Next up with my ninth grade math class: solving rational equations. I’ve been having fun with combined rate problems such as, “How long does it take Timmy and Marsha to mow the grass if it takes Timmy 2 hours on his own and Marsha 1.5 hours on her own?”
I, therefore, with great pride present you my first Vimeo video (Edit: Filling the Sink):
How I’m using it:
Put it out there as a warmup — how long do you think it’ll take to fill this sink? Show about 10 seconds of the video.
Put it out there in the lesson — what about when I combine the faucet and pitcher? Teach them combined rate problems as a specific case of rational equations.
Watch “Trial 1 (faucet only)” and “Trial 2 (pitcher only)”, then compute time to fill the sink with both working together.
Play “Trial 3″ and compare your experimental results to my actual results.
Close class with this: Assuming your computed time to fill the sink is different from the actual time, discuss what you think is the most significant source of error and how I could fix it in “Filling the Sink, Part II”.
Side note that’s aggravating but true: I’ve struggled with finding great applications of the concepts I teach because they’re rarely as complex as the stuff we’re expected to work with. With rational equations, I’m still looking for something where I’ll need to factor the numerator and denominator, cancel some terms out, and move along. My gut tells me this thing doesn’t exist.
Electrical circuits is the one area in engineering school I completely sucked at because I had a knack for letting out the magic smoke of many a project. Well, I’m back at it. Hopefully, I’m a bit more knowledgeable now & I’m definitely staying away from capacitors.
I have here a pretty cool project cribbed modified from a task published by the Georgia Department of Education.
The 8 second summary: practice solving for total resistance then assemble several resistors into an equivalent resistor using concepts of series and parallel circuits. Students will be solving rational equations throughout the project.
Below is a circuit that comes early in the project. Students are learning to apply the formula for resistors in parallel.
Here’s a more complex circuit. One of the problems is sufficiently complex that some students will need hints on solving the equation. I’ve split the hints out in a separate file, available to only those students who need it.
After students have a chance to get comfortable with the formulas for resistors in series and parallel, the project puts them in a challenging situation: build a circuit with resistance equivalent to a given value (even though none of the individual resistors have the particular value I’m looking for).
I will have actual resistors and an ohm meter on hand for the final phase of the project.
I really don’t like going this deep inside the box to think…but my kids have to prepare for major standardized tests. With that caveat, I now present resources I like to prep students for the End of Course Test after Math 1 (9th grade math – algebra, geometry, & statistics).
First up: I like the Georgia DoE’s EOCT Math 1 Study Guide (PDF, free). The 130 pages in this guide has re-teaching alongside practice problems. In my experience, the problems in this book do a great job illustrating how hard the EOCT will be. Here’s a clip from the statistics unit we recently completed:
Second up: the Released Items booklet is helpful for teacher planning. I use it to see sample problems from last year’s test & inform my quiz and test writing. Unfortunately, I realize now that the EOCT relies on at least passing knowledge of the state-authored tasks. Here’s an example:
Fellow math teachers – what EOCT resources do you like?
According to the Title Text (hover your mouse over the comic to read it), the entire iTunes music library could fit in a soda can’s worth of Micro SD cards. Could it really?
iTunes Store catalog has more than 10^6 songs. (This figure does not include podcasts and video.)
The computations:
Each Micro SD card has a volume of 15mm x 11mm x 1mm = 165 mm^3.
Each soda can has a volume of 12 fluid ounces. Google tells me 165 mm^3 in ounces is 0.00557931375, meaning 2150 Micro SD cards could fit in a 12 ounce container. Allowing for the fact a Micro SD card is rigid and a mess of ‘em won’t completely fill a soda can, let’s round that down to 2000 Micro SD cards.
Micro SD cards come in sizes up to 32 GB. 32 GB * 2000 = 64,000 Gigabytes. There are 10^3 Gigabytes in a Terabyte, so that’s 64 Terabytes of storage in a single soda can.
Songs in iTunes are around 4 Megabytes in size. 64 Terabytes / 4 Megabytes = 16,777,216 songs.
Given that the iTunes library worldwide has 10 million songs and 16 million could fit in a soda can, the comic’s claim seems to hold.
