Transcript Using PowerPoint to Animate Math Lessons

Using PowerPoint to Animate
Math Lessons
By:
Ryan Kasha
Professor of Mathematics
Valencia College: West Campus
E-mail: [email protected]
Objectives
• Discussion of motivation to create math
lessons on PowerPoint
• Discuss pros and cons
• Sample lessons
• How-to demonstration
• Discussion of other types of technology for
teaching mathematics
• Q-and-A Session
Motivation
• The initial motivation was at a FTYCMA
conference (different presentation software)
• Many presentations at conference is via
PowerPoint
• Desire to increase accessibility outside of
classroom
• Not pleased with publisher’s PowerPoint
• Needed to design PowerPoint that would
replicate writing on the board with own personal
teaching style.
Pros
• Make lessons more consistent (same material
for all classes)
• Increased accessibility – can view PowerPoint
at home and experience instructor’s style of
explanation
• Less writing for students
• Preparation is done only once – ready to go
for subsequent semesters
Cons
• Students do not write or take proper notes
• Students might view as going to class as
pointless
• “Learning by doing” is de-emphasized
• Limits spontaneous, relevant deviations from
PowerPoint slides
Solutions
• Hybrid approach – use both PowerPoint and
board
• Put main concepts and examples on
PowerPoint
• Have some examples done on board
• Emphasize what students should copy and
allow time for copying from PowerPoint slide
Sample Lessons
• The following slides are excerpt from specific
math lessons
• All lessons begin with an objective slide and
has a summary slide
• Animation is heavily emphasized in most cases
• All lessons have 1 to 3 main examples
Excerpt #1
Order of Operations
Try this problem however you like:
There are 2 ways!
Way #1:
5 + 20 ÷ 5
5 + 20 ÷ 5
25 ÷ 5
Way #2:
5 + 20 ÷ 5
5+4
5
9
Problem: We are getting 2 different answers for the
same problem.
This example is why we need to follow the same
order (Purpose of Order of Operations)!
Order of Operations (Steps)
• 1) Grouping symbols: parenthesis (), brackets
[], absolute values | |, roots/radicals
• 2) Exponents: EX: 23 , (-5)2
• 3) Multiplication & Division: Left  Right
(The way you see it, the way you read it)
• EX: 6 ÷ 2 * 3 = 3 * 3 = 9 (Divide first, then
multiply)
• 4) Addition & Subtraction: Left  Right
(The way you see it, the way you read it)
• EX: 6 – 2 + 3 = 4 + 3 = 7 (Subtract first, then add)
Order of Operations
• The next few slides will illustrate some
examples with the order of operations.
• Sayings and acronyms such PEMDAS and
“Please Excuse My Dear Aunt Sally” can be
misleading.
• However, if you choose to use these short-cuts
above to help you remember, remember it in
the following ways.
Ways of Remembering
• PEMDAS should be remembered as:
• PE MD AS
• Please Excuse My Dear Aunt Sally should be
remembered as:
• Please
• Excuse
• My Dear
• Aunt Sally!
Order of Operations (EXAMPLES)
• EX 1:
•
•
•
•
-24 + 4 |18 – 24|
Remember to break the
4
-2 + 4 |– 6|
absolute value down to a single number,
then take the absolute value of the number.
4
-2 + 4 * 6
-16 + 24
Remember a negative base with
8
no parenthesis is negative no matter the
type of exponent.
Order of Operations (EXAMPLES)
• Isn’t this fun yet?
• You should vote YES.
• With fractional problems, you should work the
numerator (top) part separate from the
denominator (bottom) part.
• At the end, you will have a fraction that
should be simplified as much as possible or
turned into a whole number
Order of Operations (EXAMPLES)
• 4[5 – 8(2 + 1)]
3 – 6 – (-4)2
• Let’s work the numerator first, then we will work
the denominator.
• Numerator: 4[5 – 8(2 + 1)]
Don’t be tempted by the 5 – 8.
•
4[5 – 8(3)]
You must multiply before subtraction.
•
4[5 – 24]
•
4[-19]
•
-76 (This is just the numerator part)
Fractional Example continued
•
•
•
•
•
•
•
•
Denominator: 3 – 6 – (-4)2
The outside negative
3 – 6 – 16
sign drops down.
-3 – 16
-19
Whole fraction: -76 / -19 = 4.
19 goes into 76 exactly 4 times.
Remember: –/– equals +!
Answer is 4.
Final Tips
•
•
•
•
•
•
Follow the order of operations carefully.
Watch your signs (remember rules)
Multiplication & Division is left to right.
Addition & Subtraction is left to right.
Remember square roots
EX: square root of 25 is 5 since 5 multiplied by
itself will yield 25.
• Practice, practice, and practice!
