Resources tagged with: Generalising

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There are 149 results

Broad Topics > Thinking Mathematically > Generalising

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?

Shear Magic

Age 11 to 14
Challenge Level

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

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.

Cubes Within Cubes Revisited

Age 11 to 14
Challenge 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?

Hidden Rectangles

Age 11 to 14
Challenge Level

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

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?

Route to Infinity

Age 11 to 14
Challenge Level

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

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?

Coordinate Patterns

Age 11 to 14
Challenge Level

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

More Number Pyramids

Age 11 to 14
Challenge Level

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

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.

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.

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?

Window Frames

Age 5 to 14
Challenge Level

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

Cuboid Challenge

Age 11 to 16
Challenge Level

What's the largest volume of box you can make from a square of paper?

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?

More Twisting and Turning

Age 11 to 16
Challenge Level

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

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.

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

Is There a Theorem?

Age 11 to 14
Challenge 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?

One, Three, Five, Seven

Age 11 to 16
Challenge Level

A game for 2 players. Set out 16 counters in rows of 1,3,5 and 7. Players take turns to remove any number of counters from a row. The player left with the last counter looses.

Squares, Squares and More Squares

Age 11 to 14
Challenge Level

Can you dissect a square into: 4, 7, 10, 13... other squares? 6, 9, 12, 15... other squares? 8, 11, 14... other squares?

Train Spotters' Paradise

Age 11 to 16

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

Tower of Hanoi

Age 11 to 14
Challenge Level

The Tower of Hanoi is an ancient mathematical challenge. Working on the building blocks may help you to explain the patterns you notice.

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?

Nim-like Games

Age 7 to 16
Challenge Level

A collection of games on the NIM theme

Finding 3D Stacks

Age 7 to 11
Challenge Level

Can you find a way of counting the spheres in these arrangements?

Adding in Rows

Age 11 to 14
Challenge Level

List any 3 numbers. It is always possible to find a subset of adjacent numbers that add up to a multiple of 3. Can you explain why and prove it?

Enclosing Squares

Age 11 to 14
Challenge Level

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

Sum Equals Product

Age 11 to 14
Challenge Level

The sum of the numbers 4 and 1 [1/3] is the same as the product of 4 and 1 [1/3]; that is to say 4 + 1 [1/3] = 4 � 1 [1/3]. What other numbers have the sum equal to the product and can this be. . . .

Special Sums and Products

Age 11 to 14
Challenge Level

Find some examples of pairs of numbers such that their sum is a factor of their product. eg. 4 + 12 = 16 and 4 × 12 = 48 and 16 is a factor of 48.

Mind Reading

Age 11 to 14
Challenge Level

Think of a number, add one, double it, take away 3, add the number you first thought of, add 7, divide by 3 and take away the number you first thought of. You should now be left with 2. How do I. . . .

Arithmagons

Age 11 to 16
Challenge Level

Can you find the values at the vertices when you know the values on the edges?

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.

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.

Winning Lines

Age 7 to 16

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

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?

Regular Hexagon Loops

Age 11 to 14
Challenge Level

Make some loops out of regular hexagons. What rules can you discover?

Keep it Simple

Age 11 to 14
Challenge Level

Can all unit fractions be written as the sum of two unit fractions?

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?

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?

Squares in Rectangles

Age 11 to 14
Challenge Level

A 2 by 3 rectangle contains 8 squares and a 3 by 4 rectangle contains 20 squares. What size rectangle(s) contain(s) exactly 100 squares? Can you find them all?

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?

Mindreader

Age 11 to 14
Challenge Level

A little bit of algebra explains this 'magic'. Ask a friend to pick 3 consecutive numbers and to tell you a multiple of 3. Then ask them to add the four numbers and multiply by 67, and to tell you. . . .

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. . . .

Steps to the Podium

Age 7 to 14
Challenge Level

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

Card Trick 2

Age 11 to 14
Challenge Level

Can you explain how this card trick works?

Magic Letters

Age 11 to 14
Challenge Level

Charlie has made a Magic V. Can you use his example to make some more? And how about Magic Ls, Ns and Ws?

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. . . .

Dotty Circle

Age 7 to 11
Challenge Level

Watch this film carefully. Can you find a general rule for explaining when the dot will be this same distance from the horizontal axis?