# Math Teachers: Raid the Physics Supply Closet!

Physics teachers are just math teachers with better toys.

I gave this talk at Twitter Math Camp 2017 in Atlanta.

Outline of this talk:

1. OMG, data!
• (Materials that) Generate Linear Data
• Generate Quadratic Data
• Generate Radical Data
• Trig Ratios & Functions
2. Physics resources
3. The #PhTBoS & how they approach teaching

# Generate Linear Data

## Tumble Buggies

What this is: a toy car that runs at constant velocity. Pro-tip: With a fairly easy hack, you can slow them down so that you can have different constant velocities.

How it’s used in physics: Sample video. When we introduce the students to constant velocity motion, we use the buggies to get them thinking about motion in terms of position and time. We’ll create graphs, data tables, and compute velocities. In my class, I like to set two teams head-to-head to predict a collision location. I provide the starting points on a number line. Pro-tip: Lay down pennies to mark the location at one second intervals.

How it can be used in math: I love to have students plot the Tumble Buggy motion using Desmos — I doubt your physics teacher is using Desmos. Warning! It’s gonna be too easy to step on your physics teacher’s toes with these — if they have the buggies, they use them for the same stuff you would, too. Pro-tip: get a metronome app for your phone so that you can easily mark equal time intervals for observing motion.

## Knots on a Rope

(all the love to Steph Reilly, @reilly1041, for this idea)

What this is: a piece of rope at least 3 meters long.

How it’s used in physics: Tie an overhand knot in the rope and measure the new length. Collect data on number of knots in rope vs. length of rope. Plot length of rope vs. number of knots. Pay particular attention to the meaning of the y-intercept and slope.

How to use it in math: Please take this idea wholesale. It fits great in math class.

## Motion Detectors

What this is: a sonic rangefinder that works by sending out high-pitched sound to locate the distance to an object. Sampling rates are pretty high, maybe 30 Hz, so you can track moving objects. Combined with software, the motion detector can produce graphs of position vs. time, velocity vs. time, and acceleration vs. time.

How it’s used in physics: Early in a course, students generally study how position, velocity, and acceleration are related. Students will sometimes perform graph matching labs where they’re given a graph and must move their own bodies in front of a motion detector to generate a matching graph. Sometimes, the motion detectors will come out again with carts that can roll down inclined planes and again with freely falling objects that fall down toward the detector.

How it could be used in math: The motion detector pairs nicely with Graphing Stories.

## Inclined Plane

What it is: a track with grooves for carts to roll in (carts optional).

How it’s used in physics: all sorts of motion labs. This is quintessential physics equipment that nearly all labs will have in the closet. In a pinch, I’ve used wood molding purchased inexpensively at a home improvement store.

How you could use it in math: Get a marble or ball bearing. Release it from somewhere on the ramp and measure where it comes to rest. Repeat with a new starting point. Repeat.

# Generate Quadratic Data

## Motion Detectors

How it’s used in physics class: Be careful! Drop a ball so that it falls directly over the motion detector. We’ll put that data on a velocity vs. time graph. The slope of that graph acceleration (Δv/Δt). We’ll calculate the acceleration due to gravity. Some teachers might then switch to objects with significant air resistance but that’s rare.

How you could use it in math: Do the same experiment — drop a ball toward the detector. This time, though, look at the position vs. time graph. The object is accelerating. You’re gonna get a nice quadratic plot.

## Video Analysis

What it is: software that pulls position and time data from videos. Tracker is free. Logger Pro is a Vernier product that costs money but your school may already have a license.

How it’s used in physics: Can do anything a motion detector can but without buying dedicated hardware. I like to have students film throwing a projectile.

How you could use it in math: Especially if your physics teacher isn’t using video analysis, this is a fun tool for generating position vs time graphs.

## Visualize Quadratic Foci with Mirrors

Edit, added March 7, 2018

Shout out to Rachael Gorsuch for showing her math students exploring the focus of a parabola using a parabolic mirror.

# Generate Radical Data

## Pendulums (Pendula?)

What it is: a string/rope with a weight at the end. Grab a chemistry ring stand, some string, and a mass from the physics lab.

How it’s used in physics: most notably, pendulums come out when we’re heading into learning about waves. We want students to understand the idea of a period (of time) for an oscillation. Fun fact: students never really believe that the mass on the end of a simple pendulum has no effect on the period. The period of a pendulum’s swing is a radical function that depends on the length of the string only.

