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#### Resources tagged with Generalising similar to Multiplication Series: Number Arrays:

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### Crossings

##### Stage: 2 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?

### Number Tracks

##### Stage: 2 Challenge Level:

Ben’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?

### Got it for Two

##### Stage: 2 Challenge Level:

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

### Lots of Lollies

##### Stage: 1 Challenge Level:

Frances and Rishi were given a bag of lollies. They shared them out evenly and had one left over. How many lollies could there have been in the bag?

### Division Rules

##### Stage: 2 Challenge Level:

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

### Growing Garlic

##### Stage: 1 Challenge Level:

Ben and his mum are planting garlic. Use the interactivity to help you find out how many cloves of garlic they might have had.

### Three Dice

##### Stage: 2 Challenge Level:

Investigate the sum of the numbers on the top and bottom faces of a line of three dice. What do you notice?

### Sums and Differences 1

##### Stage: 2 Challenge Level:

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

### Sums and Differences 2

##### Stage: 2 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?

### How Odd

##### Stage: 1 Challenge Level:

This problem challenges you to find out how many odd numbers there are between pairs of numbers. Can you find a pair of numbers that has four odds between them?

### Number Differences

##### Stage: 2 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?

### Build it up More

##### Stage: 2 Challenge Level:

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

### Broken Toaster

##### Stage: 2 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?

### Button-up Some More

##### Stage: 2 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 ...?

### More Numbers in the Ring

##### Stage: 1 Challenge Level:

If there are 3 squares in the ring, can you place three different numbers in them so that their differences are odd? Try with different numbers of squares around the ring. What do you notice?

### Centred Squares

##### Stage: 2 Challenge Level:

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

### Magic Vs

##### Stage: 2 Challenge Level:

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

### Up and Down Staircases

##### Stage: 2 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?

### Domino Numbers

##### Stage: 2 Challenge Level:

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

### Tiling

##### Stage: 2 Challenge Level:

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

### Journeys in Numberland

##### Stage: 2 Challenge Level:

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

### Play to 37

##### Stage: 2 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.

### Odd Squares

##### Stage: 2 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?

### Snake Coils

##### Stage: 2 Challenge Level:

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

### What Could it Be?

##### Stage: 1 Challenge Level:

In this calculation, the box represents a missing digit. What could the digit be? What would the solution be in each case?

### Magic Constants

##### Stage: 2 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?

### Cut it Out

##### Stage: 2 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?

### Oddly

##### Stage: 2 Challenge Level:

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

### Round and Round the Circle

##### Stage: 2 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.

### Build it Up

##### Stage: 2 Challenge Level:

Can you find all the ways to get 15 at the top of this triangle of numbers?

### Doplication

##### Stage: 2 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?

### Always, Sometimes or Never? Number

##### Stage: 2 Challenge Level:

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

### Magic Circles

##### Stage: 2 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?

### Walking the Squares

##### Stage: 2 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?

##### Stage: 1 and 2 Challenge Level:

Are these statements relating to odd and even numbers always true, sometimes true or never true?

### Strike it Out for Two

##### Stage: 1 and 2 Challenge Level:

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

### Calendar Calculations

##### Stage: 2 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?

### The Add and Take-away Path

##### Stage: 1 Challenge Level:

Two children made up a game as they walked along the garden paths. Can you find out their scores? Can you find some paths of your own?

### Roll over the Dice

##### Stage: 2 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?

### Area and Perimeter

##### Stage: 2 Challenge Level:

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

### Round the Three Dice

##### Stage: 2 Challenge Level:

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

### Round the Two Dice

##### Stage: 1 Challenge Level:

This activity focuses on rounding to the nearest 10.

### Round the Four Dice

##### Stage: 2 Challenge Level:

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

### Nim-7 for Two

##### Stage: 1 and 2 Challenge Level:

Nim-7 game for an adult and child. Who will be the one to take the last counter?

### Dice Stairs

##### Stage: 2 Challenge Level:

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

### Unit Differences

##### Stage: 1 Challenge Level:

This challenge is about finding the difference between numbers which have the same tens digit.

### Polygonals

##### Stage: 2 Challenge Level:

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

### Fault-free Rectangles

##### Stage: 2 Challenge Level:

Find out what a "fault-free" rectangle is and try to make some of your own.

### Spirals, Spirals

##### Stage: 2 Challenge Level:

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

### Dotty Circle

##### Stage: 2 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?
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