Modeling Monday: Stronger Passwords

Our second Modeling Monday lesson for the 2016-2017 school year was both intriguing and applicable to our students. Remember that Modeling Monday was designed to give our 6th grade through 12th grade math classes an opportunity to do a lesson that wasn’t necessarily tied to a specific content standard. It has more to do with thinking and reasoning and experiencing, than securing knowledge on a particular topic. Our Math Team TOSA choose Robert Kaplinsky’s lesson on How Can We Make Stronger Passwords? lesson as the basis for our lesson this go around.

We like to have something for the students to create so we made this poster for each of the groups to fill out. Most teachers, including myself, had the poster rotate between the group members to give everyone a chance to write. The lesson itself first went into the basics of simple passwords. This was especially important for the lower grades who had not experienced the idea of probability yet. After this, we explored how many possibilities a password could have if it was just 8 digits. Then we calculated the possibilities for a 10 character password using lowercase letters, uppercase letters and numbers (basically my Netflix password!). Finally we considered a 13 character password using the same options as before with having 8 symbols added to the mix of choices (this is the password I use for all my “teacher” stuff). After these calculation we looked at how “safe” they were based on an article that says a super cluster of computers can cycle though as many as 350 billion guesses per second. The students were amazed at how “unsafe” some of their own passwords really were!

The groups discussed what makes a “strong” password and what they would recommend as password requirements if they were setting the rules. Throughout the lesson we talked about the types of passwords we all have (phones, emails, debit cards, garages, online shopping sites, social media accounts, lockers, etc.) and why we even need passwords. I told them “back in my day” we didn’t really have passwords other than a locker combo.

Some levels went as far as to develop and equation that represented the number of possible passwords. We then graphed it with Desmos, and thanks to the sliders feature were able to see the impact that adding each type of character had on the overall total. Students came to the conclusion that if we just had a digit password, it takes a good 17 of them until the password gets “good” enough to not be hacked!

A colleague of mine had his students come up to his computer and enter in one of their passwords to this website How Secure is My Password. I happened to walk into his classroom when they were doing this. It was an eye-opener for many of his students!

I appreciated many things about this lesson! It was super applicable to my life and my students’ lives. It involved exponents, scientific notation, unit conversion, and probability to name a few topics. It had students working collaboratively at some points and independently in others. It used Desmos, which is always a plus. It was a good little Modeling Monday lesson and a nice way to return after our Thanksgiving break!

