Monday, October 1, 2018

Google Forms Pre-Assessment

My non-AP Calculus class is about to start our limits unit and I wanted a better picture of what they remember from last year to inform how I lay out the unit. A little background: my kids are coming from a variety of places including Pre-Calc Honors, Pre-Calc Advanced Topics (an advanced functions class- the "non-honors" version for our school), crash course community college Pre-Calc over the summer, and some even from Algebra II. I wanted to try something new to get feedback from kids that would also mean I didn't have to wait until I saw them next, so I threw together a Google Form using my answer key. 

For each question, I posted my full solution to the problem, then asked students to tell me if they got it correct or not, how confident they felt on the skill, and then an extra space for comments. Comments were optional, but kids have been sharing some interesting feedback on there. Here are some screenshots of the form:


It's been most interesting to see the correlation (or lack there of) between kids getting a question correct and their confidence. It's helpful to see that kids got something correct, but still didn't feel confident in it....a nice insight outside of just what percent of kids "knew it." 

I shared a bit.ly link on the handout and told kids they could only receive credit if they filled out the form, so there's incentive to actually do it. I'm using it to plan out where students will need support and where we can move faster than I'd expected. 

Definitely a trial run, but so far so good! 



Tuesday, September 25, 2018

Unit Circle & Exact Value of Trig Functions Review Activities

The Unit Circle is my jam. Last year, I even went to a tattoo parlor and asked them to slap one on my forearm (to which they replied that I'd need to do it much bigger if I wanted the detail I requested...so that saga continues). When I taught Pre-Calc, it was truly my favorite week of the entire year. But now that I'm teaching all things Calculus, there's less time for the beauty and elegance and just a short window for rapid fire review. My AP students are assumed to know it backwards and forwards. My school level Calculus students needed a bit more work with it based on my pre-assessments, so I did a few new things to practice with them! 

Unit Circle Hula Hoop Puzzle

I gave each group a hula hoop and had them align it with the floor tiles to form a set of axis. From there, each group was given cards with all radian measures and all coordinates of the unit circle. 


You could go even further with this and include degrees, but I wanted to make sure the students were starting to think in radians from very early on in the year. I figured I would give them 2 minutes to try to label everything, but this turned itself into a 15 to 20 minute activity with an amazing debrief. 



As I walked around the room, I noticed some great strategies. I took note of them for next year and I want to create some kind of guiding questions displayed to lead our conversation. Here's where the convo wound up going today:

  • Where did your group start? 
    • Students started with quadrantal angles (which was a word they couldn't tell me before this convo, so glad it came up), then divided from there
    • They were able to check themselves by thinking about the order the radians should go around the circle. I saw one group specifically calling each other out for putting ⅚π in the 3rd quadrant because it clearly had to be less than π. The idea made sense and I saw a few kiddos who'd clearly just tried to memorize their way through this in Pre-Calc have the logic behind it click. This took a huge working knowledge of fractions which is somehow still a struggle for kids who've successfully made it to Calculus. 
  • What did you do when you got stuck?
    • For my group, this seemed to be on the coordinates. The angles took some discussion, but they were able to reason through it together. The coordinates were a different ballgame.
    • Students were at least able to sort the coordinate into quadrants. Many were able to think about the reflections that take place to make angles with the same reference angles have related coordinates. All of these ideas were integral to where we'd go after this- reviewing the circle and how to use it. 

Exact Trig Values Speed Dating

After a brief review and a few practice problems, we were ready to practice! Instead of just a worksheet or a Kahoot and trying to get my first block to wake up already, I decided to make them start wandering. No pre-planning required...this one was easy to wing! 

1) Get a whiteboard & marker
2) Find a random partner
3) Answer the random exact value question Mrs. G puts on the board with your partner
4) Boards up!!
5) Class Discussion (if necessary)
6) Find a new partner and repeat

This not only gave me the chance to get kids working and talking, but I liked that I could go over each question and check in with kids I saw struggling. 

I have a whole library of other activities I've done with Pre-Calc classes in the past, but I really liked these for a group that only has 1 day to review all of this! 




