Factoring/Solving Quadratics – My Best Unit So Far This Year

Ok so it’s only the third unit of the year for Integrated Math 2, but my first was just meh (lots of beginning of the year trying to figure out how to teach again kind of stuff) and my second was definitely bad (very low test scores at the end even though I thought they’d do better). This unit not only felt like it was going great during it, but also ended with great test scores (highest of all the Math 2 teachers, but I don’t want to brag 🙂 )!

The unit was 19 days long, with one quiz and one test. Here’s what I did:

Day 1: Had to go over the previous test and then played this game to introduce the factoring process that I got from Simplify With Me.

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Day 2: Asked students to get a dry erase marker and eraser to write on their desk. I used Meg’s Guess and Check sheet to structure my teaching of factoring, but I added a little bit at the end for when there’s no b or c.

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docx: Factoring Notes      pdf: Factoring Notes

Yes, I know no c means there’s a GCF and no b means difference of squares, but I decided to make them just like all the other practice problems. In time, most students found the pattern themselves. Note: I taught a>1 before a=1. It was amazing. My students are used to knowing about the “invisible 1”, so when they encountered a=1 they just knew there were factors of 1 and 1. It saved so much time.

And I also accidentally left Meg’s bit about the slide and divide in there but in each class there was someone who said “But my sister did…” or “My teacher last year did…” so it was kind of nice to have it in there.

Day 3-6: Just a whole bunch of factoring practice. Each day I started by doing a problem together as a class, either from their homework or one that was challenging from the day before. Then I’d have some practice for them – A Kuta worksheet or one of the Algebra with Pizzazz worksheets. I usually let students just practice at their own pace. I also used some open middle problems as challenges for students that needed it. At the end of each class, I had students do a problem as an exit slip but then took their answers with Plickers. The next day, I would address the students that didn’t answer correctly. It was great to just have those days to practice without having the pressure to move on. On one of the days, I had students do a Desmos Card Sort with trying to find the factors.

Side note: I was in the hallway one day during the passing period and a student came out to speak to the Math 2 teacher next door to me, showing him a problem he was trying with the X method and he had to get the factors of some crazy number like 468 and was super stressed about it. I was reminded of how great the Guess and Check method is at that moment.

Day 7: Quick review and then a quiz. The quiz was awesome. I mean the students did great – only two out of 98 students had their grade go down from the quiz. Happy happy happy.

Day 8: Factor by grouping notes and practice. I started with another sheet from Meg, but really just ended up going through how to do it because of time and my students didn’t need the review of everything else. Then we just did more practice problems.

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Day 9: I described the Desmos Card Sort that I did here for practice. It was also when I had my formal observation.

Day 10: Introduction to Zero Product Property. I took Amy’s advice and did this game. It even got some students in my first hour to smile! Also, I got a laugh when I showed the first quadratic equation to solve that needed factoring and I was asking what could we do to get it to look like the problems we had already done (ones that were already factored) and someone shouted “factor” and I said “Yes, my favorite F word!” Haha still makes me laugh.

Day 11: Solving by factoring practice. Some with a GCF to factor out.

Day 12: Factor by Grouping and Solving by Factoring review and Mini-Quiz. Results were also good for this quiz.

Day 13: Showed a problem that wasn’t factorable and asked them to solve. Then introduced the quadratic formula. I showed them a video with the song to Pop Goes the Weasel. I also had the students do Sarah’s memorization assignment, which I thought I’d get some complaints from but overall the kids actually enjoyed showing off that they knew it.

Day 14-16: Solving by quadratic formula practice. I showed a different video of a quadratic formula song each day. The groans got louder and louder but I know that secretly they loved them all. I also had Plickers exit slips each day so I could see where they were at.

Crank That Quadratic Formula

One Direction Quadratic Formula

Solve Me Maybe

In these days I also threw in the discriminant to find out how many real solutions there are by having them try a bunch of quadratic formula problems with each type of discriminant to kinda push them to “discover” the rules.

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After that I also had a quick lesson about complex numbers. I had this from last year but I’m pretty sure I stole it from Meg since last year I took everything from Meg.

docx: Complex Number Notes    pdf: Complex Number Notes

BTW up until this I was able to tell students that they could do every calculation they needed with Desmos if they didn’t own a calculator, but here’s a place where the TI-84 can do a calculation that Desmos can’t. Or maybe it can. Can it?

