# Resources tagged with: Generalising

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### There are 149 results

Broad Topics > Thinking Mathematically > Generalising

### Sticky Triangles

##### Age 7 to 11Challenge Level

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

### Lost Books

##### Age 7 to 11Challenge 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?

### Move a Match

##### Age 7 to 11Challenge 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?

### Cut it Out

##### Age 7 to 11Challenge 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?

### Polygonals

##### Age 7 to 11Challenge Level

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

### Cuisenaire Squares

##### Age 7 to 11Challenge Level

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

### The Great Tiling Count

##### Age 7 to 11Challenge 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.

### Making Maths: Be a Mathemagician

##### Age 7 to 11Challenge Level

Surprise your friends with this magic square trick.

### Taking Steps

##### Age 7 to 11Challenge Level

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

### Dice Stairs

##### Age 7 to 11Challenge Level

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

### Centred Squares

##### Age 7 to 11Challenge Level

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

### Counting Counters

##### Age 7 to 11Challenge Level

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

### Sums and Differences 2

##### Age 7 to 11Challenge 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?

### Finding 3D Stacks

##### Age 7 to 11Challenge Level

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

### Steps to the Podium

##### Age 7 to 14Challenge Level

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

### Odd Squares

##### Age 7 to 11Challenge Level

Think of a number, square it and subtract your starting number. Is the number youâ€™re left with odd or even? How do the images help to explain this?

### Break it Up!

##### Age 5 to 11Challenge 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.

### Button-up Some More

##### Age 7 to 11Challenge Level

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

### Sums and Differences 1

##### Age 7 to 11Challenge Level

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

### Journeys in Numberland

##### Age 7 to 11Challenge Level

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

### Round the Three Dice

##### Age 7 to 11Challenge Level

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

### Calendar Calculations

##### Age 7 to 11Challenge Level

Try adding together the dates of all the days in one week. Now multiply the first date by 7 and add 21. Can you explain what happens?

### Triangle Pin-down

##### Age 7 to 11Challenge Level

Use the interactivity to investigate what kinds of triangles can be drawn on peg boards with different numbers of pegs.

### Circles, Circles

##### Age 5 to 11Challenge 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?

### Tiling

##### Age 7 to 11Challenge Level

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

### Broken Toaster

##### Age 7 to 11 ShortChallenge 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?

### Sitting Round the Party Tables

##### Age 5 to 11Challenge 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.

### Area and Perimeter

##### Age 7 to 11Challenge Level

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

### Doplication

##### Age 7 to 11Challenge 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?

### Division Rules

##### Age 7 to 11Challenge Level

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

### Build it up More

##### Age 7 to 11Challenge Level

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

### Simple Train Journeys

##### Age 5 to 11Challenge 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 and Round the Circle

##### Age 7 to 11Challenge 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.

### Magic Constants

##### Age 7 to 11Challenge Level

In a Magic Square all the rows, columns and diagonals add to the 'Magic Constant'. How would you change the magic constant of this square?

### Bundles of Cubes

##### Age 7 to 11Challenge Level

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

### Tumbling Down

##### Age 7 to 11Challenge Level

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

### Build it Up

##### Age 7 to 11Challenge 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.

### Cubes Within Cubes Revisited

##### Age 11 to 14Challenge 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?

### Number Tracks

##### Age 7 to 11Challenge Level

Benâ€™s class were cutting up number tracks. First they cut them into twos and added up the numbers on each piece. What patterns could they see?

### Frogs

##### Age 11 to 14Challenge Level

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

### Winning Lines

##### Age 7 to 16

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

### Walking the Squares

##### Age 7 to 11Challenge Level

Find a route from the outside to the inside of this square, stepping on as many tiles as possible.

### Round the Dice Decimals 2

##### Age 7 to 11Challenge Level

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

### Number Differences

##### Age 7 to 11Challenge 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?

### Crossings

##### Age 7 to 11Challenge Level

In this problem we are looking at sets of parallel sticks that cross each other. What is the least number of crossings you can make? And the greatest?

### Magic Letters

##### Age 11 to 14Challenge Level

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

### Spirals, Spirals

##### Age 7 to 11Challenge Level

Here are two kinds of spirals for you to explore. What do you notice?

### Magic Vs

##### Age 7 to 11Challenge Level

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

### Picturing Square Numbers

##### Age 11 to 14Challenge Level

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

### Rope Mat

##### Age 7 to 11Challenge Level

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