Lesson Planning with Google Calendar

I've done lesson planning about a dozen different ways in my 10 years of teaching - and my favorite and current way of planning is by using the Calendar application. As you can see in the picture, each activity for a given day is one of the pink boxes that shows up. In these boxes (technically they are "events") I can write as little or as much detail as I want.  Typically I just write a little bit: "Notes on Solving by Quadratic Formula" for instance. For assignments I write something simple like "Assign: Pg 189 #1, 2, 10-26evens" or "Assign: Worksheet - Multiplication".

These calendars are super easy to move items around, copy from year to year, assign over multiple days, etc. I have created four Google calendars, one for each class that I teach. These Google calendars then can be embedded into my class website.  Then students and parents can know at a glance what were studying not only this week, but they can look forward to days when they may be gone, or look back to days they've missed.  I have had on more than one occasion students who have come in after being sick and instead of asking "did I miss anything" they hand me their homework which they found on the calendar.

Whenever possible, I put links to helpful material into these events as well. This was the biggest challenge, but something a little html knowledge proves handy for. To add a link to something, you double click on the event and type into the "Add a note" section. You may type text descriptions with more details here and students will be able to read these by clicking for more details on their calendars.  Adding URL's sounds easy at first, but unfortunately, simply pasting a link into the "Add URL" section doesn't work. Perhaps this will be fixed someday? A work around that allows a clickable link to appear on the student end of things is to use a little HTML code. Copy and paste following code snippit:
  <a href = "URLgoeshere">Text goes here</a>
One thing to look out for is to make sure that your computer doesn't turn " into "smart quotes" -- because then the links won't work. I had to turn "smart quotes" off in system preferences. In addition to downloadable worksheets as assignments, I include links to quizlet vocabulary practice, math practice websites like ThatQuiz, or videos of my lessons whenever they are available.  A colleague of mine records every lesson every day, and since this year we share Algebra 2 together, I include links to her videos on youtube. I tell the students that if they don't like the way I explain something, or if they need another explanation, they can check the calendar and find Mrs. Straayer's videos.

One last plug for planning with google calendars is that students and parents can subscribe to them, and then they can have them show up on either their computers or phones. Anytime I make an update, they will have access to the most up to date plans.  This is really convenient when a snow day or something arises -- I can simply cut and paste today's events to tomorrow.  I have mine connected to my phone so I can either see what's coming up from anywhere -- or add a note or link or change something from everywhere on my phone.

QR Codes on Worksheets

Within the last year or so, I have been making efforts to include QR codes on my handouts in my classes:

Example of a QR Code:
If you scan this with your phone,
it will tell you that it's an example of a QR code.

For  those of you who don't know, a QR code stands for Quick Response code. You scan it with an app on your phone or tablet, and depending on what's encoded, stuff happens. The example above simply shows some text. Most often, a QR code is linked with a website -- and you see them all over the place from political brochures to labels in the supermarket. My wife has used QR codes to create scavenger hunts for her students that visit at the library. You can even set them up to automatically write a text for you as my step-sister did for me for those days when the girls get a little out of control:

Mom Meter:
Scan the appropriate QR code and mom receives a text like:
"come home soon dad is going to kill us!"

About a year ago I started putting them on the worksheets and notes packets I would give to my students.  It only takes up a little space in one of the corners somewhere.  Usually these are simply connected to a pdf of the document that they can view on their phone or tablet. Most of the time these files have the original blank copy of the document, as well as an answer key. My philosophy on homework is that it is practice -- and I want my students to have good practice -- not blind practice. We talk often throughout the year that they need to know whether they are doing things right, so that they don't practice mistakes and learn bad habits.

Here's how I do it:

Right-clicking files in your dropbox folder
gives you a URL link to download that file

First, I use Dropbox for all my file storage, and one of the features of Dropbox that I use most is the ability to get a sharable link to every document by simply right-clicking. I put these links on my Google Calendar, on my class website, and of course, in the QR Codes. You can create a QR code for free at a bunch of online sites such as QRStuff or QRCodeGenerator. Simply paste the link into the websites and copy the image to place it into a document.

Creating a QR Code in Quicksilver

That was too much work for me though, so I quickly learned that my favorite program Quicksilver had a QR Code generator available. If you have Quicksilver, you can simply paste the link in the first pane and choose the CopyQRCode action in the second pane and viola - you have a paste-able QR code that can be put into any program. After setting it up with it's own trigger, it literally takes me 1 second to create a QR code for a URL that i've copied onto the clipboard. For more tips on setting this up, check back later for another article.

Reflections on J-Term 2013

We just finished J-Term and I have so much to write about, but so little time to write, so let me just do quick summaries and if I have any time (this summer?) I'll come back and elaborate.

