[One-Minute Makeover] Algebra 1 • Topic 4 Assessment


If you’re just tuning in, consider checking out the first post in the series, or the most recent post.

Algebra 1 • Topic 4 Assessment, Before

We’re drifting into a little section of my Algebra 1 curriculum that I’m at least a little bit ashamed of. I have no one to blame but myself since I put the textbook on the shelf and created lessons, practice, and assessments from scratch. Big plans for improvement in the months ahead, but for now, warts and all…

Here are the two-and-only questions from Form A of my old Topic 4 assessment:

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Oh, the shame! I’ll talk more about the gap between this assessment and all-that-is-decent-in-this-world in a moment. For now I’ll just remark that what these questions actually demand of students is so far below what I originally intended that they are essentially useless as an assessment tool in Algebra 1.

Algebra 1 • Topic 4 Assessment, After

The first major flaw in the original assessment is that the questions appear out of nowhere and drift away from our attention just as suddenly. So I replaced these two unrelated questions with a sequence of five questions related to a single scenario. Here are the questions from the new Form A:

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My initial intention was for students to use expressions and/or equations to answer the questions on the assessment. On the original version, almost none of my students approached the problems algebraically. Many were able to answer the questions (and many were not), but nearly everyone who answered correctly did so with nothing more than some numerical tinkering.

While I’m not opposed to numerical tinkering (quite the contrary; I think it’s a fantastic practice for students), in this class and on this assessment I was hoping to see whether they could write an expression to model a situation and use the expression to answer another question or two in an efficient manner.

With the original assessment, this was a lost cause. With the updated version (particularly #3-5) I was able to measure at least part of what I set out to measure.

Oh, But It’s Still So… (aka “Wrap Up”)

While my current assessment is an improvement over the first version, it still strikes me as terribly inadequate. Here we are, at the end of a unit on linear modeling, and there’s a massive void when it comes to two hugely important things: (1) At no point is any connection made between the verbal/numerical/algebraic representations and a graphical one (and it would be so easy to fix this!), and (2) The scenario is decidedly boring and contrived.

I have ideas for how to address #1, but am at a loss for how to remedy #2 in the space of a single-page assessment. More to think about for the next round of revisions.

One additional minor/medium flaw I see in the updated version is this: At no point do I ask students to explain their reasoning, justify their thinking, etc. (And word on the street is that those are cool things to do.)

Until next time…


[One-Minute Makeover] Algebra 1 • Topic 3 Assessment


The first post in the series is here. The previous post (Topic 2, Part 2) is here.

Algebra 1 • Topic 3 Assessment, Before

When I first drew up this assessment, my goals were to evaluate students’ ability at simplifying linear expressions and solving linear equations. Here’s what the two questions of Form A looked like:

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I had the same all-my-eggs-in-one-basket problem with this original Topic 3 assessment as I did in an earlier assessment. If students aced these two questions, I knew they were capable of what they ought to be able to do. However, if they missed one or both, I was stuck without much information. There was no gradation in the all-or-nothing results.

Another issue: the assessment focused entirely on procedural skills and demanded nothing from students in terms of demonstrating deeper conceptual understanding.

Algebra 1 • Topic 3 Assessment, After

As was the case with Topic 2 (detailed in posts here and here), I addressed the above concerns by lengthening the assessment quite a bit. The revised Topic 3 assessment weighs in at two pages and a total of ten questions.

In the first three questions, I try to get a read on whether students understand conceptually what a solution of an equation is. (For the record, what I’m looking for is something along the lines of “this value does/does not satisfy the equation,” along with numerical support—via substitution—of that claim.)

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After that, students move through a series of four increasingly difficult linear equations, giving me the leveled progression I was lacking in the original assessment that would help me distinguish the “almost there” from the “completely lost.”

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Next up, an error-analysis/explain-your-reasoning style question:

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And to close, two more “solve” questions (including one at the same level of difficulty as the original Topic 3 assessment):

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Wrap Up

The net result of the these changes is a much stronger assessment, with improvements in at least two categories. The new assessment (1) provides me with more specific insight about student strengths and weaknesses, and (2) demands more of students in the way of critical thinking and clear communication.

I fully expect that this new assessment could be improved in half a dozen ways. Part of the beauty of teaching (and writing many of my own lessons and all of my own assessments) is the opportunity for continual improvement over the years. This job will never leave me bored!

Is there anything in particular you liked about the improvements I already made to my Topic 3 assessment? Do you have a few more ideas for making it even better? Share away!

[One-Minute Makeover] Algebra 1 • Topic 2 Assessment (One More Time!)


It all started here. In the last post, I looked at additive and multiplicative inverses. Onward!

Algebra 1 • Topic 2 Assessment, Before

The second half of my original Topic 2 assessment assessed whether students were able to evaluate expressions involving integers and various operations (including radicals, rational exponents, and a few other things). My original approach included a single question, with everything all smashed together:

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For those who were able to evaluate the expression correctly, I got precisely the information I needed (“Johnny can do this, that, and the other thing.”). But for those who answered the question incorrectly… Was it because they were lost on everything? Or because they struggled with one skill in particular? While a close look at their work would often reveal the answer to that latter question, I find that I’ve stripped one of the benefits of SBG (specific insight into specific strengths and weaknesses) right out of the question.

