Tuesday, January 16, 2018

Learning to Live-Stream: Review Sessions from my Couch

This year has been a hot mess of delays, snow days, and general schedule interruptions that have gotten me a little jumpy about my AP pacing. Yes, I know the exam is a week later this year. Yes, I know I had 5-6 weeks of review the last 2 years. Yes, I know we started behind since our Pre-Calc courses didn't get to cover the final unit as thoroughly as in years past. But like most teachers, I have my "checkpoints" of where I think I should be at certain points in the year and midterm week has gotten me feeling a little spooked. 

My kids wanted a bit more review that I just didn't have the time to give them for our last test, so we came to a compromise....I would figure out how to do a live stream review if they would watch it. We'd try for an hour the day before the test and see how that went. 

Anyone who has been around my blog for a while knows I'm a huge devotee of Notability and knew I wanted a way to live stream my iPad so  I could write by hand. After doing some research, I came across AirServer,  which took my normal airplay capabilites and allowed me to tie in live streaming directly to YouTube. Students saw my screen and a small image of me in the corner....good for the Italian in me who needs to talk with my hands constantly. 

I knew I should have majored in interpretive dance of ladders falling down a wall at a constant rate. I truly seemed to have missed my calling. 

My favorite feature of doing this was that students could interact with me live, so it wasn't just another video they were watching....they could actually chat. I gave them option of either using the chat on the live stream or if they didn't want everyone to see their questions they could send them on Remind. Questions looked mostly like this:

But occasionally like this:

A nice part of having the questions come in Remind meant that I had the power to answer whichever I chose....ignoring the horse sized duck I was about to take down until a more appropriate time in the conversation. 

The kids seemed to enjoy it and I saw big payoffs on their test. I am going to be trying it again this week for my midterm review with younger students...we will see if it's as beneficial for non-AP students. Though more than 2/3 of my class watched and interacted on the live stream, only 6 filled out my feedback form (THANKS, GUYS). Here's what they had to say:

And my final favorite feature?

YouTube archives the live stream so it can be accessed immediately by students who weren't able to watch live or who didn't want to watch live. They can speed it up or slow it down or just skip to the parts they need. 

I will definitely be tweaking for next time, but overall I thought it was a positive first attempt and reached students in a really accessible way for them on a day when they otherwise would have been unable to have the chance to review with the help of a teacher. 

Sunday, January 14, 2018

Dilation Constructions Mini-Project

As you may know from wherever you are currently reading this, it's been quite a winter so far in the great Northeast. We've already used 2 snow days and have had a 2 hour delay for cold, along with a fair number of cancelled after school activity days. Not to mention we've had a ton of stomach bugs and the flu bouncing from student to student like a pinball game. Needless to say, the best laid plans of math teachers have gone astray once or twice.

Since we run on an A/B day schedule and almost all of our time lost has been on B days, one of my geometry with lab classes inevitably zoomed in front of the other. In an effort to get them back on track, I designed this mini-project for my class that was light years ahead. I liked that it was creative, gave them some choice, and had them really practice the skills of constructing a dilation. Understanding the construction so strongly ties to the conceptual understanding of both dilations and similarity, so I knew this wouldn't be time wasted. 

You don't need much for the project. To prep, I printed tons of tiny images of famous characters. I went cartoons, but you could have kids bring in their own or design their own "logo." I had students put a dot at the center of the top of a sheet of printer paper, then glue down the original. This would be our pre-image and our center. From there, we started constructing! Students identified significant points and then created a "connect the dots" to help them draw the dilated figure. Many experimented with scale factor, trying to find the one that would be the largest without falling off of the page. 

After completing their dilations, students wrote a reflection relating what they'd done that day to the Desmos activity (Working with Dilations) we'd been working on prior to the activity. They needed to discuss center, projection lines, scale factor, and ratios. I've seen this play out in a deeper understanding of dilations in the remainder of our unit and a stronger ability to work with centers off the origin and dilations off the coordinate plane in general. 

Here are a few of my favorites! 

Thursday, January 4, 2018

Perimeter & Area of Similar Figures

We're in the heart of our dilations and similarity unit in Geometry and my students have started being surprised when we aren't using the computers that day. So thankful for our recently expanded access to more devices for our kiddos. 

I love starting my unit with this amazing Working with Dilations activity. It builds the concept of similarity from similarity transformations, which I love. It also helps students visualize how the center of dilation and the k value influence the image. It made the compass and straight-edge construction for a dilation a "duh" kind of moment....OF COURSE that's how you do it! 

