Ch 1 Sec 3: Slide

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PowerPoint Doesnt Have to be Boring Unleash
Learning
John WallaceAssociate ProfessorDevelopmental
MathematicsColumbus State Community
CollegeEmail jwallace_at_cscc.eduWebsite
www.ProfessorWallace.com
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PowerPoint Doesnt Have to be Boring Unleash
Learning

• Introduction
• History
• Example PowerPoints
• Demos
• PowerPoint, SnagIt, Camtasia
• Questions/Open Discussion

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Using the Order of Operations with Fraction Bars
EXAMPLE 7 Using the Order of Operations with
Fraction Bars
Simplify.

2

First, do the work in the numerator
Next, do the work in the denominator
4 2 ( 3 1 )2
3 4 2 3
4 2 ( 4 )2
12 2 3
4 2 ( 16 )
6 3
4 32
18
36
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Using the Order of Operations with Fraction Bars
EXAMPLE 7 Using the Order of Operations with
Fraction Bars
Simplify.

2

First, do the work in the numerator
Next, do the work in the denominator
4 2 ( 3 1 )2
3 4 2 3
4 2 ( 4 )2
12 2 3
4 2 ( 16 )
6 3
4 32
18
36
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Common Error Using the Product Rule
CAUTION
Avoid the common error of multiplying the bases
when using the product rule. Keep the same
base and add the exponents.
3 4 3 2 3 6
3 4 3 2 ? 9 6
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A Real-World Example Addition Property of
Equality
If Ali and Ty are each given 10, they will still
have the same amount of money.
If Ali and Ty each give away 50, they will still
have the same amount of money.
If you add the same number to both sides or if
you subtract the same number from both sides, the
sides will remain equal.
Alis Money
Tys Money
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Solving Linear Equations
Solving Linear Equations Step 1 Simplify each
side separately. Clear parentheses using the
distributive property, if needed, and combine
terms. Step 2 Isolate the variable term. Use the
addition property if necessary so that the
variable term is on one side of the equation and
a number is on the other. Step 3 Isolate the
variable. Use the multiplication property if
necessary to get the equation in the form x
a number. Step 4 Check. Substitute the proposed
solution into the original equation to see if a
true statement results.
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Using the Four Steps to Solve an Equation
EXAMPLE 2 Using the Four Steps to Solve an
Equation
Solve 31 ( 4 n ) 3 ( 2n 5 ).
31 ( 4 n ) 3 ( 2n 5 )
31 1( 4 n ) 3 ( 2n 5 )
Step 1 Simplify each side separately.
31 4 n 6n 15
27 n 6n 15
Step 2 Isolate the variable term on one side.
6n
6n
27 7n
15
27
27
7n
42
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Using the Four Steps to Solve an Equation
EXAMPLE 2 Using the Four Steps to Solve an
Equation
Solve 31 ( 4 n ) 3 ( 2n 5 ).
7n
42
Step 3 Isolate the variable.
7n
42

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7
n
6
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Using the Four Steps to Solve an Equation
EXAMPLE 2 Using the Four Steps to Solve an
Equation
Solve 31 ( 4 n ) 3 ( 2n 5 ).
31 ( 4 n ) 3 ( 2n
5 )
31 ( 4 ( 6 ) )
3 ( 2 ( 6 ) 5 )
Step 4 Check.
31 ( 4 6 )
3 ( 12 5 )
31 10
3 ( 7)
21
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True
The solution of the equation is 6.
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Calculator Tip TI-30X IIS
4
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Subtracting Two Integers
EXAMPLE 2 Subtracting Two Integers
Make two pencil strokes to change each
subtraction problem into an addition problem.
Then find the sum.
(a) 9 15


9 15
6

Change subtraction to addition.
Change 15 to 15
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Investigating Area
1"
It will take 21 square inch pieces that measure
one inch on each side to cover a rectangle
that measures 7 inches long and 3 inches wide.
3"

• Each square piece measures
• one inch along each side.