For those of you who don't know, at our school J-Term is a week-long opportunity for our students to take some unique classes and learn things their teachers don't normally get to do during the school year. For instance, many students took iPad video making, or an interesting Hunger Games exploration, knitting, chess class, etc. The teachers suggest offerings and the students sign up for three different classes they'd like to take.

This year I offered two classes: Astronomy (which I have taught before) and a new class which I called "Did You Get My Email?" but might more formally be called Digital Communications.

Star and Planet Locator
by Edmund Scientific

In Astronomy we learned a 15-20 constellations, discussed how to use a Planisphere, the idea of altitude and azimuth, how to find the planets along the ecliptic, and how the sun moves through different constellations (the zodiac) throughout the year. Next on the list would have been declination and right ascension, but we ran out of time.

The Star and Planet Locator made by Edmund Scientific is an great tool for teaching these concepts -- and at only $3.95 per unit it's one of the cheapest I could find.  I bought mine a few years ago and kind of remember a 25 for $50 deal so if you're interested in a classroom set, look around.

These worksheets I offered:

• Learning the Constellations: Identify the constellations you see in different maps
• Using a Star Finder:
• Using a Star Finder Part 2:
• Seasons: Questions regarding seasons and sun on star finder
• Angles Between Stars: measuring altitude and azimuth with hands, degrees, etc.
• Estimating Location of Stars: practicing altitude and azimuth with a star finder
• Celestial Coordinates: practice with declination and right ascension
• Stars and Heavens in Scripture: Bible passages referring to the stars and heavens
• The Star Clock: Using the big dipper to tell what time it is

The other class I taught was new to me -- Digital Communications. I'll admit I'm not proud of how this class turned out because I didn't put the time into it over Christmas break that I should have. In this class we learned about a ton of different technologies, leaning quite heavily on "How Stuff Works" descriptions of: the telegram, telephone, television, computers, hard drive, cd player, text messaging, email, radio, etc. We also studied binary numbers, and spent some time describing how computers convert all information into numbers, which are all converted into binary, which can mean everything can be stored ultimately as a handful of 1's and 0's somewhere.

I also did some hands on materials, though I had ambitions of doing way more. We played around with simple circuits, hooking up batteries and lights. We made a few electromagnets, and I showed them a homemade "byte" -- 8 bits -- which I made with just a piece of wood, 8 nails, and a about 40 ft of wire. I never used it in anyway besides holding it up occasionally when we discussed that 8-bits define a character in Ascii, or that three of these 8-bits define a color of an individual pixel in a picture, and so on.

I learned from this that I enjoy doing things hands-on and should take more time to make that happen in my classroom. I learned that radio shack has a lot of small circuit components for sale, such as LED's, solar panels, resistors, switches, etc and I have a lot of material now that I'll be able to use in our electricity unit in physics.  And I learned that classes will survive, even if you are fully prepped for them. Maybe that wasn't the lesson I should have learned -- but I did.

Storage Capabilities of the 8.5x11

A former student of mine had an instagram that inspired a dorky series of tweets between the two of us touting the features of this amazing new technology: the sheet of paper. I was trying to be sarcastic because I hadn't seen a sheet of paper in so long, writing all my essays and lesson plans and everything digitally.

The series of tweets:

Ian Williams ‏@ian_d_williamsThe sad tale of an engineer attempting to write an essay. tp://instagr.am/p/TwRo3sRTpt/ 

Rocky Roer ‏@RockyRoer@ian_d_williams what is that thin white note taking device in front of your laptop? Is that a new Christmas present? Wireless? Bluetooth?
Ian Williams ‏@ian_d_williams@RockyRoer It's the newest in pressed wood pulp. Functions without a processor and get's great battery life!
Rocky Roer ‏@RockyRoer@ian_d_williams what kinda storage? 200Gb?
Ian Williams ‏@ian_d_williams@RockyRoer college ruled, 56 lines, expandable to margins. Also compatible with multi-ring long-term storage devices.
Rocky Roer ‏@RockyRoer@ian_d_williams wow 56 lines! I was only familiar with older 33 line models.

Anyway, taking it a step too far I'm sure, I decided to investigate the storage capabilities of a simple sheet of paper. To begin, I found a sheet of paper -- though it took a while. I also had to find a stylus that was compatible with the paper -- after a handful of failed attempts, I found one with enough battery left (you can always count on Sharpie models!) to input text:

I counted the number of characters on each line, including spaces and punctuation.  I found 63, 62, and 65 characters on each line, and so I'm going to average them and suggest that a typical line stores 64 bytes. I'm thrilled this is a power of 2 -- it makes me confident that it's technology, because everything else in technology comes in powers of two.  Let me save that number in memory as 2^6.

