Category Archives: Precal

Alg II Files: Matrix Multiplication Application #MTBoSBlaugust

I’ve already blogged most of my matrix notes on this post (and as always, you can find all of my Algebra II Files and FAQs here), but I did do a new introduction to matrix multiplication that I liked:

Alg II T 10_2

(NTM file here, practice file here) Sure, you have to do a little teacher manipulation to make sure that the second matrix on the calzone example is a column matrix, but I think it really helps to see why we multiply matrices like we do, and what the resultant matrix tells us.

It also gives us a reason to play this in class:

 

And as an added bonus, a pretty worksheet with a calculator picture and arrows! (Also I totally skipped finding determinants and inverse matrices by hand. Sorry, but sometimes you gotta ruthlessly cut stuff.)

Alg II T 10_3

(file here) Yes, it is required that you play Jackson 5 after the last problem. REQUIRED.

The Flowchart Method: Learn It, Love it, Log it.

Astute readers of my blog may remember my ramblings of the “flowchart method” last summer (and my use of it at the start of the year in Algebra II). After not focusing on it for quite a while, I brought it back for solving logs and exponentials, and it helped so much, all the way from struggling Algebra II students to PreAP Precal rock stars. Next year I really want to focus more on carrying it through all that we do, but baby steps first.

My introduction to composition of functions remained the same, next year I want them to really focus on writing the steps of each function in order. I changed up how I introduced inverse functions, but I’m not sure if it went better than the previous year or not. I need to work on melding the two together (I also think a couple more days for this unit would have been reallllly helpful, but Spring Break!).

I started by having them do the first row on the NTM below as a bellringer. Whoa, that’s weird, 3 and 4 have the same answer! And it’s what we started with! Then we did the next row, whoa, so 7 & 8 have an output of x!  That means anything we put into it will come out the same!

from megcraig.org

(file here) (If you’re like my students, you may not get the ServPro reference: they are a disaster cleanup company with the tagline “Like it never even happened,” which became our tagline for inverse functions.)  After explaining the joke, we worked on the chart, determining inverse functions and checking with whatever number they desired (We don’t make a big deal about 1:1 functions until Precal, although we did talk it about the next day a wee bit).  And this is where building up the function machine the day before would have been super handy!  Let’s just reverse the machine!  (I also wanted to do Bob’s Inverse Function Partner Activity, but again, time!) Then the next day I felt I had to discuss some more properties of inverse functions, but again, not the greatest:

from megcraig.org

(file here) Trying to do too much at once, so we didn’t get to focus on the chart at the bottom: “Oh, so we’re really using inverse function machines when we solve equations!”

Then the next day we did exponential equations:

from megcraig.org

(file here) I really wanted to do the Zombies! Activity but, again, time! So at the end of the day we did #14 with our calculator, leaving the last two for homework. So much frustration! “Really, there’s no other way to solve these?”

Well, maybe there is….

from megcraig.org

(file here)  Thanks to Kate for the fill-in-the-blank problems at the bottom. I would probably save the beginning part for the next day, when we are actually solving equations.  But look at that glorious chart!  Oh, so you’re telling me that logs and exponentials are inverses?

The next day is when we REALLY focused on the inverses idea:

from megcraig.org

(file here) I wish I would have had them write down the actual flowchart on these, though, just to reinforce the fact that log base 6 in the inverse of 6^x. As in, the number matters! You wouldn’t undo +3 by -4! So you wouldn’t undo 7^x by taking just log!

I also always have this conflict with myself, as illustrated here:

from megcraig.org

Teach “undoing a log” by converting to an exponential equation or as exponentiating both sides? I usually stick with option 1 in Alg II, then bring in option 2 in Precal. But maybe with the flowchart option 2 would make more sense?

Anyway, speaking of the flowchart, here is where it gets super useful:

from megcraig.org

(file here) Look how beautiful that is. No one thought to make #12 into 5 ln x! And it really focuses on ln and e being inverses of each other. We held off on the homework until we had some group whiteboard practice the following day, using slides like these:

from megcraig.orgFlowchart 10

(file here) Now, don’t get me wrong, we still struggled. We spent two days on the study guide (file here, with video key part I and part II) after this and I still had students try to undo a log by using a log. However, I also saw a lot of students that have been struggling do really well on this test–because they had a strategy they could use to attack each problem. (We also talked about how hard it is to intuitively feel like your answers is correct, so let’s use the calculator to plug it back in–this was complete news to many of them that they could have been doing that for any equation we solve!)  And it wasn’t just the struggling students who were fans–I overheard one top-notch student say to another, “Hey, did you write the flowchart? It really helps!”

As I mentioned, I also used it in Precal with great success:

from megcraig.org

(File here) We also used it for actually solving equations, but I can’t seem to find that file! Doh! But hopefully you get the idea: flowchart it!

It Really Is All About Lines.

