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!!