After counting the number of available rows, I found another convenient power of 2, or 32 lines.  2^5.

Multiplying these numbers together, I get 2^11 bytes, or 2*(2^10).  2^10 is 1 KB, and so one side of one sheet of paper is 2KB. Utilizing both sides of every sheet of paper yields the following storage capabilities for the following standard models:

70 sheet 1 subject sprial notebook:  280 KB

100 sheet looseleaf unbound package: 400 KB

500 sheet ream of paper: 2 MB

Of course, using different fonts and font sizes could significantly increase or decrease storage capabilities.    

"Random" Thoughts

I hear the word "random" used all the time, and so often incorrectly. It seems like it is some of my high school students favorite words, and expressions. I bet I hear at least once a day, "That's so random!!"

 Here's a few thoughts on the word, and some alternatives that perhaps you ought to consider instead.

Random: If something happens randomly, it means that one option out of many different equally possible options occurred. This was not something someone chose. This event could have occurred a different way if things had happened just a little differently. Imagine a dice rolling and coming up a four. It could just as easily come up a 5. This is what random means. Side note: Random things will sometimes repeat. A dice will sometimes come up with the same side showing twice in a row. In fact we can predict how often that will occur (about 17%).  Your iPod does not play songs randomly -- because if it did you would complain that it wasn't "random enough".  If it really did pick a song at random, you would hear repeats occasionally, and the first music players actually did this. Your iPod probably is using a shuffled play list - which did use random choice to create the list by choosing one of the songs to play first, one of the remaining songs to go second, one of the remaining songs to go next and so on. 

Haphazard:  Lack of a plan, order or direction. A person who doesn't know where they are going is not driving "randomly". They are not flipping a coin to decide when to turn left or right.

Arbitrary: Determined by chance, whim, or impulse, and not by necessity, reason, or principle. An arbitrary decision is one that could have been lots of things, and the decider just picked one of them because a decision had to be made. Perhaps they could have made the decision randomly, by drawing draws or rolling a dice, but instead just made up their mind.

Spur-of-the-moment: occurring or done without advance preparation or deliberation; extemporaneous; unplanned. I pick a lot of numbers on the spur of the moment over the course of a day, as I make up quick examples for class. I don't pick them randomly, and I know that I favor certain numbers like 2's and 3's. There is usually little meaning behind the choice of numbers, but they were not chosen randomly.

Spontaneous: resulting from internal or natural processes, with no apparent external influence. I often hear of people described as random -- especially those that are really funny and come up with the weirdest things "from out of nowhere". These people aren't dice-rollers. They don't have thousands of thoughts rolling around in their head waiting to fall out their mouths like some sort of lottery. They are spontaneous, and the world is a better, funnier place because of them. Learn the word. Use it.

Assorted: Literally (and don't get me started about "literally" misusages) "not"-sorted. This rant was purposefully misnamed Random thoughts, thought a more appropriate word to use is assorted. I suppose I could have put these words into a shuffling algorithm and randomized them -- or sorted them alphabetically, but I just put them down as they came to me.

Unexpected: If you didn't expect something was going to happen, then describe that outcome as unexpected, not random. The fact that we had a fire alarm during third hour was not random -- in fact, it was probably planned. You just didn't expect it. Surprise! 

Aimless: Sometimes people do things that are pointless, and serve no purpose. Putting a picture of a cute penguin on a blog post about randomness might not serve any purpose, but that doesn't make it random.  

Mad Libs with Mail Merge

Every time I hear the song Let it Snow, Let it Snow, Let it Snow! I am reminded of an activity I did once several years ago when I used to teach computer applications. We were learning about mail merge features in Microsoft Word. We had finished an assignment on making form letters (actually, we made letters to send out to each of our family members informing them each of a different gift on our lists insuring that they each bought us something different we wanted) and had an extra day before leaving for break so I decided for the last day to try a funner use of mail merge.  So, we made Mad Libs.  Christmas Carol Mad Libs.

Acid Rain: (more info)

Students took 15 minutes or so to set up files, about 15 minutes to go from computer to computer filling out each others mad libs, and the last 15 minutes or so reading what ensued.  My favorite line -- the only one I remember actually, is:

"Let it Acid Rain! Let It Acid Rain! Let It Acid Rain!

The student had put "type of precipitation" in as a clue, and while most people put either rain, or snow, there's always that one kid that thinks a little differently.

If you're curious how to make it work, I copied and pasted my instructions down below.  These were based on the 2003 version of word, so the exact places you go to find these options have probably changed if you have the newer versions. Some of these instructions were specific to my students that year -- please forgive me if I didn't filter all of them out.

