My 7th graders have a question on their exam that asks them to put eight numbers (integers and fractions) in order of their distance from 0 on the number line, starting with the smallest distance.

These types of questions are tricky for me to grade, and because there are *eight* numbers in this sequence, the task of grading it **fairly** suddenly becomes thorny and irksome.

Let’s change the question to this:

Put these numbers in order from least to greatest: 5, 7, 2, 3, 1, 4, 6, 8

The correct order is 1, 2, 3, 4, 5, 6, 7, 8 (you’re welcome) — for a possible score of 8 points. How many points would this response earn?

## 1, 2, 4, 5, 3, 7, 8, 6

So, only the first two numbers —* 1 *and 2 — are placed correctly. Is the score just 2 out of 8 then? But I want to give some credit to *4* and *5* being next to each other, likewise with *7* and *8*.

I’ve tried to come up with some metrics to score this, and then I would want to apply the same metrics to different sequences to see if any would break my invisible “fairness” barometer. For example, whatever score I came up with for the above sequence, I think the below sequence should get a lower score because the *7* and *8* are farther upstream than they should be.

Anyway, I have some ideas. The above two sets are Sets *A* and *B* below.

I wonder if there’s a way to score an ordered list that half of us math teachers can agree upon. I’d like for my students to think about this too. Meanwhile, here is a spreadsheet with my scores if you’d like to take a look and play along. Just enter your name in row 1 (and link your name to your Twitter, if you want) and the scores you’d assign to these sets.

[02/01/18: @MrHonner had a similar question over 4 years ago: Order These Things From Least to Greatest.)

## 23 Comments