Modeling Monday: Election Edition

(The following post is a republishing of an article I wrote for the Los Alamitos Unified School District’s Math Newsletter “To Infinity and Beyond” from October 12, 2016.) Our first Modeling Monday event of the 2016-2017 school year can be described in one word – EPIC! All students in 4th through 12th grade experienced the same lesson on Monday, September 26th and centered around the idea of being an informed citizen and consumer of information. This being an election year has given us a unique opportunity to connect learning to current events. Here is how the project was developed, a short summary of the lesson and a few highlights on how different sites made it their own. Project Development and Rationale Back at the beginning of the summer, a group of high school teachers across the disciplines got together to explore the idea of “connected learning.” With the election as our platform, the groups came to a decision to have each subject team design a lesson(s) that focused on being an informed citizen. This project also allowed the group as a whole to address some of the Career and College Readiness Anchor Standards for Reading – which all educational stakeholders have a responsibility to contribute to. Each content area would do something that fit naturally in their domain. The math team wanted to be the subject to “kick it off” the event that would take place in various classrooms during the month of October. After much hard work and sifting through lesson ideas, it was decided to have a two-part lesson. Are You Informed? Lesson Summary The first part of the Modeling Monday lesson focused on graphical representations of data. This would include lots of discussion between students and would ask students questions they don’t normally get during a math lesson. The students were guided through a series of charts and maps all representing voting data from the 2012 Presidential Election. Each map had a new story to tell! Students were asked what they wondered about the chart breaking down the electoral college vote and the popular vote, how they could make the maps better, as well as make observations and look for patterns. They were asked how a certain map made them feel and if they preferred one map representation over another one. The discussions students had as they progressed from map to map were priceless. They were asked to think about the maps as a type of text to examine. The second part of the lesson was on gerrymandering and provided a chance for students to try their hand at district boundary drawing. After watching a short video explaining the concept of gerrymandering, students tried to create boundaries that satisfied a specific outcome. The students got really creative and clever about the district boundaries and were able to create so many viable options according to the constraints! Lesson Extensions and Adaptations What made this lesson exceptionally cool was the way that each teacher made the lesson their own! There were so many spots in the lesson that individual teachers and content or grade level teams interjected a spin of their own. Here are a few examples from around the district: History teachers from Oak took the reigns on the Friday before Modeling Monday to frontload all of the students with important vocabulary on the electoral college vote versus the popular vote and what gerrymandering was all about. (Fun fact: The following week when the 6th graders were asked to vote on how they wanted to review for their upcoming test, they replied with, “Popular vote or electoral vote?”) 4th and 5th grade students at Lee and Hopkinson watched a couple of Brain Pop videos on voting and presidential elections. A few high school classes went into more detail about the fifth map. They investigated and tried to synthesize why certain areas voted the way they did by comparing the various shades of red and blue to other maps they looked up which included cities and roads as well as maps with geographical features. The sixth grade math classes at McAuliffe took two days to finish the lesson, did not include some of the later maps and instead spent quality time digging deeper into the early ones and then on gerrymandering. Several teachers at multiple sites gave their students something to vote on right there in class to illustrate the differences between the electoral college and popular vote. A teacher from Oak asked their students to respond on a sticky note which map was their overall favorite and write a sentence explaining why. Lots of classes, at all levels, decided to not do the gerrymandering part of the lesson and instead spend more time on the maps. These are just some of the examples of how various teachers were able to adapt the lesson to fit their own needs! A Team Effort I would be remiss if I did not give credit to the fantastic team of teachers that worked on this lesson! Vicki Gallagher and Josh Pixler, along with myself, worked on putting the lesson together from scratch (with a lot of help from Google Image search!), Math Team TOSA (Juliet Gardner, Bret Lynes and myself) worked on the specific, simple but thoughtful, questions we wanted to ask our students, and several other English and Social Science teachers at the high school helped us define vocabulary, refine our targets for the lesson and help us use the correct academic vocabulary. To everyone who helped put together what some are calling, “The best Modeling Monday yet!” – THANK YOU!!

Series Foldable – AP Calc BC

Ahhh, the dreaded chapter in AP Calc BC, SERIES (sing dun-dun-duuun!!). I get it, there is a lot to remember, especially when it comes to the tests for convergence or divergence. We have been using a wonderful packet of material from Master Math Mentor, but we need something a little bit more “handheld” as an easy reference guide. A foldable to the rescue! (I got the foldable idea from a fellow colleague, who got it from another colleague. Yay, for sharing is caring!)

I wanted this one to be slimmer so I cut the paper in half lengthwise and we needed lots of spots for writing, so I needed 6 different colors. We gave each test a section (filled it in as we learned them) and on the back pair of pages we glued in a flow chart to help us decide which test to use. I actually got the flow chart from Teachers Pay Teachers, it was one of the best I could find and I figured my students were worth it. 🙂

Here is a picture of the foldable one section at a time in case you want to make something similar with your class.

I have seen and given to students many different charts and summaries of these tests for convergence and divergence over the years, but I am really digging this year’s version! It is slim, compact, stays all together, has a flow chart. What I like best, though, is that is all all in one place, but unlike a grid or a table, students can look at one test at a time and not have the other tests vying for their attention.

A Murder Mystery ala Precalculus

A team member of mine has a really great lesson using Newton’s Law of Cooling to solve a murder. We like to make it more fun than just “doing the math” to solve the problem, so we create a little scene to inspire our students! Here is this year’s set up complete with a dead body under a sheet and a “chalk” outline on the floor (gotta thank my son for getting on the floor so I could create that part!). We got smart this year and did one set up in a central location so all the precalc classes could use it (why we had never thought of that before this year is a mystery in and of itself!) I love this day and this activity!

Speaker and Scribe – Calculator Style

Knowing how to work your own calculator is sometimes just as important as knowing how to solve a math problem especially when it comes to logs! In my precalculus class we did an activity through our notes the other day to practice calculator work. We were focusing on word problems using log, ln and e. Once we got the problem set up to solve it was time for “Speaker and Scribe!” Here are the instructions:

It was very revealing for students if they knew how to operate their own calculator real quick! Knowing the right amount of parentheses to use was a huge eye opener! Plus this way they couldn’t just fake their way thought it, they were forced to work with someone and they only way to get the answer was with their partner.

