Being Resourceful is part of our Developing Mathematical Habits of Mind collection.
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.
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.
list
Being Resourceful - Algebra
Challenge level
Algebra problems that require careful consideration.
list
Being Resourceful - Geometry
Challenge level
Geometry problems that require careful consideration.
list
Being Resourceful - Statistics
Challenge level
Statistics problems that require careful consideration.
game
Favourite
Quadrilaterals game
A game for 2 or more people, based on the traditional card game Rummy.
game
Favourite
Dicey Operations in Line
Who said that adding, subtracting, multiplying and dividing couldn't be fun?
problem
Favourite
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?
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
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
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?
problem
Favourite
Attractive Tablecloths
Age
14 to 16
Challenge level
Charlie likes tablecloths that use as many colours as possible, but insists that his tablecloths have some symmetry. Can you work out how many colours he needs for different tablecloth designs?
problem
Favourite
In a box
Age
14 to 16
Challenge level
Chris and Jo put two red and four blue ribbons in a box. They each pick a ribbon from the box without looking. Jo wins if the two ribbons are the same colour. Is the game fair?
problem
Favourite
Heads and Feet
Age
5 to 7
Challenge level
On a farm there were some hens and sheep. Altogether there were 8 heads and 22 feet. How many hens were there?
problem
Favourite
Twenty Divided into Six
Age
7 to 11
Challenge level
Katie had a pack of 20 cards numbered from 1 to 20. She arranged the cards into 6 unequal piles where each pile added to the same total. What was the total and how could this be done?
problem
Favourite
Square Corners
Age
7 to 11
Challenge level
What is the greatest number of counters you can place on the grid below without four of them lying at the corners of a square?
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
Sealed Solution
Age
7 to 11
Challenge level
Ten cards are put into five envelopes so that there are two cards in each envelope. The sum of the numbers inside it is written on each envelope. What numbers could be inside the envelopes?
problem
Favourite
Frogs
Age
11 to 14
Challenge level
How many moves does it take to swap over some red and blue frogs? Do you have a method?
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
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?
problem
Favourite
Eggs in Baskets
Age
5 to 7
Challenge level
There are three baskets, a brown one, a red one and a pink one, holding a total of 10 eggs. How many eggs are in each basket?
problem
Favourite
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?
problem
Favourite
Sponge Sections
Age
7 to 11
Challenge level
You have been given three shapes made out of sponge: a sphere, a cylinder and a cone. Your challenge is to find out how to cut them to make different shapes for printing.
problem
Favourite
Cut Nets
Age
7 to 11
Challenge level
Each of the nets of nine solid shapes has been cut into two pieces. Can you see which pieces go together?
problem
Favourite
The Tall Tower
Age
5 to 7
Challenge level
As you come down the ladders of the Tall Tower you collect useful spells. Which way should you go to collect the most spells?
problem
Favourite
The Spider and the Fly
Age
14 to 16
Challenge level
A spider is sitting in the middle of one of the smallest walls in a
room and a fly is resting beside the window. What is the shortest
distance the spider would have to crawl to catch the fly?
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
On the Edge
Age
11 to 14
Challenge level
If you move the tiles around, can you make squares with different coloured edges?
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
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
Odds and Evens
Age
11 to 14
Challenge level
Are these games fair? How can you tell?
problem
Favourite
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?
problem
Favourite
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?
problem
Favourite
Substitution Cipher
Age
11 to 14
Challenge level
Find the frequency distribution for ordinary English, and use it to help you crack the code.
problem
Favourite
Torn Shapes
Age
7 to 11
Challenge level
These rectangles have been torn. How many squares did each one have inside it before it was ripped?
problem
Favourite
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...
problem
Favourite
Four Go
Age
7 to 11
Challenge level
This challenge is a game for two players. Choose two of the numbers to multiply or divide, then mark your answer on the number line. Can you get four in a row?
problem
Favourite
Shape Times Shape
Age
7 to 11
Challenge level
These eleven shapes each stand for a different number. Can you use the number sentences to work out what they are?
problem
Favourite
Difference Sudoku
Age
14 to 16
Challenge level
Use the differences to find the solution to this Sudoku.
problem
Cows and Sheep
Age
7 to 11
Challenge level
Use your logical reasoning to work out how many cows and how many
sheep there are in each field.
problem
Favourite
Which spinners?
