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.

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Being resourceful - number

Challenge level

Number problems that require careful consideration.

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Being resourceful - algebra

Challenge level

Algebra problems that require careful consideration.

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Being resourceful - geometry

Challenge level

Geometry problems that require careful consideration.

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Being resourceful - statistics

Challenge level

Statistics problems that require careful consideration.

game

Favourite

Quadrilaterals game

Age

11 to 14

Challenge level

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

game

Favourite

Transformation game

Age

11 to 14

Challenge level

Why not challenge a friend to play this transformation game?

problem

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

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

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

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

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?

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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

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

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

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

Shady symmetry

Age

11 to 14

Challenge level

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

problem

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

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

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

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

Odds and evens

Age

11 to 14

Challenge level

Are these games fair? How can you tell?

problem

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

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

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

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

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

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

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

Which spinners?

Age

14 to 18

Challenge level

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

problem

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

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

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

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

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

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

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

Box plot match

Age

14 to 16

Challenge level

Match the cumulative frequency curves with their corresponding box plots.

problem

Cryptarithms

Age

11 to 14

Challenge level

Can you crack these cryptarithms?

problem

Forwards add backwards

Age

11 to 14

Challenge level

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

problem

Reversals

Age

11 to 14

Challenge level

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

problem

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

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

Satisfying four statements

Age

7 to 11

Challenge level

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

problem

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

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

Repeating patterns

Age

5 to 7

Challenge level

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

problem

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

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

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

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

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

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

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

Arithmagons

Age

11 to 16

Challenge level

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

problem

Agile algebra

Age

16 to 18

Challenge level

Observe symmetries and engage the power of substitution to solve complicated equations.

problem

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

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

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.

game

Favourite

The remainders game

Age

7 to 14

Challenge level

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

problem

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

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

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

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

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

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

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

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

Product Sudoku

Age

11 to 16

Challenge level

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

problem

Difference Sudoku

Age

14 to 16

Challenge level

Use the differences to find the solution to this Sudoku.

problem

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

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

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

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

Baravelle

Age

7 to 16

Challenge level

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

problem

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

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.

problem

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

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

Nice or nasty

Age

7 to 11

Challenge level

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

problem

Xavi's T-shirt

Age

7 to 16

Challenge level

How much can you read into a t-shirt?

problem

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

The animals' sports day

Age

5 to 7

Challenge level

One day, five small animals in my garden had a sports day. Who do you think won each race?

problem

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

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

Finding factors

Age

14 to 16

Challenge level

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

problem

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

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

Dozens

Age

7 to 14

Challenge level

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

problem

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

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

On the edge

Age

11 to 14

Challenge level

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

problem

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?