Sunday, September 23, 2018

Methods of Finding Limits Error Analysis

My AP Calculus students just took their big Limits quiz and before we dive into Continuity and IVT, I wanted to make sure we solidified some sloppy issues I saw pop up.  I designed this activity based off actual errors from student work, hoping for a little personal reflection before they ever get their quizzes handed back to them. I'm planning to use this as an intervention tool with my struggling AP kids, but then a teaching tool with my school level Calculus kids.



I started this by simply having students choose a technique to evaluate each limit, without actually evaluating. I hope this will be a catalyst for conversations within the group and a baseline for students as they move into the next part of the activity.


The 2nd part of the activity shows examples of mistakes from the quiz that I rewrote in my own handwriting to avoid any embarrassment. Student will need to find the mistake and then fix it. One of my favorite parts of these mistakes is that often they do not lead to an incorrect answer. My Calculus students need to get very used to attending to notational precision in their work and there's no better time than the present for that!

There's a good mix of Algebra and Calculus mistakes throughout the activity, but they definitely lean heavier on notational fluency than anything else.  

Feel free to use as is or modify as you see fit! Also, if you have any common issues that you see with your students and limits, feel free to send them to me so I can add them to this! 


Monday, September 17, 2018

Rational Functions Who Am I? Activity

Pre-Calculus has always been my first baby. As a new teacher, I was thrown into Pre-Calculus and it quickly became my pride and joy...I experimented, learned, and fell in love with teaching it. Not only was it the best preparation I could have had for when I finally got to teach my real, true love (Calculus), but it also helped me connect my knowledge of algebra, geometry, and more in a way I'd never done as a student.

This year I've started teaching a school level Calculus class and it's been so much fun to delve back into some Pre-Calculus topics that I don't normally get to review with my AP kids. This activity was a great review for my students to get them talking, factoring, and thinking. It didn't take long, but generated some good conversations. It would also be a fun extension to have students write one of these "Who Am I?" activities, which could be used for any topic in any course! 


Feel free to steal or adapt! Let me know if you make any meaningful changes! Here is the file:


Here's some more of my thoughts about rationals from past posts, if your in the market! 




Tuesday, August 14, 2018

#MTBoSBlaugust Day 8: Oh The Places You'll Go!

I have been lucky in all my years of teaching to have a "senior" level class each year. For a few years, it was 8th graders- top dogs going off to the wide world of high school. For the majority, it's been Pre-Calculus or AP Calculus with some of the most wonderful 18 year old humans the world has ever seen.

One of the things I try to do with my seniors is give them a space in the classroom that is all their own. I bought this poster as a heading for the corner:


I chose it for a few very specific reasons:
  • Dr. Seuss is a boss
  • It was available as a Prime item (an instant sales tactic)
  • I like that it doesn't specifically mention "college" or anything else like that- just "the places"
I keep a set of blank "pennants" in a folder near the wall and I encourage kids to post anything they're excited about there. They can decorate to their hearts content or they can just fill it in. They can fill out as many as they want.  For some, that looks like this. 
Always an added bonus when you get to celebrate an acceptance to your alma mater (Go Bearcats!)

Some students have upwards of 10-15 pennants on the wall by March, posting every acceptance they want to share there. This board has seen big names: Yale, Cornell, Duke, Syracuse, UNC Chapel Hill, University of Texas, and many more. But I wanted this board to be a place to celebrate anything that my seniors are celebrating about their life outside high school. For some of those kids, that doesn't mean a 4 year school. I've had kids post military commitments, jobs, community college, missionary work, and gap years. Not only is this good for my seniors- giving them a sense of pride and ownership- but it's also a place where my underclassmen can get inspired by the things their older counterparts are accomplishing. Most fun for me, it brings kids rushing into my room first thing in the morning- sometimes long before their class-  to share happy news with me or confide in me if they're disappointed. They ask their friends to "wait up" after class so they can stay and share something with me. It's such a simple thing, but it's been a powerful tool in helping me connect to my kiddos at a scary and exciting time in their lives.

