Transcript Evaluating Expressions, Mean, Median, Mode and Data Graphs

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 Mathematics
College of Education and Psychology
Calculator: Evaluating expressions,
mean, median, mode and data
graphs
Day Seven
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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)
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Day Seven of (SM)2I
1.
Calculator Activities
• Evaluating expressions
• Boolean Algebra
2. Mean, median, mode
• Calculator spreadsheets from
created lists
• Box-and-Whisker Plot
• More calculator spreadsheets-from applications
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Day Seven of (SM)2I
.
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Evaluating Expressions
• Example: Evaluate 2/3 x + 100
when x = 16.5
Keystrokes:
(16.5 will be x until you store a new value for x.)
* advise your students to always put fractions in parentheses!!!!
• Example: Evaluate 5/(8x) when x = 2.
Is 5/8x the same expression? Evaluate and see if you
obtain the same answer for x = 2.
Moral of story: using “( )” makes it clear what you
mean: to others and your calculator!
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Practice: Evaluate the following expressions
1. if x = 4, m = 5, and p = -2
 xmp
 m2/px,
 m p  x,

m2 p
m2
2 p
, m ,
p
x
x x
m2p/x,
2. 4y3z
2
m2
 px 
if y = -2 and z = 10
3. -x - (-a + b) if x = 2, a = -4, and b = -6
4. x - y( - a2 + x )
if x = -2, y = 3, and a = - 4
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Suppose you want to evaluate a formula: V =  r2 h if the radius of
a right cylinder is 12.5 inches and the height is 18 inches. You
would store the values for r and h just like the above example and
then type the formula on the home screen. Suppose you were
comparing the volume of two right cylinders and the other cylinder
had a radius of 18 inches and a height of 12.5 inches. Simply store
the new values for r and h, but in stead of retyping the formula use
the “replay” feature:
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Boolean Algebra
(True or False)
This activity will allow students to check their work without
getting the answer from the calculator.
Example:
+ 47
=
102
The student wants to check her answer of 54
Assign the box an alphabetical letter such as X.
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Keystrokes:
The calculator will either show a 1 which means TRUE ( their
answer is correct) or a 0 which means false ( their answer is
incorrect ).
Students can check any kind of problems that they encounter
using the “Boolean” method.
Try these:
1.
X - 47 = 229,
2.
½ + ¼
X = ______
= _____
(ALWAYS PUT FRACTIONS IN PARENTHESIS)
3.
2.97 x 104
4.
34 = _____
= ______
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Mean, Median and Mode
Let’s use Smart Notebook!
Find the mean, median and mode and graph data in a
Box-and-Whisker Plot.
85 72 94 85 76 94 81 52 79
50
52
55
60
65
70
75
76
80
83
85
100
90
95
94
100
100
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12
Mean, Median and Mode
82
91 74
78
94
68
74
88
64
42
72
82 79
99
98
75
61
78
86
69
Enter this data in
L1
To clear list
Enter data
The calculator will put this in ascending or descending order
for you.
or
T To access:
1 var-stats
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Note: If your information is not in L1 you must tell the
calculator where it is with a comma and the correct list. List numbers
are in blue above the numbers 1 – 6.
Ex.
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This whisker
shows the
lowest value
This line shows
the lower
quartile
This line shows
the median
This line shows
the upper
This whisker
quartile
shows the
highest value
The width of the box shows
the interquartile range
This shows an outlier
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Box-and-Whisker Plots
To Graph your data:
To select the type of graph:
(use arrows)
and
Select your Xlist (L1) and Ylist (1)
Manually set your window according to the data.
For our data:
To see your graph and data:
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More Lists on the TI-84 Plus Silver Edition
• To access the lists 
There are six preset lists
 L1, L2, L3, L4, L5 and L6. These names** can also be
accessed through
and numbers 1 to 6
on the face of the calculator
• Names can also be given to lists. To name** a list 
. The calculator will be in alpha mode. Type
the name of the list using up to five characters. Once a
list has been named, the calculator is automatically in
SetUpEditor mode. Use the arrow keys to highlight the
name placeholder and type a name in a new column
using up to five characters.
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A Practice Problem: There are 20 units of string. By
making as many rectangles as possible with integer
lengths and widths, which rectangle has the largest area?
• Create four lists titled length, width, perimeter, and area
• Enter the numbers 1 – 9 into list length
• Use the formula  “(20 – 2*LLENGT)/2” for the WIDTH
list
• Use the formula  “(2*LLENGT + 2*LWIDTH)” for the
PERIM list
• Use the formula  “(LLENGT *LWIDTH)” for the AREA
list
NOTE: YOU MUST USE THE NAMES** OF
THE LISTS IN THE FORMULA
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TI Screen One
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TI Screen Two
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Editing and Deleting of Lists
• To delete a list 
To delete
the name of a list after the entries have been
cleared 
To delete the name of the
list from the name menu 
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Spreadsheet on TI-84 Plus Silver Edition Using APPS
• To activate the Spreadsheet through [APPS] 
• The CellSheet Help window shows which buttons access the
functions needed to do operations.
• The top left hand corner shows the name of the spreadsheet (S01)
• A Problem: Listed is check amounts before taxes for eating out:
– $ 42.95
– $ 13.77
– $ 78.00
– $ 25.88
• Use the spreadsheet to compare 15% tips with 20% tips. Also
compare the 15% tip rate with the estimation method of doubling
the tax.
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Collecting and Graphing Data
“Biloxi” Random Number Generators
Outcomes
2
3
4
5
6
7
8
9
10
11
12
Frequency
0
1
2
1
3
8
6
2
0
2
0
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Collecting and Graphing Data
Activity: Roll two “Random Number Generators” 25 times. Record the
results in a table.
To enter data in the calculator:
Put the possible outcomes in L1 ( 2, 3, 4, …, 12)
Put the frequency results in L2
To generate a bar graph:
Other ideas: Sort Skittles, Sort M & M’s, Count shapes in the classroom…..
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More on Random Number Generators
•
•
•
•
•
•
•
Press
Use
Press
Select
Press
Press
Press
to <Prob Sim> press
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Mean, Median and Mode
Let’s use Smart Notebook!
Find the mean, median and mode and graph data in a
Box-and-Whisker Plot.
85 72 94 85 76 94 81 52 79
50
52
55
60
65
70
75
76
80
83
85
100
90
95
94
100
100
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