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1TTO §8.2 Powers
Now comes a powerful paragraph!
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Wiskunde
Middelbare school
havo, vwo
Leerjaar 1
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Now comes a powerful paragraph!
Slide 1 - Tekstslide
§8.2 Powers
Slide 2 - Tekstslide
When using your calculator:
5 kwadraat kun je op twee manieren doen:
tik 5
tik kwadraat teken
tik =.
Of: tik 5 en dan 'dakje' [dus ^] en dan 2 en dan =
x
2
Slide 3 - Tekstslide
When using your calculator:
tik 3
tik dakje [ = ^-knop)
tik 4
en tik dan =
3
4
=
Slide 4 - Tekstslide
Here is a table with length = 2 m and also width = 2 m.
The Area (=oppervlakte) = 2 x 2 = 4
Multiplying a number by itself -in this case 2 muliplied by 2- is called:
SQUARING a number.
The result is the SQUARE of a number. Let's look at a few more examples!
m
2
Square = vierkant!
Slide 5 - Tekstslide
Square = vierkant = 'kwadraat'
3 kwadraat =
3
2
=
3
x
3
=
3
k
w
a
d
r
a
a
t
=
9
Slide 6 - Tekstslide
In the next slide
give the answers to these 5 exercises.
First copy in your notebook:
1
2
,
2
2
,
3
2
,
4
2
,
5
2
Slide 7 - Tekstslide
The 4 answers to the SQUARES of 1,2,3,4, and 5 are:
A
1, 2, 3, 4 and 5
B
1, 4, 9, 16 and 25
C
2, 4, 6, 8 and 10
Slide 8 - Quizvraag
Solutions:
So, for example:
the SQUARE of 5 is
5 x 5 = 25.
Slide 9 - Tekstslide
However ...
sometimes you want to multiply a number by itself more than once. Then we can use a similar Notation as for the Square:
+ For example: 3 x 3 x 3 x 3 =
+ See the next slide for more! New examples and the new Words that come with this.
+ Like the word: POWER.
3
4
Slide 10 - Tekstslide
Slide 11 - Tekstslide
Slide 12 - Tekstslide
is the same as ........
4
3
A
4 x 4 x 4
B
4 + 4 +4
C
4 x 3
D
64
Slide 13 - Quizvraag
Explanation:
means the same as:
4 x 4 x 4,
but it also means: 64, because that is the outcome.
It doesn't mean 4 + 4 + 4, which you could write as 3 x 4 = 12.
Once more: = 4 x 4 x 4 = 64
Remember: a POWER is about multiplying, not adding!
4
3
4
3
Slide 14 - Tekstslide
is the same as .....
(more answers possible!)
2
4
A
8
B
2 x 2 x 2 x 2
C
16
D
2 + 2 + 2 + 2
Slide 15 - Quizvraag
Explanation:
is the same as:
+ 2 x 2 x 2 x 2 , because a power is a multiplication, that is repeated.
+ 16, because that's the outcome.
+ however, it's not about adding, so not 2 + 2 + 2 +2.
2
4
Slide 16 - Tekstslide
REMEMBER THIS? IT'S FROM FROM §8.1!
HOWEVER, THE POWERS HAVE TO HAVE A PLACE IN THIS NOW!
SEE NEXT SLIDE.
Slide 17 - Tekstslide
Watch below: between the 'brackets' and the 'multiplying/dividing' the POWERS are placed!
So it comes 2nd in place.
Slide 18 - Tekstslide
Hoe Haakje
Moeten Machten
Wij wortel
Van Deze vermenigvuldigen delen
------------>
Onvoldoendes Afkomen? optellen aftrekken
------------------------------>
Slide 19 - Tekstslide
THINK about this one for a while ... (You don't have to actually work it out, yet!)
How to work it out and what is the final answer?
Slide 20 - Tekstslide
Here is the Solution:
(Study it carefully, because you're going to make one yourself!)
H
M
W
VD ->
OA ->
Slide 21 - Tekstslide
Task:
1. Work this one out on paper.
2. Take a pic and
3. Send it in in next slide!
Slide 22 - Tekstslide
My work in a Photo:
Slide 23 - Open vraag
Solution:
The POWERS between the BRACKETS have to be worked out first!
Following the PRIORITY rules we get:
7 x ( 36 - 32) = 7 x 4 = 28
A common mistake would be:
7 x ( 12 - 10 ) = 7 x 2 = 14 In this case you've done 6 x 2 and 2 x 5 instead of
calculating POWERS!
Slide 24 - Tekstslide
Homework time.
+ §8.2 make 11, 14, 15, 16.
Slide 25 - Tekstslide
As for 18, above, use the remark :
'Calculate as in the example above' !
So don't just give the answers -they are in the Solutionsbook too- but show the process of Calculating!
Slide 26 - Tekstslide
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