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#### Resources tagged with Generalising similar to Farhan's Poor Square:

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### Semi-square

##### Age 14 to 16 Challenge 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?

### Pareq Calc

##### Age 14 to 16 Challenge Level:

Triangle ABC is an equilateral triangle with three parallel lines going through the vertices. Calculate the length of the sides of the triangle if the perpendicular distances between the parallel. . . .

### Generating Triples

##### Age 14 to 16 Challenge Level:

Sets of integers like 3, 4, 5 are called Pythagorean Triples, because they could be the lengths of the sides of a right-angled triangle. Can you find any more?

### Converging Means

##### Age 14 to 16 Challenge Level:

Take any two positive numbers. Calculate the arithmetic and geometric means. Repeat the calculations to generate a sequence of arithmetic means and geometric means. Make a note of what happens to the. . . .

### 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.

### In a Spin

##### Age 14 to 16 Challenge Level:

What is the volume of the solid formed by rotating this right angled triangle about the hypotenuse?

### 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?

### Equilateral Areas

##### Age 14 to 16 Challenge 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.

### 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?

### Areas of Parallelograms

##### Age 14 to 16 Challenge Level:

Can you find the area of a parallelogram defined by two vectors?

### 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.

### Steps to the Podium

##### Age 7 to 14 Challenge Level:

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

### Of All the Areas

##### Age 14 to 16 Challenge Level:

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

### Magic Squares

##### Age 14 to 18

An account of some magic squares and their properties and and how to construct them for yourself.

### Chocolate 2010

##### Age 14 to 16 Challenge Level:

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

### Pentanim

##### Age 7 to 16 Challenge Level:

A game for 2 players with similarities to NIM. Place one counter on each spot on the games board. Players take it is turns to remove 1 or 2 adjacent counters. The winner picks up the last counter.

### Dotty Triangles

##### Age 11 to 14 Challenge 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?

### Winning Lines

##### Age 7 to 16

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

### Magic Squares II

##### Age 14 to 18

An article which gives an account of some properties of magic squares.

### Beelines

##### Age 14 to 16 Challenge Level:

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

### One O Five

##### Age 11 to 14 Challenge Level:

You can work out the number someone else is thinking of as follows. Ask a friend to think of any natural number less than 100. Then ask them to tell you the remainders when this number is divided by. . . .

### 2001 Spatial Oddity

##### Age 11 to 14 Challenge Level:

With one cut a piece of card 16 cm by 9 cm can be made into two pieces which can be rearranged to form a square 12 cm by 12 cm. Explain how this can be done.

### Painted Cube

##### Age 14 to 16 Challenge 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?

### Nim

##### Age 14 to 16 Challenge 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.

### Picturing Square Numbers

##### Age 11 to 14 Challenge Level:

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

### Seven Squares - Group-worthy Task

##### Age 11 to 14 Challenge Level:

Choose a couple of the sequences. Try to picture how to make the next, and the next, and the next... Can you describe your reasoning?

### Take Three from Five

##### Age 14 to 16 Challenge Level:

Caroline and James pick sets of five numbers. Charlie chooses three of them that add together to make a multiple of three. Can they stop him?

### Pair Products

##### Age 14 to 16 Challenge Level:

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

### Nim-7 for Two

##### Age 5 to 14 Challenge Level:

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

### Sums of Pairs

##### Age 11 to 16 Challenge Level:

Jo has three numbers which she adds together in pairs. When she does this she has three different totals: 11, 17 and 22 What are the three numbers Jo had to start with?”

### Nim-like Games

##### Age 7 to 16 Challenge Level:

A collection of games on the NIM theme

### 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.

### 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?

### Jam

##### Age 14 to 16 Challenge Level:

A game for 2 players

### Route to Infinity

##### Age 11 to 14 Challenge Level:

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

### 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.

### What Numbers Can We Make Now?

##### Age 11 to 14 Challenge Level:

Imagine we have four bags containing numbers from a sequence. What numbers can we make now?

### All Tangled Up

##### Age 14 to 18 Challenge Level:

Can you tangle yourself up and reach any fraction?

### 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 for Two

##### Age 7 to 14 Challenge Level:

Got It game for an adult and child. How can you play so that you know you will always win?

### Tourism

##### Age 11 to 14 Challenge 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.

### Shear Magic

##### Age 11 to 14 Challenge Level:

What are the areas of these triangles? What do you notice? Can you generalise to other "families" of triangles?

### Steel Cables

##### Age 14 to 16 Challenge Level:

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

### More Number Pyramids

##### Age 11 to 14 Challenge Level:

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

### More Twisting and Turning

##### Age 11 to 16 Challenge Level:

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

### 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.

### 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?

### What Numbers Can We Make?

##### Age 11 to 14 Challenge Level:

Imagine we have four bags containing a large number of 1s, 4s, 7s and 10s. What numbers can we make?

### Partly Painted Cube

##### Age 14 to 16 Challenge 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?

### Christmas Chocolates

##### Age 11 to 14 Challenge Level:

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