How you could use it in math: Set up a pendulum and collect data on length of string and period. Plot it. Bam! Now, I love a good function transformation, so this might be fun to play with a function stretch.

# Trigonometric Ratios & Functions

## Angle Indicator

What it is: a protractor and a plum bob, often designed to attach to a track, to measure the angle of tilt. Can easily be made with a straw and protractor. I also have used a phone app (iHypsoLite is one of several).

How it’s used in physics: to measure the angle of a track.

How you can use it in math: Go outside and measure the height of the flagpole, height of the school, or height of the football goalpost.

## Force Table

What it is: a set of masses that can be hung over the edge of a table, marked off with angle measurements. These strings make visible force vectors.

How we use it in physics: In the study of two dimensional force-balancing, we haul these tables out and set up equilibrium scenarios. Lots of possibilities here but my favorite is “what force will bring this system into equilibrium?”

How you could use it in math: OMG, vector addition! Dudes, just use this the same way we do in physics. Have a chat with your physics teacher that you’re not stepping on their toes by borrowing the equipment, though.

# Physics Resources We’ll Let You Use

We like to share as much as the #MTBoS does, so I asked the physics teachers if I could share these with you. They said yes:

• Frank Noschese’s Physics Lab Modeling resources from NCTM15.
• PhET simulations: Most of what you’ll want for algebra is under motion and for trigonometric functions is under waves. Ooh, there is a math section though I’ve never explored it.
• Direct Measurement Videos: This guy (Peter Bohacek, @bohacekp) up in Minnesota put together a video library and activity guides for a host of physics concepts. The cool bit is that each contains on-screen tools for taking all necessary measurements.

# The #PhTBoS

The physics teachers on Twitter may not be as large as the math teacher group, but we make up for it in enthusiasm. Seriously, here are some of the most helpful folks I know, regardless of content area. If you’re looking for a hands-on activity to do in math class but don’t know what lab equipment might already exist on campus, hit one of us up.

• Steph Reilly (@reilly1041) — was at #TMC17. Steph has taught physics and math and helped me prep this talk. She’s done many physics-y things in her math classes.
• John Burk (@occam98) — was at #TMC17 and is on Twitter 24/7, I suspect. John has taught math, so can understand where you’re coming from.
• Frank Noschese (@fnoschese) — he pretty much invented the 180 blog and his archives will give you plenty of ideas. Probably the most helpful person on Twitter, too.

Generally, physics teachers on Twitter are left of center on their pedagogies:

• We tend to eschew long labs heavy on procedures (“cookie-cutter labs”) for shorter, open-ended questions (“single-sentence labs“).
• A good number of us teach via modeling. There’s a Modeling Physics course some have taken, which emphasizes multiple representations, student construction of knowledge, and scientific argumentation. The Modelers use #modphys on Twitter. (My take as someone who dabbles on the fringes of this group.)

Meanwhile, the majority physics teachers probably teach the way you learned physics. A few notes about these folks, so that you can make friends and borrow equipment:

• Be careful that you’re not using the exact idea they tend to teach, especially if you’ll be stealing their thunder.
• Ask if they have ideas for experiments that generate a certain type of data. We don’t really think of the content that way but can totally pull out a phenomena that will give you a nice rational function graph if you need it (I’m looking at you resistors in parallel).

Good luck raiding the physics supply closet! And if you find some equipment you can’t identify, Tweet it out to me and #iteachphysics — someone will be able to tell us what it’s for.

# HOWTO Participate in #Twittereen

#Twittereen is a virtual costume day for the mathtwitterblogosphere and beyond. The rules are simple:

1. Change your avatar to “be” someone else for Halloween (that’s Thursday, Oct 31 in 2013).
2. Tweet something about being in costume with the #Twittereen hashtag.
3. Obsessively read Twitter all day long to see everyone’s costumes.

How did all this get started? I gotta be honest with ya, last year was my first year participating. I knew there was at least one before that. Thankfully, our #MTBoS-historian and Twitter Math Camp organizer, Lisa pinned down the origins for me: #Twittereen began in 2009, where it looks like Sean (@SweenWSweens) dressed as Sam (@samjshah).

