Resources tagged with: Generalising

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There are 147 results

Broad Topics > Thinking Mathematically > Generalising

Circles, Circles

Age 5 to 11 Challenge Level:

Here are some arrangements of circles. How many circles would I need to make the next size up for each? Can you create your own arrangement and investigate the number of circles it needs?

Taking Steps

Age 7 to 11 Challenge Level:

In each of the pictures the invitation is for you to: Count what you see. Identify how you think the pattern would continue.

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.

Cunning Card Trick

Age 11 to 14 Challenge Level:

Delight your friends with this cunning trick! Can you explain how it works?

Cuboid Challenge

Age 11 to 16 Challenge Level:

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

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?

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?

Odd Squares

Age 7 to 11 Challenge Level:

Think of a number, square it and subtract your starting number. Is the number you’re left with odd or even? How do the images help to explain this?

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.

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?

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?

Triangle Pin-down

Age 7 to 11 Challenge Level:

Use the interactivity to investigate what kinds of triangles can be drawn on peg boards with different numbers of pegs.

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?

Tumbling Down

Age 7 to 11 Challenge Level:

Watch this animation. What do you see? Can you explain why this happens?

Finding 3D Stacks

Age 7 to 11 Challenge Level:

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

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?

Nim-like Games

Age 7 to 16 Challenge Level:

A collection of games on the NIM theme

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.

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.

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?

Winning Lines

Age 7 to 16

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

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?

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.

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?

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.

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.

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?

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?”

Cuisenaire Squares

Age 7 to 11 Challenge Level:

These squares have been made from Cuisenaire rods. Can you describe the pattern? What would the next square look like?

Arithmagons

Age 11 to 16 Challenge Level:

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

Play to 37

Age 7 to 11 Challenge Level:

In this game for two players, the idea is to take it in turns to choose 1, 3, 5 or 7. The winner is the first to make the total 37.

Making Maths: Be a Mathemagician

Age 7 to 11 Challenge Level:

Surprise your friends with this magic square trick.

Always, Sometimes or Never? Shape

Age 7 to 11 Challenge Level:

Are these statements always true, sometimes true or never true?

Build it Up

Age 7 to 11 Challenge Level:

Can you find all the ways to get 15 at the top of this triangle of numbers? Many opportunities to work in different ways.

Dice Stairs

Age 7 to 11 Challenge Level:

Can you make dice stairs using the rules stated? How do you know you have all the possible stairs?

Strike it Out for Two

Age 5 to 11 Challenge Level:

Strike it Out game for an adult and child. Can you stop your partner from being able to go?

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?

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?

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...

Route to Infinity

Age 11 to 14 Challenge Level:

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

Steps to the Podium

Age 7 to 14 Challenge Level:

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

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?

Polygonals

Age 7 to 11 Challenge Level:

Polygonal numbers are those that are arranged in shapes as they enlarge. Explore the polygonal numbers drawn here.

Button-up Some More

Age 7 to 11 Challenge Level:

How many ways can you find to do up all four buttons on my coat? How about if I had five buttons? Six ...?

Strike it Out

Age 5 to 11 Challenge Level:

Use your addition and subtraction skills, combined with some strategic thinking, to beat your partner at this game.

Broken Toaster

Age 7 to 11 Short Challenge Level:

Only one side of a two-slice toaster is working. What is the quickest way to toast both sides of three slices of bread?

Centred Squares

Age 7 to 11 Challenge Level:

This challenge, written for the Young Mathematicians' Award, invites you to explore 'centred squares'.

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

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.