Assessing “Upper Level” Math Students on Algebra I


I am teaching Algebra II/TRIG! Not Algebra II. First time ever. Last December, I gave the kids a packet with the following letter:

Hi! I’m looking forward to our course.

Attached is a packet of Algebra I review work to prepare you for our class. If you are comfortable with linear and quadratic equations, then you’re in good shape. If you’re not, it’s time to study up!
Our course will be challenging and fast-paced, and I will not be teaching linear equations and quadratics in their entirety—that is, I expect you to know and demonstrate mastery of Algebra I concepts. We will be modeling equations and working with applied knowledge (the dreaded word problems) almost constantly. I don’t just expect you to regurgitate solutions. You’ll need to know what they mean.
I’m not trying to scare you off—just put you on your toes! But you should put in some time on this, because we will be having a test when you come to class the first full day. That test will go in the gradebook, but more importantly, it will serve as notice. You’ll know if you’re prepared for the class.

Have a great holiday.

Reminder: My school is on a full-block schedule, which means we teach a year’s content in a semester, then repeat the whole cycle with another group of students. A usual teacher schedule is three daily 90-minute classes, with a fourth period prep. I taught algebra II, pre-calc, and a state-test prep course (kids killed) last semester, and this semester I have A2/Trig and two precalcs.

(Notice that I am getting more advanced math classes? Me, too. It’s not a seniority thing. It’s not at my request. It’s possible, and tempting, to think they noticed the kids are doing well. I know the first decision to put me in pre-calc last year was deliberate, a decision to give me more advanced classes because they wanted a higher pass rate. But I honestly don’t know why it’s happening. Maybe they cycle round at this school, moving teachers from high to low and back again.)

So I said the first full day, and today was a half day, but the kids had a whole packet to work on and I wanted to understand I wasn’t screwing around. If they’d done the work, they’d do fine on the test. If they were planning on cramming, too bad so sad.

I was originally going to do a formal test, but decided to just throw a progression of problems on the board. Then I typed it up for next time, if I teach the class again.


How’d they do? About a third of them did well, given the oddball nature of the test. A couple got everything right. Most of them stumbled with graphing the parabola, which is fine. Some of them knew the forms (standard, point slope), but weren’t sure how to convert them.

Another three passed–that is, answered questions, showed they’d worked some of the packet. The rest failed.

Of the ones who failed, easily half of them had just blown off the packet but have the chops. The other half of that third I’m not sure of.

If you are thinking that kids in Algebra II/Trig should know more, well, they were demonstrably a step ahead of my usual algebra 2 classes. And I think some of them just didn’t know I was serious. Wait until that F gets entered, puppies. Like I told them today: “There’s a lower level option here. Take it if you can’t keep up.” Whoo and hoo.


I’ve now taught pre-calc twice. The first time, last spring, I was stunned at the low abilities of the bottom third, which I didn’t really understand fully for two or three weeks, leaving some of them hopelessly behind. I slowed it down and caught the bulk of the class, with only four to five students losing out on the slower pace (that is, they could have done more, but not all that much more). So when I taught it again in the fall, I gave them this assessment to see how many students could graph a line, identify a parabola from its graph, factor, and use function notation. If you’re thinking that’s pretty much the same thing I do with the A2/Trig classes, well, yeah. Generally, non-honors version of course is equivalent of honors version of previous year.

I don’t formally grade this; the assessment happens while they’re working. I can see who stumbles on lines, who stumbles on parabolas, who needs noodging, who works confidently, and so on. I was able to keep more kids moving forward in the semester/year just ended using this assessment and a slightly slower pace. One of the two classes is noticeably stronger; half the kids made it through to the function operations before asking for assistance.

This assessment also serves as a confidence booster for the weaker kids. Convinced they don’t understand a single bit of it, they slowly realize that by golly, they do know how to graph a line and multiply binomials. They can even figure out where the vertex should be, and they might have forgotten about the relationship between factors and zeros, but the memory wasn’t that far away.


While I just threw together the A2/Trig course, I put a huge amount of thought into this precalc assessment last fall. I think it’s elegant, and introduces them to a lot of the ideas I’ll be covering in class, while using familiar models.

Part II is just a way of seeing how many of them remember trig and right triangle basics:



If you’re interested in assessing kids entering Algebra (I or II) or Geometry, check out this one–multiple choice, easy to grade, and easy to evaluate progress.

About educationrealist

10 responses to “Assessing “Upper Level” Math Students on Algebra I

  • vijay

    Which grade are these students?

