Next-door Numbers
Age 5 to 7
Challenge Level
Florence, Ethan and Alma have each added together two 'next-door' numbers. What is the same about their answers?
Eightness of Eight
Age 5 to 7
Challenge Level
What do you see as you watch this video? Can you create a similar video for the number 12?
Five Steps to 50
Age 5 to 7
Challenge Level
Use five steps to count forwards or backwards in 1s or 10s to get to 50. What strategies did you use?
Little Man
Age 5 to 7
Challenge Level
The Man is much smaller than us. Can you use the picture of him next to a mug to estimate his height and how much tea he drinks?
Ring a Ring of Numbers
Age 5 to 7
Challenge Level
Choose four of the numbers from 1 to 9 to put in the squares so that the differences between joined squares are odd.
Colouring Triangles
Age 5 to 7
Challenge Level
Explore ways of colouring this set of triangles. Can you make symmetrical patterns?
Chain of Changes
Age 5 to 7
Challenge Level
Arrange the shapes in a line so that you change either colour or shape in the next piece along. Can you find several ways to start with a blue triangle and end with a red circle?
Light the Lights
Age 5 to 7
Challenge Level
Investigate which numbers make these lights come on. What is the smallest number you can find that lights up all the lights?
More Numbers in the Ring
Age 5 to 7
Challenge Level
If there are 3 squares in the ring, can you place three different numbers in them so that their differences are odd? Try with different numbers of squares around the ring. What do you notice?
Shaping It
Age 5 to 11
Challenge Level
These pictures were made by starting with a square, finding the half-way point on each side and joining those points up. You could investigate your own starting shape.
Digit Addition
Age 5 to 11
Challenge Level
Try out this number trick. What happens with different starting numbers? What do you notice?
If the World Were a Village
Age 5 to 11
Challenge Level
This activity is based on data in the book 'If the World Were a Village'. How will you represent your chosen data for maximum effect?
Tumbling Down
Age 7 to 11
Challenge Level
Watch this animation. What do you see? Can you explain why this happens?
Number Differences
Age 7 to 11
Challenge Level
Place the numbers from 1 to 9 in the squares below so that the difference between joined squares is odd. How many different ways can you do this?
Brush Loads
Age 7 to 11
Challenge Level
How can you arrange the 5 cubes so that you need the smallest number of Brush Loads of paint to cover them? Try with other numbers of cubes as well.
Two Clocks
Age 7 to 11
Challenge Level
These clocks have only one hand, but can you work out what time they are showing from the information?
Curious Number
Age 7 to 11
Challenge Level
Can you order the digits from 1-3 to make a number which is divisible by 3 so when the last digit is removed it becomes a 2-figure number divisible by 2, and so on?
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.
Subtraction Surprise
Age 7 to 14
Challenge Level
Try out some calculations. Are you surprised by the results?
Triangle Transformation
Age 7 to 14
Challenge Level
Start with a triangle. Can you cut it up to make a rectangle?
Nice or Nasty
Age 7 to 14
Challenge Level
There are nasty versions of this dice game but we'll start with the nice ones...
Your Number Is...
Age 7 to 14
Challenge Level
Think of a number and follow the machine's instructions... I know what your number is! Can you explain how I know?
Statement Snap
Age 7 to 14
Challenge Level
You'll need to know your number properties to win a game of Statement Snap...
The Number Jumbler
Age 7 to 14
Challenge Level
The Number Jumbler can always work out your chosen symbol. Can you work out how?
Three Neighbours
Age 7 to 14
Challenge Level
Take three consecutive numbers and add them together. What do you notice?
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?
Tilted Squares
Age 11 to 14
Challenge Level
It's easy to work out the areas of most squares that we meet, but what if they were tilted?
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?
Special Numbers
Age 11 to 14
Challenge Level
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?
Largest Product
Age 11 to 14
Challenge Level
Which set of numbers that add to 10 have the largest product?
What Numbers Can We Make?
