Skip to main content
### Number and algebra

### Geometry and measure

### Probability and statistics

### Working mathematically

### For younger learners

### Advanced mathematics

# Being Resourceful - Secondary Students

*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.*
### 4 Dom

### How Old Am I?

### Funny Factorisation

### Where Can We Visit?

### Two and Two

### Marbles in a Box

### Attractive Tablecloths

### In a Box

### Heads and Feet

### Twenty Divided Into Six

### Mystery Matrix

### A Puzzling Cube

### Square Corners

### Triangles to Tetrahedra

### Sealed Solution

### Frogs

### Shady Symmetry

### Hexy-metry

### Eggs in Baskets

### Special Numbers

### Sponge Sections

### Cut Nets

### Ladybird Count

### The Tall Tower

### The Spider and the Fly

### Cuboids

### On the Edge

### Square It

### Isosceles Triangles

### Stars

### Arithmagons

### Quadrilaterals Game

### Shapely Pairs

### Property Chart

### Two's Company

### Cosy Corner

### Semi-regular Tessellations

### Product Sudoku

### Substitution Cipher

### Torn Shapes

### Wallpaper

### Transformation Game

### Turning Man

### A Chance to Win?

### Four Go

### Shape Times Shape

### Difference Sudoku

### First Connect Three

### Cows and Sheep

### Repeating Patterns

### Which Spinners?

### M, M and M

### Magic Vs

### Eight Hidden Squares

### Treasure Hunt

### The Remainders Game

### Baravelle

### Coded Hundred Square

### Nice or Nasty

### Dicey Operations

### How Much Can We Spend?

### Tower of Hanoi

### Shifting Times Tables

### A Little Light Thinking

### Charlie's Delightful Machine

### Sociable Cards

### Last One Standing

### What Does Random Look Like?

### Which Solids Can We Make?

### Dotty Six

### Missing Multipliers

### Multiplication Arithmagons

### Finding Factors

### Poly Plug Rectangles

### The Animals' Sports Day

### Constructing Triangles

### Play to 37

### Through the Window

### Perception Versus Reality

### WipeoutLive

### Box Plot Match

### Forwards Add Backwards

### Reversals

### Unequal Averages

### Gabriel's Problem

### Seeing Squares

### Dicey Operations in Line

### Satisfying Four Statements

### Number Lines in Disguise

Or search by topic

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!

Age 5 to 11

Challenge Level

Use these four dominoes to make a square that has the same number of dots on each side.

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?

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?

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?

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.

Age 11 to 16

Challenge Level

How many winning lines can you make in a three-dimensional version of noughts and crosses?

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?

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?

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?

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?

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.

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?

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?

Age 11 to 14

Challenge Level

Imagine you have an unlimited number of four types of triangle. How many different tetrahedra can you make?

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?

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?

Age 11 to 14

Challenge Level

How many different symmetrical shapes can you make by shading triangles or squares?

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?

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?

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?

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.

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?

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.

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?

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?

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?

Age 11 to 14

Challenge Level

If you move the tiles around, can you make squares with different coloured edges?

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.

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?

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?

Age 11 to 16

Challenge Level

Can you find the values at the vertices when you know the values on the edges?

Age 11 to 14

Challenge Level

A game for 2 or more people, based on the traditional card game Rummy.

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...

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?

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?

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?

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?

Age 11 to 16

Challenge Level

The clues for this Sudoku are the product of the numbers in adjacent squares.

Age 11 to 14

Challenge Level

Find the frequency distribution for ordinary English, and use it to help you crack the code.

Age 7 to 11

Challenge Level

These rectangles have been torn. How many squares did each one have inside it before it was ripped?

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?

Age 11 to 14

Challenge Level

Why not challenge a friend to play this transformation game?

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.

Age 11 to 14

Challenge Level

Imagine you were given the chance to win some money... and imagine you had nothing to lose...

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?

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?

Age 14 to 16

Challenge Level

Use the differences to find the solution to this Sudoku.

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?

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.

Age 5 to 7

Challenge Level

Try continuing these patterns made from triangles. Can you create your own repeating pattern?

Age 14 to 18

Challenge Level

Can you work out which spinners were used to generate the frequency charts?

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?

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?

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?

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?

Age 7 to 14

Challenge Level

Play this game and see if you can figure out the computer's chosen number.

Age 7 to 16

Challenge Level

What can you see? What do you notice? What questions can you ask?

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?

Age 7 to 14

Challenge Level

There are nasty versions of this dice game but we'll start with the nice ones...

Age 11 to 14

Challenge Level

Who said that adding, subtracting, multiplying and dividing couldn't be fun?

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?

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.

Age 11 to 14

Challenge Level

Can you find a way to identify times tables after they have been shifted up or down?

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?

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?

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?

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?

Age 11 to 14

Challenge Level

Engage in a little mathematical detective work to see if you can spot the fakes.

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?

Age 5 to 11

Challenge Level

Dotty Six is a simple dice game that you can adapt in many ways.

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?

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?

Age 14 to 16

Challenge Level

Can you find the hidden factors which multiply together to produce each quadratic expression?

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?

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.

Age 11 to 14

Challenge Level

Generate three random numbers to determine the side lengths of a triangle. What triangles can you draw?

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.

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?

Age 14 to 18

Challenge Level

Infographics are a powerful way of communicating statistical information. Can you come up with your own?

Age 11 to 16

Challenge Level

Can you do a little mathematical detective work to figure out which number has been wiped out?

Age 14 to 16

Challenge Level

Match the cumulative frequency curves with their corresponding box plots.

Age 11 to 14

Challenge Level

What happens when you add a three digit number to its reverse?

Age 11 to 14

Challenge Level

Where should you start, if you want to finish back where you started?

Age 11 to 14

Challenge Level

Play around with sets of five numbers and see what you can discover about different types of average...

Age 11 to 14

Challenge Level

Gabriel multiplied together some numbers and then erased them. Can you figure out where each number was?

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.

Age 7 to 11

Challenge Level

Who said that adding, subtracting, multiplying and dividing couldn't be fun?

Age 7 to 11

Challenge Level

Can you find any two-digit numbers that satisfy all of these statements?

Age 7 to 14

Challenge Level

Some of the numbers have fallen off Becky's number line. Can you figure out what they were?