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

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### Always, Sometimes or Never? Number

##### Stage: 2 Challenge Level:

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

### Always, Sometimes or Never?

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

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

### 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?

### 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?

### Spirals, Spirals

##### Stage: 2 Challenge Level:

Here are two kinds of spirals for you to explore. What do you notice?

### 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 ...?

### 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.

### 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?

### 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?

### 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?

### Roll over the Dice

##### Stage: 2 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?

### Snake Coils

##### Stage: 2 Challenge Level:

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

### Walking the Squares

##### Stage: 2 Challenge Level:

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

### 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?

### Nim-7 for Two

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

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

### 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?

### Centred Squares

##### Stage: 2 Challenge Level:

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

### Always, Sometimes or Never? KS1

##### Stage: 1 Challenge Level:

Are these statements relating to calculation and properties of shapes always true, sometimes true or never true?

### Sums and Differences 1

##### Stage: 2 Challenge Level:

This challenge focuses on finding the sum and difference of pairs of two-digit numbers.

### Unit Differences

##### Stage: 1 Challenge Level:

This challenge is about finding the difference between numbers which have the same tens digit.

### Circles, Circles

##### Stage: 1 and 2 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?

### Sums and Differences 2

##### Stage: 2 Challenge Level:

Find the sum and difference between a pair of two-digit numbers. Now find the sum and difference between the sum and difference! What happens?

### Build it Up

##### Stage: 2 Challenge Level:

Can you find all the ways to get 15 at the top of this triangle of numbers?

### Build it up More

##### Stage: 2 Challenge Level:

This task follows on from Build it Up and takes the ideas into three dimensions!

### 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?

### Tiling

##### Stage: 2 Challenge Level:

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

### Division Rules

##### Stage: 2 Challenge Level:

This challenge encourages you to explore dividing a three-digit number by a single-digit number.

### 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?

### 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.

### Number Tracks

##### Stage: 2 Challenge Level:

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

### Play to 37

##### Stage: 2 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.

### Got it for Two

##### Stage: 2 Challenge Level:

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

### Round the Four Dice

##### Stage: 2 Challenge Level:

This activity involves rounding four-digit numbers to the nearest thousand.

### 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.

### 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.

### What Could it Be?

##### Stage: 1 Challenge Level:

In this calculation, the box represents a missing digit. What could the digit be? What would the solution be in each case?

### 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?

### Round the Two Dice

##### Stage: 1 Challenge Level:

This activity focuses on rounding to the nearest 10.

### Stop the Clock for Two

##### Stage: 1 Challenge Level:

Stop the Clock game for an adult and child. How can you make sure you always win this game?

### 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.

### 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.

### Polygonals

##### Stage: 2 Challenge Level:

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

### Strike it Out for Two

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

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

### 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?

### 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.

### Fault-free Rectangles

##### Stage: 2 Challenge Level:

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

### 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.

### 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.

### 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?