Grading With Points, Half Marks and Partial Credit

Questions correct vs points earned

If every question is worth one point, "number correct out of number of questions" and "points earned out of points possible" are the same thing. As soon as questions have different values they aren't, and using the wrong one can change the grade a lot.

Take a 20-question test with 15 one-point questions and 5 three-point questions. That's 15 + 15 = 30 points possible. A student gets all 15 one-point questions right and only 2 of the 3-point questions:

• By questions: 17 of 20 correct = 85%.
• By points: 15 + 6 = 21 of 30 points = 70%.

Fifteen percentage points apart, for the same paper. If you've decided the 3-point questions deserve more weight, the points method is the correct one, and the "questions correct" number shouldn't be used at all.

How to calculate a percentage from points

You can use any of our tools with points instead of questions: in the test grader enter the total points as "total questions" and points lost as "wrong answers", or use the calculator on any grading chart page, which accepts half points and decimals such as 27.5 out of 30.

Giving partial credit consistently

Partial credit is where grading quietly becomes inconsistent. On a stack of 120 papers, the 4-point problem you graded at 8 a.m. and the one you graded at 10 p.m. may not have been held to the same standard. Three habits help:

• Write the partial-credit rules before you start. For a 4-point problem: 1 point for setting it up correctly, 2 for correct method with an arithmetic error, 3 for a correct answer without units, 4 for a complete correct answer. Keep the list next to you.
• Grade one question across all papers before moving to the next. You apply the same rule to every student while it's fresh, and you notice common errors that might mean the question itself was unclear.
• Shuffle the stack between questions, so the same students aren't always graded first while you're freshest or last when you're tired.

Half marks on one-point questions

Half marks are common on short answers: half a point for the right idea with a missing detail. They work well, with two cautions. First, a test of many half-marked one-point questions produces scores like 17.5/20 (87.5%), which is fine, but make sure your gradebook accepts decimals rather than silently rounding to 18. Second, decide whether half marks are allowed on multiple-choice questions. Usually they shouldn't be, because there's no work to give credit for.

Weighting whole sections

Sometimes you want a section to count for a fixed share regardless of its point total: a 10-point vocabulary section and a 40-point essay where you want each to count for half. Points alone won't do that (the essay would be 80% of the grade). Convert each section to a percentage first, then average the sections with the weights you want, exactly like a weighted grade:

A quick checklist before you grade

• Does every question have a stated point value?
• Have you written the partial-credit rules for any multi-point question?
• Are you entering points (21/30), not a rounded percentage, in the gradebook?
• If sections should count equally, have you converted them to percentages first?

Quick answers

This guide explains common practice and the math behind it. Grading rules differ between schools, so always check your school or district policy. Spotted an error? Let us know and we'll fix it.