Reality Math
Dot Sulock, University of North Carolina at Asheville
Grades, GPAs, and Avoiding Suspension at UNCA
1. Weighted Averages
The average of a set of numbers is the sum of the numbers divided by the number of
numbers. Sometimes multiplication helps.
1. Find the average of these grades:
(a) 95, 88, 67, 89, 90
(b)
grade
A = 95
number of grades
3
B = 85
11
C = 75
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Often a teacher will use a strategy involving percents to determine a grade in a class.
Grade:
20% homework
50% tests
20% final
10% attendance and participation
If Sri had a 95 on homework, 87 test average, 75 on the final, and 95 for attendance and
class participation, the grade would be determined this way:
0.20 (95) + 0.50 (87) + 0.20 (75) + 0.10 (95) = 87
2. Sri is in the class above and and has all the grades given except the final. If Sri
averages 90 or more in the class, he can get an A. What is the least he can get on
the final and still make an A? (Guess and check works well here)
3. In Reality Math, each of 4 tests, the final, the homework and attendance count
1/7 of the grade, so all those scores can be added and the sum divided by 7. In
addition, a higher final grade can replace the lowest test grade. Salome has a
homework average of 85, attendance average of 81, and tests of 55, 75, 92, and
60. What numerical average will Salome have for the course if she makes each of
the following grades on the final?
(a) 70
(b) 80
(c) 90.
(d) In Reality Math, 90 is an A. Can Salome get an A in the course? If
so, she would have to get at least what score on the final?
(e) In Reality Math, 80 is a B. Can Salome get a B in the course? If so,
she would have to get at least what score on the final?
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2. The Danger of the Invisible Zero.
Hamlet has been happily informing his parents of his good grades on homework. So far
he has 4 A’s and 11 B’s. Hamlet kind of ignores his 5 zeros. He never sees them and has
sort of forgotten about them. However Hamlet’s homework average is not the B+ he is
imagining, it is actually a D.
4.
(a) Using A = 95 and B = 85, calculate Hamlet’s homework average.
(b) If Hamlet had had F = 50 instead of zeros on those 5 homeworks,
what would his homework average be?
3. Determining Grade Point Average (GPA)
GPA =
Quality Point Total
--------------------------Total Hours Attempted
Quality Points for a course = (Credit Hours) X (Quality Points for the Grade)
Quality Points for the grades that have quality points are:
A
4.00
AB+
3.33
B
3.0
BC+
2.33
C
2.00
CD+
1.33
D
1.00
F
Lazi
Hours
attempted
4
4
3
3
3
1
Grade
3.67
2.67
1.67
0
QP for grade
QP for course
Hum 124
C1.67
4(1.67) = 6.68
Math 155
D
Span 110
F
HWP 153
B
Chem 132
F
Chem 111
C
Total hours
Total QP =
attempted
5.
(a) Determine the GPA for Lazi with the courses and grades given in the
table above. Need accuracy to thousandths, that is, 3 decimal places.
(b) The previous semester, his first, Lazi had taken a lighter load and
worked harder, obtaining a GPA of 2.000 on 13 hours attempted. How many QP
did Lazi have from the previous semester?
(c) Determine Lazi’s cumulative GPA after two semesters. (GPA is
always total QP / total hours attempted, not the numerical average of the two
semesters.)
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4. Getting Kicked out of UNCA for a Semester
At UNCA a student whose cumulative grade-point average falls below 2.00 at the
end of any semester is placed on academic warning, must consult with his or her advisor
on how to improve, and can only take 14 hours the next semester.
Also, if the student falls below the minimum GPA’s given in the following table,
the student will be suspended for one semester. If the student returns after this “time-off”
experience, the student must make a 2.25 GPA every semester and stay above these
levels to avoid being dismissed from the university.
Hours attempted
(includes transfer hours)
Minimum GPA
0-23
24-44
45-75
75 -
1.00
1.50
1.75
2.00
6. After two semesters
(a) How many total hours attempted did Lazi have?
(b) What minimum GPA did he need to stay in school?
(c) Did he have that minimum cumulative GPA?
(d) Was Lazi placed on academic warning after his second semester?
What does the future hold for Lazi?
Third Semester
Scenarios
Hours attempted
QP
GPA for the
semester
Cumulative
GPA
Good (B average)
Bad (C average)
Ugly (D average)
14
14
14
42
28
14
3.00
2.00
1.00
(a)
(b)
(c)
7.
(a)
(d)
(e)
(f)
- (c) questions from table
How many hours attempted will Lazi have after the third semester?
Under which scenarios will Lazi be suspended for a semester?
Can Lazi get off academic warning under the Good scenario?
5. The Benefits of Replacing an F
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At UNCA if a student retakes a course he or she can replace an F, D, D+ or even a C-,
with up to 15 hours of such replacing allowed. Let’s look at Lazi at the end of two
semesters. He has
Total QP = 26 + 21.68 = 47.68
Total Hours Attempted = 13 + 18 = 31 hours
Cumulative GPA = 47.68 / 31 = 1.538
Lazi’s future looks kind of shaky right now. If Lazi retakes Spanish 110 and Chem 132
in his third semester and gets a B in both, his original F’s will disappear from his GPA.
What that actually means is that the QP of the past will not change since the F did not
produce any QP, but the hours attempted will go down by 6 as both F’s are removed from
the GPA. Suppose Lazi takes 14 hours in his third semester, getting all B’s and
replacing those two F’s. Now his grade history looks like this:
semester
Total hours
Total QP
first
13
26
second
18 – 6 = 12
21.68
third
14
42
8.
Determine Lazi’s new cumulative GPA after three semesters.
9.
Determine Lazi’s cumulative grade point average after three semesters if
he got all B’s on 12 hours in semester three but did not retake the classes that he
had made F in.
10. Reflect. Why does UNCA have the replacement of F option?
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