Other tags that relate to Opposite Vertices
Regular polygons and circles. Pythagoras' theorem. Circle properties and circle theorems. Squares. 2D shapes and their properties. Area - triangles, quadrilaterals, compound shapes. Quadrilaterals. Visualising. Mathematical reasoning & proof. Logo.There are 59 results
Broad Topics > Habits of Mind > Resourceful
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?
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?
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...
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?
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?
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.
On the Edge
Age 11 to 14 Challenge Level:
If you move the tiles around, can you make squares with different coloured edges?
Quadrilaterals Game
Age 11 to 14 Challenge Level:
A game for 2 or more people, based on the traditional card game Rummy.
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?
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?
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?
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?
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?
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.
Difference Sudoku
Age 14 to 16 Challenge Level:
Use the differences to find the solution to this Sudoku.
Product Sudoku
Age 11 to 16 Challenge Level:
The clues for this Sudoku are the product of the numbers in adjacent squares.
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?
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?
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?
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?
Shady Symmetry
Age 11 to 14 Challenge Level:
How many different symmetrical shapes can you make by shading triangles or squares?
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?
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?
Arithmagons
Age 11 to 16 Challenge Level:
Can you find the values at the vertices when you know the values on the edges?
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?
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?
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?
Transformation Game
Age 11 to 14 Challenge Level:
Why not challenge a friend to play this transformation game?
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?
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?
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?
Substitution Cipher
Age 11 to 14 Challenge Level:
Find the frequency distribution for ordinary English, and use it to help you crack the code.
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?
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?
Dicey Operations
Age 11 to 14 Challenge Level:
Who said that adding, subtracting, multiplying and dividing couldn't be fun?
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?
Dozens
Age 7 to 14 Challenge Level:
Do you know a quick way to check if a number is a multiple of two? How about three, four or six?
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?
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?
Finding Factors
Age 14 to 16 Challenge Level:
Can you find the hidden factors which multiply together to produce each quadratic expression?
Two and Two
Age 11 to 16 Challenge Level:
How many solutions can you find to this sum? Each of the different letters stands for a different number.
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...
The Remainders Game
Age 7 to 14 Challenge Level:
Play this game and see if you can figure out the computer's chosen number.
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?
Stars
Age 11 to 14 Challenge Level:
Can you find a relationship between the number of dots on the circle and the number of steps that will ensure that all points are hit?
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?
Which Spinners?
Age 14 to 18 Challenge Level:
Can you work out which spinners were used to generate the frequency charts?
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?
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.
NRICH is part of the family of activities in the Millennium Mathematics Project.