Good thinkers are resourceful and reflective. They think critically and can explain and justify the choices that they make. They become absorbed in what they are doing and show attention to detail. They look back on what they have done in order to learn from both successes and failures.
Want to become more resourceful?
These problems may require careful consideration. Immerse yourself in them - we think they are worth the effort!
You can browse through the Number, Algebra, Geometry or Statistics collections, or scroll down to see the full set of problems below.
Quadrilaterals game
Dicey Operations in Line
How old am I?
Funny Factorisation
Where can we visit?
Marbles in a box
Attractive Tablecloths
In a box
Heads and Feet
Twenty Divided into Six
Square Corners
Triangles to Tetrahedra
Sealed Solution
Frogs
Shady Symmetry
Hexy-Metry
Eggs in Baskets
Special Numbers
Sponge Sections
Cut Nets
The Tall Tower
The Spider and the Fly
Cuboids
On the Edge
Isosceles Triangles
Stars
Two's company
Cosy corner
Substitution Cipher
Torn Shapes
A Chance to Win?
Four Go
Shape Times Shape
Cows and Sheep
Which spinners?
Magic Vs
Eight hidden squares
Nice or Nasty
How much can we spend?
Tower of Hanoi
Sociable Cards
Last one standing
What does random look like?
Which solids can we make?
Finding factors
Constructing Triangles
Play to 37
Perception versus reality
Wipeout
Box plot match
Forwards Add Backwards
Unequal Averages
Gabriel's Problem
Satisfying Four Statements
Number Lines in Disguise
Coded hundred square
Treasure Hunt
Repeating Patterns
First Connect Three
Turning Man
4 Dom
Mystery Matrix
Poly Plug Rectangles
A Puzzling Cube
Missing Multipliers
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?
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?
Shifting Times Tables
Can you find a way to identify times tables after they have been shifted up or down?
Multiplication arithmagons
Can you find the values at the vertices when you know the values on the edges of these multiplication arithmagons?
Arithmagons
Can you find the values at the vertices when you know the values on the edges?
M, M and M
If you are given the mean, median and mode of five positive whole numbers, can you find the numbers?
Shapely pairs
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...
Agile Algebra
Observe symmetries and engage the power of substitution to solve complicated equations.
Square It
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.
Dicey Operations
Who said that adding, subtracting, multiplying and dividing couldn't be fun?
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?
Seeing Squares
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.
Two and Two
How many solutions can you find to this sum? Each of the different letters stands for a different number.
Wallpaper
These pieces of wallpaper need to be ordered from smallest to largest. Can you find a way to do it?
The animals' sports day
One day five small animals in my garden were going to have a sports day. They decided to have a swimming race, a running race, a high jump and a long jump.
Through the Window
My local DIY shop calculates the price of its windows according to the area of glass and the length of frame used. Can you work out how they arrived at these prices?
Ladybird Count
Some children were playing a game. Make a graph or picture to show how many ladybirds each child had.
Property chart
A game in which players take it in turns to try to draw quadrilaterals (or triangles) with particular properties. Is it possible to fill the game grid?
Product Sudoku
The clues for this Sudoku are the product of the numbers in adjacent squares.
The Remainders Game
Play this game and see if you can figure out the computer's chosen number.