THE WHOLE NUMBERS : THE WHOLE NUMBERS Z
+3 -5 -9 . . .
Slide 2 : From the hot-air balloon, the radar falls down into the water. What is the distance from the hot-air balloon to the radar?
What is the distance from the helicopter to the subamarine?
Slide 3 : How many floors are there between the shop (0) and the parking (-2)?
And how many floors are there between the restaurant (1) and the gymnasium (-1)?
Slide 4 : What’s the avg. temperature in the Sahara Desert?
What’s the avg. temperature in Alaska?
1.- The Whole Numbers Set. : 1.- The Whole Numbers Set. As you can see, the Natural Numbers N = {0, 1, 2, ...} are not enough to express many life situations (places under the sea, flats under ground, temperatures below zero,...)
We need more numbers.
We must add new numbers to the set of the Natural Numbers, the Negative Numbers {..., -3, -2, -1}
All these numbers are called The Whole Numbers Z = {..., -3, -2, -1, 0, 1, 2, ...}
Slide 6 : The sign of a whole number
If the whole number is a natural number, we can writte it with the sign + before it. Ex: +5, +7
The sign is positive
If the whole number is not a natural number, we must writte it with the sign – before it:
Ex: -5, -9
The sign is negative
Slide 7 : The absolute value of a whole number.
The absolute value of a whole number is the same number but always positive.
Ex: I -7 I = 7
I 4 I = 4
The opposite number of a whole number.
The opposite number of a whole number is the same number but with the opposite sign.
Ex: The opposite of 5 = -5
The opposite of -3 = 3
2.- Addition and Subtraction : 2.- Addition and Subtraction 1 case: Both numbers have the same sign
We add the absolute values and we put the sign. Ex: 5 + 2 = 7
-2 -10 = -10
2 case: The numbers have different signs
We subtract the absolute values and we put the sign of the greatest. Ex: -2 + 7 = 5
4 - 9 = -5
3.- Multiplication and Division : 3.- Multiplication and Division The sign rule:
(+) * (+) = (+) (+) : (+) = (+)
(+) * ( - ) = ( -) (+) : ( - ) = ( -)
(-) * (+) = (+) (-) : (+) = (+)
(-) * (-) = (+) (-) : (-) = (+)
Slide 10 : Example:
(+5) * ( - 4) = - 20
(-5) * ( - 4) = + 20
(+9) * ( + 7) = + 63
(-9 ) * ( + 7) = - 63
Slide 11 : Example:
(-20) : ( - 4) = + 5
(-20) : ( + 4) = - 5
( +63 ) : ( + 7) = + 63
( +63 ) : ( - 7) = - 63
4.- Operations hierarchy : 4.- Operations hierarchy 1st. First, solve the parenthesis
2nd. After that, solve the multiplication and division operations.
3rd. Finally, solve the addition and the subtraction operations.
Slide 13 : Example:
15 – 3 * [ 7 – ( -6 ) : (+3)] =
15 - 3 * [ 7 - (-2)] =
15 – 3 * [ +9] =
15 – 27 =
-12
5.- Activities : 5.- Activities 1. Use whole numbers, positive or negative, to express each situation:
A helicopter flies at 100 m .................
A diver swims 15 m underwater...........
A submarine navigates 50 m underwater....................................................
An airplane flies 10.000 m above the sea..
Mt. Everest rises 8.845 m above sea level.
6.- On the internet : 6.- On the internet http://bilingualproject.wikispaces.com/Resources
http://www.youtube.com/watch?v=0wteb5T2PmM
http://www.mathgoodies.com/lessons/toc_vol3.html