1. Create a folder in your personal space called "madlib"
2. Open a new Microsoft word document save it as "mymadlibsong" in that madlib folder.
3. Find the lyrics to a christmas song of your choosing online, and paste them into "mymadlibsong".
4. Go through your song, and remove certain keywords which you would like to be blanks that need to be filled in with words.  Delete the old word and in its place type some type a field name that you will replace it with.  e.g.  Rudolph the ADJECTIVE1-nosed ANIMAL1...  (Notice that I have a 1 after adjective, that's because each field needs a unique name -- otherwise EVERY adjective in the song would be replaced by the same word.  If I have another adjective later, I would ADJECTIVE2, etc.
5. From Tools, choose Mail Merge...
1. Click create main document, form letters, Active Window
2. . Get Data, Create Data Source...
3. Remove all the prearranged field names that Word gives you
4.  Go through your whole story from top to bottom and add the fields that you created above.  Remember that each field name requires a unique name, which is why I have adjective1, adjective2, etc.  
5.  Click OK and save it as "mywordlist" in madlib folder
6. Choose "Edit Data Source"  The Data source is what MsWord calls the document which contains all the information that will be placed into the main document, or in this assignment, the data source is the wordlist, and the main document is the story.
7. You can words if you'd like, enter at least one set of words.  If you have come up with one set of words -- called a record -- either enter another set, or have a friend or neighbor enter a set
8. When you are finished entering words (at least for now) hit OK.
6. Notice now the Merge toolbar has been added to your bar. The first available button is insert Merge field.  If you click on that button, you'll see your list of fields that you can place in your document in the appropriate locations.  Go through your document and replace each of the field names you typed earlier with the appropriate mergefield. It should look like <<ADJECTIVE1>>.  
7.  When you are complete finished, press the button with <<>>ABC on it and you'll find that each of the merge fields has been filled with the lyrics that you and your friends have come up with!  Click the > button to read through each of the records you created.
8. To make another verse. Click the MailMergeHelper button, and you'll see the familiar menu. This time click Edit Source Document.  Add another verse, either yourself, or by asking me or a different friend to fill yours out.  Before you hit ok, click View source.  You should see another word document pop up with a table containing your words -- much like an excel spreadsheet.  Both can be used.  Typically it is easier to create a file this way, but sometimes, if you already have an Excel document made up, it will be easier to use that information already. Close the source file, saving any changes you may have made, and try reading the new verses you made.

If you try it and come across any issues, comment below and I can try to help. If you try it and come up with a cool verse, comment that too!

Answer Key's to Worksheets

I believe that students do need to practice a skill in order to get good at something. This often translates into lots of questions and problems and opportunities for students to practice. Typically, for my math and physics classes, this takes the form of worksheets or practice problems out of the book. 

One thing I try to make sure I have for my worksheets or assignments however is some way for the students to know if they are getting it right. 

For my algebra assignments out of the book -- I remind my students that math textbooks almost always have an answer section in the back, and I tell them to check their work as they go. (One thing I have not done that just came to mind is model to them what that looks like in practice, and how to deal with mistakes...) For assignments that do not have answers, I have been known to write all the answers on the board, or on the bottom of a worksheet, but in random order. This way the students have to come up with an answer, but if they see that answer on the board then they have some confidence that they did it right. To avoid process of elimination at the end, I usually throw a few more answers up than I assigned.

My physics assignments typically come from several sources -- a hardcopy textbook, made up questions on worksheets, or several handouts of supplementary practice problems. Most of these do not have a ready made answer sheet, or have multiple parts that should be checked along the way before arriving at the "final answer". For many of these assignments, I provide the answers in a multiple choice format:

      m = {1.20,     1.47,      1.93,       2.31,     2.88,    3.06} kg

One of the six options listed is the correct mass, and the other 5 are just random distractors. The idea came to me when one of the students complained to me "Can you just give us the answers?".  At first I thought, "Of course not!" but then I remembered my assignments at MSU where we had to enter our answers in online, and they would tell us if we were right or not. I remember being frustrated at these assignments, but in a good way because I kept returning to the problem and trying to figure out what was wrong until finally I found an answer that worked. I haven't taken the time to find a way to do that with my assignments yet, but having the answers available for students is a step in that direction perhaps.  

To help me come up with such answers, I set up an excel file that I can enter the correct answer in one cell, and it will come up with six answers that are all reasonably close in size compared to that answer.  The correct answer is randomly placed somewhere in those numbers:

If you want to try it for yourself, you may download it here.  To adjust where the answers round to, select the options and push the rounding button in the number tab above, highlighted in yellow above. 

To create a worksheet for the students then, I typically have this file open and copy and paste the answers in.  One thing I have found necessary is to "Special Paste" them in -- by pressing Alt E, S and paste them as unformatted text instead of cells from a spreadsheet. That way the formatting looks good, and the numbers in the worksheet are fixed instead of linked to the constantly changing excel file.  