Algebra 1 • Topic 2 Assessment, After

To address that weakness, I bumped this section of the assessment up from a single question to several (three, in fact):

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I lose a minute or two more of class time to administer the assessment, though I gain a quick and clear sense of who’s struggling with exponentiation, rational exponents, and simplifying expressions involving multiple radicals. Note that while grouping symbols are entirely absent from #9 above, they make an appearance in some of the other assessment forms, including this one:

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Something’s Still Missing…

Even with this more discrete-ified set of questions—which I view as an improvement over the original—I still feel like this assessment is short on critical thinking and “explaining your reasoning.” A nice quick addition might be to present students with an expression (similar to #9 above) with two (or three) incorrect step-by-step approaches (each of which has exactly one error). Ask the students to identify the error in each approach and then show their own (100% correct) step-by-step solution. Here’s a quick mockup:

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Wrap Up

I’ve now written four of these “better-assessments-in-sixty-seconds” posts. Since I’ve taken two posts to address each topic (the content fell rather naturally into four categories, rather than only two), I might want to consider breaking these apart for the purpose of grade book entries. I might even leave the assessment handout itself unchanged, but the idea of more refined grade book categories for tracking student mastery certainly has its appeal.

Thoughts on that last thought? Comments on something else? You know what to do.


P.S. Disclaimin’ the Naming’

I’m terrible at coming up with imaginary student names for my handouts. So I often use my students’ names or my kids’ names (I have lots to choose from in this second category, now!). Today I borrowed some names from a list of fictional butlers. Oh, I also have a preference for names to follow an A, B, C, etc., pattern.

[One-Minute Makeover] Algebra 1 • Topic 2 Assessment


Last time in this quick-look-at-improving-assessment series (which began here) I shared my attempt at improving the questions related to distribution on an Algebra 1 assessment. As always, you can check out the topic list here (or here, if you want “I can…” statements as well).

Algebra 1 • Topic 2 Assessment, Before

This time we’ll take a look at a series of questions related to operations on numbers. Here’s the rubbish version (from the original Form A):

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I was trying to get a read on whether students understood what additive and multiplicative properties are. For reasons similar to those shared in the first post in the series, this question type wasn’t particularly effective. Also, there’s the issue of “What am I actually trying to accomplish with these questions?” I don’t think I had that settled in my mind when I wrote the original assessment, and that led to the lackluster questions shown above.

Algebra 1 • Topic 2 Assessment, After

If this assessment was going to improve at all, I first needed to nail down what I wanted to accomplish. Then I needed to work on better ways to ask questions (even just spicing up the originals with “explain your reasoning” or “defend your answer” would have been a nice start.

At any rate, I decided on three goals, so I wrote three mini-sections of the assessment. Here they are:

Goal 1: Students will know the colloquial nicknames for additive inverse (opposite) and multiplicative inverse (reciprocal)

And here’s how I attempt to measure that on the new-and-hopefully-improved assessment:

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Simple, but to the point. On to the next one…

Goal 2: Students will be able to use the idea of additive and multiplicative inverse (possibly without even knowing their names) in order to “make one” and “make zero”

Here’s how I tried to assess that skill:

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I decided that this was actually the main reason we were exploring additive and multiplicative inverses in the first place, so a rather direct assessment question seemed appropriate. On to the third goal related to inverses…

Goal 3: Students will justify their reasoning with verbal and numerical support

The content isn’t profound or complex, so I thought it might provide a nice opportunity for students to create their first “mathematical” argument, one with complete sentences and mathematical “evidence.” With these two questions, I’m really trying to pave the way for more complex arguments students will make in Geometry, Algebra 2, Precalculus, and Calculus.

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Wrap Up

Now that I’ve written three of these posts, I’m wondering if I should add student work. I don’t have anything for the original versions, but for some of the revamped assessments I took pictures of strong and weak responses in order to facilitate in-class discussions the following day. If I can dig those images up, would they be worth posting? Share your thoughts (on this last question, or in general) below.


[One-Minute Makeover] Algebra 1 • Topic 1 Assessment (The Sequel!)

Welcome Back!

Two posts and this is officially a series, right? Off we go!

Algebra 1 Assessment, Before

Let’s spend a little more time (how about 60 seconds?) looking at the second half of that old, filthy Topic 1 assessment:

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That’s it. One measly simplification question. Nothing inherently wrong about the question itself, but…

Algebra 1 Assessment, After

With the updated Topic 1 assessment, I wanted to address to potential weaknesses to the approach I took on the original. First, I felt like one question wasn’t enough to get a sense of student mastery of distribution. For students who have mastered this, each question takes between 5 and 20 seconds, so time wasn’t an issue. With that in mind, I added two more “standard” distribution questions and scaled their difficulty:

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(If the “compact form” comment doesn’t make sense and you wish it did—rare combination, possibly—let me know in the comments.)

Next, I wanted to add a question that required students to think outside the box, even if just a little, and at the same time would provide them with an opportunity to explain their thinking. It’s not terribly profound, but since we didn’t even hint at factoring during the lessons leading up to this assessment, I think this rather bland factoring problem, when appearing in this context, actually demands some critical thinking on the students’ part. Enough yammering, here’s the question:

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Thoughts? Comments? Questions? Outrage? Share any and all in the comments!

(Bonus Material: Confession)

The “original” revamped version of the Topic 1 assessment only included 7 questions. I added #8 just to spice up the blog post.  Actually, in thinking about writing the post, I had an idea for how to—potentially—make this assessment even less terrible for next year. So it’s sort of a lie, and sort of not, with an emphasis on the latter, at least in/from the future. Errrr… Time travel. Brain hurts. 12:12 am. Time for bed.