Other tags that relate to Polycircles
Making and proving conjectures. Interactivities. Dynamic geometry. 2D shapes and their properties. Visualising. Mathematical reasoning & proof. Regular polygons and circles. Creating and manipulating expressions and formulae. Generalising. Simultaneous equations.There are 105 results
Broad Topics > Physical and Digital Manipulatives > Interactivities
Polycircles
Age 14 to 16 Challenge Level:
Show that for any triangle it is always possible to construct 3 touching circles with centres at the vertices. Is it possible to construct touching circles centred at the vertices of any polygon?
Matter of Scale
Age 14 to 16 Challenge Level:
Prove Pythagoras' Theorem using enlargements and scale factors.
Tilted Squares
Age 11 to 14 Challenge Level:
It's easy to work out the areas of most squares that we meet, but what if they were tilted?
Right Angles
Age 11 to 14 Challenge Level:
Can you make a right-angled triangle on this peg-board by joining up three points round the edge?
Tilting Triangles
Age 14 to 16 Challenge Level:
A right-angled isosceles triangle is rotated about the centre point of a square. What can you say about the area of the part of the square covered by the triangle as it rotates?
Squaring the Circle and Circling the Square
Age 14 to 16 Challenge Level:
If you continue the pattern, can you predict what each of the following areas will be? Try to explain your prediction.
Rolling Around
Age 11 to 14 Challenge Level:
A circle rolls around the outside edge of a square so that its circumference always touches the edge of the square. Can you describe the locus of the centre of the circle?
Subtended Angles
Age 11 to 14 Challenge Level:
What is the relationship between the angle at the centre and the angles at the circumference, for angles which stand on the same arc? Can you prove it?
Triangles in Circles
Age 11 to 14 Challenge Level:
Can you find triangles on a 9-point circle? Can you work out their angles?
More Number Pyramids
Age 11 to 14 Challenge Level:
When number pyramids have a sequence on the bottom layer, some interesting patterns emerge...
Colour in the Square
Age 7 to 16 Challenge Level:
Can you put the 25 coloured tiles into the 5 x 5 square so that no column, no row and no diagonal line have tiles of the same colour in them?
Magic W
Age 14 to 16 Challenge Level:
Find all the ways of placing the numbers 1 to 9 on a W shape, with 3 numbers on each leg, so that each set of 3 numbers has the same total.
Cogs
Age 11 to 14 Challenge Level:
A and B are two interlocking cogwheels having p teeth and q teeth respectively. One tooth on B is painted red. Find the values of p and q for which the red tooth on B contacts every gap on the. . . .
Inside Out
Age 14 to 16 Challenge Level:
There are 27 small cubes in a 3 x 3 x 3 cube, 54 faces being visible at any one time. Is it possible to reorganise these cubes so that by dipping the large cube into a pot of paint three times you. . . .
Excel Interactive Resource: Interactive Division
Age 11 to 16 Challenge Level:
Use an Excel to investigate division. Explore the relationships between the process elements using an interactive spreadsheet.
Have You Got It?
Age 11 to 14 Challenge Level:
Can you explain the strategy for winning this game with any target?
A Tilted Square
Age 14 to 16 Challenge Level:
The opposite vertices of a square have coordinates (a,b) and (c,d). What are the coordinates of the other vertices?
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?
Poly Plug Rectangles
Age 5 to 14 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?
Countdown Fractions
Age 11 to 16 Challenge Level:
Here is a chance to play a fractions version of the classic Countdown Game.
Disappearing Square
Age 11 to 14 Challenge Level:
Do you know how to find the area of a triangle? You can count the squares. What happens if we turn the triangle on end? Press the button and see. Try counting the number of units in the triangle now. . . .
Got It
Age 7 to 14 Challenge Level:
A game for two people, or play online. Given a target number, say 23, and a range of numbers to choose from, say 1-4, players take it in turns to add to the running total to hit their target.
Number Pyramids
Age 11 to 14 Challenge Level:
Try entering different sets of numbers in the number pyramids. How does the total at the top change?
Thank Your Lucky Stars
Age 14 to 16 Challenge Level:
A counter is placed in the bottom right hand corner of a grid. You toss a coin and move the star according to the following rules: ... What is the probability that you end up in the top left-hand. . . .