Word Blanks using Microsoft Word's Styles

I have notes available in Microsoft Word for my students, and one of the things I have found most helpful is creating and using styles. Styles are quick formatting options that can be used and reused from file to file.

To find Styles in Microsoft Word, press Ctrl-Shift-S. A list of available styles should come up. These are probably preset styles that come automatically. To apply a style, select some text and click on one of those styles and you will see it change.

While applying the built-in styles is kind of helpful, the real power of styles is when you adjust and control what you want styles to look like. Or when you create new styles of your own. One thing I found myself doing over and over again was creating fill in the blanks for my students in their notes. One problem I had was I would often forget what the word was myself. I found myself making two files all the time -- one which had blanks in it, and another that had the answers. This was a nightmare to manage and I found a solution with styles.

I created a new style called WordBlank. Then I typed up my "answer key" version of the notes, and as I found words that I wanted to blank out, I applied this new WordBlank style to them. When I was done typing it, I modified the WordBlank style by pressing the Modify... button.

Several formatting features made the blanks look just the way I wanted them to.

• Set to underline.
• Set the underline color to Black
• Set the words to be e x p a n d e d.  This is because students handwriting takes up more space then text does, and so the blanks needed to be wider than they would naturally appear.  Alternatively you could just make the font size a little bigger than normal too, or some combination of both.

When I was done, all the words in the document that I had applied the style to looked like this:

Now I could print if I wanted to and have an answer key.

But the real genius was that in this one file, now I could modify the style and change one thing:

• Set the font color to white

And now the file changed to this:

Then I could print off student copies!  

Now, all of my notes files have this style in them. To make that easier, I pushed "Manage Styles" and made sure to copy that style into my Normal file, so that every time I start a new word document, WordBlank is one of the options I have available.  

Also, since I have all these files available on my class website for students to download, they can access them. Since the blanks are there -- if the students are sick or absent, all they have to do to get the notes is to select the blanks and change them to a different color. And yes, I show them how to do this early on in the year.

If you want to download a document that has my wordblank style in it, try these Momentum Notes.

Geogebra Activities In My Classroom

I have been spending a lot of time playing around with Geogebra lately -- in my algebra and precalc classes. I love this program because of how easy it is to make functions come alive and allow you to tweak things and see the effect they have. Below I have embedded an example of a geogebra activity I made to help illustrate how transformations change the graph of the basic sine curve.

Sorry, the GeoGebra Applet could not be started. Please make sure that Java 1.5 (or later) is installed and active in your browser (Click here to install Java now) If you can not see it, you might need to update or install Java on your computer. If you can see it, play around with the sliders in the corner -- move them and you will see how the graph adjusts. These are concepts that we delve out in more details of course in class, but this is a tool I use at the beginning of the unit to introduce the idea. It is also something I allowed as an option for my students to make at the end of the unit as an assessment of their knowledge. It takes minimal knowledge to create a graph that moves with sliders -- I can show a student how to do that in about two minutes.  But to add to the graph the other colored lines and line segments that make it so clear what a, b, c, and d do require more advanced programming thinking, and a strong knowledge of the keypoints that are on a graph.

I have made other geogebra activities too -- another of my favorites is to make a guessing game of graphs. By assigning some code to a button, you can have geogebra create a new random graph. So I do that, and then create another controllable graph and have the students try to match the random graph. Here is an example I just had my algebra students playing with the other day:
Sorry, the GeoGebra Applet could not be started. Please make sure that Java 1.5 (or later) is installed and active in your browser (Click here to install Java now)
After a quick demonstration in class, we moved the the computer lab and they spent some time playing around trying to type the equation of the blue line. I could have just given them a worksheet to do, (and seriously thought of it as bad as I was feeling yesterday with a pounding headache) but I preferred this activity instead. It was:

• A change of pace and scenery
• Motivating - there is something satisfying in "getting it!" 
• Self-checking. I believe this is one of the most critical points of an drill-like activity in a math class. If students don't have instant feedback that they are doing something correct, or incorrect, they will quickly develop habits that are hard to undo.

If you are interested in learning more about creating geogebra activities like these, be sure to check out future posts.  

Chutes and Ladders (or Tangents and Cotangents)

Chutes and Ladders - a game for ages 4 and up
Tangents and Cotangents - a game for ages 16 and up

Last week I was playing Chutes and Ladders with my daughter (well, I was playing and she was arguing with me about why I kept moving my piece three spaces forward and didn't just put it on a space that had a three in the number, like 3, 13, 23, etc like she must have thought were the rules) and I made the amazingly smart observation that there were six spaces in the spinner, and there were six basic trig functions. Before long I had gotten board and wanted to find ways to add strategy to the game, and found that at times it was more beneficial to go backwards several spaces instead of forward, if by doing so I could avoid a chute or land on a ladder.

