Other tags that relate to Königsberg
Interactivities. Creating and manipulating expressions and formulae. Visualising. Working systematically. Combinatorics. Topology. Networks/Graph Theory. Generalising. Mathematical reasoning & proof. Mathematical modelling.There are 92 results
Broad Topics > Physical and Digital Manipulatives > Interactivities
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.
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.
Instant Insanity
Age 11 to 18
Challenge Level
Given the nets of 4 cubes with the faces coloured in 4 colours, build a tower so that on each vertical wall no colour is repeated, that is all 4 colours appear.
Olympic Magic
Age 14 to 16
Challenge Level
in how many ways can you place the numbers 1, 2, 3 … 9 in the nine regions of the Olympic Emblem (5 overlapping circles) so that the amount in each ring is the same?
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.
Square Coordinates
Age 11 to 14
Challenge Level
A tilted square is a square with no horizontal sides. Can you devise a general instruction for the construction of a square when you are given just one of its sides?
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. . . .
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.
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?
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?
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.
More Number Pyramids
Age 11 to 14
Challenge Level
When number pyramids have a sequence on the bottom layer, some interesting patterns emerge...
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.
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. . . .
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?
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?
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.
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.
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?
Jam
Age 14 to 16
Challenge Level
To avoid losing think of another very well known game where the patterns of play are similar.
Have You Got It?
Age 11 to 14
Challenge Level
Can you explain the strategy for winning this game with any target?
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
Matter of Scale
Age 14 to 16
Challenge Level
Prove Pythagoras' Theorem using enlargements and scale factors.
Nine Colours
Age 11 to 16
Challenge Level
Can you use small coloured cubes to make a 3 by 3 by 3 cube so that each face of the bigger cube contains one of each colour?
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.
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?
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?
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.
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. . . .
Excel Interactive Resource: Fraction Multiplication
Age 11 to 16
Challenge Level
Use Excel to explore multiplication of fractions.
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?
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.
Countdown Fractions
Age 11 to 16
Challenge Level
Here is a chance to play a fractions version of the classic Countdown Game.
Interactive Number Patterns
Age 14 to 16
Challenge Level
How good are you at finding the formula for a number pattern ?
Excel Interactive Resource: Haitch
Age 11 to 16
Challenge Level
An Excel spreadsheet with an investigation.
Excel Interactive Resource: Fraction Addition & Fraction Subtraction
Age 11 to 16
Challenge Level
Use Excel to practise adding and subtracting 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: Multiples Chain
Age 11 to 16
Challenge Level
Use an interactive Excel spreadsheet to investigate factors and multiples.
Excel Interactive Resource: Long Multiplication
Age 11 to 16
Challenge Level
Use an Excel spreadsheet to explore long multiplication.
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!
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?
Excel Interactive Resource: Number Grid Functions
Age 11 to 16
Challenge Level
Use Excel to investigate the effect of translations around a number grid.
Spot the Card
Age 14 to 16
Challenge Level
It is possible to identify a particular card out of a pack of 15 with the use of some mathematical reasoning. What is this reasoning and can it be applied to other numbers of cards?
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...
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?
NRICH is part of the family of activities in the Millennium Mathematics Project.