Day 17-18: Review – my department has a rule where we give students a study guide that looks exactly like the test. Something I wish could be different after seeing Tyrone and Kelly present about Revamping your Review Day. So I did a review Quizizz and then spent a day on the study guide.

Day 19: Test that was a big morale boost for me and my students 🙂

Overall, I think the #1 reason this went so well was that there was time. It was the first time all year that I felt like I was not rushed. I know the students appreciated this, too.

J’aimerais avoir le temps de ralentir tout le temps.

 

Planning a Graph Transformation Unit

After Thanksgiving, we will be MAP testing for two days and then will have 11 days to complete the last unit of the semester in Math 2. This would give 4 days of final exam review. It is what all the other Math 2 teachers have. I would like to plan this before Thanksgiving so I can have everything ready just in case something happens that means I can’t do MAP testing (because we all know that technology can be difficult at the worst times). This is what they will have to do on their test:

  • Graph a transformation on an exponential function
  • Use the graph of a function to evaluate f(#)
  • Graph a transformation on a radical function
  • Use a radical function model to find when the population reaches a number
  • Graph a piecewise linear function (no evaluating)
  • State the piecewise definition for an absolute value function
  • Graph a transformation of another graph
  • Perform operations on functions (with a word problem thrown in there)

The other teachers are going straight lecturing from the textbook, two days on each section, two days of review, test on day 11. I will say right out that I don’t like lecturing for 8 days in a row. I’m determined to make my students actually think about functions over these two weeks. Take into account I have 50 minute periods, a class set of Chromebooks that take roughly 8 minutes to take out, login, and put away, a class set of TI-84s, and students that have never graphed anything more than lines and parabolas in standard form. I also just had the tech department put Desmos Test Mode on my Chromebook cart so I’m hoping that I can just have students use that on the test but we’ll see if my department approves.

What I want to do is:

Day 1: Discover exponential function properties (something with Desmos would seem fitting – Marbleslides?), make sure to write down what we’ve found, which should be:

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Day 2: Practice graphing exponential functions

Day 3: Compare transformations on exponential functions to radical functions. Possibly make a DAB. They should know this at the end:

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Day 4: Oh wait, these rules can be used for any function. Practice graphing transformations on functions in general.

Day 5: Graphing piecewise functions – I had done Lisa’s http://www.teachesmath.com/?p=60 in the past but I think because I have way less time I’ll try Amy’s method http://squarerootofnegativeoneteachmath.blogspot.com/2011/05/color-coding-for-sketching-piecewise.html because it seems pretty straight forward and fun.

Day 6: Practice graphing piecewise, try to throw some other functions in there so they keep practicing those. If time, do some Graphing Stories because those are fun and actually make you think about math from something besides a worksheet, but don’t really have a link to the test so not sure I’ll feel like I can do them.

Day 7: Operations on Functions – I’m intrigued by this from Sarah: http://mathequalslove.blogspot.com/2016/02/operations-with-functions-notes-and.html

Day 8: Practice more operations on functions, and graphing

Day 9: Review -probably Quizizz because their test is all multiple choice and they like it and I like it

Day 10: Review – go over most missed Quizizz problems, go over questions from study guide, if time do another game, like maybe Quizlet.live or Deal or No Deal or something small and low-key.

Day 11: Test

To be honest, I’m pretty down in the dumps about this unit in general. I feel like it has the potential to be really great but with the time and the way the test was made and the pushback I get from doing anything besides the textbook I feel like it won’t be so awesome. Maybe I’m just being pessimistic. I am really starting to miss the freedom I had to build my own curriculum in my old school. But then I think back at how stressed I was planning for 4 classes and I don’t know what I’d rather have.

Je suis désolée pour le pessimisme de ce post. Je suis un peu frustrée avec ma situation en ce moment.

Weekly Summaries and Class Twitter

I’ve written about my Weekly Summaries before. I still do them but I’ve updated them a little. Now, the questions are:

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  1. What did you learn in class this week?
  2. What activities did you do in class this week?
  3. How are you feeling about math class?
  4. Type your tweet (I am following after Annie Forest with her class tweets)
  5. Other comments

 

 

 

 

 

 

When they click submit, their parents (if they have given the school or me an email address) and I get an email that looks like this:

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So the grade automatically gets put in and the parents see their responses to 1, 2, 3, and 5 (that’s this student’s joke about the mathematician).

