# Being Resourceful

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.

How do we help our students to become more resourceful?

These problems require careful consideration. If you allow your students time to immerse themselves in the problems, they may learn to appreciate that the journey is often as important as the destination.

You can browse through the Number, Algebra, Geometry or Statistics collections, or scroll down to see the full set of problems below.

### Being Resourceful - Number

Number problems that require careful consideration.

### Being Resourceful - Algebra

Algebra problems that require careful consideration.

### Being Resourceful - Geometry

Geometry problems that require careful consideration.

### Being Resourceful - Statistics

Statistics problems that require careful consideration.

### Dozens

##### Age 7 to 14Challenge Level

Can you select the missing digit(s) to find the largest multiple?

### How Old Am I?

##### Age 14 to 16Challenge 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?

### Funny Factorisation

##### Age 11 to 16Challenge Level

Using the digits 1 to 9, the number 4396 can be written as the product of two numbers. Can you find the factors?

### Where Can We Visit?

##### Age 11 to 14Challenge 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?

### Two and Two

##### Age 11 to 16Challenge Level

How many solutions can you find to this sum? Each of the different letters stands for a different number.

### Marbles in a Box

##### Age 11 to 16Challenge Level

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

### Attractive Tablecloths

##### Age 14 to 16Challenge 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?

### In a Box

##### Age 14 to 16Challenge 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?

### Triangles to Tetrahedra

##### Age 11 to 14Challenge Level

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

### Frogs

##### Age 11 to 14Challenge Level

How many moves does it take to swap over some red and blue frogs? Do you have a method?

##### Age 11 to 14Challenge Level

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

### Hexy-metry

##### Age 14 to 16Challenge 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?

### Special Numbers

##### Age 11 to 14Challenge 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?

### The Spider and the Fly

##### Age 14 to 16Challenge 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?

### Cuboids

##### Age 11 to 14Challenge 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?

### On the Edge

##### Age 11 to 14Challenge Level

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

### Square It

##### Age 11 to 16Challenge 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.

### Isosceles Triangles

##### Age 11 to 14Challenge 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?

### Stars

##### Age 11 to 14Challenge Level

Can you work out what step size to take to ensure you visit all the dots on the circle?

### Arithmagons

##### Age 11 to 16Challenge Level

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

##### Age 11 to 14Challenge Level

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

### Shapely Pairs

##### Age 11 to 14Challenge 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...

### Property Chart

##### Age 11 to 14Challenge 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?

### Odds and Evens

##### Age 11 to 14Challenge Level

Are these games fair? How can you tell?

### Two's Company

##### Age 11 to 14Challenge Level

Seven balls are shaken. You win if the two blue balls end up touching. What is the probability of winning?

### Cosy Corner

##### Age 11 to 14Challenge Level

Six balls are shaken. You win if at least one red ball ends in a corner. What is the probability of winning?

### Semi-regular Tessellations

##### Age 11 to 16Challenge Level

Semi-regular tessellations combine two or more different regular polygons to fill the plane. Can you find all the semi-regular tessellations?

### Product Sudoku

##### Age 11 to 16Challenge Level

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

### Substitution Cipher

##### Age 11 to 14Challenge Level

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

### Transformation Game

##### Age 11 to 14Challenge Level

Why not challenge a friend to play this transformation game?

### A Chance to Win?

##### Age 11 to 14Challenge Level

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

### Difference Sudoku

##### Age 14 to 16Challenge Level

Use the differences to find the solution to this Sudoku.

### Which Spinners?

##### Age 14 to 18Challenge Level

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

### M, M and M

##### Age 11 to 14Challenge Level

If you are given the mean, median and mode of five positive whole numbers, can you find the numbers?

### Treasure Hunt

##### Age 7 to 14Challenge Level

Can you find a reliable strategy for choosing coordinates that will locate the treasure in the minimum number of guesses?

### The Remainders Game

##### Age 7 to 14Challenge Level

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

### Nice or Nasty

##### Age 7 to 14Challenge Level

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

### Dicey Operations

##### Age 11 to 14Challenge Level

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

### How Much Can We Spend?

##### Age 11 to 14Challenge 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?

### Tower of Hanoi

##### Age 11 to 14Challenge Level

The Tower of Hanoi is an ancient mathematical challenge. Working on the building blocks may help you to explain the patterns you notice.

### Shifting Times Tables

##### Age 11 to 14Challenge Level

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

### A Little Light Thinking

##### Age 14 to 16Challenge Level

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

##### Age 11 to 16Challenge Level

Here is a machine with four coloured lights. Can you develop a strategy to work out the rules controlling each light?

### Sociable Cards

##### Age 11 to 14Challenge Level

Move your counters through this snake of cards and see how far you can go. Are you surprised by where you end up?

### Last One Standing

##### Age 14 to 16Challenge Level

Imagine a room full of people who keep flipping coins until they get a tail. Will anyone get six heads in a row?

### What Does Random Look Like?

##### Age 11 to 14Challenge Level

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

### Which Solids Can We Make?

##### Age 11 to 14Challenge 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?

### Missing Multipliers

##### Age 7 to 14Challenge Level

What is the smallest number of answers you need to reveal in order to work out the missing headers?

### Multiplication Arithmagons

##### Age 14 to 16Challenge Level

Can you find the values at the vertices when you know the values on the edges of these multiplication arithmagons?

### Finding Factors

##### Age 14 to 16Challenge Level

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

### Constructing Triangles

##### Age 11 to 14Challenge Level

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

### Perception Versus Reality

##### Age 14 to 18Challenge Level

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

### Wipeout

##### Age 11 to 16Challenge Level

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

### Box Plot Match

##### Age 14 to 16Challenge Level

Match the cumulative frequency curves with their corresponding box plots.

### Cryptarithms

##### Age 11 to 14Challenge Level

Can you crack these cryptarithms?

##### Age 11 to 14Challenge Level

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

### Reversals

##### Age 11 to 14Challenge Level

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

### Unequal Averages

##### Age 11 to 14Challenge Level

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

### Gabriel's Problem

##### Age 11 to 14Challenge Level

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