Transcript USM Summer Math Institute: Cabri Jr. on Calculator, Powers of 10

2008 USM Summer Math Institute
Co-Sponsored by
Institutions of Higher Learning (IHL)
U.S. Department of Education
(No Child Left Behind Funding)
The Center for Science and Mathematics Education
The Department of Mathematics
College of Science and Technology
College of Education and Psychology
Cabri Jr on calculator, powers of 10,
expanded form, scientific notation,
moving the decimal point, grant writing
Day
Fourteen
1
2008 USM Summer Math Institute
Your Mathematics Instructors, Staff and Partners
• Ms. Michelle Green, Co-Director and CoInstructor for (SM)2I
– Stringer Attendance Center
– National Board Certified/Early Adolescence
– Email [email protected] , Phone 601428-5508
• Dr. Myron Henry, Director and Co-Instructor for
(SM)2I
– Department of Mathematics and the Center for
Science and Mathematics Education
– Johnson Science Tower 314
– Email [email protected], Phone 601-266-4739 or
266-6516
• All Participants (that’s you)
2
Day Fourteen (SM)2I Outline
1. CabriJr Geometry
2. Powers of 10


Expanded form
Scientific notation
3. Moving the decimal place


Multiplication
division
4. Grant Writing (Mrs. Shauna
Hedgepeth
4
Math Query of the Day
What did the
acorn say when it
grew up?
5
Geometry
( Gee, I’m a tree!)
CabriJr
6
Tips for CabriJr
Menus are on F1, F2, F3, F4, and F5
You must have the arrow to drag.
Press
when you are pointing to
what you want to drag to get a hand.
7
Powers of Ten
1
10 .
• Multiples of 10, multiples of
• 10 to powers or exponents, 1 to powers or
10
exponents.
• Expanded form.
• The decimals 10., 1., .1, .01, .001, are names
for what rational numbers or fractions?
12
1
1000 100 10
1
10
1000. 100. 10.
1.
10
3
10
2
10
1
10
0
10
1
.1
1
1
100 1000
10
2
10
3
.01 .001
Top row: multiples of tens
Middle row: powers of ten (just names for multiples of ten)
Bottom row: decimal names for multiples of ten
13
Use Expanded Form to Find the Fractions
• 264.1
• 354.129
• 8435.0296
14
Expanded Form and Scientific Notation
A number is in scientific notation if the number is in the
form of
A  10 where A is an integer,
1  A  10, and n is an Integer
n
A Problem: To change 342.67 to scientific notation by first
writing the number in expanded form and then in scientific
notation.
Scientific
Notation is handy
for working with
very large and
very small
numbers.
15
6
7

10 100
 1
 1 
342.67  3  102  4  101  2  100  6     7   2 
 10 
 10 
342.67  3  100  4  10  2  1 
2

 1
 1   10
2
1
0
342.67   3  10  4  10  2  10  6     7   2    2
 10 
 10   10


 1 
 1 
 1 
 1  1 
 1   1 
342.67   3  102   2   4  101   2   2  100   2   6      2   7   2    2    102 
 10 
 10 
 10 
 10   10 
 10   10  


 1 
 1 
 1 
 1 
342.67   3  4   1   2   2   6   3   7   4    102 
 10 
 10 
 10 
 10  

342.67   3.4267  102 
342.67  3.4267  102
16
Use expanded form and an appropriate representation
of “1” to express the these numbers in scientific form.
• 264.1
• 354.129
17
Division: moving the decimal point
.052 54.08
We learned that the way we do
this is to “move the decimal point.”
.052 54.080
052. 54080.
18
How do we explain “moving the
decimal point” in division?
1
 1 
 1 
.052  (0) *    5 * 
  2*

 10 
 100 
 1000 
 1 
 1 
 50 * 
  2*

 1000 
 1000 
52
 1 
 52 * 

 1000  1000
19
How do we explain “moving the
decimal point” in division?
 1 
1
54.08  5 * (10)  4 *1  (0) *    8 * 