    Here, they offer it in middle school, eighth grade, or in the HS freshman year, such that most kids forget Algebra II and trigonometry by the time they are juniors. Hence, we have the issue of people doing AP stat/AP Calc, but struggling in some SAT questions.

    • educationrealist

      A2/Trig is generally sophomores and juniors. Precalc is usually juniors and seniors.

      I don’t see how “forgetting algebra” is anything other than a serious fail. Algebra is the damn mother ship.

      • Vijat

        Oh my god! You should come and teach freshmen and sophomores in our great universities. They ask questions like how to solve quadratic equations after reducing the problem to a quadratic. Actual questions asked in my class include how do you know air is oxygen+nitrogen. What is the value of gravity, and what is a nonlinear equation, and why are you using equations and chemistry in thermodynamics.

      • Sideways

        ER: I wouldn’t say I “forgot” algebra, but the kind of math you do on the SAT is just not what you’ve been doing for years by the time you take the SAT on the advanced path.

        I can’t prove I would have gotten a perfect score instead of near perfect if I’d taken it years earlier, but I do remember finding the Math 2c test easier.

        Also, your post has me embarrassed by just how rusty my algebra is.

  • Hattie

    OT, but I’m not on Twitter: You mention that, unless someone is writing Richard Sherman’s column for him, he can construct coherent sentences. Fact is, most practising athletes who write columns would have journalists ghost writing for them, at least here in the British Isles. (Maybe it’s different in the US, but I can’t think of a single reason that it would be.)

    Doesn’t make them stupid; it just means that it’s very difficult to be able to both play to a professional standard and write a regular column to anything approaching a professional standard. Personally, I’d be astonished if any current athlete, regardless of race or SES, wrote his own columns. There just aren’t enough hours in the day.

    Personally, I think both that Sherman is a very bright man and that he behaved like a thug. The two aren’t mutually exclusive. But I get the horrible feeling, listening to people rhapsodise about how bright he is, that it’s a bit like Dr Johnson talking about female preachers. That is, they’re so surprised to see a halfway bright black man with street cred that they put an already impressive guy to a standard that he can’t meet and shouldn’t have to. Can’t he just be a fairly intelligent dude with seemingly great leadership skills? We have to pretend he’s a genius and above reproach?

  • Tort

    “(Notice that I am getting more advanced math classes? Me, too. It’s not a seniority thing. It’s not at my request. It’s possible, and tempting, to think they noticed the kids are doing well. I know the first decision to put me in pre-calc last year was deliberate, a decision to give me more advanced classes because they wanted a higher pass rate. But I honestly don’t know why it’s happening. Maybe they cycle round at this school, moving teachers from high to low and back again.)”

    I’m not surprised to see you rapidly ascending to the top and I’m sure the admin recognizes your analytic skills as a teacher. Teaching is becoming more scientific and those who can analyze data, make observations, tactical adjustments, etc., will be more successful than those who don’t. I learned that my planning focus must also be on what “they” will be doing as much as what I am to do.

    Are you a relatively new member of the department? How are some of the other teachers handling your rise and your apparent good standing with the admin?

    • educationrealist

      Relatively new, yes. As for the second, I started to answer fully and decided better of it. I get along with all the members of the math department, and some of them are really interested in my work and talking to me about it.

      As for not being surprised, thanks, but the last school I was at–despite being the teacher with the lowest fail rate and solid test scores–the district wanted younger teachers and made it clear I wasn’t welcome. So I take any good will of admins happily, but I never forget that it could all change.

      Thanks for the good words, though!

  • Tort

    Reformers have picked up the “young is better theme.” What bs. Younger teachers might have more energy, but not the same wisdom or experience as older teachers. So, I am befuddled as to why they think youth is more desirable (I am typing while my students are doing a warm up). Younger teachers are certainly cheaper and won’t be able to point out the inherent flaws in the educational system–flaws that existed long before any of us started teaching. It is uncanny that so many people who wield power and influence lack so little real information about what actually occurs in the classroom.

    They will keep making mistakes in the name of reform, and will not set things straight until they finally realize that ultimately the parents and students are responsible for improved learning outcomes. I often see good teachers not getting all their students to learn due to the gaps in their overall understanding. You seem to be able to fill those gaps, if I am not mistaken, thus helping the students to learn and pass their subjects.

    Too bad the other school discriminated against you and let you go.
    Oh, when do the reformers reform the administrative side? A typical conservative reformer will believe that empowering management is all that is needed in education. We’ll see.

  • Jim

    I’m sure your students are in good hands.

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