# Resources tagged with: Generalising

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### There are 128 results

Broad Topics > Thinking Mathematically > Generalising

### Mini-max

##### Age 11 to 14Challenge 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. . . .

### Repeaters

##### Age 11 to 14Challenge 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.

### Three Times Seven

##### Age 11 to 14Challenge Level

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

### Have You Got It?

##### Age 11 to 14Challenge Level

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

### One O Five

##### Age 11 to 14Challenge 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. . . .

### Plus Minus

##### Age 14 to 16Challenge Level

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

### Number Pyramids

##### Age 11 to 14Challenge Level

Try entering different sets of numbers in the number pyramids. How does the total at the top change?

### Chocolate Maths

##### Age 11 to 14Challenge 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. . . .

### Counting Factors

##### Age 11 to 14Challenge Level

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

### What Numbers Can We Make Now?

##### Age 11 to 14Challenge Level

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

### Got it for Two

##### Age 7 to 14Challenge Level

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

### Special Sums and Products

##### Age 11 to 14Challenge 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.

##### Age 11 to 14Challenge 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 16Challenge 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?”

### Chocolate 2010

##### Age 14 to 16Challenge Level

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

### Card Trick 2

##### Age 11 to 14Challenge Level

Can you explain how this card trick works?

### Sum Equals Product

##### Age 11 to 14Challenge 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 ï¿½ 1 [1/3]. What other numbers have the sum equal to the product and can this be. . . .

### Summing Consecutive Numbers

##### Age 11 to 14Challenge 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?

### Take Three from Five

##### Age 11 to 16Challenge 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?

##### Age 11 to 14Challenge 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. . . .

### Regular Hexagon Loops

##### Age 11 to 14Challenge Level

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

### 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.

### Nim-like Games

##### Age 7 to 16Challenge Level

A collection of games on the NIM theme

### Nim

##### Age 14 to 16Challenge 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.

### Hypotenuse Lattice Points

##### Age 14 to 16Challenge Level

The triangle OMN has vertices on the axes with whole number co-ordinates. How many points with whole number coordinates are there on the hypotenuse MN?

### Got It

##### Age 7 to 14Challenge 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.

### Multiplication Square

##### Age 14 to 16Challenge Level

Pick a square within a multiplication square and add the numbers on each diagonal. What do you notice?

### One, Three, Five, Seven

##### Age 11 to 16Challenge 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.

### Winning Lines

##### Age 7 to 16

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

### 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.

### Pentanim

##### Age 7 to 16Challenge 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.

##### Age 7 to 14Challenge Level

I added together some of my neighbours' house numbers. Can you explain the patterns I noticed?

### Cunning Card Trick

##### Age 11 to 14Challenge Level

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

### Elevenses

##### Age 11 to 14Challenge Level

How many pairs of numbers can you find that add up to a multiple of 11? Do you notice anything interesting about your results?

### Charitable Pennies

##### Age 7 to 14Challenge Level

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

### Nim-7 for Two

##### Age 5 to 14Challenge Level

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

### Steps to the Podium

##### Age 7 to 14Challenge Level

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

### Magic Letters

##### Age 11 to 14Challenge Level

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

##### Age 11 to 14Challenge 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. . . .

### What Numbers Can We Make?

##### Age 11 to 14Challenge Level

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

### Window Frames

##### Age 5 to 14Challenge Level

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

##### Age 11 to 14Challenge 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?

### Janine's Conjecture

##### Age 14 to 16Challenge Level

Janine noticed, while studying some cube numbers, that if you take three consecutive whole numbers and multiply them together and then add the middle number of the three, you get the middle number. . . .

### Consecutive Negative Numbers

##### Age 11 to 14Challenge Level

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

### 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.

### Harmonic Triangle

##### Age 14 to 16Challenge Level

Can you see how to build a harmonic triangle? Can you work out the next two rows?

### Tourism

##### Age 11 to 14Challenge 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 Number Pyramids

##### Age 11 to 14Challenge Level

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

### Partitioning Revisited

##### Age 11 to 14Challenge 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

### Arithmagons

##### Age 11 to 16Challenge Level

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