There are **220** NRICH Mathematical resources connected to **Generalising**, you may find related items under Using, Applying and Reasoning about Mathematics.

Try out this number trick. What happens with different starting numbers? What do you notice?

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

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

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

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

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

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

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?

Can you find all the ways to get 15 at the top of this triangle of numbers? Many opportunities to work in different ways.

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

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

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

Use two dice to generate two numbers with one decimal place. What happens when you round these numbers to the nearest whole number?

What happens when you round these numbers to the nearest whole number?

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

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.

How many ways can you find to do up all four buttons on my coat? How about if I had five buttons? Six ...?

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

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?

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

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

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?

Jo made a cube from some smaller cubes, painted some of the faces of the large cube, and then took it apart again. 45 small cubes had no paint on them at all. How many small cubes did Jo use?

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

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

Use the animation to help you work out how many lines are needed to draw mystic roses of different sizes.

The Tower of Hanoi is an ancient mathematical challenge. Working on the building blocks may help you to explain the patterns you notice.

How could Penny, Tom and Matthew work out how many chocolates there are in different sized boxes?

A country has decided to have just two different coins, 3z and 5z coins. Which totals can be made? Is there a largest total that cannot be made? How do you know?

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

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

Charlie has moved between countries and the average income of both has increased. How can this be so?

What's the largest volume of box you can make from a square of paper?

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

Imagine you have a large supply of 3kg and 8kg weights. How many of each weight would you need for the average (mean) of the weights to be 6kg? What other averages could you have?

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

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

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

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

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

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?”

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

Can you describe this route to infinity? Where will the arrows take you next?

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

Explore the effect of combining enlargements.

Explore the effect of reflecting in two intersecting mirror lines.

Explore the effect of reflecting in two parallel mirror lines.

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?

Can you find the area of a parallelogram defined by two vectors?