# Doing #Twittereen

How do you do #Twittereen? First of all, let’s bring Lisa (@lmhenry9) in to eliminate some stress:

My approach is to first get inspired by browsing avatars of folks in the #MTBoS (or peripherally associated with us!). Then, I choose my target. In 2012, my target was @mrpicc112 who was at the time using one of those arrays of nails that you press your hand into to make cool 3D images. I had spotted one of those thingys in a colleague’s room, so I knew it was achievable. Finally, get set up to represent or recreate your target’s avatar, and simply tweet using #Twittereen on Oct 31 while wearing your new avatar. Don’t give it away right off the bat — the guessing is half the fun.

Probably the most unintended of consequences are the new people I follow because of #Twittereen. What? You want an example? So, last year, Sadie (@wahedahbug) dressed as Lusto (@lustomatical), some well-tattooed dude I wasn’t following at the time. But if he’s cool enough for Sadie to emulate, he’s cool enough for me to follow (good guy BTW):

Some people look forward to #Twittereen for most of October. They plan multiple costume changes during the day. Well, to be honest, I’m mostly just describing @approx_normal. I asked her why she loves #Twittereen and she responded:

@approx_normal changed costume four times in 2012 #truestory

@druinok on why she loves #Twittereen

And now, a tour through #Twittereens past:

# Twittereen 2013 Contest

(updated Monday 10/28 at 2pm EDT) A challenge for y’all from @approx_normal: GO TO APPROXIMATELY NORMAL IN THE CLASSROOM TO READ AND ENTER

TWITTEREEN WITH A TWIST!!

Last year we submitted our character changes and then voted on our favorite. We are still going to do that, but this time we are going to add some extras.

If you’ve already put on your “costume”, please change back to “normal” for a few days. Why? We will need your original avatar for comparison. Aaaaaand, everyone loves “reveal day”.

So, here are the rules for submission (if you want – totally optional):

1) You must fill out the form at the bottom of the blog post to submit your Twittereen costume by October 30th 7:00 p.m. EST to qualify to win. There are a bazillion of you now, and it will take me a few hours to compile. 🙂

2) Reveal starts on October 31st! And so will the voting for best Twittereen “costume”! This year we are adding a few extra awards:

a) Best Copy

b) Most Creative Interpretation

c) Best Burn

GO TO APPROXIMATELY NORMAL IN THE CLASSROOM TO ENTER

So again, please DON’T change your avatar until people have had a chance to do the copy. Here is the direct link to the form if you need it. Have fun and we’ll see the “new you” on the 31st!

# Twittereen 2012

Love, love, love the way Timon (@mrpicc112, at left above) swapped the hedgehog in the image for this. There are a few leaps you have to make to get it.

More Twittereen blog posts from 2012: mine and @approx_normal’s.

# Twittereen 2011

You want Lisa’s blog “Twittereen 2011 — for Sam” because she kept record of the Tweets as folks revealed themselves.

# Twittereen 2010

And it looks like 2010 was the year of “dress up as Kate”. Sam blogged about 2010 #Twittereen and has more pictures. I do remember #Twittereen 2010 but had forgotten it till Lisa pointed me to Sam’s blog.

# Twittereen 2009

This, apparently, is where it all started. October 2009 and Sam was using this picture as his Twitter avatar:

I’m gonna let Sam’s blog do the big reveal. See the first ever #Twittereen costume.

# Updates

(7:15pm Sunday) Greg (@sarcasymptote) reminds us if  you’re doing twittereen you should save the pic of the person you are dressing as. In his words, “shit gets real confusing otherwise when trying to pull together compilations.” Spoken like a true veteran, Greg.

(4:50pm Friday) Why should someone very new to the mathtwitterblogosphere particpate in #Twittereen? I mean, after all, it’s not like your inspiration would even notice (yeah right, that’s what @ mentions are for). Kate (@k8nowak) mentions all the good feels your target gets when you dress as them:

Holy crap, yes! I can only speak for me, but I LOVED seeing Julie dress as me last year. What an honor that *she* picked *me*. Y’know?

(4:50pm Friday) Struggling to find someone to impersonate? Katie (@fourkatie) who dressed as @cheesemonkeysf suggests the following for inspiration:

Here’s her costume:

Nailed it.

In my attempt to write about the history of #Twittereen, I’m pretty sure I left important people and details out. Won’t you help me fill them in with comments, below?

