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#### Resources tagged with Generalising similar to Andy's Marbles:

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### Number Tracks

##### Age 7 to 11 Challenge 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?

### 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!

### Calendar Calculations

##### Age 7 to 11 Challenge 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?

### 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.

### Surprising Split

##### Age 7 to 11 Challenge Level:

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

### 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.

### 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?

### 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?

### Snake Coils

##### Age 7 to 11 Challenge Level:

This challenge asks you to imagine a snake coiling on itself.

### Magic Constants

##### Age 7 to 11 Challenge 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 11 Challenge Level:

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

### Centred Squares

##### Age 7 to 11 Challenge Level:

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

### 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.

##### Age 5 to 11 Challenge Level:

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

### Crossings

##### Age 7 to 11 Challenge 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 Circles

##### Age 7 to 11 Challenge 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?

### 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?

### 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 ...?

### Strike it Out for Two

##### Age 5 to 11 Challenge Level:

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

### 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.

### 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?

### Oddly

##### Age 7 to 11 Challenge Level:

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

### 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.

### 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?

### 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.

### Domino Numbers

##### Age 7 to 11 Challenge Level:

Can you see why 2 by 2 could be 5? Can you predict what 2 by 10 will be?

### 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?

### 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.

### Special Sums and Products

##### Age 11 to 14 Challenge Level:

Find some examples of pairs of numbers such that their sum is a factor of their product. eg. 4 + 12 = 16 and 4 × 12 = 48 and 16 is a factor of 48.

### 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?

### Tiling

##### Age 7 to 11 Challenge Level:

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

### 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?

### 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?

### Round the Four Dice

##### Age 7 to 11 Challenge Level:

This activity involves rounding four-digit numbers to the nearest thousand.

### Have You Got It?

##### Age 11 to 14 Challenge Level:

Can you explain the strategy for winning this game with any target?

### 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?

### Tumbling Down

##### Age 7 to 11 Challenge Level:

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

### Always, Sometimes or Never? Number

##### Age 7 to 11 Challenge Level:

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

### Walking the Squares

##### Age 7 to 11 Challenge Level:

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

### 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?

### 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?

### Got it for Two

##### Age 7 to 14 Challenge Level:

Got It game for an adult and child. How can you play so that you know you will always win?

### 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?

### Division Rules

##### Age 7 to 11 Challenge Level:

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

### 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.

### 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?

### Round the Three Dice

##### Age 7 to 11 Challenge Level:

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

### Spirals, Spirals

##### Age 7 to 11 Challenge Level:

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

### 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.