Resources tagged with: Generalising

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There are 149 results

Broad Topics > Thinking Mathematically > Generalising

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"?

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?

Cuisenaire Squares

Age 7 to 11
Challenge Level

These squares have been made from Cuisenaire rods. Can you describe the pattern? What would the next square look like?

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?

Steps to the Podium

Age 7 to 14
Challenge Level

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

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.

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.

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 ...?

Counting Counters

Age 7 to 11
Challenge Level

Take a counter and surround it by a ring of other counters that MUST touch two others. How many are needed?

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?

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.

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.

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?

Making Maths: Be a Mathemagician

Age 7 to 11
Challenge Level

Surprise your friends with this magic square trick.

Cuboid Challenge

Age 11 to 16
Challenge Level

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

Finding 3D Stacks

Age 7 to 11
Challenge Level

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

More Number Pyramids

Age 11 to 14
Challenge Level

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

Centred Squares

Age 7 to 11
Challenge Level

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

Squares, Squares and More Squares

Age 11 to 14
Challenge Level

Can you dissect a square into: 4, 7, 10, 13... other squares? 6, 9, 12, 15... other squares? 8, 11, 14... other squares?

What Numbers Can We Make?

Age 11 to 14
Challenge Level

Imagine we have four bags containing a large number of 1s, 4s, 7s and 10s. What numbers can we make?

Hidden Rectangles

Age 11 to 14
Challenge Level

Rectangles are considered different if they vary in size or have different locations. How many different rectangles can be drawn on a chessboard?

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?

Tiling

Age 7 to 11
Challenge Level

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

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.

Sliding Puzzle

Age 11 to 16
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.

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.

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?

Picturing Square Numbers

Age 11 to 14
Challenge Level

Square numbers can be represented as the sum of consecutive odd numbers. What is the sum of 1 + 3 + ..... + 149 + 151 + 153?

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?

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.

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.

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?

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?

Frogs

Age 11 to 14
Challenge Level

How many moves does it take to swap over some red and blue frogs? Do you have a method?

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?

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?

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?

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!

Round the Three Dice

Age 7 to 11
Challenge Level

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

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.

Always, Sometimes or Never? Shape

Age 7 to 11
Challenge Level

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

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?

Tumbling Down

Age 7 to 11
Challenge Level

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

Division Rules

Age 7 to 11
Challenge Level

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

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.

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?

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?

Cunning Card Trick

Age 11 to 14
Challenge Level

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