 100 
 10 
 1 
 1 
 1 
 1 
 5000 * 

  8*
  (0) * 
  400 * 
 100 
 100 
 100 
 100 
 1   5408 
 5408 * 


 100   100 
20
So,
.052 54.08 
 5408 


 100 
 52 


 1000 
subtraction : a  b  x  a  b  x
division : a  b  x  a  b  x
r p
r p
division :   x    x
s q
s q
21
An example of “inverting and multiplying”
r p
r p
division :   x    x
s q
s q
3 2
3 2
  x   x
5 9
5 9
3 9 2
9
    x
5 2 9
2
3 9 2 9
    x (communativity )
5 2 9 2
3 9
  x
5 2
Therefore
3 2 3 9
  
We have inverted and multipled !
5 9 5 2
22
r p
r p
division :   x    x
s q
s q
r p
 x
s q
r q p q
   x
s p q p
x
r q p
q
   x
s p q
p
r q
 x
s p
r p
But   x. Therefore
s q
r p r q
  
We have inverted and multiplied .
s q s p
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.052 54.08 
 5408   52 

   1000 

 100  
 5408   1000   (5408)  (10) 

 
 

52

 100   52  
 54080 


 52 
052 54080
 052. 54080.
24
One More Division Example
.27 2.781  2.781  .27
2781 27


1000 100
2781 100


1000 27
2781 1


10 27
278.1

27
 27. 278.1
2
7
2 10
7
27




10 100 10 10 100 100
781 2 1000 781 2000  781
2.781  2 



1000
1000
1000
1000
2781

1000
.27 
2781 2000 700 80 1




10
10
10 10 10
1
 200  70  8 
10
 278.1
25
Moving the Decimal Point: Multiplication
54.8
.052
2.8496
2.8496
548
52
1096
2740
28496
26
Expanded Form: Again
8
54.8  5 10  4 1 
10
5 100 4 10 8



10
10 10
500  40  8 548


10
10
0
5
2
52
.052  


10 100 1000 1000
548 52
548  52
(54.8)  (.052) 


10 1000 10000
27
548 52
548  52
(54.8)  (.052) 


10 1000 10000
28496 20000  8000  400  90  6


10000
10000
20000 8000
400
90
6





10000 10000 10000 10000 10000
8
4
9
6
 2 


10 100 1000 10000
 2.8496
We moved the decimal point four places to the left!
Wow!
28
Show and use an appropriate representation of “1”
and “moving the decimal point” to express the
numbers below in scientific form. Check by TI-84.
• 8345.0679
• .0016045
• Each of the above numbers is a terminating
decimal number. Express each of these numbers
as a whole number and/or fraction and explain .
29
Applying for
Grants!
30
2006 USM Summer Mathematics Institute Recipients of Jordon Grants
1.
2.
3.
4.
Michael Cox, Hattiesburg, MS Oak Grove Middle School
David Dunlap, Hattiesburg, MS Hawkins Elementary
Susan Lott, Hattiesburg, MS Purvis Middle School
Theresa Rose, Wiggins, MS Stone Elementary
5. Shauna Hedgepeth, Oak Grove Middle School
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Mrs. Shauna Hedgepeth
The University of Southern Mississippi
•
M.S. The University of Southern Mississippi: Science
Education with a Mathematics Emphasis (CSME) 2008
•
B.A. The University of Southern Mississippi: Mathematics
(Licensure) 1999
•
Graduate Assistant in summers 2005, 2006, and 2007 for
the USM Summer Mathematics Institute
Mathematics Teacher Oak Grove Middle
School Teacher
•
Seventh Grade Mathematics
Teacher
•
MathCounts Coach
•
Academic Content Leader
(2003-2007)
•
2005 Teacher of the Year
32
Mrs. Shauna Hedgepeth (continued)
Pearl River Community College
•
Adjunct faculty member
Professional Memberships
•
National Council of Teachers
of Mathematics
•
Mississippi Professional
Educators
Grants
•
•
Michael Jordan Grant (2006)
Cisco Strategic Initiative Pilot Project
Technology Skills
•
Internet, Microsoft Word, Excel, PowerPoint, SmartBoard,
and the Promethean Interactive Whiteboard
•
TI 84 graphing calculator