Being Resourceful - Secondary Students
4 Dom
Use these four dominoes to make a square that has the same number of dots on each side.
How Old Am I?
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
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?
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
How many solutions can you find to this sum? Each of the different letters stands for a different number.
Marbles in a Box
How many winning lines can you make in a three-dimensional version of noughts and crosses?
Attractive Tablecloths
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
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?
Heads and Feet
On a farm there were some hens and sheep. Altogether there were 8 heads and 22 feet. How many hens were there?
Twenty Divided Into Six
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?
Mystery Matrix
Can you fill in this table square? The numbers 2 -12 were used to generate it with just one number used twice.
A Puzzling Cube
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?
Square Corners
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?
Triangles to Tetrahedra
Imagine you have an unlimited number of four types of triangle. How many different tetrahedra can you make?
Sealed Solution
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?
Frogs
How many moves does it take to swap over some red and blue frogs? Do you have a method?
Shady Symmetry
How many different symmetrical shapes can you make by shading triangles or squares?
Hexy-metry
A hexagon, with sides alternately a and b units in length, is inscribed in a circle. How big is the radius of the circle?
Eggs in Baskets
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?
Special Numbers
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?
Sponge Sections
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.
Cut Nets
Each of the nets of nine solid shapes has been cut into two pieces. Can you see which pieces go together?
Ladybird Count
Some children were playing a game. Make a graph or picture to show how many ladybirds each child had.
The Tall Tower
As you come down the ladders of the Tall Tower you collect useful spells. Which way should you go to collect the most spells?
The Spider and the Fly
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
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
If you move the tiles around, can you make squares with different coloured edges?
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.
Isosceles Triangles
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
Can you work out what step size to take to ensure you visit all the dots on the circle?
Arithmagons
Can you find the values at the vertices when you know the values on the edges?
Quadrilaterals Game
A game for 2 or more people, based on the traditional card game Rummy.
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...
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?
Two's Company
Seven balls are shaken. You win if the two blue balls end up touching. What is the probability of winning?
Cosy Corner
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
Semi-regular tessellations combine two or more different regular polygons to fill the plane. Can you find all the semi-regular tessellations?
Product Sudoku
The clues for this Sudoku are the product of the numbers in adjacent squares.
Substitution Cipher
Find the frequency distribution for ordinary English, and use it to help you crack the code.
Torn Shapes
These rectangles have been torn. How many squares did each one have inside it before it was ripped?
Wallpaper
These pieces of wallpaper need to be ordered from smallest to largest. Can you find a way to do it?
Transformation Game
Why not challenge a friend to play this transformation game?
Turning Man
Use the interactivity to find out how many quarter turns the man must rotate through to look like each of the pictures.
A Chance to Win?
Imagine you were given the chance to win some money... and imagine you had nothing to lose...
Four Go
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?
Shape Times Shape
These eleven shapes each stand for a different number. Can you use the number sentences to work out what they are?
Difference Sudoku
Use the differences to find the solution to this Sudoku.
First Connect Three
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?
Cows and Sheep
Use your logical reasoning to work out how many cows and how many sheep there are in each field.
Repeating Patterns
Try continuing these patterns made from triangles. Can you create your own repeating pattern?
Which Spinners?
Can you work out which spinners were used to generate the frequency charts?
M, M and M
If you are given the mean, median and mode of five positive whole numbers, can you find the numbers?
Magic Vs
Can you put the numbers 1-5 in the V shape so that both 'arms' have the same total?
Eight Hidden Squares
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?
Treasure Hunt
Can you find a reliable strategy for choosing coordinates that will locate the treasure in the minimum number of guesses?
The Remainders Game
Play this game and see if you can figure out the computer's chosen number.
Baravelle
What can you see? What do you notice? What questions can you ask?
Coded Hundred Square
This 100 square jigsaw is written in code. It starts with 1 and ends with 100. Can you build it up?
Nice or Nasty
There are nasty versions of this dice game but we'll start with the nice ones...
Dicey Operations
Who said that adding, subtracting, multiplying and dividing couldn't be fun?
How Much Can We Spend?
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
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
Can you find a way to identify times tables after they have been shifted up or down?
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?
Sociable Cards
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
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?
Engage in a little mathematical detective work to see if you can spot the fakes.
Which Solids Can We Make?
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?
Dotty Six
Dotty Six is a simple dice game that you can adapt in many ways.
Missing Multipliers
What is the smallest number of answers you need to reveal in order to work out the missing headers?
Multiplication Arithmagons
Can you find the values at the vertices when you know the values on the edges of these multiplication arithmagons?
Finding Factors
Can you find the hidden factors which multiply together to produce each quadratic expression?
Poly Plug Rectangles
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?
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.
Constructing Triangles
Generate three random numbers to determine the side lengths of a triangle. What triangles can you draw?
Play to 37
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.
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?
Perception Versus Reality
Infographics are a powerful way of communicating statistical information. Can you come up with your own?
Wipeout
Can you do a little mathematical detective work to figure out which number has been wiped out?
Box Plot Match
Match the cumulative frequency curves with their corresponding box plots.
Forwards Add Backwards
What happens when you add a three digit number to its reverse?
Reversals
Where should you start, if you want to finish back where you started?
Unequal Averages
Play around with sets of five numbers and see what you can discover about different types of average...
Gabriel's Problem
Gabriel multiplied together some numbers and then erased them. Can you figure out where each number was?
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.
Dicey Operations in Line
Who said that adding, subtracting, multiplying and dividing couldn't be fun?
Satisfying Four Statements
Can you find any two-digit numbers that satisfy all of these statements?
Number Lines in Disguise
Some of the numbers have fallen off Becky's number line. Can you figure out what they were?