The End
Order of Operations Game
• Click on the link below:
• http://www.mathplayground.com/order_of_o
perations.html
• Or click on button below:
CLICK HERE
Excerpt #2
Translating Phrases  Equations
Translating Sentences to
Equations
Beginning Algebra/
Developmental Math II
(MAT 0024C/MAT 0028C)
Translation
• This is similar to translating phrases to
expressions, but except that we will need to
know key words for equals as well.
• After translating the word sentence to the
correct equation, we are required to solve the
equation as directed.
• The next few slides will review key words for
mathematical operations and equals.
• The only thing new here is “equals”.
Example #1
Translate & Solve:
Nineteen more than a triple a number
is one hundred.
Example #1
Translate & Solve:
Nineteen more than a triple a number
is one hundred.
3x
Example #1
Translate & Solve:
Nineteen more than a triple a number
is one hundred.
3x + 19
Example #1
Translate & Solve:
Nineteen more than a triple a number
is one hundred.
3x + 19 =
Example #1
Translate & Solve:
Nineteen more than a triple a number
is one hundred.
3x + 19 = 100
Example #1
Translation: 3x + 19 = 100
-19 -19
Now,
we solve the equation.
Subtract 19 from both sides.
3x = 81
3
3
x = 27
Divide both sides by 3.
Example #2
Translate & Solve:
Two less than the quotient of a number
and five is six.
Example #2
Translate & Solve:
Two less than the quotient of a number
and five is six.
Remember that the
word than flips the order.
–2
Example #2
Translate & Solve:
Two less than the quotient of a number
and five is six.
Remember that the
word than flips the order.
x
5
–2
Example #2
Translate & Solve:
Two less than the quotient of a number
and five is six.
Remember that the
word than flips the order.
x
5
–2 =6
Example #2
Translation: x
5
–2 =6
+2 +2
Now we solve this equation.
Add 2 to both sides.
x* 5
= 8* 5
5
x = 40
Multiply both sides by 5.
Remember that fraction bar
means division
and multiplication is the
opposite operation.
Example #3
Translate & Solve:
Ten is the result when one is subtracted
from the ratio of a number to four.
Example #3
Translate & Solve:
Ten is the result when one is subtracted
from the ratio of a number to four.
10 =
Example #3
Translate & Solve:
Ten is the result when one is subtracted
from the ratio of a number to four.
10 =
–1
Example #3
Translate & Solve:
Ten is the result when one is subtracted
from the ratio of a number to four.
10 =
The word from flips order.
–1
Example #3
Translate & Solve:
Ten is the result when one is subtracted
from the ratio of a number to four.
10 =
x
4
–1
Now we’re going to solve the above equation!
Example #3
Translation: 10 =
+1
x
4
x
11*4=
*4
4
–1
+1
Add 1 to both sides.
Multiply both sides by 4.
44 = x
Check your solution. This solution works!!
Excerpt #3
Screen Shots for Accessing
Competency Review Materials
NOTE: This is older material and is not current – use webct.
Introduction
• This presentation is meant to help you access
your on-line lab &competency review material
easily
• The following contains screenshots and
helpful websites
• This presentation does not cover everything
but covers major highlights
Where to begin?
Go to www.valenciacc.edu
Click on
Quick Links
&
Select Online Courses
Click on Online Courses
Online Courses
Log in is same as your atlas log in!
Log In with the
same user name
& password as
your atlas account!
Same as your atlas log in:
Click on your math course:
For you, it should be
easy since you are not taking
more than 1 math course
Home screen
This screen should appear
Or you can click on
Course Content to load/reload.
Everything you need access to is on
this screen!
Lab assignments
Competency
Information
&
Registration
On-line Review Access
Follow
Review Link
First Link is General Information
On-Line Review
Second Link is
the practice test
The following links
are the 7 learning modules
containing 15 questions each
Excerpt #4
Graphing
Graphing
Graph the following:
(3, 2)
(5, 0)
(-2, 4)
(5, -3)
(0, -2)
Graphing
(3, 2)
x=3
y=2
Graphing
(1, 5)
Graph y = 2x + 3
using the slope and
y-intercept.
(0, 3)
The y-intercept is (0, 3).
Slope is 2 which is the
same as 2 over 1.
We’ll move up 2 spaces, then
go across 1 space.
Brainteaser
How many squares are there?
Squares
16 1 by 1
9 2 by 2
4 3 by 3
Of course,
1 16 by 16
(The whole thing)
Total =
16 + 9 + 4 + 1
= 30
How-to Demonstration Slide
• Slide left intentionally blank!
Other Technology to Consider
•
•
•
•
Livescribe Smartpen
Videos and links
Wolfram Alpha
Youtube videos
Questions ???