I love love love these Weekly Summaries. The hardest part is getting students to do them. Usually it’s me who forgets to have them get the Chromebooks. It’s not something they like doing on their phones because they have to log in to their account and that takes longer than a microsecond so they’re just not into it.

But I get a lot of good feedback (like this student who was failing but was feeling great about the current topic and ended up raising her grade to a D in the next week!). And parents (except two that asked me to stop emailing them unless it was an emergency) have told me that they really like getting these. It’s a good conversation starter at home and it makes them feel like they are more in the loop about their child. I loved getting these comments at conferences and frequently get responses back from parents over the weekend with questions or comments so it definitely has helped my communication.

You may have noticed that the tweets aren’t seen by the parents. That’s because I curate the tweets to put on our class Twitter. I usually use one tweet per period. I have the Twitter feed on my class website and currently have 5 followers…but some students have said that they just look on my website. I also post pictures from class on the class Twitter. I haven’t gotten any parent comments about it yet. Honestly I don’t know if any look at it. I just keep putting reminders that it’s there when I send my unit emails and, if nothing else, it’s nice for me to chronicle the year.

J’espère que les parents apprécient les mises à jour.

Desmos Card Sort Is More Than Just Technology for Technology’s Sake

I just had my first formal observation and it was scheduled for last period on day 2/2 of factoring by grouping (polynomials with four terms). I was a little stressed when I found out about the observation.

Luckily the #MTBoS is the best and Meg @mathymeg07 and Sarah @mathequalslove gave me great ideas that helped me de-stress. I ended up settling on a Desmos card sort for practice, mainly because my evaluator has already said how impressed she is with my technology use. I would just make a sort where the students would match a polynomials with its factors (3 cards for each set). That led me to tweet about how it was a perfect example of technology for technology’s sake, which made me feel bad but my plans were due the day before already (even though I had just been assigned the observation).

But then I was thinking about it…and it really isn’t just technology for technology’s sake. Using the Desmos card sort gave me and the students way more information than a regular old worksheet. Ok well for the students they got confirmation that their answers could be correct if they were on the screen (which is not much more than me just giving a scrambled answer key or something). But also they gained engagement. There’s something about being on the Chromebooks that is just 10x more engaging than a worksheet. Like, seriously, in all of my classes there wasn’t one time where I caught a group on something they weren’t supposed to be on. Maybe I’m just bad at catching it, but I’m gonna go with they were engaged. And no, my classes are not perfect little angels who just do whatever I ask them. But the pairs that were just sitting there doing nothing were quickly caught and re-engaged (read on for how).

Also, I gained so much more with the card sort than I would have with just a worksheet. Students were in pairs and I had them make their names both of their first names together so I could manage better. I walked around with my iPad showing the dashboard, and I was able to see their work in real time! No more making rounds around the room and not finding out until 2 minutes before ending that a group did everything wrong. No more letting a group wait there for 10 minutes because they finished early (or just weren’t working) and just didn’t say anything!

I wish I had taken a screenshot in the middle of the class (this is just the first four groups from a class that had already finished) but, for instance, I could see right away that the Stefan Banach pair had a mismatch and could go over to them as soon as I was available before they made more mistakes like that. I could also see, for instance, that Diego and Kurt were ready for some extension questions and challenges since they were done earlier. Or I could use this to see that Mary’s pair needed someone from Diego’s pair to help them out since they were stuck on that screen for a while.

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Also, it was pretty easy to make. I made an 8 question Kuta worksheet, made sure none of the factors were the same but that there were some similar ones, and then typed them in. I think it took me half an hour while I watched TV to make.

So yeah, I wanted to use Desmos to impress my assistant principal. But really, in the end, I did what I think helped my students and me have the best practice for this topic.

Here’s the links to the card sorts that I’ve done like this:

Factor by Grouping: https://teacher.desmos.com/activitybuilder/custom/581e0a5a39d984e1059501f3

Factor quadratic trinomials: https://teacher.desmos.com/activitybuilder/custom/5812d0b1b9d4312e2ae3f184

J’adore Desmos et je vais trouver n’importe quelle raison de l’utiliser.