Algebra 2 Quiz • Stephanie Reilly

Introduction

Our first assessment submission comes from Stephanie Reilly (@reilly1041, mrsreillyblog.wordpress.com) in the form of an Algebra 2 quiz on exponents and adding polynomials. Links for the assessment and commentary are below. Questions to consider:

  • What do you like?
  • How would you make it better?
  • What questions do you have for Stephanie?

Submission Type

“Share an assessment you don’t hate…”

Assessment

https://docs.google.com/file/d/0BytS9twTZ9tlVElfUGZ2MHp6aW8/edit

Author’s Commentary

https://docs.google.com/document/d/1o71FlRPQ5LdyD3B0k-LZjgXdEWiT0HUnzFC1slftaPc/edit

Bonus Request

Since this is the first assessment submission post, please let me know in the comments, via Twitter (@mjfenton), or via email (mjfenton at gmail dot com) if you have any suggestions for how better to facilitate this assessment conversation.

Coming Soon

Next in line: A Precalculus Honors test from Jim Doherty.

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10 thoughts on “Algebra 2 Quiz • Stephanie Reilly

  1. Great to see the site up. Looking forward to some learning from virtual colleagues!

    A few reactions here
    The first #1 (the explain question) is terrific. I often ask my students to pretend that I am their annoying younger sibling asking them a question. Having the table there to support their answers is VERY helpful here.

    In the simplify section – Do they have calculators? Are they expected to know that 3 ^ 6 is 729?
    My guess is that the most common mistake is to apply the laws of exponents to variables and to either ignore those laws or make up new ones when working with constants.

    For #12 and #13 – I assume that they know not to simply invoke identity properties here. Perhaps instructions could be clearer, but by this point of the year students should certainly know the lay of the land with their teacher.

    Questions 14 – 18 seem odd here but I had already asked Mrs. Reilly about this in another venue.

    I love question 19 as a procedural question to get kids to explain a problem solving process.

    Thanks for getting this live!

  2. I very much like this also! It taps a lot of different types of thinking.

    For #1, I would think it would be a powerful thing to give more space to answer. I would think I would give around 1/2 a page so they could flesh out their ideas, provide examples for the Algebra II kid, etc. I don’t know how I would answer it in two lines, personally. Also, is the table and the question related — do you want kids to refer to the table in helping them explain their answer? If so, maybe say that?

    Most importantly for that problem, I love that you ask it. So many kids just take it as this mechanized thing — negative exponents!

    For the simplify problems #1-#10, I see a lot of thought and care put into making sure you ask a variety of different questions which cover different things, but without repeating any of those things to death (e.g. there aren’t 4 problems with a 0 exponent). Depending on where you are at, questions like (-2x^3)^5 can be good (with a negative coefficient) because I have noticed my kids struggle with negative numbers being raised to a positive exponent.

    I love #11 — but I would just be careful with the word “prove” as they aren’t proving it true — just finding some evidence supporting the idea that it does hold true.

    #12 and #13 are my favorites! You’re asking the backwards question! I can see many of my kids putting something super easy down… but maybe you could say (if you believe in/use extra credit)… if you finish the assessment early, go back to #12 and #13 and come up with super complicated expressions which yield the same results… if they are of sufficient complexity and work, you’ll get a half point extra credit for each. So make them complicated and weird!

    If this were a longer thing, you could even do the backwards question for #14-#18! That would highlight that factoring and FOILING are really opposites of each other! If you did do this, I would divide the test into two columns in this section, and on the left hand column, ask the forwards question, and on the right hand column, ask the backwards question.

    I love that you have an inside joke (“call it a day”) with your class.

    Love it! Thanks for sharing. You have given me so many good ideas. Now I’m sad (but happy) that the year is OVER, though!!!

  3. My first instinct is to wonder whether the assessment needs to be this long. Lot’s of good problems/tasks, but are they all necessary to evaluate proficiency? Would it be possible to narrow the assessment to evaluate the skill first and then the deeper learning second? I think this is a great opportunity to throw your evaluative intentions with this assessment out there for a little bit of collaborative editing. Editable Google Doc? Thanks for sharing.

  4. Samshah- you know, I cringed when I wrote (and bolded) “prove” in that question. My Pitt profs would kill me. I went with kid-friendly “prove” in the colloquial sense. Wouldn’t do that in an advanced class.
    My kids didn’t “phone it in” on #12 or 13, by just using identity. I have them make up problems often, so I didn’t have to put in explanation or warning, they just did it.
    I like the idea of forwards and backwards for #14-18, of course, that would make it even longer!
    The inside joke is nice to add because it drives home that I’m not using some book-test or a test that I’ve been using for the last 20 yrs. like this quiz is just for them. even for my physics final, I included a joke question about a students “physics” tshirt (a Nike tshirt that says I DO WORK). Fun.
    Mrdardy-I find students can figure out (x^2)(x^3)=x^5 but (5^2)(5^3)=25^5.
    Thx for commenting and for going gently! Scary putting an assessment out there!
    Stephanie

  5. Great site, Michael. Thank you for starting this!! Stud muffin you.

    Thank you, Stephanie, for being brave and awesome in sharing the first assessment here!! I love ALL the questions, no redundancy, just solid. You have HS kids, so it may not be long for them, but I’m in middle-school mindset and I’d break this test into two.