If you teach seniors, I really recommend trying this. I don't have pictures of last year's wall since my room is being used for summer school, but I'll take some and post them in the future! 

Wednesday, August 8, 2018

#MTBoSBlaugust Day 7: Using Google Drawings to Encourage Student Independence with Technology

One of the things that was most daunting about beginning to integrate technology into my every day instruction was the thought of having to do any instruction in the actual use of the tech. As much as we think our kids are digital natives, there's a cruel reality we must face. For many our my kiddos, this was the extent of what they could do with technology:


If it wasn't social media or a video game, my kids weren't buying it. And trying to explain the things that need to be clicked in the correct order to a class of 30 kids who may or may not be listening was daunting. I can vividly remember saying the same thing over...and over...and over...and over the first few times I tried a new tech tool. And while some of the kids caught on quickly, I found it hard to balance the kids who were moving ahead of me and the kids who were lagging behind. 

Looking for a tool to create more student independence, I started playing with Google Drawings and it's been my go to tool ever since! If you haven't tried it before, start in your Google Drive: 

See how you just did that....on your own? 

That's because you just used a Google Drawing I made to show you exactly where to look! 

It's very easy to insert images (often screen captures of the tool you're using) and then edit then by adding text, shapes, arrows, callouts, and more. You can also add multiple pictures to one drawing, add charts and diagrams, and add word art. 


You can download the image as many different things, but I usually use JPEG since it's easily inserted into a Word document or uploaded to my website. 


Here are some examples some I've made for my kids in the past:





These can be easily copied, pasted, uploaded, and shared! I put them into student worksheets so kids can work at their own pace and I'm free to move about the cabin and help as needed! It's been a life saver for me (and my own sanity) when teaching with tech! 

Tuesday, August 7, 2018

#MTBoSBlaugust Day 6: Continuity, Limits, & L'Hopitals, Oh My!

PLT PICs at NASA
I was extremely lucky to have an out of this world (get it, get it???) PD experience this summer- going to Houston to attend the Advanced Placement Annual Conference. On top of that, I got to attend with my Calculus PLT PIC (yup....professional learning team partner in crime- because there are never enough acronyms in a school setting). She just finished her first year of teaching AP and I finally have enough under my belt to apply to be a reader, so we were coming from slightly different perspectives. Both of us knew one thing for sure, though....we could not stand to hear another word about L'Hopital's Rule by the time we left.
Anti-L'H's sentiment on conference notes

The big issue was this- there's been a lot of debate online all year about the way L'Hopital's rule is justified. Understandably, the College Board has asserted that it is mathematically incorrect to say that something equals 0/0 since 0/0 is indeterminate. This caused some unrest in the Calculus community, since many teacher have allowed students to write this for years. Easy enough adjustment for my PLT to make...make sure students evaluate each limit separately. But we got a new curve ball this year that brought some amazing scoring statistics with it. Question #5 from the AB exam was a relatively straight forward question- average rate of change, evaluating derivative, candidate test for absolute extrema, L'Hopital's Rule. 



So why oh why did only 0.013% of students (under 30 worldwide) get full credit on this question? 

The answer came from the scoring guidelines, which allocated 3 points to part d instead of a more typical 2 points:


If a student didn't state that g was continuous, they missed a point. Any while logically we know that this must be true, I think very few of us as Calculus teachers would have expected our students to state this explicitly. This was discussed ad nauseam in many sessions and left me thinking how I could better prepare my students for this type of more rigorous justification. I knew it needed to start during my limits unit and then continue throughout the year. Most importantly, it needed to have my students analyzing why a limit can be evaluated and when it does not exist vs cannot be evaluated because we are missing necessary information. 

Here's the activity I designed to start my students thinking about this during the first unit. 



I've attempted to use multiple representations, lots of notation to build fluency, and to scaffold up to 2 questions more like the part d on the AP. I also am trying to help kids distinguish between when we need more information, when we have enough information, and how to justify all of that. I will be emphasizing that it doesn't just saw "evaluate," but it also says justify! Please feel free to send feedback! This is still rough and a work in progress!