# Exam Review That Doesn’t Suck

It’s nearly exam time (hey, no complaining, y’all with a month or more of school left made me jealous last August!). In the past, I’ve been a huge proponent of Waterfall Trivia and math stations as review techniques. Both helped me wrangle large, unruly classes that didn’t really want to review for an exam or test. This year I have a blessing and a curse wrapped into one: my students would actually prefer to sit and listen to me recap the entire semester over 2 or 3 days. “Re-lecturing” is just not valuable in my opinion. The kids are passive, so they’re not likely actually getting anything new from the activity. I’d prefer activities where the kids do most/all of the in-class work — Quadrant I in my chart below. Some teachers aren’t so lucky as to have such academically-minded students, so their review activities need to get the kids who don’t want to, working — Quadrant II.

My criteria for a good review activity with this batch of kids:

• avoids cutsey gimmicks
• hits >= 80% of content covered this semester
• allows serious problem-solving in class
• has me not recapping the whole semester at the board for n days.

With my criteria in mind, here are the best ideas shared by my Twitter peeps.

Recitation Problems from Kelly O’Shea. Kelly writes:

About two weeks before the end of the semester, my students get a big (usually 24 pages), intimidating packet. It has one problem per student*, and the problems are problem+blank-page type of questions (that is, juicy ones that require multiple steps without breaking the question into parts that would structure the work for you). They tend to cover most of the main skills, but especially the ones that my students have found most difficult.

When they get to class the next day, we pick letters A through however-many-students-there-are. Then I give them my pep talk about how they should choose their problem. Whichever problem they choose, they will get to present the solution the class. They will have to become an expert on that problem. So I encourage them to pick the one that looks scariest to them. Pick the one that you would least like to see show up on the exam. Pick the one that will be hardest for you (it will be different for different students, of course).

Recitation Problems hits all my criteria without adding a ton of stress to the kids in their last week of regular classes.

Math Basketball from Dan Meyer. Dan writes:

1. You bring in a set of questions related to the previous two week’s instruction.
2. You put up a question.
3. A kid stands up with an answer, either correct or incorrect:
• If it’s incorrect, the student sits down, reworks the problem, and you wait for another student to stand.
• If it’s correct, the student takes two shots with a miniature basketball into a lined trashcan. You award points according to a) the student’s distance from the trash can, and b) the competitive mode you’ve selected below.
4. Repeat.

Review Activities Aplenty from Becky Rahm

I wound up doing math stations because they’re pretty easy to set up and help me carve out time to ask individual questions. Here’s the setup:

1. Print a set of problems for about 10 minutes of work on a sheet of paper. Repeat for each topic. Spread the problem sets around the room. I taped mine to cabinets, Julie Reulbach uses acrylic frames (way cooler).
2. Print answers and hang them in one spot near you.
3. Set a 10 minute timer tell students to choose a station with <5 people already there, work problems, and check answers at will. If they can’t get their problems answered by a classmate, they stay with me until station time’s up or question is answered.

Stations are easier to set up if you collaborate with a colleague.

I’ll be sharing, along with Matt Vaudrey, about Exam Review That Doesn’t Suck on Tuesday, May 21 at the Global Math Department. Join us! It’s completely free and online at 9pm Eastern / 6 Pacific.

# Hexaflexagon Folding Fun

You need to start making hexaflexagons. These:

Vi’s video not helpful enough? I learned to make simple hexaflexagons here. Maybe you can, too.

# Global Math Behind the Scenes

Global Math Department is heading into its fourth meeting this week (Exeter problem sets with @gwaddellnvhs. This is meant as an update to members as well as a behind the scenes tour of running a Global * Department.

The first two meetings were hosted at our free community on BigMarker. Overall, folks liked the environment but we were plagued by conference issues — mainly, folks were losing audio too frequently.

I love that BigMarker integrates a bunch of separate tools into a single community. Not only does it host our conferences, but also our recordings, and has a “wall” where we can ask questions and get feedback.

For our third meeting, we talked Algebra II big ideas on a Google+ Hangout OnAir.  Normal Hangouts are limited to 10 participants, so OnAir is the broadcasting option for larger conferences. We had no technical issues — video and audio quality were both excellent. Folks main gripe was that interaction with each other and the presenter was difficult as it’s handled through live YouTube comments.

Google+, as robust as it is technically, is harder to use and not as integrated as BigMarker. A number of participants gave me the feedback that they wanted the community of BigMarker and the stability of Google+.