I have heard about “Speaker and Scribe” used in other ways, but this really worked out well for my precalc kids!

Making Examples…Not My Job Today!

They say (whoever they are!) that the best way to learn something is to teach it. Today as part of my Precalc lesson on log rules they students did just that! We went over the rules, which are actually a review from last year’s math class, and then we did one example together. Then it was the students’ turn to be the teacher. Each student created their own example on their whiteboard. Then they traded whiteboards with a someone around them. Students then had to solve the problem in front of them and when they had completed it give it back to the author for checking. Students were thinking at that higher level that we strive for when they were creating their own problems. A lot of students found that creating and correcting their problem was not as easy as they first thought it would be. It was a simple thing to change in my lesson and it had great benefits. A deeper understanding of log rules…yes, a deeper appreciation for their lovely teacher…maybe that too! 🙂

Rational Exponents – “Teach My Lesson”

(#MTBoS Blogging Initiative Assignments #4)

Second semester has just begun and we spent the first four days of Precalc doing a little SBAC preparation by taking the computer based ICA and the performance task, and then going over it as a class. (Another post on that later.) So yesterday was our first time being back to our “normal” schedule. We started our chapter on Exponents and Logs (which makes students terrified because they totally didn’t “get” this topic last year in Algebra 2/Trig) and first up was “Rational Exponents.”

Janelle’s Brain: That was a good idea I had to make them grab their whiteboard when they came in the room – I hate passing out those things and the students just do it so very slowly. Having that reminder right on the first slide of the PowerPoint a good idea.

First was to review the “rules.”

Janelle’s Brain: This slide is super overwhelming! Good thing I have it showing just a bit at time. And is there a better way to get this info out to the students? I mean, these rules go way back to Algebra 1 class, they do still mix them up sometimes and but really the lesson isn’t designed to LEARN these, just be reminded of them, so maybe it is okay. Plus I know the lesson gets better later. But maybe this is not the best way to start.

The first example we do together. The students have whiteboards because of another part of the lesson, I decide to have them do the first part of the question on their whiteboards – writing the expression in radical form.

Janelle’s Brain: Good thing I did, because – yay!!! – spur of the moment teaching moment. I noticed that across the class the kids had three types of answers and only two of them were correct. I nab three boards from kids in the front and show them to the class. We talk about how they are the same and how they are different and how two of them are great and one of them could be better and how important parentheses are and remind them about order of operations. I reassure the one I grab the “not so good one” from that she was totally not the only one who had that answer and she is good with that. I think I have developed that “safe classroom culture” that experts always talk about so students are okay with making mistakes. Win – high five to self.

Now we get to the part of the lesson I am proud of and that we adapted a couple of years ago – “Two Truths and a Lie.” It is a good way to have lots of examples and the students can get exposure to common mistakes that they themselves might make. Plus we ask them to fix the mistakes and say what went wrong.

Janelle’s Brain: Hmmmm, these exponents, especially the fractions ones are super hard to read!! I hustle up to the front and read each problem off in my super slow teacher voice. I am reminded that I DESPERATELY NEED (okay, WANT) a new projector with higher lumins. And how do I even spell that word? And who do I need to talk to to make that happen. I thought that one day the Assistant Supe was in here we talked about that. Hmmmm…oh yeah, I am teaching right now…back to the students.

We plug along. We do one example together and then “Two Truths and a Lie” for another set.

Janelle’s Brain: Ooh, let’s explain WHAT we are going to have to do, before we do it for this example. I tell them to quickly write on their board what they have to do to simply with those fractional exponents. As a “class” they come up with a good answer. I have three students read off what their board says and we have the idea.

Last set of examples.

Janelle’s Brain: Yikes, this last set is crazy…30 seconds in I instruct the students to work together with their peeps around them. That new girl in the back who just transferred to me is working super well with the girl in front of her – good for them, that was easy.

Last example, a word problem, the students favorite. They answer it on their whiteboards.

