# Resources tagged with: Generalising

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### There are 128 results

Broad Topics > Thinking Mathematically > Generalising

### Konigsberg Plus

##### Age 11 to 14Challenge 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.

### Semi-square

##### Age 14 to 16Challenge Level

What is the ratio of the area of a square inscribed in a semicircle to the area of the square inscribed in the entire circle?

### Polycircles

##### Age 14 to 16Challenge 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?

### Sliding Puzzle

##### Age 11 to 16Challenge 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.

### Jam

##### Age 14 to 16Challenge Level

To avoid losing think of another very well known game where the patterns of play are similar.

### Maths Trails

##### Age 7 to 14

The NRICH team are always looking for new ways to engage teachers and pupils in problem solving. Here we explain the thinking behind maths trails.

### A Tilted Square

##### Age 14 to 16Challenge Level

The opposite vertices of a square have coordinates (a,b) and (c,d). What are the coordinates of the other vertices?

### Number Pyramids

##### Age 11 to 14Challenge Level

Try entering different sets of numbers in the number pyramids. How does the total at the top change?

### Partitioning Revisited

##### Age 11 to 14Challenge 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

##### Age 11 to 16

Dave Hewitt suggests that there might be more to mathematics than looking at numerical results, finding patterns and generalising.

### Cubes Within Cubes Revisited

##### Age 11 to 14Challenge Level

Imagine starting with one yellow cube and covering it all over with a single layer of red cubes, and then covering that cube with a layer of blue cubes. How many red and blue cubes would you need?

### Window Frames

##### Age 5 to 14Challenge Level

This task encourages you to investigate the number of edging pieces and panes in different sized windows.

### Chocolate 2010

##### Age 14 to 16Challenge Level

First of all, pick the number of times a week that you would like to eat chocolate. Multiply this number by 2...

### Equilateral Areas

##### Age 14 to 16Challenge Level

ABC and DEF are equilateral triangles of side 3 and 4 respectively. Construct an equilateral triangle whose area is the sum of the area of ABC and DEF.

### More Number Pyramids

##### Age 11 to 14Challenge Level

When number pyramids have a sequence on the bottom layer, some interesting patterns emerge...

### Of All the Areas

##### Age 14 to 16Challenge Level

Can you find a general rule for finding the areas of equilateral triangles drawn on an isometric grid?

### More Twisting and Turning

##### Age 11 to 16Challenge Level

It would be nice to have a strategy for disentangling any tangled ropes...

### Tilted Squares

##### Age 11 to 14Challenge Level

It's easy to work out the areas of most squares that we meet, but what if they were tilted?

### Jam

##### Age 14 to 16Challenge Level

A game for 2 players

### More Magic Potting Sheds

##### Age 11 to 14Challenge 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?

### Overlap

##### Age 11 to 14Challenge 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. . . .

### Attractive Tablecloths

##### Age 14 to 16Challenge 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?

### Christmas Chocolates

##### Age 11 to 14Challenge Level

How could Penny, Tom and Matthew work out how many chocolates there are in different sized boxes?

### Games Related to Nim

##### Age 5 to 16

This article for teachers describes several games, found on the site, all of which have a related structure that can be used to develop the skills of strategic planning.

### Coordinate Patterns

##### Age 11 to 14Challenge Level

Charlie and Alison have been drawing patterns on coordinate grids. Can you picture where the patterns lead?

### Route to Infinity

##### Age 11 to 14Challenge Level

Can you describe this route to infinity? Where will the arrows take you next?

### Picturing Triangular Numbers

##### Age 11 to 14Challenge Level

Triangular numbers can be represented by a triangular array of squares. What do you notice about the sum of identical triangle numbers?

### Is There a Theorem?

##### Age 11 to 14Challenge Level

Draw a square. A second square of the same size slides around the first always maintaining contact and keeping the same orientation. How far does the dot travel?

### Enclosing Squares

##### Age 11 to 14Challenge Level

Can you find sets of sloping lines that enclose a square?

### Steel Cables

##### Age 14 to 16Challenge Level

Some students have been working out the number of strands needed for different sizes of cable. Can you make sense of their solutions?

### Partly Painted Cube

##### Age 14 to 16Challenge Level

Jo made a cube from some smaller cubes, painted some of the faces of the large cube, and then took it apart again. 45 small cubes had no paint on them at all. How many small cubes did Jo use?

### Beelines

##### Age 14 to 16Challenge Level

Is there a relationship between the coordinates of the endpoints of a line and the number of grid squares it crosses?

### Shear Magic

##### Age 11 to 14Challenge Level

Explore the area of families of parallelograms and triangles. Can you find rules to work out the areas?

### Hidden Rectangles

##### Age 11 to 14Challenge Level

Rectangles are considered different if they vary in size or have different locations. How many different rectangles can be drawn on a chessboard?

### Dotty Triangles

##### Age 11 to 14Challenge Level

Imagine an infinitely large sheet of square dotty paper on which you can draw triangles of any size you wish (providing each vertex is on a dot). What areas is it/is it not possible to draw?

##### Age 14 to 16Challenge 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. . . .

### Got It

##### Age 7 to 14Challenge 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.

### Nim

##### Age 14 to 16Challenge Level

Start with any number of counters in any number of piles. 2 players take it in turns to remove any number of counters from a single pile. The loser is the player who takes the last counter.

### Pair Products

##### Age 14 to 16Challenge Level

Choose four consecutive whole numbers. Multiply the first and last numbers together. Multiply the middle pair together. What do you notice?

### Picturing Square Numbers

##### Age 11 to 14Challenge Level

Square numbers can be represented as the sum of consecutive odd numbers. What is the sum of 1 + 3 + ..... + 149 + 151 + 153?

### Winning Lines

##### Age 7 to 16

An article for teachers and pupils that encourages you to look at the mathematical properties of similar games.

### Tourism

##### Age 11 to 14Challenge Level

If you can copy a network without lifting your pen off the paper and without drawing any line twice, then it is traversable. Decide which of these diagrams are traversable.

### Go Forth and Generalise

##### Age 11 to 14

Spotting patterns can be an important first step - explaining why it is appropriate to generalise is the next step, and often the most interesting and important.

### Painted Cube

##### Age 14 to 16Challenge Level

Imagine a large cube made from small red cubes being dropped into a pot of yellow paint. How many of the small cubes will have yellow paint on their faces?

### Frogs

##### Age 11 to 14Challenge Level

How many moves does it take to swap over some red and blue frogs? Do you have a method?

### Multiplication Square

##### Age 14 to 16Challenge Level

Pick a square within a multiplication square and add the numbers on each diagonal. What do you notice?

### Nim-like Games

##### Age 7 to 16Challenge Level

A collection of games on the NIM theme

### Beach Huts

##### Age 11 to 14Challenge Level

Can you figure out how sequences of beach huts are generated?

### Nim-7 for Two

##### Age 5 to 14Challenge Level

Nim-7 game for an adult and child. Who will be the one to take the last counter?

### Steps to the Podium

##### Age 7 to 14Challenge Level

It starts quite simple but great opportunities for number discoveries and patterns!