I’m sure this has never happened to you, my wonderful smart readers, but sometimes I read/hear something about math and outside I’m:

But inside I’m really:

Case in point: Glenn’s (@gwaddellnvhs) obsession about how everything is just made up of lines (It’s somehow comforting to know that Dylan struggled with this idea as well.).

Well guess what, y’all? NOW I GET IT!

It was all thanks to a presentation by John Abby Khalilian that I attended at the Alabama CTM Fall Forum, where he not only presented an activity that involved multiplying lines, but actually had us do the activity. And I was fortunate enough to be seated next to another attendee (but I don’t remember his name!) who was super excited about joining me in a conversation about extending it past the Algebra I level at which it was intended.

I modified the original file slightly (with permission from Dr Khalilian):
files from megcraig.org

files from megcraig.org(File here) I urge you to work through the first page–I promise you this whole made-up-of-lines-thing will finally make sense!  Note: I would make some modifications for next year. First, Dr Khalilian gave us two versions and I used the one we did in class. However, his first version used two positive-sloped lines, which I think would work better as the first example (Just use the lines from #10) Second, instead of giving them the equations of the lines in #10 and 11, I would have them already graphed and ask them to sketch the result?

Also, I know what you’re thinking, “Man, those are some Algebra I level questions on the first sheet.” I agree, and yet it was definitely a review that my Precal students needed.

After the worked on this, we then reviewed graphing polynomials, tying it together with the idea that we were just adding another line and what that would do. I was also made sure to focus on the fact that, “Oh, we have two negative lines and a positive, that would make it positive” because I knew what was upcoming:

Polynomial and Rational Inequalities.

Well, it went stunningly this year. All we had to talk about was the fact that sometimes drawing all those lines could be tedious and messy, when all we really care about are the places where a line is positive and negative. And if the line has a positive slope, it will be negative before its x-intercept and positive after. Like most math things, easier to see than to tell:

files from megcraig.org

The red represents the sign of the red line, blue of the blue line, and black is the final result. So now sign charts are SUPER EASY.  We don’t plug things in! Who wants to do that? MATH BABIES, that’s who. We are going to use our BRAINS instead:

files from megcraig.org

note the two rows needed for 0 in #5, since it is a double root, meaning there were TWO lines that had zero as an intercept

files from megcraig.org

(file here) Note: I started them on the first page with making sure that we always got rid of a negative leading coefficient (you have to “flip the sign”–get it??). This made it easier on the back when we had -x-5 hanging around; yes we could have pictured a negative line and write the chart as + – – but I felt like they would forget that one was negative. Easier just to take care of it than remember it!  They all did fantastic with this on their test!

I know, could this whole “everything is lines” thing get any more exciting and awesome? Yes. Hold on to your hats, I’m going to change your Rational Function Graphing World.

Maybe your world use to be like this: Find your horizontal and vertical asymptotes (and holes) using these rules that I told you. Then make a t-chart of all the values on either side of the vertical asymptotes and plug in to find points to graph:

files from megcraig.org

See, I hated doing the arithmetic so much I made it into a powerpoint. (But the powerpoint is pretty awesome for introducing horizontal asymptotes).

But then I used Kate’s wonderful introduction to rational functions worksheet that I always admired but never quite saw how it fit we how I graph rationals, but NOW I GET IT! It’s just like polynomials, except dividing! (modified only because I did not want to pay scribd to download it, plus one page, amirite?)

files from megcraig.org

(File here)  I’m going to modify some more for next year by (a) replacing trash panda (I have a serious problem where I can’t leave blank space) with the questions “what is the equation/zeros of f(x)/g(x)?” and (b) adding some more graphs, mostly stealing from being inspired by Sam’s worksheet. Instead we spent a few minutes the next day talking about what would happen if we were dividing a line by itself in order to lead into the idea of a hole.

So NOW! we can graph rationals THE SUPER EASY AWESOME WAY.

H: Find the horizontal aysmptote

F: Factor and find holes

Z: Find zeros of the numerator (x-intercepts) and denominator (vertical asymptotes)

S: Make a sign chart with all the zeros you found in the previous step and then graph!

When I asked the students to come up with a mnemonic, the most memorable was, “Horses Fart, Zebras Smell.”

So here it is in all its glory:files from megcraig.org

(file here, with more practice on page 2!) More modifications to make: Now that I don’t need all that space for a sign chart, I can add another example to the front!  The one we did in class involved two factors in both the numerator and denominator. Also, I would change #2 so the horizontal asymptote isn’t 1/3! If you notice, in #1, I did the sign chart below the graph, but that got super confusing in #2 with everything so close together, so we started drawing it separately. We almost finished up the front page (including introducing horizontal asymptotes with the above-mentioned powerpoint) in one day, then did a couple more examples and practice on the back the following day.  When we get back from spring break, we’ll do another day involving Weird Things That Can Happen like 1/x^2, but I think the sign chart is going to work nicely again!

I hope this helped you figure out the power of understanding the whole “everything is lines” idea and how it can carry through to so many things!