1"
7"
Each row contains 7 square pieces.
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Functions
NOTE
Another way to think of a function relationship
is to think of the independent variable as an
input and the dependent variable as an output.
This is illustrated by the input-output
(function) machine (below) for the function
defined by y 3x.
(Output y)
(Input x)
6
2
5
4
2
(Input x)
15
5
12
4
12
y 3x
15
6
(Output y)
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5.3 Applications of Systems of Linear Equations

• EXAMPLE 3

Solving a Mixture Problem
How many ounces each of 10 hydrochloric acid and
25 hydrochloric acid must be combined to get 40
oz of solution that is 22 hydrochloric acid?
Step 1
Read the problem. Two solutions of different
strengths are being mixed together to get a
specific amount of a solution with
an in-between strength.
Step 2
Assign a variable. Let x the number of ounces
of 10 solution and y the number of ounces of
25 solution.
25


22
10
25
10
x oz
y oz
40 oz
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5.3 Applications of Systems of Linear Equations

• EXAMPLE 3

Solving a Mixture Problem
How many ounces each of 10 hydrochloric acid and
25 hydrochloric acid must be combined to get 40
oz of solution that is 22 hydrochloric acid?
Step 2
Assign a variable. Let x the number of ounces
of 10 solution and y the number of ounces of
25 solution.
Percent (as a decimal)
Ounces of Pure Acid
Number of Ounces
.10x
x
10 .10
.25y
y
25 .25
.22(40)
40
22 .22
Step 3
Write a system of equations.
x
y
40
(1)




22
10
25
.10x
.25y
8.8
(2)


x oz
y oz
40 oz
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Practice with Quadratic Functions
Match each description to the graph that
illustrates it best.
(1) a 0, a is small. ____
(2) a 0, a is large. ____
C
B
(3) a (4) a D
A
(A)
(B)
(C)
(D)
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The Rectangular Coordinate System
y Axis
Origin
Positive y-values
Positive x-values
Negative x-values
x Axis
Negative y-values
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The Rectangular Coordinate System
Graph A(2, 5), B(-7, -4), C(-5, 3), D(4, -3)
A
C
D
B
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4.5 Solving Systems of Linear Inequalities
Graph the solution of the system
y 2
x 4
3x 2y 6.
Recall that y 2 is a horizontal line
through the point (0, 2).
Recall that x 4 is a vertical line through
the point (4, 0).
Now graph the inequality 3x 2y 6.
The graph of the solution is the shaded (bright
yellow) triangular region in the figure,
including all boundary lines.
The test point (0, 0) makes this inequality
false, so we shade the other side of the boundary.
To graph the inequality y 2, we shade the
region that makes the inequality true.
To graph the inequality x region that makes the inequality true.
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Rate x Time Distance
A car is speeding at a rate of 80 mph as it
passes a highway patrol station. One hour later,
a highway patrol officer leaves the patrol
station traveling at a rate of 120 mph. How long
will it take for the highway patrol officer to
catch up with the speeding car?
One hour later, the highway patrol officer leaves
the station.
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Running Cool Stuff During Presentations
Marking up worksheets
Doing examples using the black (or white)
screen
Opening the web
Opening applications
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Screen Capturing Software
SnagIt
www.TechSmith.com
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Screen Capturing Software
Adobe Captivate 3
www.Adobe.com
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More on Software

• PowerPoint
• OneNote
• Windows Journal
• Word
• Snipping Tool 2.0
• Paint
• Audacity (http//audacity.sourceforge.net/)

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Where-to-Buy for Educators
www.AcademicSuperstore.com
www.JourneyEd.com
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Fun Stuff
Johnnys mother has exactly three children.
After each child was born, she would reach into
her pocket and pulled out a coin thinking she
might name each child after the coin she pulled
out.
2nd Child
1st Child
3rd Child
Penny
Nicholas
?
Johnny
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Demo


Weak
Strong
Mixture