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#### Resources tagged with Generalising similar to Odd Times Even:

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### How Odd

##### Stage: 1 Challenge Level:

This problem challenges you to find out how many odd numbers there are between pairs of numbers. Can you find a pair of numbers that has four odds between them?

### Lots of Lollies

##### Stage: 1 Challenge Level:

Frances and Rishi were given a bag of lollies. They shared them out evenly and had one left over. How many lollies could there have been in the bag?

### Cut it Out

##### Stage: 2 Challenge Level:

Can you dissect an equilateral triangle into 6 smaller ones? What number of smaller equilateral triangles is it NOT possible to dissect a larger equilateral triangle into?

### Make 37

##### Stage: 2 and 3 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.

### GOT IT Now

##### Stage: 2 and 3 Challenge Level:

For this challenge, you'll need to play Got It! Can you explain the strategy for winning this game with any target?

### GOT IT

##### Stage: 2 and 3 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.

### Growing Garlic

##### Stage: 1 Challenge Level:

Ben and his mum are planting garlic. Use the interactivity to help you find out how many cloves of garlic they might have had.

### Crossings

##### Stage: 2 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?

### Button-up Some More

##### Stage: 2 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 ...?

### Snake Coils

##### Stage: 2 Challenge Level:

This challenge asks you to imagine a snake coiling on itself.

### More Numbers in the Ring

##### Stage: 1 Challenge Level:

If there are 3 squares in the ring, can you place three different numbers in them so that their differences are odd? Try with different numbers of squares around the ring. What do you notice?

### Broken Toaster

##### Stage: 2 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?

### Nim-7

##### Stage: 2 Challenge Level:

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

### Number Differences

##### Stage: 2 Challenge Level:

Place the numbers from 1 to 9 in the squares below so that the difference between joined squares is odd. How many different ways can you do this?

### Number Tracks

##### Stage: 2 Challenge Level:

Ben’s class were making cutting up number tracks. First they cut them into twos and added up the numbers on each piece. What patterns could they see?

### Oddly

##### Stage: 2 Challenge Level:

Find the sum of all three-digit numbers each of whose digits is odd.

### Magic Vs

##### Stage: 2 Challenge Level:

Can you put the numbers 1-5 in the V shape so that both 'arms' have the same total?

### Magic Constants

##### Stage: 2 Challenge Level:

In a Magic Square all the rows, columns and diagonals add to the 'Magic Constant'. How would you change the magic constant of this square?

### Tiling

##### Stage: 2 Challenge Level:

An investigation that gives you the opportunity to make and justify predictions.

### Masterclass Ideas: Generalising

##### Stage: 2 and 3 Challenge Level:

A package contains a set of resources designed to develop pupils’ mathematical thinking. This package places a particular emphasis on “generalising” and is designed to meet the. . . .

### Move a Match

##### Stage: 2 Challenge Level:

How can you arrange these 10 matches in four piles so that when you move one match from three of the piles into the fourth, you end up with the same arrangement?

### Sliding Puzzle

##### Stage: 1, 2, 3 and 4 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.

### Fault-free Rectangles

##### Stage: 2 Challenge Level:

Find out what a "fault-free" rectangle is and try to make some of your own.

### Strike it Out

##### Stage: 1 and 2 Challenge Level:

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

### Journeys in Numberland

##### Stage: 2 Challenge Level:

Tom and Ben visited Numberland. Use the maps to work out the number of points each of their routes scores.

### Steps to the Podium

##### Stage: 2 and 3 Challenge Level:

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

### Doplication

##### Stage: 2 Challenge Level:

We can arrange dots in a similar way to the 5 on a dice and they usually sit quite well into a rectangular shape. How many altogether in this 3 by 5? What happens for other sizes?

### The Add and Take-away Path

##### Stage: 1 Challenge Level:

Two children made up a game as they walked along the garden paths. Can you find out their scores? Can you find some paths of your own?

### Sitting Round the Party Tables

##### Stage: 1 and 2 Challenge Level:

Sweets are given out to party-goers in a particular way. Investigate the total number of sweets received by people sitting in different positions.

### Three Dice

##### Stage: 2 Challenge Level:

Investigate the sum of the numbers on the top and bottom faces of a line of three dice. What do you notice?

### Round and Round the Circle

##### Stage: 2 Challenge Level:

What happens if you join every second point on this circle? How about every third point? Try with different steps and see if you can predict what will happen.

### Stop the Clock

##### Stage: 1 Challenge Level:

This is a game for two players. Can you find out how to be the first to get to 12 o'clock?

### Domino Numbers

##### Stage: 2 Challenge Level:

Can you see why 2 by 2 could be 5? Can you predict what 2 by 10 will be?

### Up and Down Staircases

##### Stage: 2 Challenge Level:

One block is needed to make an up-and-down staircase, with one step up and one step down. How many blocks would be needed to build an up-and-down staircase with 5 steps up and 5 steps down?

### Odd Squares

##### Stage: 2 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?

### Calendar Calculations

##### Stage: 2 Challenge Level:

Try adding together the dates of all the days in one week. Now multiply the first date by 7 and add 21. Can you explain what happens?

### Maths Trails

##### Stage: 2 and 3

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.

### Break it Up!

##### Stage: 1 and 2 Challenge Level:

In how many different ways can you break up a stick of 7 interlocking cubes? Now try with a stick of 8 cubes and a stick of 6 cubes.

### Games Related to Nim

##### Stage: 1, 2, 3 and 4

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

##### Stage: 2, 3 and 4 Challenge Level:

A collection of games on the NIM theme

### Sticky Triangles

##### Stage: 2 Challenge Level:

Can you continue this pattern of triangles and begin to predict how many sticks are used for each new "layer"?

### Dotty Circle

##### Stage: 2 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?

### Simple Train Journeys

##### Stage: 1 and 2 Challenge Level:

How many different journeys could you make if you were going to visit four stations in this network? How about if there were five stations? Can you predict the number of journeys for seven stations?

### Polygonals

##### Stage: 2 Challenge Level:

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

### Triangle Pin-down

##### Stage: 2 Challenge Level:

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

### Area and Perimeter

##### Stage: 2 Challenge Level:

What can you say about these shapes? This problem challenges you to create shapes with different areas and perimeters.

### The Great Tiling Count

##### Stage: 2 Challenge Level:

Compare the numbers of particular tiles in one or all of these three designs, inspired by the floor tiles of a church in Cambridge.

### Lost Books

##### Stage: 2 Challenge Level:

While we were sorting some papers we found 3 strange sheets which seemed to come from small books but there were page numbers at the foot of each page. Did the pages come from the same book?

### Counting Counters

##### Stage: 2 Challenge Level:

Take a counter and surround it by a ring of other counters that MUST touch two others. How many are needed?

### Winning Lines

##### Stage: 2, 3 and 4 Challenge Level:

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