3Thavo §7.2 Directly and inversely proportional

§ 7.2 Directly and inversely proportional
Before working on this paragraph, let's look at these words and their meaning first!

1 / 15
next
Slide 1: Slide
WiskundeMiddelbare schoolhavoLeerjaar 3

This lesson contains 15 slides, with interactive quiz and text slides.

time-iconLesson duration is: 50 min

Items in this lesson

§ 7.2 Directly and inversely proportional
Before working on this paragraph, let's look at these words and their meaning first!

Slide 1 - Slide

Directly proportional 1.
 Proportional is 'evenredig' in Dutch. 
Question: But what does 'evenredig' mean?
All think about this!

Slide 2 - Slide

Directly proportional 2.
Answer: Proportional or 'evenredig' means in Maths that 
a variable gets bigger when another variable gets bigger.

Slide 3 - Slide

Directly proportional 3.
Now we added the word 'directly' and it becomes very concrete:
When x becomes 3 times as large, then y also becomes 3 times as large.
In a formula:      y = 6x  or  y = 10x
For example: fill in x = 2 in y = 6x    We get y = 6 x 2 = 12
Now fill in x = 6 (so 3 times as large as 2):     y = 6 x 6 = 36
If we now compare 12 to 36, we see that y is done x 3 too!           

Slide 4 - Slide

For example:
 y = 5x  Now divide by 5, you get
y/x = 5  !

Slide 5 - Slide

Homework time!
Using what you just learnt, try to do the exercises 8 and further.
Skip the Introduction.
Later on this LessonUp will be continued.

Slide 6 - Slide

Inversely proportional
From exercise 13 on you need some more information.
This we will go through together, right now!
It is about another kinda proportionality.
Question: What does 'Inversely' mean?

Slide 7 - Slide

Inversely?!
Inversely means: 'omgekeerd',
 in good German.
Let's see what this means for our Math subject.

Slide 8 - Slide

Slide 9 - Slide

Task: Find at least 2 differences
between the tables for 'Directly proportional' and 'Inversely proportional'.
Look up both tables, on pages 250 and 252!

Slide 10 - Slide

Solution to task:
Differences:
1. For Directly prop., if you do x times 4, you also do y times 4,
for Inversely prop., if you do x times 4, you do y divided by 4!
2. For Inversely prop. the product (that is doing: times)
stays the same always, for Directly proportional this is not the case.

Slide 11 - Slide

Finally...
For Directly proportional you were shown a graph.
Watch Theory p.250 again: a straight line, through the origin.
But...why is there no graph shown for Inversely proportional?!
Anyway, look at page 255!
This kinda graph is called a HYPERBOLA.

Slide 12 - Slide

Homework time again!
Good luck and make sure you do not have that much homework.

Slide 13 - Slide

What did you learn this lesson?

Slide 14 - Mind map

Slide 15 - Slide