Resources tagged with: Generalising

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There are 143 results

Broad Topics > Mathematical Thinking > Generalising

Walking the Squares

Age 7 to 11 Challenge Level:

Find a route from the outside to the inside of this square, stepping on as many tiles as possible.

Generalising

Age 5 to 11

These tasks give learners chance to generalise, which involves identifying an underlying structure.

Triangle Numbers

Age 11 to 14 Challenge Level:

Take a look at the multiplication square. The first eleven triangle numbers have been identified. Can you see a pattern? Does the pattern continue?

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?

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.

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.

Have You Got It?

Age 11 to 14 Challenge Level:

Can you explain the strategy for winning this game with any target?

Nim-7

Age 5 to 14 Challenge Level:

Can you work out how to win this game of Nim? Does it matter if you go first or second?

Handshakes

Age 11 to 14 Challenge Level:

Can you find an efficient method to work out how many handshakes there would be if hundreds of people met?

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?

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.

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.

Consecutive Negative Numbers

Age 11 to 14 Challenge Level:

Do you notice anything about the solutions when you add and/or subtract consecutive negative numbers?

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?

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.

Winning Lines

Age 7 to 16

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

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?

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.

Always, Sometimes or Never?

Age 5 to 11 Challenge Level:

Are these statements relating to odd and even numbers always true, sometimes true or never true?

Enclosing Squares

Age 11 to 14 Challenge Level:

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

Nim-like Games

Age 7 to 16 Challenge Level:

A collection of games on the NIM theme

Card Trick 2

Age 11 to 14 Challenge Level:

Can you explain how this card trick works?

Keep it Simple

Age 11 to 14 Challenge Level:

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

Summing Consecutive Numbers

Age 11 to 14 Challenge Level:

15 = 7 + 8 and 10 = 1 + 2 + 3 + 4. Can you say which numbers can be expressed as the sum of two or more consecutive integers?

More Number Pyramids

Age 11 to 14 Challenge Level:

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

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.

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.

Make 37

Age 7 to 14 Challenge Level:

Four bags contain a large number of 1s, 3s, 5s and 7s. Pick any ten numbers from the bags above so that their total is 37.

Finding 3D Stacks

Age 7 to 11 Challenge Level:

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

Cunning Card Trick

Age 11 to 14 Challenge Level:

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

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.

Egyptian Fractions

Age 11 to 14 Challenge Level:

The Egyptians expressed all fractions as the sum of different unit fractions. Here is a chance to explore how they could have written different fractions.

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?

Mastering Mathematics: the Challenge of Generalising and Proof

Age 5 to 11

This article for primary teachers discusses how we can help learners generalise and prove, using NRICH tasks as examples.

Roll over the Dice

Age 7 to 11 Challenge Level:

Watch this video to see how to roll the dice. Now it's your turn! What do you notice about the dice numbers you have recorded?

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.

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!

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?

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?

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?

Charitable Pennies

Age 7 to 14 Challenge Level:

Investigate the different ways that fifteen schools could have given money in a charity fundraiser.

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.

Crossings

Age 7 to 11 Challenge Level:

In this problem we are looking at sets of parallel sticks that cross each other. What is the least number of crossings you can make? And the greatest?

Always, Sometimes or Never? Number

Age 7 to 11 Challenge Level:

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

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.

More Twisting and Turning

Age 11 to 16 Challenge Level:

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

Arithmagons

Age 11 to 16 Challenge Level:

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

Tumbling Down

Age 7 to 11 Challenge Level:

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