Resources tagged with: Generalising

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Broad Topics > Thinking Mathematically > Generalising

Charitable Pennies

Age 7 to 14 Challenge Level:

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

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?

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?

Cunning Card Trick

Age 11 to 14 Challenge Level:

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

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?

Card Trick 2

Age 11 to 14 Challenge Level:

Can you explain how this card trick works?

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. . . .

Repeaters

Age 11 to 14 Challenge Level:

Choose any 3 digits and make a 6 digit number by repeating the 3 digits in the same order (e.g. 594594). Explain why whatever digits you choose the number will always be divisible by 7, 11 and 13.

Winning Lines

Age 7 to 16

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

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?

Plus Minus

Age 14 to 16 Challenge Level:

Can you explain the surprising results Jo found when she calculated the difference between square numbers?

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.

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...

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.

Odd Differences

Age 14 to 16 Challenge Level:

The diagram illustrates the formula: 1 + 3 + 5 + ... + (2n - 1) = n² Use the diagram to show that any odd number is the difference of two squares.

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.

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?

Attractive Tablecloths

Age 14 to 16 Challenge 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?

Three Times Seven

Age 11 to 14 Challenge Level:

A three digit number abc is always divisible by 7 when 2a+3b+c is divisible by 7. Why?

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?

...on the Wall

Age 11 to 14 Challenge Level:

Explore the effect of reflecting in two intersecting mirror lines.

Mini-max

Age 11 to 14 Challenge Level:

Consider all two digit numbers (10, 11, . . . ,99). In writing down all these numbers, which digits occur least often, and which occur most often ? What about three digit numbers, four digit 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.

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.

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?

Mirror, Mirror...

Age 11 to 14 Challenge Level:

Explore the effect of reflecting in two parallel mirror lines.

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?

Have You Got It?

Age 11 to 14 Challenge Level:

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

Counting Factors

Age 11 to 14 Challenge Level:

Is there an efficient way to work out how many factors a large number has?

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?

Magic Squares

Age 14 to 18

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

Chocolate Maths

Age 11 to 14 Challenge Level:

Pick the number of times a week that you eat chocolate. This number must be more than one but less than ten. Multiply this number by 2. Add 5 (for Sunday). Multiply by 50... Can you explain why it. . . .

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?

Great Granddad

Age 11 to 14 Challenge Level:

Great Granddad is very proud of his telegram from the Queen congratulating him on his hundredth birthday and he has friends who are even older than he is... When was he born?

Litov's Mean Value Theorem

Age 11 to 14 Challenge Level:

Start with two numbers and generate a sequence where the next number is the mean of the last two numbers...

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?

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?

Who Is the Fairest of Them All ?

Age 11 to 14 Challenge Level:

Explore the effect of combining enlargements.

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. . . .

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.

Problem Solving, Using and Applying and Functional Mathematics

Age 5 to 18 Challenge Level:

Problem solving is at the heart of the NRICH site. All the problems give learners opportunities to learn, develop or use mathematical concepts and skills. Read here for more information.

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...

Arithmagons

Age 11 to 16 Challenge Level:

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

More Twisting and Turning

Age 11 to 16 Challenge Level:

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

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.

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.

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?

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?