Get 4 rounds of Probability Trivia (PowerPoint | PDF). Set your Adobe Reader to scroll (View menu > Automatically Scroll or Shift + Ctrl + H). Put on music the kids might actually like. Then roam the room to help kids who struggle.
I’m not much at expounding, but if I had to list the benefits this little game has given me,
used days before a unit test, I can identify areas the whole class needs to work on
I have the freedom to work in very small groups with kids who struggle with a particular problem (because the game part kinda runs itself)
the teamwork aspect means that kids justify their work – I hear the best arguments from kids who know they solved the problem right but their teammates are being meatheads
the scrolling questions puts the kids under pressure to solve problems quickly
The question set covers counting principles (for number of outcomes), permutations & combinations, mutually exclusive events, dependent events, and conditional probabilities.
Bonus for Georgia teachers: this is Math 1, Unit 4 standards MM1D1 and MM1D2.
1) Two months since my last post? Here’s my quick update: my schedule was completely swapped the day before second semester started. I had about 21 hours to get ready to teach my new students AND move classrooms across the building. I’m starting to find my feet again.
2) Big thanks to Kate Nowak for including me in her “Blogs you aren’t reading but should be” post.
I hope you’ll steal my trivia format because it’s proven a great balance between fun and problem solving that lasts the whole period. The format is loosely modeled on Team Trivia, which you may have played at a local eatery. While I’ve designed time pressure, it’s not about answering the question first (which removes incentive for everyone else).
The trickiest part to Waterfall Trivia was developing a sense of problem-solving urgency. My solution was an auto-scrolling series of questions that come at the students in rounds of three to five questions. I explain below how to generate an auto-scrolling set of Waterfall Trivia questions.
Where’s the Teaching?
I use time between rounds to review especially tricky problems (often those that more than half the students get wrong). In addition, I keep the answer slips to identify groups of students who need remediation (and on what kinds of problems they need the work).
What Do the Winners Win?
In my games, the winning team usually wins candy, pencils, or a couple bonus points on the upcoming test. A broad spectrum of students will compete hardest for the bonus points.
Musical Stylings
I usually play music from Pandora.com during the rounds. If you can stand it, the Classic Hip Hop station is quite entertaining.
Setting Up Waterfall Trivia
Set up your questions in a Powerpoint file (a sample is here).
Export the Powerpoint file to a PDF file.
Open the PDF in Adobe Reader.
From the View menu, choose Reading Mode to eliminate clutter.
From the View menu, choose Automatically Scroll.
Adjust scrolling speed with up and down arrow keys.
Voila! A trivia game that paces itself. Sit back, collect answer slips, tally scores, and explain solutions.
Last year, I wrote about a service called Group2Call that I was using to send homework reminders via SMS to my students. It worked great but now that I’m in a public school, it was going to be too costly to continue. After fits and starts, I’ve finally found a solution that works for me: sending email that gets transmitted as a text message.
Here’s how you can set it up:
Get your students to give you their phone number and carrier’s name (MetroPCS, AT&T, Sprint, etc).
Find out the email-to-SMS gateway addresses for the carriers on your list. For your convenience, I’ve included the ones I’m using below.
Send an email in the usual way, but to your student’s SMS email address. Keep messages under 160 characters because that’s the limit for text messages. Don’t forget to trim your signature!
Email to SMS gateways for several major mobile carriers:
Methinks this could be used in math class. “Hey kids, we’re going to play Corporate Spin today. You’ll hide a disappointing stat in a graph so the public doesn’t realize how much we’re polluting/raising prices/whatever.” (My, I didn’t realize I was feeling so cynical today…)
What time of day was this photo of the Washington Monument taken?
While writing this warm-up question, I came across the Sun or Moon Altitude/Azimuth Table page. Supply a location and a date and this page will tell you the angle of sun in the sky for any time of day. (Interesting side note: This photo of the Washington Monument could not have been taken between November and February because the sun never gets that high in the sky.)
I can already imagine all sorts of interesting extension problems based on this picture but for now I will keep it simple: my students need to practice the inverse trig functions.