It wasn't long before I had decided upon a few rules, and come up with a game we could play in precalculus, which I decided to call "Tangents and Cotangents".  I thought the name was a nerdy way of describing Chutes and ladders, because the graph of cotangents is always decreasing like chutes, and the graphs of tangents are always increasing like ladders.

I brought the game to school, and described the following rules to the students:

• Students (in teams) would answer estimation questions like sin(25) or tan(258).  (NO CALCULATORS ALLOWED!) Each trig function was worth a different amount of points. If the students estimated within 10% of the correct value, they moved forward that many spaces. If not, the other teams would be able to steal the points if they had estimated correctly -- so everyone was interested in every question. The points were defined as follows:
• sine = 1pt
• cosine = 2pt
• tangent = 3pt
• secant = 4pt
• cotangent = 5pt
• cosecant = 6pt
• If the team guessed the value within 10%, but had the opposite sign, they went backwards that many spaces. While this might seem like an annoying penalty, eventually one of the teams caught on that it could be used their advantage to land on the coveted 28 square, and it wasn't long before teams were "purposely" getting the sign wrong to their advantage. I didn't mind, because it made them think about and practice the signs of the values too -- part of my objective for the day.
• Once per game, I allowed the teams to choose what point value they wanted to play for -- typically they were chosen at random like normally in the game. This added an element of strategy for the students who would wait to the opportune time to try to hit a big ladder. I think I would change this rule next time to reward REALLY close guesses (say, within 1%) with an additional free choice.  
• Occasionally we would play a question that was available for all four teams. Any team that guessed within range was awarded the points (forward or backwards as necessary)

In order to help facilitate the random choosing of the game, I created an excel file that gave me a random trig estimation question every time I pressed F9, and then displayed the answer and the acceptable range of values when I pressed F9 again. When students chose a particular point value, I had to press F9 repeatedly until the appropriate value came up -- for instance, when one group wanted a 4 point question in order to land on space 80 for the win, I had to press F9 over and over again until a secant question came up. You may download this excel file here, and you can read about the underlying workings of it at my post here.  For more on estimating trig functions, I suggest you read on the unit circle definitions of trig functions.

Online Graphing Calculator

I just wanted to do a quick promotion of my favorite online graphing calculator:
http://my.hrw.com/math06_07/nsmedia/tools/Graph_Calculator/graphCalc.html

I like as a teacher because it is very similar to the TI-83 and TI-84 model calculators in the steps you need to perform to create a graph -- which makes it a handy tool for students to use at home if they don't have a calculator. There is a "y=" screen, which you can see in the graph, and then a settings page where they need to type in xmin, xmax, xscale, ymin, ymax, yscale just like we practice in my algebra classes. It has a trace feature, and a table feature, and can find the intersections between lines or curves. It can even do graphs of inequalities fairly easily -- much easier than the calculator can naturally, but in basically the same manner as the common application Inequalz which most new calculators come with.

I do wish it had an easier way to capture graphs -- like a copy button somewhere, but I suppose there's always screen capturing tools for that sort of thing. That's a topic for another post.

Metric System Prefix Fufu Song

Little basic FuFu, hopping through the forest
Scooping up the millipedes and boppin' 'em on the head
(spoken) Down came the 10-to-the-third fairy, and she said:
  "Little basic FuFu, I don't want to see you,
   scooping up the millipedes and boppin' 'em on the head.
   ... (spoken) Now I shall decrease each of your three dimensions by a factor of ten: poof!


Little milli-FuFu, hopping through the forest
Scooping up the micropedes and boppin' 'em on the head
(spoken) Down came the 10-to-the-third fairy, and she said:
  "Little milli-FuFu, I don't want to see you,
   scooping up the micropedes and boppin' 'em on the head.
   ... (spoken) Now I shall decrease each of your three dimensions by a factor of ten: poof!

Little micro-FuFu, hopping through the forest
Scooping up the nanopedes and boppin' 'em on the head
(spoken) Down came the 10-to-the-third fairy, and she said:
  "Little micro-FuFu, I don't want to see you,
   scooping up the nanopedes and boppin' 'em on the head.
   ... (spoken) Now I shall decrease each of your three dimensions by a factor of ten: poof!

Repeat with, nano,pico/femto/atto/zepto/yocto.

  ... (spoken) I suppose you'll never learn, will you?  Back to normal!

