Good thinkers are curious and ask good questions. They are excited by new ideas and are keen to explore and investigate them.
Want to become a more curious mathematician?
We hope these problems will provoke you to ask good mathematical questions. Take a look, we think you'll get hooked on them!
You can browse through the Number, Algebra, Geometry or Statistics collections, or scroll down to see the full set of problems below.
Digit Addition
Try out this number trick. What happens with different starting numbers? What do you notice?
Shaping It
If the World Were a Village
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?
Five Steps to 50
Next-door Numbers
Eightness of Eight
Ring a Ring of Numbers
Colouring Triangles
Explore ways of colouring this set of triangles. Can you make symmetrical patterns?
Chain of Changes
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?
Little Man
Light the Lights
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
Consecutive Numbers
An investigation involving adding and subtracting sets of consecutive numbers. Lots to find out, lots to explore.
Fruity Totals
In this interactivity each fruit has a hidden value. Can you deduce what each one is worth?
Number Differences
The Number Jumbler
Brush Loads
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.
Nice or Nasty
Your number is...
Statement Snap
Tumbling Down
Watch this animation. What do you see? Can you explain why this happens?
Two Clocks
These clocks have only one hand, but can you work out what time they are showing from the information?
Three neighbours
Pouring Problem
What do you think is going to happen in this video clip? Are you surprised?
Curious number
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?
Your number was...
Summing Consecutive Numbers
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?
Semi-regular Tessellations
Semi-regular tessellations combine two or more different regular polygons to fill the plane. Can you find all the semi-regular tessellations?
Blue and White
What numbers can we make?
Imagine we have four bags containing a large number of 1s, 4s, 7s and 10s. What numbers can we make?
What's it worth?
There are lots of different methods to find out what the shapes are worth - how many can you find?
Elevenses
Can they be equal?
Perimeter Possibilities
Special Numbers
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?
Number Pyramids
Try entering different sets of numbers in the number pyramids. How does the total at the top change?
How much can we spend?
Shifting Times Tables
Can you find a way to identify times tables after they have been shifted up or down?
Tilted Squares
It's easy to work out the areas of most squares that we meet, but what if they were tilted?
Satisfying Statements
Charlie's delightful machine
Here is a machine with four coloured lights. Can you develop a strategy to work out the rules controlling each light?
Dicey Operations
Who said that adding, subtracting, multiplying and dividing couldn't be fun?
Arithmagons
Can you find the values at the vertices when you know the values on the edges?
Right angles
Two's company
Cosy corner
Opposite vertices
Can you recreate squares and rhombuses if you are only given a side or a diagonal?
Marbles in a box
Think of Two Numbers
Non-Transitive Dice
Take Three From Five
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)
What numbers can we make now?
Imagine we have four bags containing numbers from a sequence. What numbers can we make now?
Cuboid Challenge
What's the largest volume of box you can make from a square of paper?
Estimating time
Wipeout
More Number Pyramids
When number pyramids have a sequence on the bottom layer, some interesting patterns emerge...
Unequal Averages
On the Edge
Sending a Parcel
Square coordinates
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?
Stars
Which solids can we make?
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?
Litov's Mean Value Theorem
A Chance to Win?
Cola Can
An aluminium can contains 330 ml of cola. If the can's diameter is 6 cm what is the can's height?
Last one standing
How old am I?
Beelines
Vector journeys
Which spinners?
Curvy areas
Pair Products
Choose four consecutive whole numbers. Multiply the first and last numbers together. Multiply the middle pair together. What do you notice?
Circles in quadrilaterals
Explore when it is possible to construct a circle which just touches all four sides of a quadrilateral.
A little light thinking
Here is a machine with four coloured lights. Can you make two lights switch on at once? Three lights? All four lights?
Same Number!
Triangle midpoints
You are only given the three midpoints of the sides of a triangle. How can you construct the original triangle?
What's Possible?
Arclets
Trapezium Four
Multiplication arithmagons
Can you find the values at the vertices when you know the values on the edges of these multiplication arithmagons?