Students doodling on pattern
block mats to show their thinking. 

I designed the next activity so students could discover the relationship between scale factor and ratios of perimeter and area. Students use a combo of interactive shapes and pattern block mats to discover the pattern! I took the idea from a Big Ideas Math activity and adapted it:

Perimeter and Area of Similar Shapes Desmos Activity

Overall, it went well. My students this year are struggling a bit more with abstraction that they have in the past, but they enjoyed the activity and once one person in the group saw that pattern they were excited to see it for themselves.

Feel free to steal, adapt, or offer suggestions for improvement!

Monday, November 20, 2017

WODB for First Derivative Test

Using this as a warm up after our first day of curve sketching. Feel free to use or offer feedback, if you have any! 

Wednesday, November 15, 2017

Find My Mistake Activity- CPCTC

A CPCTC activity where each proof has something wrong and students need to find and correct it! I usually have students work in teams at stations around the room and record what they find wrong with each. Often, I'll put in one "correct" proof so they have to find the one that has no mistakes, but I decided not to on this one. Since I'm using this for my Geometry with Lab class, I wanted to give them a chance to practice proof analysis without the extra confusion. I'll add in that layer as we move on into more sophisticated proofs. 

Side Note: I don't let my kids say CPCTC until like February. By that time, some tutor or another has told them my well-kept secret and they're begging to use it. Until they can perfectly explain to me what it means, they don't touch it. You'll see no mention of it in these proofs! We instead talk about the fact that is triangles are congruent, the corresponding sides or corresponding angles. 

Mean Value Theorem Free Response Critique

Every year the justification of Mean Value Theorem is something we spend a lot of time finessing (a new favorite word of the senior class here...any other schools seeing this?) over the course of a year in AP Calculus. The students understand the concept, but struggle with accurately justifying the situation. We started MVT last class and as a warm up today I did this activity with them. 

I gave each set of partners about 5 minutes to complete the front page and then we discussed- what are the "giveaways" that you should be thinking about MVT? What are the conditions that need to apply? How would YOU answer this? 

Then, I had them flip over to the back and do a critique of 3 arguments with their partner. Each one could some tweaking, although one did receive full credit on the AP Exam. 

The third section I left blank intentionally, so I could move around the room and see what students were putting on the front side of the page. This way they could critique their own answers in light of the responses they saw. Here's what I had them write in based on what they were writing with their partners:
We got to discuss the importance of using the same notation for the function in the problem (using g, not f) and the importance of the justification part. 

Here's the activity! 

We will be building on this next class as we spend an entire day trying to differentiate between when to use which existence theorem and looking at some more interesting AP style questions. Feel free to send any suggestions or other favorite MVT activities my way! 

Sunday, November 12, 2017

Basic Triangle Congruence Proof Tools

I'll be honest- I wasn't quite sure how the start of triangle proofs would go with my Geo with Lab students this year. Not because they aren't capable, but because they were so scared! With students who already have some math anxiety, the anticipation of starting a famously formidable topic was hanging ominously over the classroom our very first day. They had heard things from their older sibling and friends and judged proofs before they ever even gave them a chance. So far, so good, though. No tears. A few "why did everyone make such a big deal of this?" comments. I count all of those in the W column. 

I've been scaffolding proofs slowly, a little more each day. We've been using this super basic graphic organizer to plan before writing anything, making a constant analogy to how your English teacher asks you to outline a paper before you write the final draft. Knowing where your headed before you ever start makes the destination easier to get to, for sure. I printed about 8 of these to a page and have them in sheet protectors in my room so kids can write on them with dry erase markers with no commitment as they plan. I also have a bunch of extras that they can pick up for homework or use on quizzes/tests if it helps them. 

Here's how it looked in action on our first day:

Here's a link if you're interested in using or adapting: 

I also designed this really basic sorting activity for triangle congruence. I know there are a ton of these out there already, but I wanted something targeted for my type of kiddos, who need to build some confidence and hadn't been exposed to everything yet. I didn't even use this with my standard level class because they were ready for more open-ended activities more quickly. There are 3 proofs and all the statements and reasons scrambled for each. My students at this point hadn't seen HL or CPCTC yet, so these are really just getting them to engage with the very first steps of proof. It went well with my kiddos and made them feel some success, which is really half the battle in a lab class. 

Steal away if this would be helpful to you! And as always, feel free to offer suggestions if you see room for improvement! Happy proving!