Other tags that relate to Polycircles
GeoGebra. Interactivities. Visualising. Making and proving conjectures. Creating and manipulating expressions and formulae. Simultaneous equations. Dynamic geometry. Regular polygons and circles. Generalising. 2D shapes and their properties.There are 93 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?
Tessellation Interactivity
Age 7 to 16
Challenge Level
An environment that enables you to investigate tessellations of regular polygons
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?
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.
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?
More Number Pyramids
Age 11 to 14
Challenge Level
When number pyramids have a sequence on the bottom layer, some interesting patterns emerge...
Jam
Age 14 to 16
Challenge Level
To avoid losing think of another very well known game where the patterns of play are similar.
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.
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?
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. . . .
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?
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.
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. . . .
Interactive Number Patterns
Age 14 to 16
Challenge Level
How good are you at finding the formula for a number pattern ?
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?
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. . . .
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.
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.
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.
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.
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.
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
An Unhappy End
Age 11 to 14
Challenge Level
Two engines, at opposite ends of a single track railway line, set off towards one another just as a fly, sitting on the front of one of the engines, sets off flying along the railway line...
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?
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. . . .
Excel Interactive Resource: Fraction Multiplication
Age 11 to 16
Challenge Level
Use Excel to explore multiplication of fractions.
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?
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?
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.
More Magic Potting Sheds
Age 11 to 14
Challenge Level
The number of plants in Mr McGregor's magic potting shed increases overnight. He'd like to put the same number of plants in each of his gardens, planting one garden each day. How can he do it?
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!
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: Fraction Addition & Fraction Subtraction
Age 11 to 16
Challenge Level
Use Excel to practise adding and subtracting fractions.
Excel Interactive Resource: Haitch
Age 11 to 16
Challenge Level
An Excel spreadsheet with an investigation.
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?
Got it Article
Age 7 to 14
This article gives you a few ideas for understanding the Got It! game and how you might find a winning strategy.
Excel Interactive Resource: Multiples Chain
Age 11 to 16
Challenge Level
Use an interactive Excel spreadsheet to investigate factors and multiples.
Speeding Up, Slowing Down
Age 11 to 14
Challenge Level
Experiment with the interactivity of "rolling" regular polygons, and explore how the different positions of the red dot affects its speed at each stage.
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"
NRICH is part of the family of activities in the Millennium Mathematics Project.