Random images from Global Math meetings

Giving BigMarker a chance

With the mix of features we wanted in mind, I spoke with a representative from BigMarker who told me our audio glitches were likely because we were overcrowding the free conference room (there were 68 at @jreulbach’s foldables talk). We talked through my technical concerns and they made changes on their end that should alleviate the majority of the audio glitches.

If you listen to the recording of the Foldables meeting, the audio is flawless. Meaning that the problem wasn’t on the presenter’s end. Rather, the BigMarker server was struggling to send out 60+ feeds to the attendees. BigMarker moved us to their bigger server for our upcoming meeting. We expect to hear better audio quality.

I understand the need for stability in a new community. If folks get confused about where we’re meeting and how to use the tools, we wil lose people. It was a tough decision to return to BigMarker to see if the dropped audio is fixed. We can’t test it out unless there are a *lot* of us in the room at one time. BigMarker also can’t test this easily, so they want to work with us to improve their service.

Our community

#GlobalMath is our community. I’m just the one investing time on the back end to keep it running smoothly. We need to provide honest and thoughtful feedback at every turn.

Are you starting a community that holds live meetings?

You need to decide what you want to do at your meetings. Video conferencing? Application sharing? Slide presentations? Do you want folks on mobile phones to have easy access?

The major players in the online conferencing arena, as well as pros and cons as I see them are:

 Site Pros Cons BigMarker Free community version (test it out, good for small communities), free accounts for teachers to use with students. Members can join the community OR attend conferences anonymously.In archive, the chat remains synched with the video, providing a more integrated experience. Recordings don’t capture the video feed and don’t play on iOS. We have a history of glitchy audio (though the recordings are crystal clear) which BigMarker is committed to fixing. Google+ OnAir Hangouts Tech is rock-solid. Archives are Youtube videos, thus are mobile and iOS friendly. Free.It’s easy to have multiple presenters at one meeting. The person speaking takes over the main portion of the video screen, which people said they liked.Integrated with Google Docs, so we can collaborate on a doc live. It’s a patchwork of several technologies (Google+, YouTube, and something else if you want a backchannel) so can be difficult for attendees to figure out.Some of our teachers didn’t like that their YouTube conference comments were public and under the name on their Google accounts. They prefer a degree of anonymity online. Also, the comments are not synched with the video so become relatively useless. Finally, YouTube blocks posting links in comments — a huge part of our meetings. Elluminate Robust technology. Industry leader. Many have used it elsewhere, so it’s familiar.Throttles the quality of the video/audio feed so that if your internet connection is slow, you will get a lower quality but you’ll still get the feed. Relatively expensive. I ruled this out because I don’t want my members on the hook for a bill each month.

In all cases, the conference consists of a slide window, an audio feed, and (optionally) a video feed. You can broadcast anything on your computer’s desktop, too. (to learn about other players in the online conferencing market, check out this list).

Global * Departments

1. First on the scene was the Global Physics Department. They’ve been running since early 2011.
2. Global Math Department began in August 2012.

Do you have a Global * Department? Drop me your name and link in the comments and I’ll add you to this list.

# My #Made4Math 5: Global Math Department

It’s begun! The Global Math Department meets every Tuesday at 9pm ET. Modeled on the Global Physics Department, we are a passionate group of math teachers who engage in weekly professional development that’s live, online, and FREE.

Who Should Join

Right now, our primary membership includes math teachers for students aged 12 to 18. What I might call junior high and high school. I’d like to see college professors and elementary teachers find a home with us, too.

How it Works

Global Math Department is a community-driven effort. We are the presenters, the attendees, and the decision-makers. Here’s some advice on how to join in the fun:

• Join the community because you’ll get invitations as we create new meeting topics and we can track the number of members.
• Attend the meetings you want and skip the ones you don’t want. You can expect the main presentation to last about 45 minutes.
• Visit the meeting archive to listen to a session you missed. (I was shy for the first meeting and didn’t record Interactive Notebooks. Starting with August 14, we will record and archive ’em.)
• Stick around after the meeting to plan future topics and participate in open discussion time.
• Follow the #globalmath hashtag on Twitter for updates and conversation.

What We Talk About

Topics are all over the place on purpose — we want to include as many teachers as possible under our umbrella. Sometimes they’re very practical (interactive notebooks and foldables, for example), sometimes very philosophical (standards-based grading in Algebra II), and sometimes they help us see other ways to get students doing math (solving problems the Exeter way).

The first few meetings will include one 45-minute presentation by a single presenter. In the future, I’d like to string together several 5-10 minute long “My Favorite” presentations.