Janelle’s Brain: Yep, they all got the right number, but not all of them put the units. I am usually super lazy about labels, so I remember that I am not supposed to be lazy and I am supposed to “attend to precision” so I make them all look around at each other whiteboards and put them back down to fix something if they feel they are missing something. Good teaching moment, even if it was a short moment. And a good reminder to myself.

Lesson over. Boards go back into the bin.

Janelle’s Brain: Overall that was good…I liked the discussions we had about the mistakes we made ourselves as well as the mistakes from the “Lie.” Lunch is next, happy face. I wonder if lessons like this are okay. Was it too boring? Was it effective? We will see when it comes to Monday and I see how the homework went.

 

Questions on Tests…Okay to Better

I have attended some trainings lately that have focused on asking better questions on tests, not just the same ol’ solve ’em kind. Here is a few that we had come up for our last Precalc test.

• We added this one. It really showed if the students knew their vocabulary and the differences between the graphs. (We were proud of this one!)

• We also added this one. I like that the students had to categorize the choices into what worked and what doesn’t. It felt very SBAC-ish.

• I had thought of including this question, but it ended up on the cutting room floor. Mostly this is because i felt we didn’t give the names of these tools quality time in class and this particular problem may be better suited to a group quiz situation where the students can discuss it with one another and then formulate a response. (So I am keeping in my brain as a quiz question for next year!)

• This last one was a test question, but I really felt it could have been better. I could have made it more open and creative for the students. I think a better version would have been to ask students to create their own polynomial of a particular degree, say 4, that had a specific number of each of the roots. Maybe next year on that one!

Writing test questions that cover the material but at the same time challenge the students to really show their mathematical understanding is a hard job! But I am always trying to improve and increase the amount of thinking I ask my students to demonstrate to me!

These Are A Few of My Favorite Things

(I hope you sang the title…I totally did as I was typing it!)

There are two things that are currently among my favorites that make my life easier as a a teacher. One is the Remind App and the other is my favorite review game.

Remind App

I first encountered this app with my twins’ first grade teacher. She used it to send reminders and updates by text to the parents. It was quicker and more reliable than e-mail. I thought it was so great that I should use it with my own students (who all seem to be very connected to their own cell phones). Here is how it works. I downloaded the free app, signed up and created my classes. One day in class I had everyone take out their phones and text a code to a special number. That’s it. We were all connected! I can text every single one of my students now. They don’t have my number, I don’t have theirs, but I can send them a quick message anytime I want. I send them reminders about study sessions, a note if I happen to change an assignment, pictures of an example we didn’t quite get to during class, a note telling them when their tests are graded and are up in Aeries, and I even once sent a recording of a song I made up to remember a rule by. I can even schedule them to go out at a later time. It is awesome, I use it weekly and my students appreciate the communication with them!

Fast Track

I totally got the idea for this review game from someone else, gave it a new name and adopted it as my favorite way to review. It is basically “Speed Dating” without any of the weirdness you might get between students. In southern California many of our freeways have a Fast Track lane that you can go in if you have a carpool buddy or pay a fee. (I went with the carpool direction.) I make my desks into rows. Each set of two rows, I turn the desks towards each other so that when the students sit down they are facing each other. (I also make sure to put spaces between the desks in the rows so the students can get in and out easily.) I have them put all their belongings along the edges of the classroom too, so no one trips over anything. Each pair of student gets a whiteboard, marker and eraser. Then we get to work. I put up a problem on the PowerPoint, they work on it with their “carpool buddy” and then at an appropriate time record and hold up their answer on their whiteboards. I check the class, usually there is some high-fiving if they get it right, and then it is time to move on to a new “car.” Only one “side” of the row moves at a time – they move to their left (or snake around to a new row) – and then it is on to the next question with their new carpool buddy. The new pair works together, report their answer and then the other side of the row moves to their left. This way you never work with the same person twice! I even created a playlist in YouTube of songs that have to do with cars or driving or roads and I play it from my iPad connected to my speakers when the students are moving to their new car. I have done lot of different games over the years and this one seems to work the best for me as a teacher and, most importantly, for the students. They have told me that they like working with all the different people in class and that having a time limit for problems really keeps them on task. Here are a few links to a PowerPoint and a worksheet for one of the times I used Fast Track to review with my Precalculus class.