    Just some numbering seemed off: you had the great fill-in table, then question #1, then question #1 again. And not all the questions had points value indications.

    These questions are all algebra 1 topics though so I can steal these!! Thank you, Stephanie!

  6. Yes, Fawn, I am awful at putting point values on quizzes. Sometimes I forget totally. For this one, I didn’t have time to coax Word into handling columns and equations and little parentheses for the big middle section. Would’ve been better to just hand write them in!
    Funny about the difference between MS and HS, this was just a quiz, not even a whole period.
    A lot of our alg2 class is alg1 review or even intro. District is still working on curriculum alignment. For example, they don’t do systems at all in alg1. That’s why I use so much of your stuff.
    Thx for the feedback!

  7. Love assessment, and so I am loving this project. Big thumbs up to Michael!

    Ok, I’m going to launch into some ideas:

    What do I like?
    I love #1, #12 and #13. I’d probably add a line like “explain your thinking” or “explain your reasoning” to try to bait some more student thinking as evidence of understanding. But nonetheless, I love the fact it will involve some genuine understanding.

    How would you make it better?
    I wouldn’t necessarily say better, but I’d probably do a couple of things differently. First, I haven’t marked with points in a long time. I would probably provide the expectations I am evaluating (I think you US people use the words “Standards” instead), and my evaluation would be a holistic judgement on overall understanding. Second, if I had full control in creating this quiz for my students (not worrying about other colleagues teaching the same course), I would probably just include questions 1, 12, and 13. Then I’d do something similar for polynomial manipulation.

    What questions do you have for Stephanie?
    What do you give back to the students? What do you do with them? What do they do with them?

    Thanks for starting us off!

  8. Stephanie,

    First of all, I’m so glad you shared your assessment. It proved to be a great conversation starter as the blog launched last week. Many of my thoughts have already been shared by others, so I’ll just mention a few of them.

    I love #1, and echo Sam’s comment about considering leaving more space for student answers. It got me thinking about how we support and spur our students on in other ways by using scaffolding, and I began to wonder if test formatting (especially space for answers) is a way to scaffold as well. If a student sees two lines, they may be tempted to think, “Oh, this answer should be short.” Contrast that with an “explain” style question followed by a large space, which might say to (some) students, “Hey, this question has the potential for a thoughtful, detailed response. Go for it!” I often tinker with formatting on my handouts in an effort to save space/pages/paper/trees, but I think I might start leaving more space for responses, especially on assessments.

    While #1-10 (the second #1, that is) don’t get me too excited, they do seem like a good (hopefully quick) way to test a variety of skills/concepts related to exponents. Avoiding redundancy is key, and it does appear you’ve done so. I’m happy you have a second problem with a zero exponent (#7 and #9), because I’m terribly curious to know what percentage of students (if any) answered #7 correctly but #9 incorrectly. If anyone did, I think it would be a great “combo” math mistake to send to Michael Pershan (@mpershan). It certainly seems related to his thoughts on this (http://rationalexpressions.blogspot.com/2013/04/figuring-out-why-kids-mess-up-exponents.html).

    I think #11-13 are fantastic as well. #11 got me thinking… Is there a related question along the lines of “Give a numerical example to show that *** is not true”? Maybe take a commonly applied misconception, and ask them to disprove it with a counterexample during the assessment.

    I would remove #14-19 entirely and place them on a separate quiz, even if you gave it immediately after this one. I think having two separate scores would better communicate to you and the students regarding strengths and weaknesses.

    Okay, so it turns out I won’t “just mention a few.” Once I got rolling I was having too much fun. 🙂

    Thanks again for sharing! I hope you’ll submit another assessment in the future.

  9. Thx for the comments. I love the idea of asking Ss to show something isn’t true. I have asked Ss to show that (x+3)^2 is not equal to x^2+9 before on tests. Of course, some students are puzzled bc they so desperately want to believe that to be true.
    Ok you all have convinced me to separate out the polynomials onto a different quiz!! 🙂

  10. I’m late to the discussion and don’t have much to add, but I just want to say that I love this! I love that you mixed traditional questions (#1-10 and #14-18) with more innovative ones (LOVE the first #1 and #11-13!). I agree with the comment above that I would probably put #14-19 on a separate assessment, but they’re not completely out of line here. Great job and thanks so much for sharing and for being brave enough to go first!

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