Little basic Fufu, running through the forest

Hiding from the kilo-birds who bop him on the head

(spoken) Down came the 10-to-the-third fairy and she said,

   "Little basic Fufu, how I hate to see you,

    Hiding from the kilo-birds who bop you on the head"

    (spoken) Lets try increasing each of your three dimensions by a factor of 10: poof!

Little kilo-Fufu, running through the forest

Hiding from the mega-birds who bop him on the head

(spoken) Down came the 10-to-the-third fairy and she said,

   "Little kilo Fufu, how I hate to see you,

    Hiding from the mega-birds who bop you on the head"

   (spoken) Lets try increasing each of your three dimensions by a factor of 10: poof!

   Repeat with Mega/Giga/Tera/Peta/Exa/Zetta/Yotta

Skills

• I CAN celebrate my unique strengths and abilities
• I CAN choose to dwell on the positives
• I CAN treat everyone with respect even if I’m angry or disagree with them
• I CAN take responsibility for my actions without making excuses or blaming others
• I CAN choose my attitude and behavior, no matter what happens to me
• I CAN make things happen for me instead of watching them happen to me
• I CAN encourage myself with positive words
• I CAN choose to try and learn from my mistakes instead of being paralyzed by what-ifs
• I CAN set goals that are achievable and worthwhile
• I CAN see myself being what I know I want later, by sacrificing what I feel I want now

Uneditted Videos

I have been struggling for some time now about creating and posting videos for my students and classes, because I am a perfectionist.  If I'm going to post something, I want it to be done well. When creating a video, I have yet to record myself perfectly. I constantly will make mistakes, say things twice, repeat myself, or say things twice constantly. Even if I don't make a mistake, my speech is so littered with "um" and "so" that it's embarrassing counting how many times I eliminate those.

Typically, when I create a video, it takes me 3-4 times the length of the video to edit it and do what I would consider a "great" job. For day-to-day lessons, that has proven to be unfeasible.

On the trip home today I listened to live radio and was reminded that the real world has a lot of mistakes, but that doesn't stop them.  So I decided that I would start publishing more videos -- but in a raw, uneditted format.  I will still produce high quality videos, especially for my physics class which is "flipped" and depends highly on video lectures for input, but I don't feel I need to do as high quality a job with my algebra videos, which aren't as highly viewed.

The same thinking, by the way, is the reason I don't blog very often -- maybe once a week.  I feel like I need my entries to be deep, rich, well written entries -- but they really don't.  After my Master's project is finished, I'll try to express more thoughts in rougher un-editted form.  Be ye warned....

Some Systems Videos

Hey guys,

It's been a while since I've posted anything since I've been working especially hard creating a lot of videos for my classes at school.  I'm now back into a flipped unit in physics, studying Torque and rotation with my students. If you're curious, you can follow the unit at our class website. I am creating this unit as a sample of a flipped unit for my Masters project at Cornerstone University, so I'm taking more time perfecting it than I normally might -- thinking about tying all the things I've learned together.

I've also recently created several videos for my algebra 1 students.  Though I am not flipping that class -- I do have a lot of students who are absent a lot, and I thought it might be worth it for those students for me to post videos of the lectures online.  Since I already have all my equipment up and out and ready for my physics classes, I talked through my algebra lessons too and here are those videos:

This is an introduction to systems of equations, and my explanation of the graphing method of solving systems:

z

Here's the substitution method, which we'll be studying next week -- I like the colors in this video -- it turned out pretty:

And here's the elimination method, or what my text book calls "linear combinations".  Elimination is a much sweeter name.

This is probably one of my favorite lessons to teach -- I just think the combining equations and one variable disappearing is a beautiful magic trick -- makes me feel like a mathmagician, as some of my students say.  The only thing cooler than adding two equations together and having variables cancel out, is dividing two equations together and having variables cancel out, a trick I often do in physics, especially when sine and cosine values are around.

Standard Form Fight Song

Standard form usually get's a bad rep, perhaps because slope-intercept (or y=mx+b) form is so popular due to its ease in graphing. Standard form, while not as easy to graph, does have its benefits, a few of which I'll list below.

As a recap, standard form is writing an equation as Ax+By = C, with the stipulation that A, B, and C must be integers.  I prefer the form Ax-By=C instead of + because then the A and the B values end up being the rise and the run of the line.  For example, 2x-5y=20 has a rise of 2 units for every run of 5 units, for a slope of 2/5.  Additionally, the example x+3y=15 rises 1 unit for every run of 3 units backward -- backwards because it was written with + instead of -.