Jam
Age 14 to 16 Challenge Level:
To avoid losing think of another very well known game where the patterns of play are similar.
Overlap
Age 11 to 14 Challenge Level:
A red square and a blue square overlap so that the corner of the red square rests on the centre of the blue square. Show that, whatever the orientation of the red square, it covers a quarter of the. . . .
Tessellation Interactivity
Age 7 to 16 Challenge Level:
An environment that enables you to investigate tessellations of regular polygons
Sliding Puzzle
Age 11 to 16 Challenge Level:
The aim of the game is to slide the green square from the top right hand corner to the bottom left hand corner in the least number of moves.
Bow Tie
Age 11 to 14 Challenge Level:
Show how this pentagonal tile can be used to tile the plane and describe the transformations which map this pentagon to its images in the tiling.
Interactive Number Patterns
Age 14 to 16 Challenge Level:
How good are you at finding the formula for a number pattern ?
Konigsberg Plus
Age 11 to 14 Challenge Level:
Euler discussed whether or not it was possible to stroll around Koenigsberg crossing each of its seven bridges exactly once. Experiment with different numbers of islands and bridges.
Partitioning Revisited
Age 11 to 14 Challenge Level:
We can show that (x + 1)² = x² + 2x + 1 by considering the area of an (x + 1) by (x + 1) square. Show in a similar way that (x + 2)² = x² + 4x + 4
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.
Changing Places
Age 14 to 16 Challenge Level:
Place a red counter in the top left corner of a 4x4 array, which is covered by 14 other smaller counters, leaving a gap in the bottom right hand corner (HOME). What is the smallest number of moves. . . .
Picturing Triangular Numbers
Age 11 to 14 Challenge Level:
Triangular numbers can be represented by a triangular array of squares. What do you notice about the sum of identical triangle numbers?
Proof Sorter - Quadratic Equation
Age 14 to 18 Challenge Level:
This is an interactivity in which you have to sort the steps in the completion of the square into the correct order to prove the formula for the solutions of quadratic equations.
Excel Interactive Resource: Fraction Multiplication
Age 11 to 16 Challenge Level:
Use Excel to explore multiplication of fractions.
Excel Interactive Resource: Number Grid Functions
Age 11 to 16 Challenge Level:
Use Excel to investigate the effect of translations around a number grid.
Excel Interactive Resource: Haitch
Age 11 to 16 Challenge Level:
An Excel spreadsheet with an investigation.
Excel Interactive Resource: the up and Down Game
Age 11 to 16 Challenge Level:
Use an interactive Excel spreadsheet to explore number in this exciting game!
Just Rolling Round
Age 14 to 16 Challenge Level:
P is a point on the circumference of a circle radius r which rolls, without slipping, inside a circle of radius 2r. What is the locus of P?
Excel Interactive Resource: Equivalent Fraction Bars
Age 11 to 16 Challenge Level:
A simple file for the Interactive whiteboard or PC screen, demonstrating equivalent fractions.
Excel Interactive Resource: Long Multiplication
Age 11 to 16 Challenge Level:
Use an Excel spreadsheet to explore long multiplication.
Excel Interactive Resource: Multiples Chain
Age 11 to 16 Challenge Level:
Use an interactive Excel spreadsheet to investigate factors and multiples.
Excel Interactive Resource: Fraction Addition & Fraction Subtraction
Age 11 to 16 Challenge Level:
Use Excel to practise adding and subtracting fractions.
Icosian Game
Age 11 to 14 Challenge Level:
This problem is about investigating whether it is possible to start at one vertex of a platonic solid and visit every other vertex once only returning to the vertex you started at.
Cushion Ball Interactivity
Age 14 to 16 Challenge Level:
The interactive diagram has two labelled points, A and B. It is designed to be used with the problem "Cushion Ball"
Guesswork
Age 14 to 16 Challenge Level:
Ask a friend to choose a number between 1 and 63. By identifying which of the six cards contains the number they are thinking of it is easy to tell them what the number is.
Factors and Multiples Game
Age 7 to 16 Challenge Level:
A game in which players take it in turns to choose a number. Can you block your opponent?
NRICH is part of the family of activities in the Millennium Mathematics Project.