Age 11 to 14
Challenge Level
Imagine we have four bags containing a large number of 1s, 4s, 7s and 10s. What numbers can we make?
Blue and White
Age 11 to 14
Challenge Level
Identical squares of side one unit contain some circles shaded blue. In which of the four examples is the shaded area greatest?
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?
Perimeter Possibilities
Age 11 to 14
Challenge Level
I'm thinking of a rectangle with an area of 24. What could its perimeter be?
Dicey Operations
Age 11 to 14
Challenge Level
Who said that adding, subtracting, multiplying and dividing couldn't be fun?
Satisfying Statements
Age 11 to 14
Challenge Level
Can you find any two-digit numbers that satisfy all of these statements?
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?
Your Number Was...
Age 11 to 14
Challenge Level
Think of a number and follow my instructions. Tell me your answer, and I'll tell you what you started with! Can you explain how I know?
How Much Can We Spend?
Age 11 to 14
Challenge Level
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?
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?
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?
Opposite Vertices
Age 11 to 14
Challenge Level
Can you recreate squares and rhombuses if you are only given a side or a diagonal?
Think of Two Numbers
Age 11 to 14
Challenge Level
Think of two whole numbers under 10, and follow the steps. I can work out both your numbers very quickly. How?
On the Edge
Age 11 to 14
Challenge Level
If you move the tiles around, can you make squares with different coloured edges?
What Numbers Can We Make Now?
Age 11 to 14
Challenge Level
Imagine we have four bags containing numbers from a sequence. What numbers can we make now?
Sending a Parcel
Age 11 to 14
Challenge Level
What is the greatest volume you can get for a rectangular (cuboid) parcel if the maximum combined length and girth are 2 metres?
Reversals
Age 11 to 14
Challenge Level
Where should you start, if you want to finish back where you started?
Unequal Averages
Age 11 to 14
Challenge Level
Play around with sets of five numbers and see what you can discover about different types of average...
Right Angles
Age 11 to 14
Challenge Level
Can you make a right-angled triangle on this peg-board by joining up three points round the edge?
Square Coordinates
Age 11 to 14
Challenge Level
A tilted square is a square with no horizontal sides. Can you devise a general instruction for the construction of a square when you are given just one of its sides?
More Number Pyramids
Age 11 to 14
Challenge Level
When number pyramids have a sequence on the bottom layer, some interesting patterns emerge...
Two's Company
Age 11 to 14
Challenge Level
Seven balls are shaken. You win if the two blue balls end up touching. What is the probability of winning?
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?
Non-transitive Dice
Age 11 to 14
Challenge Level
Alison and Charlie are playing a game. Charlie wants to go first so Alison lets him. Was that such a good idea?
Cosy Corner
Age 11 to 14
Challenge Level
Six balls are shaken. You win if at least one red ball ends in a corner. What is the probability of winning?
Who's the Best?
Age 11 to 14
Challenge Level
Which countries have the most naturally athletic populations?
Estimating Time
Age 11 to 14
Challenge Level
How well can you estimate 10 seconds? Investigate with our timing tool.
Cola Can
Age 11 to 14
Challenge Level
An aluminium can contains 330 ml of cola. If the can's diameter is 6 cm what is the can's height?
Litov's Mean Value Theorem
Age 11 to 14
Challenge Level
Start with two numbers and generate a sequence where the next number is the mean of the last two numbers...
Which Solids Can We Make?
Age 11 to 14
Challenge Level
Interior angles can help us to work out which polygons will tessellate. Can we use similar ideas to predict which polygons combine to create semi-regular solids?
A Chance to Win?
Age 11 to 14
Challenge Level
Imagine you were given the chance to win some money... and imagine you had nothing to lose...
Semi-regular Tessellations
Age 11 to 16
Challenge Level
Semi-regular tessellations combine two or more different regular polygons to fill the plane. Can you find all the semi-regular tessellations?
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?
Arithmagons
Age 11 to 16
Challenge Level
Can you find the values at the vertices when you know the values on the edges?
