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How to figure your grade

One of the questions that I get asked most frequently is "What is my grade in this class?" The second is like it: "What do I need to get on the exam in order to get an A?" The varients of these two questions go on, but at the root of them all is finding grades. Here is a little lesson on how grades are figured out in my classes and in the school. All that is needed is a little simple math and perhaps a little simple algebra.

In my classes, different types of assignments/assessments get different weights. Tests and quizzes are worth more than labs, homework and participation. Each category is worth a specific percent of the quarter grade. For example, in Algebra II, the tests are worth 40% of the quarter grade. This means that all of the tests for that quarter add up to 40% of the total. The exact weights depend upon the class (see the syllabus).

Quarter Grade Method 1: There are three basic steps to find the quarter grade. First, for each category of assignment, add up the number of points received by the student, then divide the result by the total number of points possible for that category. The result will most likely be a decimal less than one unless there is extra credit involved. Once you have done this, you multiply each of these by the weight (for example, if tests are worth 40%, multiply the test grade by 40). Finally, add these up to get the grade for the quarter (97 = 97%).

Semester Grade Method 1: Finding the smester grade is very similar. The school-wide weighting scale is 40% for each quarter and 20% for the semester exam. To find the semester grade, take each grade and multiply it by the appropriate percent, this time as a decimal (If the 1st quarter grade was a 97%, multiply 97 by .40). Once you had done this for each category, add them together to get the semester grade.

Method 2 for both: If you are fluent in Algebra, here is another quicker way to do the above tasks using equations. I will use an example for my Algebra II class where tests are 40%, quizzes are 30%, homework is 25%, and participation is 5%. Each letter stands for the grade for that section (points received divided by points possible)

Quarter Grade = 40T + 30Q + 25H + 5P

Semester grade = .4(Q1) + .4(Q2) + .2(E)
(Q1 = 1st quarter grade, etc.)

Finding what you need on an exam: To find what you need on an exam, use the following formula. If you are not fluent in algebra, follow the verbal instructions afterward.

E = [S - .4(Q1) - .4(Q2)]/.2

S = desired semester grade, Q's = quarter grade, E = minimum exam grade needed

Step 1: multiply each quarter grade by .4

Step 2: Take desired semester grade and subtract both results from step 1

Step 3: divide result from step 2 by .2

See the examples below to see how this actually works!

Sample Gradebook: Quarter Grade

Here is a sample Algebra II gradebook for a quarter. The actual number of grades is much smaller than an actual quarter, but it has enough to show how things work. Below that is work showing how to find the quarter grade. Tests are worth 40%, Quizzes 30%, Homework 25%, and Participation 5%

AssignmentTypePoints ReceivedPoints Possible%
Homework 1.1H2020100
Homework 1.2H253083
Chapter 1 QuizQ121580 
Homework 1.3H2525100
Homework 1.4H2840 70
Chapter 1 TestT233077
Homework 2.1H283093
Homework 2.2H3030100
Chapter 2 QuizQ182090
Homework 2.3H4040100
Homework 2.4H303586
Chapter 2 TestT415082
ParticipationP2020100

Homework Grade = (20+25+25+28+28+30+40+30)/(20+30+25+40+30+30+40+35)
                            = 226/250
                            = .904   (90.4%)

Quiz Grade = (12+18)/(15+20) = 30/35 = .857   (85.7%)

Test Grade = (23+41)/(30+50) = 64/80 = .8    (80%)

Participation Grade = 20/20 = 1   (100%)

Quarter Grade = 40T + 30Q + 25H + 5P
                        = 40(.8) + 30(.857) + 25(.904) + 5(1)
                        = 32 + 25.7 + 22.6 + 5
                        = 85.3% = B-

One thing that you might notice is that while this student got a 80% and a 90% for his quiz grades, his overall quiz grade was not exactly in the middle (85%) but slightly larger (85.7). This is because the second quiz was worth more points. In a class where each quiz was worth the same number of points, this would not happen.

Another thing to note is that the final grade may be slightly different when done all in one step on a calculator, which in turn may be slightly different than what is derived by Skyward, the grading program. These differences are due to rounding. Doing it all in one step is the most accurate, which is what the computer does. Calculating the quarter grade in one step will be less accurate, but more accurate than what was done above for the last set. If you are using a TI calculator, it will automatically do multiplication before addition (order of opperations).

Sample Gradebook: Semester

1st Quarter grade = 85.3% (B-)
2nd Quarter grade = 82.1% (C+)
Exam Grade = 78% (C)

Semester Grade = .4(Q1) + .4(Q2) + .2(E) = .4(85.3) + .4(82.1) + .2(78) = 82.56 (C+)

Again, there may be some differences due to rounding, but this is a good approximation

What if...

Let's say wants to know what they need to get on the exam in order to get an A. Their first quarter grade is an 89.7 (B+) and their second quarter grade is an 87.5 (B). The minimum percent for an A is 94%.

E = [S - .4(Q1) - .4(Q2)]/.2
   = [94 - .4(89.7) - .4(87.5)]/.2
   = [94 - 35.88 - 35]/.2
   = 23.12/.2
   = 115.6%

So, the student needs to get about a 115% in order to get an A. In other words, this student cannot get an A due to the fact that I only offer 3% extra credit (which would total to a maximum score of 103%). Once again, we must keep rounding in mind, but this should be very close to the actual value. But let's get some good news. Let's find what minimum score this student needs to get on the exam in order to pass the class for the semester. The minimum passing grade is a 67%.

E = [S - .4(Q1) - .4(Q2)]/.2
   = [67 - .4(89.7) - .4(87.5)]/.2
   = [67 - 35.88 - 35]/.2
   = -3.88/.2
   = -19.4%

In other words, this student cannot fail the class. In fact, the student could even not take the exam (which would result in a 0%) and still pass (thought their grade would be significantly lower). This basically shows that while it is difficult to get an A in my class, it is also difficult to fail.