What you should learn

To find the absolute value of a number

To add and subtract integers

NCTM Curriculm Standards 2, 6 - 10

 

In doing this the teacher wants to make sure that the following words are incorporated into the introductory lesson:

Absolute Value

Additive Inverse

Matrix

Discrete Mathematics

Introduction: On February 10, 1995, Dr. Bernard A. Harris, Jr. became the first African-American to walk in space. During the walk, he and Dr. Michael Foale, a British-born astronaut who is a U.S. citizen, were exposed to temperatures as cold as -125 degrees Farenheit. The scheduled five-hour spacewalk was cut short by 30 minutes because the astronauts expreienced icy fingers.

Usually, spacewalkers spend some of their time basking in the sun's rays where temperatures can be as high as 200 degrees Farenheit. But throughout the spacewalk, Dr. Harris and Foale remained in the shadow of the shuttle Discovery and Earth, the coldest possible spot.

As you can see, spacewalkers must be able to survive in extreme temperatures. You can use a number line to determine the range of the temperature extremes. -125 and 200 are graphed on the number line below. NBotice that -125 is 125 units from 0 and 200 is 200 units from 0. So, the total number of units form -125 to 200 is 125 + 200 or 325.

The temperature range from -125 to 200 is 325.

You used the idea of absolute value to find the range from -125 to 200.

Definition of Absolute Value: The absolute value of a number is its distance from zero on a number line.

 

The symbol for the absolute value of a number is two vertical bars around the number.

You can evaluate expressions involving absolute value.

Exercise 1: Evaluate -|x + 6| if x = -10

-|x + 6| = -|-10 + 6| = -|-4| = -4

 

 

You can use absolute value to add integers.

Same Sign

a. 4 + 3 = 7

b. -4 + (-3) = -7

Different Sign

c. 6 + (-8) = -2

d. -6 + 8 = 2

These examples suggest the following rules.

Adding Integers: To add integers with the same sign, add their absolute values. Give the result the same sign as the integers.

To add integers with different signs, subtract the lesser absolute value from the greater absolute value. Give the result the same sign as the integer with the greater absolute value.

Exercise 2: Find each sum

a. -10 + (-17)

b. 39 + (-22)

c. -28 + 16

 

 

Every positive integer can be paired with a negative integer. These pairs are called opposities. For example, the opposite of +2 is -2.

A number and its opposite are called additive inverses of each other. Look at the sumof each number and its additive inverse below. What pattern do you notice?

These examples suggest the following rule.

Additive Inverse Property: For every number a, a + (-a) = 0.

 

Additive inverses can be used when you subtract numbers.

It appears that subtracting a number is equivalent to adding its additive inverse.

Subtracting Integers: To subtract a number, add its additive inverse. For any numbers a and b, a - b = a + (-b).

 

Exercise 3: Find each difference.

a. 6 - 14

b. -12 - (-8)

c. 43 - (-26)

A matrix is a rectangluar arrangement of elements in rows and columns. Although matrices are sometimes used as a problem-solving tool, their importance extends to another branch of mathematics called discrete mathematics. Discrete mathematics deals with finite or discontinuous quantities. The distinction between continuous and discrete quantities is one that you have encountered throughout your life. Think of a staircase. Yhou can slide your hand up the banister, but you have to climb the stairs one by one. The banister represents a continuous quantity, like the graph of {all numbers greater than 3}. However, each step represents a discrete quantity, like an element in a matrix, or a point in the graph of {2, 4, 7, 12}.

When entries in corresponding positions of two matrics are equal, the matrices are equal.

You can add or subtract matrices only if they have the same number of rows and columns. You add and subtract matrices by adding or subtracting corresponding entries.

Closing Activity: Check for understanding by using this as a quick review before class is over. It should take about the last five to ten minutes. I would use it for my students as their 'ticket out the door'. Click Here.

Homework: The homework to be assigned for tonight would be: 25 - 61 odd, 62, 63, 65, 67 - 78

Alternative Homework: Enriched: 26 - 60 even, 62 - 78

Extra Practice: Students book page 759 Lesson 2-3

Extra Practice Worksheet: Click Here.

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