No topic is too big or small for us!

Why We Do This

After all the excitement that was Twitter Math Camp, we wanted a way to continue sharing with each other. I like to think that the Global Math Department is the year-round version.

Expansion

Where do we go from here?*

Well, I think we should consider having open office hours so folks can pop in and out with live discussions. After a long Twitter exchange on Sunday, I have concluded that’s not a great place to hash out big ideas (anything requiring more than about 5 tweet-exchanges). A chat room would be a wonderful place to brainstorm or work through ideas.

All our administrators are pushing for it and we even acknowledge it’s really cool, so I’d like to see Global Math be a place to develop interdisciplinary studies/projects.

# My #Made4Math 3: Bloom’s Question Starters

Somehow the Twitter math teacher universe has come to know me for my use of interactive notebooks (really not sure how that happened). Giving credit where credit is due, I need y’all to know I was inspired by my colleague, Jennifer Marshall, who taught me 90% of what I know.

Last week, we spent two hours at a coffee shop brainstorming about Interactive Notebooks and the following #Made4Math idea came out of that discussion. Ms. Marshall says “Give your students a copy of Bloom’s Question Starters to glue in their notebooks. During the year, ask them to write questions about their learning. They will refer to the question starters until they get a really strong handle of Bloom’s vocabulary.”

Ms. Marshall recommends the following type of assignment:

At the close of class, ask students to write several questions about the day’s learning. They’ll put the questions on a left page (reserved for student output or processing) of their interactive notebooks.

Students can answer their questions in groups (crowdsourcing for the most popular or most important ones), for homework, or for a unit review.

# Finally: A Chance to Merge Math & Physics

Because my students took the statewide End Of Course Test (EOCT) earlier this week, my school allows me to give a final project instead of an exam. This was a big break for me because my kids are tested out and I have no desire to write a 50 question comprehensive multiple guess test that can be graded within mere minutes of it being turned in so that I can close out my gradebook on the insane end-of-semester schedule we all have.

I’ve included the project below for you to enjoy steal. [Galileo’s Ramp (Word, 622kb)]

I start the kids off with understanding position-time and velocity-time graphs

Here’s a little snip:

Later, we move into understanding how quadratic functions can be transformed

There’s more in the full version (I guess that’s kinda obvious). Hit the link above.

I owe a huge debt of gratitude to @occam98, @fnoschese, and @jsb16 for brainstorming with me via Twitter the other night. Y’all were amazing. I opened with, “give me some phenomena that fit a quadratic function.” Also, I would never have finished writing this project tonight if I hadn’t had a horrible day at work. Something about a lousy day makes me want to do better the next.

This project gets students to understand position-time and velocity-time graphs in a rudimentary way, gets them thinking about the quadratic equations that describe those graphs, and helps them begin to understand how to collect data accurately.

# Stuff I’m Doing This Week: Math Taboo

Thanks, Bowman Dickson (@bowmanimal), for Math Taboo! Whenever I tell my kids to give me a definition in their own words, I get some regurgitation of what I already said. No real understanding needed. Enter Math Taboo:

The idea of the real game is to get your partner to guess a word by describing without using any of the five taboo words, which are usually the first words that anyone would go to in a description. So the obvious math equivalent is to pick a term that you are throwing around in your class and get students to describe it without using their go-to math descriptors.

As someone who teaches courses made of 60% English Learners and 40% students who failed math last semester, I’m eager to put this game out there. My students may just enjoy this one.

Dude, I love the comment that students make the Taboo cards.

# Finding the Best Lock

Can you help me make this into a 3 Acts problem? I was thinking some thing along these lines:

• Act 1: movie clip of someone trying to crack a combination lock. I want to set up the question “how long will it take?”
• Act 2: What are the rules for these combination locks? Maybe I could even be so lucky as to find these listed on a website with the number of permutations.
• Act 3: Which lock will take longer to crack?*
* Interesting factoid: I started this idea with the extension, not the first act. That is, I knew I wanted to present my students with a permutations-of-a-lock problem. I spotted these two locks on a website. Then wondered if kids could tell me which was more secure. For those who have written 3 Acts problems, is this a typical workflow?

Standard schmandard…

Georgia Performance Standards (GPS) for Math: MM1D1b
MM1D1. Students will determine the number of outcomes related to a given event. b. Calculate and use simple permutations and combinations.