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Grade 7: The Learning Equation Math
11.09 Introduction to Integers 

Learning
Outcomes: The student will:
+ = 0
source: Thermometer Applet Demo 
The initial temperature displayed below the thermometer is 32^{o}F.
If you follow the directions carefully you will see what you need displayed in the
liquid level of the thermometer and may not have to wait for the temperature to be
displayed(unfortunately this part of the applet runs slowly). Click on three times
and
twice to reduce the temperature by 32^{o}. The level
of the liquid in the thermometer should be and the temperature displayed should
be 0^{o}F.
Click on . The liquid level should be: Now click on . The
liquid level should be: and the temperature displayed should be 0^{o}F.
Click on and check the temperature displayed. It should be zero.
Try other combinations to demonstrate the sum of opposite integers is zero. 
Click on the following to see the the groups of
integers:

FUNBRAIN
 Number Line
Lesson
on Introduction to Integers
Number
Line
Integer
Bars: Learning Fractions and more with Online Manipulatives
 Study the following animated gif to learn the parts of the Cartesian Plane.

Now let us investigate ordered pairs. An ordered pair is the
location (x, y) of a point on the grid. In this case the x and yaxis both extend
from 5 to 5. The integers for this range are: {5, 4, 3, 2, 1,
0, 1, 2, 3, 4, 5}
Move the mouse over the applet from 5 to 5 over the xaxis. Notice the value of
the integer gets larger. The value of the integer gets smaller when you move your
mouse from 5 to 5 on the xaxis. Similarly the value of the integer gets smaller as
you move the mouse for 5 to 5 on the yaxis and smaller when you move the mouse from 5
to 5. The applet is pretty sensitive so you will need to be patient. 

source: http://www.coe.tamu.edu/~strader/Mathematics/Algebra/Cartesian/cartesian.html 
Lesson on
Comparing and Ordering Integers

Directions 
Example(s) 
3458 and 3472
If both numbers are positive:
Line up the ones digit for the numbers.
Compare the place value for each digit starting from the left. When you find the
first difference, the number with the largest digit is the largest number.

 3458
 3472
The ones digits are lined up. Starting from the left, the first difference is in
the tens column.
Since 7>5, then 3472 > 3458 
If one number is positive and the other is negative, then the positive
number has the greatest value 
34 > 3458 
3458 and 3472
If both numbers are negative:
Line up the ones digit for the numbers.
Compare the place value for each digit starting from the left. When you find the
first difference, the number with the largest digit is the smallest
number. 
 3458
 3472
The ones digits are lined up. Starting from the left, the first difference is in
the tens column.
Since 7<5, then 3472 < 3458 
Comparing
Integers
Integer
Inequalities 
Source:
http://cs.georgefox.edu/~ewheeler/310hw/1.20/ 

Review:
Lesson
on Comparing and Ordering Integers
Integer
Inequalities
Comparing
Integers

Enrichment:


integer, negative, positive, whole number, average, infinite

Prerequisite
Skills:
..., 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 0,
1, 2, 3, 4, 5, ...
The counting(natural) numbers are: positive whole
numbers (1,2,3...) 
An integer is:
 a positive whole number (1,2,3...),
 a negative whole number (1,2,3...)
 or zero (0).

The whole numbers are: positive whole numbers and zero
(0,1,2,3...) 
Watch what happens to the liquid level in the thermometer when you
increase (+) or decrease () the temperature. The new temperature will be shown
eventually, but unfortunately this part of the applet runs slowly.
source: Thermometer Applet Demo
The Applet of Thermometer shows minus quantities by
comparing the difference in temperature between two days. Applet of
Thermometer 

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