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?
Cuboid Challenge
Age 11 to 16
Challenge Level
What's the largest volume of box you can make from a square of paper?
Wipeout
Age 11 to 16
Challenge Level
Can you do a little mathematical detective work to figure out which number has been wiped out?
Take Three from Five
Age 11 to 16
Challenge Level
Caroline and James pick sets of five numbers. Charlie tries to find three that add together to make a multiple of three. Can they stop him?
Searching for Mean(ing)
Age 11 to 16
Challenge Level
If you have a large supply of 3kg and 8kg weights, how many of each would you need for the average (mean) of the weights to be 6kg?
Marbles in a Box
Age 11 to 16
Challenge Level
How many winning lines can you make in a three-dimensional version of noughts and crosses?
How Old Am I?
Age 14 to 16
Challenge Level
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?
Last One Standing
Age 14 to 16
Challenge Level
Imagine a room full of people who keep flipping coins until they get a tail. Will anyone get six heads in a row?
Beelines
Age 14 to 16
Challenge Level
Is there a relationship between the coordinates of the endpoints of a line and the number of grid squares it crosses?
Curvy Areas
Age 14 to 16
Challenge Level
Have a go at creating these images based on circles. What do you notice about the areas of the different sections?
A Little Light Thinking
Age 14 to 16
Challenge Level
Here is a machine with four coloured lights. Can you make two lights switch on at once? Three lights? All four lights?
Pair Products
Age 14 to 16
Challenge Level
Choose four consecutive whole numbers. Multiply the first and last numbers together. Multiply the middle pair together. What do you notice?
Circles in Quadrilaterals
Age 14 to 16
Challenge Level
Explore when it is possible to construct a circle which just touches all four sides of a quadrilateral.
Triangles and Petals
Age 14 to 16
Challenge Level
An equilateral triangle rotates around regular polygons and produces an outline like a flower. What are the perimeters of the different flowers?
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?
Same Number!
Age 14 to 16
Challenge Level
If everyone in your class picked a number from 1 to 225, do you think any two people would pick the same number?
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?
Odds and Evens Made Fair
Age 14 to 16
Challenge Level
In this follow-up to the problem Odds and Evens, we invite you to analyse a probability situation in order to find the general solution for a fair game.
Where to Land
Age 14 to 16
Challenge Level
Chris is enjoying a swim but needs to get back for lunch. How far along the bank should she land?
Multiplication Arithmagons
Age 14 to 16
Challenge Level
Can you find the values at the vertices when you know the values on the edges of these multiplication arithmagons?
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.
Arclets
Age 14 to 16
Challenge Level
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".
Triangle Midpoints
Age 14 to 16
Challenge Level
You are only given the three midpoints of the sides of a triangle. How can you construct the original triangle?
Trapezium Four
Age 14 to 16
Challenge Level
The diagonals of a trapezium divide it into four parts. Can you create a trapezium where three of those parts are equal in area?
Fit for Photocopying
Age 14 to 16
Challenge Level
Explore the relationships between different paper sizes.
Mathsland National Lottery
Age 14 to 16
Challenge Level
Can you work out the probability of winning the Mathsland National Lottery?
Hexy-metry
Age 14 to 16
Challenge Level
A hexagon, with sides alternately a and b units in length, is inscribed in a circle. How big is the radius of the circle?
Data Matching
Age 14 to 18
Challenge Level
Use your skill and judgement to match the sets of random data.
Which Spinners?
Age 14 to 18
Challenge Level
Can you work out which spinners were used to generate the frequency charts?
Vector Journeys
Age 14 to 18
Challenge Level
Charlie likes to go for walks around a square park, while Alison likes to cut across diagonally. Can you find relationships between the vectors they walk along?
Three by One
Age 16 to 18
Challenge Level
There are many different methods to solve this geometrical problem - how many can you find?
NRICH is part of the family of activities in the Millennium Mathematics Project.