Proportional sizes

Proportional sizes

INDEX

table with data

Let's define!

1st example

What does "k" means?

Selection of x and y

Number k!

Is it proportional ?

2nd example

again...choose x and y

Take a challenge!

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More tasks !

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How to do ?

At the end...

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1st exampleThe printer writes 30 pages for 3 minutes. There is an equal amount od text and drawings on each page. 1. How many such pages will be printed for 1 minutes ? 2. How long will it take time for three times as many pages ? 3. How many pages will the printer print if it runs 5 times as long ?

click on the picture and play true-false

1st example: table with data

Two sizes, x and y are proportional:

• How many times the size of x increases, so many times the size of y must also increase
• How many times the size od x decreases, so many times the size of y must also decreases

Click on the sign and play a game!

Let's calculate the proportionality coefficient

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The quotient of proportional sizes is always equal and is called the proportionality coefficient - k

In the 1st example, the proportionality coefficient represents the velocity of printing one page.

How to choose x and y ?

After we establish that two sizes are proportional...

...let's ask ourselves: What is more logical ?

for 1st example : How many minutes does it take to print 1 page? How many pages are printed for 1 minutes ?

It is more logical to say how many pages are printed for 1 minutes, therefore size y is number of pages and x is the print time.

The size x represents a unit value. In a 1st example it represent how many pages are printed for 1 minutes.

2nd example: 125 dag of sugar is needed to bake 5 equal cake.

Are the number of cakes and amount of sugar proportional quantities ?

If we increase the number of egual cakes to 10, how much sugar is needed ?

What is more logical to say ? How many cakes is needed for 1 dag of sugar ? How much sugar is needed for baking 1 cake ?

It is more logical to say how much sugar is needed for baking 1 cake, therefore the size y is amount od sugar and x is the number of cakes.

click on picture to see solution of 2nd example.

In which table the proportional sizes are shown ?

VS

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Two ways of solving tasks with proportional sizes

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Start

Try to solve tasks!

when you solve the task 3, click here to reveal solution.

When you solve the task 2, click here to reveal the solution.

When you solve the task 1, click here to reveal the solution.

Take the challenge !

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Graphical display of proportionality

At the end click here and play a game!

P.S. There are inversal proportional in size,... but that is completely different story...maybe next time!