Age
14 to 18
Challenge level
Can you work out which spinners were used to generate the frequency charts?
problem
Favourite
Magic Vs
Age
7 to 11
Challenge level
Can you put the numbers 1-5 in the V shape so that both 'arms' have the same total?
problem
Favourite
Eight hidden squares
Age
7 to 14
Challenge level
On the graph there are 28 marked points. These points all mark the vertices (corners) of eight hidden squares. Can you find the eight hidden squares?
problem
Favourite
Baravelle
Age
7 to 16
Challenge level
What can you see? What do you notice? What questions can you ask?
problem
Favourite
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...
problem
Favourite
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?
problem
Favourite
Tower of Hanoi
Age
11 to 14
Challenge level
The Tower of Hanoi is an ancient mathematical challenge. Working on the building blocks may help you to explain the patterns you notice.
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
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?
problem
Favourite
What does random look like?
Age
11 to 14
Challenge level
Engage in a little mathematical detective work to see if you can spot the fakes.
problem
Favourite
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?
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
Constructing Triangles
Age
11 to 14
Challenge level
Generate three random numbers to determine the side lengths of a triangle. What triangles can you draw?
problem
Favourite
Play to 37
Age
7 to 11
Challenge level
In this game for two players, the idea is to take it in turns to choose 1, 3, 5 or 7. The winner is the first to make the total 37.
problem
Favourite
Perception versus reality
Age
14 to 18
Challenge level
Infographics are a powerful way of communicating statistical information. Can you come up with your own?
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
Box plot match
Age
14 to 16
Challenge level
Match the cumulative frequency curves with their corresponding box plots.
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
Reversals
Age
11 to 14
Challenge level
Where should you start, if you want to finish back where you started?
problem
Favourite
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...
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
Satisfying Four Statements
Age
7 to 11
Challenge level
Can you find any two-digit numbers that satisfy all of these statements?
problem
Favourite
Number Lines in Disguise
Age
7 to 14
Challenge level
Some of the numbers have fallen off Becky's number line. Can you figure out what they were?
problem
Favourite
Coded hundred square
Age
7 to 11
Challenge level
This 100 square jigsaw is written in code. It starts with 1 and ends with 100. Can you build it up?
problem
Favourite
Treasure Hunt
Age
7 to 14
Challenge level
Can you find a reliable strategy for choosing coordinates that will locate the treasure in the minimum number of guesses?
problem
Favourite
Repeating Patterns
Age
5 to 7
Challenge level
Try continuing these patterns made from triangles. Can you create your own repeating pattern?
problem
Favourite
First Connect Three
Age
7 to 11
Challenge level
Add or subtract the two numbers on the spinners and try to complete a row of three. Are there some numbers that are good to aim for?
problem
Favourite
Turning Man
Age
5 to 7
Challenge level
Use the interactivity to find out how many quarter turns the man must rotate through to look like each of the pictures.
problem
Favourite
Dozens
Age
7 to 14
Challenge level
Can you select the missing digit(s) to find the largest multiple?
problem
Favourite
4 Dom
Age
5 to 11
Challenge level
Use these four dominoes to make a square that has the same number of dots on each side.
problem
Favourite
Mystery Matrix
Age
7 to 11
Challenge level
Can you fill in this table square? The numbers 2 -12 were used to generate it with just one number used twice.
problem
Favourite
Poly Plug Rectangles
Age
5 to 11
Challenge level
The computer has made a rectangle and will tell you the number of spots it uses in total. Can you find out where the rectangle is?
problem
Favourite
A Puzzling Cube
Age
7 to 11
Challenge level
Here are the six faces of a cube - in no particular order. Here are three views of the cube. Can you deduce where the faces are in relation to each other and record them on the net of this cube?
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
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?
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
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
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?
problem
Favourite
Arithmagons
Age
11 to 16
Challenge level
Can you find the values at the vertices when you know the values on the edges?
problem
Favourite
Dotty Six
Age
5 to 11
Challenge level
Dotty Six is a simple dice game that you can adapt in many ways.
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
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
Agile Algebra
Age
16 to 18
Challenge level
Observe symmetries and engage the power of substitution to solve complicated equations.
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.
game
Favourite
Dicey Operations
Who said that adding, subtracting, multiplying and dividing couldn't be fun?
problem
Favourite
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?
problem
Favourite
Seeing Squares
Age
5 to 11
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
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
Wallpaper
Age
5 to 7
Challenge level
These pieces of wallpaper need to be ordered from smallest to largest. Can you find a way to do it?
problem
Favourite
The animals' sports day
Age
5 to 7
Challenge level
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.
problem
Favourite
Through the Window
Age
7 to 11
Challenge level
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?
problem
Favourite
Ladybird Count
Age
5 to 7
Challenge level
Some children were playing a game. Make a graph or picture to show how many ladybirds each child had.
problem
Favourite
Property chart
Age
11 to 14
Challenge level
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?
problem
Favourite
Product Sudoku
Age
11 to 16
Challenge level
The clues for this Sudoku are the product of the numbers in adjacent squares.
game
Favourite
The Remainders Game
Play this game and see if you can figure out the computer's chosen number.