 

Here is a worksheet of the review problems Fast Track Ch 9 WS

Here is the accompanying PowerPoint PC Ch 9 Fast Track

Here is my YouTube playlist Fast Track Songs

A Day in the Life of Mrs. Fox

(Here is my #MTBoS Assignment #1 – Tuesday, January 12, 2016 Total disclaimer, not all days are this crazy, but many of them are!)

5:45 Alarm goes off

6:05 Finally roll out of bed (ooh, that snooze button) and start getting ready

6:31 Go wake up my three kids, go back to getting ready

6:38 Go back and wake daughter up again. (Two thoughts to self..1-I really need to buy alarms clocks for the kids on Amazon, 2-The blow dryer I picked up yesterday at Target is working great.) Boys start making their own breakfasts, I make mine and daughter’s and help son load up that dishwasher we forgot to do last night, and eat while doing a quick e-mail check.

7:22 We are all out the door, in the car and headed to school

7:37 Kids are dropped off in the loop and I am headed down the street. The line of cars to get into school at this time of the day is always so lovely (hope you sensed the sarcasm).

7:45 I am in my classroom, time to finish up the things that were on yesterday’s Things To Do post-it, put the finishing touches on the Calc project I am introducing today

8:03 Get in line for the only copy machine that will take colored paper that is working today

8:05 Short line, I am copying, woot! Drop by the main secretary’s desk to pick up something she printed in color for me, return the extra pink paper to the math office, remember I have to wrap that wedding gift for Faculty Club

8:22 It is back to my classroom, I need to update the side board with today’s agendas, locate the calc project notes for myself and remind myself how to introduce it and how to do the Excel spreadsheet, make a mistake, sort it out, look at precalc lesson for later today, draw picture from yesterday’s notes on the board that we didn’t quite have time for yesterday to do it justice

8:55 Time for class! Give Calc BC their warm-up quiz, call a colleague to answer his question about the precalc notes for today, go to stamp homework , get reminded that I am not stamping today (yep, oops!), talk about that problem from the notes from yesterday about rotating a region around a line that is parallel to an axis, answer lots of questions and what-ifs (this section is a doozy!). Introduce project, do a baby example and show how the Excel speadsheet works, set the students to work, they get into groups of their own choosing, and I rotate through the classroom checking in, offering advice and answering questions

10:03 Rinse, repeat. Remember to mention the previous classes “what-ifs” when going over that example from yesterday which inspire even more what-ifs.

11:04 Time for precalc, no time for homework questions today (Thoughts to self while I am teacning: bummer that notes take forever, I am probably taking extra time getting whiteboard feedback from them, maybe this chapter should have fill-in notes, I should talk with other precalc teachers about this idea soon for next year, and it is a good thing that we have an extra review day before the quiz)

11:58 Lunch! Time to find my math teacher friends and talk about things that have nothing to do with teaching

12:35 Head over across campus to a LAHS TOSA meeting we called ourselves. The Tech TOSA, English TOSA and Math TOSA are hashing out what is the best way to attack having practically all our students take the  SBAC ICAs right at the beginning of second semester. We chat, catch up, think about the best way to schedule and borrow some carts of chromebooks from the social science teachers and we think about what our less technological colleagues will need from us in terms of an instruction guide. We each have our assignments and we are going to pow-wow back together next Friday. (Tech TOSA was super excited to hear about my #MTBoS assignment and is proud that I am getting my Twiiter on.)

2:00 We are done, I head back to classroom, run into department chair and I quickly fill him in on what we just met about, he fills some in on a couple of other things, I rush out to head to a different TOSA meeting

2:20 Head over to one of the middle schools for a Math TOSA meeting. We meet every Tuesday at this time. Today I and my two fellow TOSAs from each of the middle schools are joined by the assistant superintendent. We have much to discuss as first semester is coming to a close. We talk about SBAC ICA, registration and class placement, some philosophical questions about what teaching looks like at the elementary level versus the middle school level versus the highs school level (that is a heavy subject, I am going to have to spend some more brain time on that one). When assistant supe heads off, we take care of some other TOSA business, Modeling Monday at the elementary level and last minute newsletter ideas.

4:18 Meeting over, chat for 5 minutes in parking lot with fellow TOSA whose daughter (who I had as my student a few years back) has just started a semester in Spain

4:40 Finally pull in driveway, super weird traffic on the freeway on the way home (it is only three miles…sheesh!)

