Resources tagged with: Generalising

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There are 92 NRICH Mathematical resources connected to Generalising, you may find related items under Thinking Mathematically.

Broad Topics > Thinking Mathematically > Generalising

Digit Addition

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? KS1

Age 5 to 7
Challenge Level

Are these statements relating to calculation and properties of shapes 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.

Unit Differences

Age 5 to 7
Challenge Level

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

What Could it Be?

Age 5 to 7
Challenge Level

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

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 Two Dice

Age 5 to 7
Challenge Level

This activity focuses on rounding to the nearest 10.

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.

The Add and Take-away Path

Age 5 to 7
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?

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.

How Odd

Age 5 to 7
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?

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?

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.

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?

Stop the Clock

Age 5 to 7
Challenge Level

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

Growing Garlic

Age 5 to 7
Challenge Level

Ben and his mum are planting garlic. Can you find out how many cloves of garlic they might have had?

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?

More Numbers in the Ring

Age 5 to 7
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?

Lots of Lollies

Age 5 to 7
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?

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?

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?

Make 37

Age 7 to 14
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

Age 7 to 14
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.

Nim-7

Age 5 to 14
Challenge Level

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

Cut it Out

Age 7 to 11
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?

Sticky Triangles

Age 7 to 11
Challenge Level

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

Round and Round the Circle

Age 7 to 11
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.

Doplication

Age 7 to 11
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?

Charitable Pennies

Age 7 to 14
Challenge Level

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

Surprising Split

Age 7 to 11
Challenge Level

Does this 'trick' for calculating multiples of 11 always work? Why or why not?

Unexpected Ordering

Age 5 to 7
Challenge Level

Watch the video of Fran re-ordering these number cards. What do you notice? Try it for yourself. What happens?

Truth or Lie

Age 7 to 11
Challenge Level

Take a look at the video of this trick. Can you perform it yourself? Why is this maths and not magic?

Neighbourly Addition

Age 7 to 14
Challenge Level

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

Window Frames

Age 5 to 14
Challenge Level

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

Bundles of Cubes

Age 7 to 11
Challenge Level

Watch this animation. What do you notice? What happens when you try more or fewer cubes in a bundle?

Next-door Numbers

Age 5 to 7
Challenge Level

Florence, Ethan and Alma have each added together two 'next-door' numbers. What is the same about their answers?

Roll over the Dice

Age 7 to 11
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?