# Resources tagged with: Generalising

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### There are 149 results

Broad Topics > Thinking Mathematically > Generalising

### 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?

### 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?

### 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?

### 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?

### Magic Circles

##### Age 7 to 11Challenge Level

Put the numbers 1, 2, 3, 4, 5, 6 into the squares so that the numbers on each circle add up to the same amount. Can you find the rule for giving another set of six numbers?

### Oddly

##### Age 7 to 11Challenge Level

Find the sum of all three-digit numbers each of whose digits is odd.

### 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.

### Centred Squares

##### Age 7 to 11Challenge Level

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

### Build it up More

##### Age 7 to 11Challenge Level

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

### 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?

### 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?

### Sums and Differences 1

##### Age 7 to 11Challenge Level

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

### 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?

### Making Maths: Be a Mathemagician

##### Age 7 to 11Challenge Level

Surprise your friends with this magic square trick.

### 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?

##### Age 5 to 11Challenge Level

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

### Polygonals

##### Age 7 to 11Challenge Level

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

### Round the Three Dice

##### Age 7 to 11Challenge Level

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

### 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 ...?

### 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.

### 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.

### 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?

### 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

##### 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.

### 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?

### 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?

### 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.

### Tiling

##### Age 7 to 11Challenge Level

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

### 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.

### 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"?

### 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?

### Round the Dice Decimals 2

##### Age 7 to 11Challenge Level

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

### 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.

### Steps to the Podium

##### Age 7 to 14Challenge Level

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

### 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.

### Surprising Split

##### Age 7 to 11Challenge Level

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

### Strike it Out

##### Age 5 to 11Challenge Level

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

### Sums of Pairs

##### Age 11 to 16Challenge 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?”

### 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?

### Round the Dice Decimals 1

##### Age 7 to 11Challenge Level

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

### Repeaters

##### Age 11 to 14Challenge Level

Choose any 3 digits and make a 6 digit number by repeating the 3 digits in the same order (e.g. 594594). Explain why whatever digits you choose the number will always be divisible by 7, 11 and 13.

### 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?

### 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?

### Charitable Pennies

##### Age 7 to 14Challenge Level

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

### 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?

### 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?

### Strike it Out for Two

##### Age 5 to 11Challenge Level

Strike it Out game for an adult and child. Can you stop your partner from being able to go?

### Regular Hexagon Loops

##### Age 11 to 14Challenge Level

Make some loops out of regular hexagons. What rules can you discover?

### Winning Lines

##### Age 7 to 16

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

### Generalising

##### Age 5 to 11

These tasks give learners chance to generalise, which involves identifying an underlying structure.