4:45 Head right back out the door after changing into some comfy jeans and grabbing my Starbucks cup, stop at Subway to pick up a $6 special of the day dinner (Thought to self: radio advertising is really working, I am only here because of the commercial I just heard), get to Starbucks a few minutes early, get bummed because the one big table is already taken, but at least there are available tables, get my iced tea and get ready

5:00 My first tutoring appointment arrives, it is a precalc student from another school, we go over lots of stuff from trig. My principal calls during the session, but I can’t pick up, shoot!

6:00 Get a text saying my person is running late. Not a total bust though since I can eat part of that aforementioned sandwich I picked up plus check that voicemail from the principal. Big table becomes available, I swoop in and set up camp for the rest of the evening.

6:25 Tutoree finally arrives, (that was some traffic!), we cram in lots of precalc learning in 35 minutes, we make sure to schedule his times for his upcoming final next week (he is from a different school too)

6:45 Hair is officially now in a messy bun

7:00 Third tutor of the evening is here. Advanced Math Trig student from my school. He forgot his notes stuff at school, nice. We manage…at least he has his book. We bust out lots of work going over previous sections as well as hitting the current section really hard. (I see this student twice a week, he lets me take a tutoring selfie with him, gotta love him).

7:40 I get refill of iced tea (Thought to self: super love my Starbucks gold card and free refills!)

8:00 Fourth tutor, Advanced Math Trig again, so I am already in the zone! I have tutored her for several years now, so we take a tutoring selfie too.

9:00 Finally done with my marathon tutoring session!! So, so drained. Head over to my mom and dad’s to get my kids. (They have been there ever since my mom picked them up from school at 2:30. This usually doesn’t happen…weird schedule today with husband having to take in a dinner with the big bosses that are in from Wisconsin. So blessed to have them live so close and have my mom be recently retired from teaching herself that she can do this for our family.) They are bathed and homework is all done too. I catch up on the news of the day on the short car ride home.

9:20 We all walk in the door, husband got home just 5 minutes before we did. Kids make their lunches for tomorrow. I get all the homework signed off like we do every night.

9:31 Kids are in bed (Thought to self: yikes that is late, oops!). I get to work…first up, final edits on my To Infinity and Beyond newsletter that goes out tomorrow morning. Husband is watching the state of the union address, I am half listening. Add a section to request ideas for our net Modeling Monday, add a new link for Mathematics Framework from the CA Department of Ed, read over it two times, and schedule it to go out in the morning.

10:06 Catch up on emails, send out a few dropbox file requests for yearbook pictures (yep, I am the gal who foolishly volunteered to create the 5th grade yearbook), read the Marshall Memo I got this morning (Thought to self: Good stuff to think about, maybe for next time’s newsletter), check bank, Facebook (for just 5 minutes…okay, 8), back to emails, look over Coinstar Modeling Monday lesson I am previewing with the 4th and 5th grade teachers at my kids elementary school tomorrow (no pressure there).

11:04 Finally shut down computer, get out clothes for tomorrow, plug in phone (Thought to self: how in the world did it get all the way down to 17%? Probably all those pictures I and my students kept taking all day.)

11:35 Bed time (Thought to self as I am nodding off: I didn’t have time to write that precalc test I was supposed to, shoot…I will break news to the team tomorrow and promise to get it done on Wednesday.)

**When I choose this assignment for this day, I had no idea that the day would get so crowded. I guess it is because I kinda have three jobs…teacher, TOSA and tutor for my side gig. I truly do love all of my work, though, so I will keep at it. Here is I super funny thing I found out by taking on this assignment – I make all kinds of weird faces when I teach, maybe a good thing, maybe not. My husband says this is not a surprise to him. Another thing…the students I asked to take pictures of me teaching didn’t even blink an eye when I asked them to, I love those kids. One set of girls even made a little title on their whiteboard, too cute! I also had a fun thought that all jobs should have spots where the people around them just start clapping in appreciation at something well said like during the state of the union. I mentioned that to one of my calc classes yesterday, they dug it, they clapped a lot for me during the lesson – I admit it felt good!**

So, phew, there it is…a day in the life of Janelle Fox!