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There are 141 NRICH Mathematical resources connected to Generalising, you may find related items under Using, Applying and Reasoning about Mathematics.

Broad Topics > Using, Applying and Reasoning about Mathematics > Generalising Age 5 to 11 Challenge Level:

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

Age 7 to 11 Challenge Level:

Watch this animation. What do you see? Can you explain why this happens? Finding 3D Stacks

Age 7 to 11 Challenge Level:

Can you find a way of counting the spheres in these arrangements? Always, Sometimes or Never? Shape

Age 7 to 11 Challenge Level:

Are these statements always true, sometimes true or never true? Always, Sometimes or Never? Number

Age 7 to 11 Challenge Level:

Are these statements always true, sometimes true or never true? Always, Sometimes or Never?

Age 5 to 11 Challenge Level:

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

Age 5 to 11 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? Build it Up

Age 7 to 11 Challenge Level:

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

Age 7 to 11 Challenge Level:

This challenge encourages you to explore dividing a three-digit number by a single-digit number. Round the Dice Decimals 1

Age 7 to 11 Challenge Level:

Use two dice to generate two numbers with one decimal place. What happens when you round these numbers to the nearest whole number? Round the Dice Decimals 2

Age 7 to 11 Challenge Level:

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

Age 7 to 11 Challenge Level:

This activity involves rounding four-digit numbers to the nearest thousand. Play to 37

Age 7 to 11 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. Button-up Some More

Age 7 to 11 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 ...? Journeys in Numberland

Age 7 to 11 Challenge Level:

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

Age 7 to 11 Challenge Level:

What can you say about these shapes? This problem challenges you to create shapes with different areas and perimeters. Sitting Round the Party Tables

Age 5 to 11 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

Age 7 to 11 Challenge Level:

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

Age 11 to 14 Challenge Level:

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

Age 11 to 14 Challenge Level:

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

Age 11 to 14 Challenge Level:

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

Age 11 to 14 Challenge Level:

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? Strike it Out

Age 5 to 11 Challenge Level:

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

Age 11 to 14 Challenge Level:

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

Age 11 to 16 Challenge Level:

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

Age 11 to 14 Challenge 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? Searching for Mean(ing)

Age 11 to 14 Challenge Level:

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? Magic Vs

Age 7 to 11 Challenge Level:

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

Age 11 to 16 Challenge Level:

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

Age 11 to 16 Challenge 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?” Triangle Numbers

Age 11 to 14 Challenge Level:

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

Age 11 to 14 Challenge Level:

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

Age 11 to 14 Challenge Level:

Delight your friends with this cunning trick! Can you explain how it works? Who Is the Fairest of Them All ?

Age 11 to 14 Challenge Level:

Explore the effect of combining enlargements. ...on the Wall

Age 11 to 14 Challenge Level:

Explore the effect of reflecting in two intersecting mirror lines. Mirror, Mirror...

Age 11 to 14 Challenge Level:

Explore the effect of reflecting in two parallel mirror lines. 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? 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... Squares in Rectangles

Age 11 to 14 Challenge Level:

A 2 by 3 rectangle contains 8 squares and a 3 by 4 rectangle contains 20 squares. What size rectangle(s) contain(s) exactly 100 squares? Can you find them all? Cubes Within Cubes Revisited

Age 11 to 14 Challenge Level:

Imagine starting with one yellow cube and covering it all over with a single layer of red cubes, and then covering that cube with a layer of blue cubes. How many red and blue cubes would you need? Partitioning Revisited

Age 11 to 14 Challenge 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 Number Differences

Age 7 to 11 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? 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? Break it Up!

Age 5 to 11 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. Up and Down Staircases

Age 7 to 11 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? More Number Pyramids

Age 11 to 14 Challenge Level:

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

Age 7 to 11 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?