Here's some reasons I think standard form is useful:

• It's neat and orderly, with no fractions or decimals
• It's easy to plug in points (because x and y are in order and the multipliers are always integers) which is how you check if a point is on a line
• It still reveals rise and run, with some understanding that the terms must be subtracted
• It is easier to answer questions like finding equation of lines through (3,7) and (8, 2) because you don't have to find the y-intercept
• It can describe vertical lines (x=___) that have undefined slope
• It can be scaled by multiplying.  (by the way, dividing everything by C gives you an interesting form, x/dx-y/dy=1....)
• It is the form of choice for combining equations when systems of equations rolls around... my favorite topic in the algebra curriculum.
• It can easily be expanded into 3 (or more) dimensions, where y=mx+b has no easy expansion

To celebrate standard form, and praise some of its merits, I wrote a fight song for it, which is to the tune of the greatest college fight song out there, Michigan State.  The lyrics are posted below, as well as a link to a tune on Youtube so you can sing along.

A x + b Y equals C

is known as standard form by all

It always graphs a straight line

The only form that does them ALL

Other forms can't do straight up lines

'cause their slopes are undefined

We simply let x equals ___

 we'll be fine!

Chorus:

A's the rise and B's the run

As long as we subtract 'em!

Plug in a point to find the C

And make sure they are nice IN-TE-GERS!

Multi-pl'ing   by  de -nom'-na-tors

Makes fractions disappear! (poof!)

X's!  Y's!  Equals C!

Standard form's the one for me!

(Dance during musical interlude, then sing chorus again)

Sobering thoughts on physics

Read two blogs back-to-back today which hit hard about my teaching of physics. The first article called "No credit for ridiculous answers" was one teachers experience with fostering an attitude of always checking the reasonableness of an answer. While I do this naturally in my head -- I do not do a good job of developing this in my students. I'd like them to think as I do -- with estimations, and a sense of what answers are reasonable and unreasonable, and the post showed some ways the teacher graded to develop that.

The second article describes how our physics classrooms so often become areas of plug-and-chug formula application, rather than conceptual thinking. The author describes "How we create a context of Formula worship" listing many of the dry dead questions that require no more thought than deciding which formula contains the correct letters in it - letters which I know all but one of. I saw in my past few weeks of teaching several of those questions being asked on my worksheets and my PowerPoint presentations. How come in algebra I am always teaching how many different ways there are of looking at a problem, but in physics I am always simplifying things to plug-and-chug?

On a more encouraging note -- I think my students are this week doing a valuable experience of using video analysis to determine how effective seatbelts and airbags are in reducing injury in a crash.  I had to use some interesting thinking to determine the framerate of the video -- which I may write about later.

Article Reviews

Just read two interesting articles on grading, from the magazine Educational Leadership which is published monthly by ASCD. Their November 2011 issue focuses on standard based grading, which is something I'm considering doing my final Master's project or thesis on. 

   The first article was The Case of Illogical Grades by Lissa Pijanowski. In the article, Lissa describes her school districts efforts to reform their grading system. She described that teachers in the district had all sorts of different philosophies, which amounted to meaningless numbers that were inconsistent from teacher to teacher and year to year. She described the process the schools took to revamp their policies and become more consistent.  

   One of the things the teachers did was separate out of the grades behavioral concerns, so the grade was based entirely on what the students know from the required learning standards. This meant students grades were no longer lowered for missing assignments, participation, or late work -- but neither were students grades inflated for simply turning in work on time.  These sorts of things, specifically the four categories: Assignment Completion, Participation, Responsibility, and Interpersonal Skills were listed separately and graded on a 1-4 scale.  I like this idea, as my grades this year are based directly on knowledge of standards, and so I had been looking for way to communicate these other social skills.  

   The second article I read was Finding Your Grading Compass by grading guru Carol Ann Tomlinson.  This short article describes several revelations Tomlinson encountered during her teaching with regards to grading, several of which I have been learning in my seven years so far.  Some of these revelations are paraphrased below:

• No matter how hard I try to remove my personal judgement with foolproof criteria for grades, there will always be an element of subjectivity. This means I will always need to use my professional judgement, and that I should not be threatened by that.
• Consistent and specific feedback is more helpful and powerful than a letter or number grade will ever be
• I need to grade fewer assignments, as these are places where students can and should be free to make errors and mistakes.  Coaches don't grade the first time you're learning a new move or play in basketball, but how well you use the move in a game when the time comes. Teachers should do similarly   
• If I have a student who consistently have low grades, there's something I'm not doing well in reaching or connecting with that student. Also, if I have a student who consistently reaches high grades, with no struggle or needs, I'm underestimating their capability, and wasting their time. I need to find a way to challenge them to learn too.

Each of these has been something I have struggled with in my own grading philosophy. Though I know and believe the statements above to be true, in past years my actions have proven otherwise. Likewise, I still often feel differently. These things I am working to change this year, beginning with my actions in implementing a standards-based grading system and moving away from a points based system as I have had in the past.