Resources tagged with: Generalising

Filter by: Content type:
Age range:
Challenge level:

There are 149 results

Broad Topics > Thinking Mathematically > Generalising

Triangle Pin-down

Age 7 to 11
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

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.

Broken Toaster

Age 7 to 11 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?

Rope Mat

Age 7 to 11
Challenge Level

How many centimetres of rope will I need to make another mat just like the one I have here?

Tiling

Age 7 to 11
Challenge Level

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

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.

Dice Stairs

Age 7 to 11
Challenge Level

Can you make dice stairs using the rules stated? How do you know you have all the possible stairs?

Dotty Circle

Age 7 to 11
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?

Move a Match

Age 7 to 11
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?

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 ...?

Maths Trails

Age 7 to 14

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.

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"?

Taking Steps

Age 7 to 11
Challenge Level

In each of the pictures the invitation is for you to: Count what you see. Identify how you think the pattern would continue.

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?

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.

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.

Steps to the Podium

Age 7 to 14
Challenge Level

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

Lost Books

Age 7 to 11
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?

Sums and Differences 2

Age 7 to 11
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?

Sums and Differences 1

Age 7 to 11
Challenge Level

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

Games Related to Nim

Age 5 to 16

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.

Polygonals

Age 7 to 11
Challenge Level

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

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?

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.

Centred Squares

Age 7 to 11
Challenge Level

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

The Great Tiling Count

Age 7 to 11
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.

Simple Train Journeys

Age 5 to 11
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?

Round the Three Dice

Age 7 to 11
Challenge Level

What happens when you round these three-digit numbers to the nearest 100?

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.

Build it up More

Age 7 to 11
Challenge Level

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

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?

Round the Dice Decimals 2

Age 7 to 11
Challenge Level

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

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.

Coordinate Patterns

Age 11 to 14
Challenge Level

Charlie and Alison have been drawing patterns on coordinate grids. Can you picture where the patterns lead?

Finding 3D Stacks

Age 7 to 11
Challenge Level

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

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?

Picturing Triangular Numbers

Age 11 to 14
Challenge Level

Triangular numbers can be represented by a triangular array of squares. What do you notice about the sum of identical triangle numbers?

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.

Route to Infinity

Age 11 to 14
Challenge Level

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

More Twisting and Turning

Age 11 to 16
Challenge Level

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

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?

Magic Letters

Age 11 to 14
Challenge Level

Charlie has made a Magic V. Can you use his example to make some more? And how about Magic Ls, Ns and Ws?

Shear Magic

Age 11 to 14
Challenge Level

Explore the area of families of parallelograms and triangles. Can you find rules to work out the areas?

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?

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?

Winning Lines

Age 7 to 16

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

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

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?

Konigsberg Plus

Age 11 to 14
Challenge Level

Euler discussed whether or not it was possible to stroll around Koenigsberg crossing each of its seven bridges exactly once. Experiment with different numbers of islands and bridges.

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.