problem
Favourite
Add to 200
Age
11 to 14
Challenge level
By selecting digits for an addition grid, what targets can you make?
problem
Favourite
Farey Sequences
Age
11 to 14
Challenge level
There are lots of ideas to explore in these sequences of ordered fractions.
problem
Favourite
Parallelogram It
Age
11 to 16
Challenge level
Players take it in turns to choose a dot on the grid. The winner is the first to have four dots that can be joined to form a parallelogram.
problem
Favourite
Going round in circles
Age
11 to 14
Challenge level
Mathematicians are always looking for efficient methods for solving problems. How efficient can you be?
problem
Favourite
Where can we visit?
Age
11 to 14
Challenge level
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?
problem
Favourite
Forwards Add Backwards
Age
11 to 14
Challenge level
What happens when you add a three digit number to its reverse?
problem
Favourite
Number Pyramids
Age
11 to 14
Challenge level
Try entering different sets of numbers in the number pyramids. How does the total at the top change?
problem
Favourite
Product Sudoku
Age
11 to 16
Challenge level
The clues for this Sudoku are the product of the numbers in adjacent squares.
problem
Favourite
Shifting Times Tables
Age
11 to 14
Challenge level
Can you find a way to identify times tables after they have been shifted up or down?
problem
Favourite
Nine Colours
Age
11 to 16
Challenge level
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?
problem
Favourite
Overlaps
Age
11 to 14
Challenge level
Can you find ways to put numbers in the overlaps so the rings have equal totals?
problem
Favourite
Peaches today, Peaches tomorrow...
Age
11 to 14
Challenge level
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?
problem
Favourite
Factors and Multiples Puzzle
Age
11 to 14
Challenge level
Using your knowledge of the properties of numbers, can you fill all the squares on the board?
problem
River Crossing
Age
11 to 18
Challenge level
There is nothing half so much worth doing as simply messing about in boats...
problem
Favourite
Difference Sudoku
Age
14 to 16
Challenge level
Use the differences to find the solution to this Sudoku.
problem
Favourite
Which is cheaper?
Age
14 to 16
Challenge level
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?
problem
Favourite
Training schedule
Age
14 to 16
Challenge level
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?
problem
Favourite
CD Heaven
Age
14 to 16
Challenge level
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?
problem
Favourite
LCM Sudoku
Age
14 to 16
Challenge level
Here is a Sudoku with a difference! Use information about lowest common multiples to help you solve it.
problem
Favourite
Latin Numbers
Age
14 to 16
Challenge level
Can you create a Latin Square from multiples of a six digit number?
problem
Favourite
Finding factors
Age
14 to 16
Challenge level
Can you find the hidden factors which multiply together to produce each quadratic expression?
problem
Favourite
Nutrition and Cycling
Age
14 to 16
Challenge level
Andy wants to cycle from Land's End to John o'Groats. Will he be able to eat enough to keep him going?
problem
Favourite
Expenses
Age
14 to 16
Challenge level
What is the largest number which, when divided into 1905, 2587, 3951, 7020 and 8725 in turn, leaves the same remainder each time?
problem
Symmetricality
Age
14 to 18
Challenge level
Five equations and five unknowns. Is there an easy way to find the unknown values?
problem
Favourite
Pick's Theorem
Age
14 to 16
Challenge level
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.
problem
Favourite
Surprising Transformations
Age
14 to 16
Challenge level
I took the graph y=4x+7 and performed four transformations. Can you find the order in which I could have carried out the transformations?
problem
Favourite
Fair Shares?
Age
14 to 16
Challenge level
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?
problem
Favourite
What's Possible?
Age
14 to 16
Challenge level
Many numbers can be expressed as the difference of two perfect squares. What do you notice about the numbers you CANNOT make?
problem
Favourite
Warmsnug Double Glazing
Age
14 to 16
Challenge level
How have "Warmsnug" arrived at the prices shown on their windows? Which window has been given an incorrect price?
problem
Favourite
Partly Painted Cube
Age
14 to 16
Challenge level
Jo made a cube from some smaller cubes, painted some of the faces of the large cube, and then took it apart again. 45 small cubes had no paint on them at all. How many small cubes did Jo use?
problem
Favourite
Parabolic Patterns
Age
14 to 18
Challenge level
The illustration shows the graphs of fifteen functions. Two of them have equations $y=x^2$ and $y=-(x-4)^2$. Find the equations of all the other graphs.
problem
Favourite
Painted Cube
Age
14 to 16
Challenge level
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?
problem
Favourite
Matchless
Age
14 to 16
Challenge level
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 ?