Things I Thought I Knew

Some days this job can be a bit ho-hum. Teach a lesson you’ve taught 37 times before, grade a few tests, make some copies, go home. And then some days you get to learn math that you totally thought you knew, but you had no idea. Friday was one of those days.  I’ve been teaching long enough that I probably should have known this stuff, but I didn’t. So here I am to enlighten you as well. Just be prepared for the following to occur:

Topic 1: Classification of Systems

Am I the only one that is really bad at reading directions? But then the students actually read it word for word and ask questions that I didn’t see coming because knew what the question was really asking without having to closely read it. This week, we had a question about making an independent and inconsistent system, which I read as “inconsistent” and knew what the goal was, but then that pesky “independent” thing was brought up by students.

So I always thought there were three types of systems:
Independent: One Solution
Dependent: Infinite Solutions
Inconsistent:  No Solutions

TURNS OUT I was mushing two different categories together:
Category One: Is there at least one solution?
Yes: Consistent  No: Inconsistent
Category Two: Are they the same line? (Technically, “can one be formed from the other with algebraic manipulation?”)
Yes: Dependent No: Independent

So the correct categorization would be:
Independent and Consistent: One Solution
Dependent and Consistent: Infinite Solutions
Independent and Inconsistent: No Solutions

When you realize you’ve been teaching something wrong for your entire teaching career:

Topic 2: Logs grow really really slowly.

“Yes, Meg, we know that.” No, I don’t think you do. The wonderful MTBoS Search Engine led me to this GREAT activity from @Johnberray. I modified it a bit, first of all by making some pretty 1-inch graph paper:

inch graph paper

(file here) Each group got a sheet in a dry erase pocket and used their calculator to find the decimal values to graph y = log x. Then I asked them to calculate how many inches it would take for it to function to reach 2, 4, 6, and 8 inches high. (At least one group each period said 20, 40, 60, 80 so we may not have the idea of logs down pat just yet). Then I asked them to describe each distance in some way–is it the size of a pencil? classroom? from here to the front office? as tall as basketball goal?  I let them use the internet and a student showed me that if you put a measurement into Wolfram Alpha, it will give you real world comparisons! Pretty neat!

You really need to try it for yourself!  What fun we had when we started talking about how long the paper would be for a height 6, 7, and 8 inches (oh, plus go ahead and try 9!) using this draw-a-circle-on-a-map site that John had linked to. Then it turned into, how high will it be if the paper reaches the moon? The sun? Pluto? I won’t give it away, but guys, logs grow really really really really really slowly. 

Yet they still go to infinity.

One raised to any power is equal to one, oh, unless that power is infinity.

So I’m pretty good with limits. Then my Calculus teacher friend mentioned, hey, isn’t it weird that the limit of (1 + 1/r) ^ r is e, not 1?  Wait, that doesn’t make sense.  But it turns out 1^infinity is indeterminate. WHAT? But I thought 1 to any power is 1!  WHAT IS HAPPENING TO EVERYTHING I THOUGHT I KNEW?  The best answer I saw was that “we don’t know if the one is really a one”, which ok, I guess, since 1 + 1/r is never exactly one. But what if the number IS actually 1? Not like “kind sorta” close to one but ONE. If 1^infinity isn’t one, at what number does it STOP being equal to one?

I was discussing all this mind-blowing math with my friend right as class was starting, complete with dramatic re-enactments of how high the graph of log will be on Pluto and what was happening to my brain. When I came into class, a student asked what we were talking about and I said “Math!” and she said, “You really do like math a lot, don’t you?”

Yes, yes I do. 🙂

Category: Alg II, Precal | Tags: , ,

Hey, Make This Exponentially More Awesome for Me, Okay?

Monday I spent a couple hours falling into the #MTBoS trap of lesson planning: having so many shiny pretty ideas that I can’t decide what to do! I was trying to figure out how I wanted to start my exponential unit for PreAP Precal. Yes, they’ve seen it before, but I didn’t think they had a concept of EXPONENTIAL BEATS EVERYTHING (I know I really didn’t until my [REDACTED] year of teaching math.)  So this is what I came up with:

You just started a new job. Pick the best salary option and be prepared to support your opinion:
Option 1: $50,000 a week, increased by $5000 each week.
Option 2: $100 times the square of the number of weeks you have been working (I didn’t really know a better way to describe this?)
Option 3: Start at $10 a week, increase by 10% each week.

It was a weird day yesterday with some classes half-full due to class meetings, plus I had some tests to go over, so we only had about 25 minutes to work on it. I let them have 10-15 minute to discuss in their groups. Many people started with a table, which is quite deceiving at the start. A few groups finally asked, “how long are you working there?” To which I replied, “That’s a good question, how long are you working there?”

Most decided to focus on one year, and thus chose option 1. A few ventured out further and chose option 2. (Maybe next year I’ll make so option 2 overtakes option 1 just before year one instead of just after?) Most could not figure out an equation for option 3 (which didn’t bother me, especially when they haven’t seen exponentials in over a year), so just crossed that one out immediately based on the first few weeks.

After each group gave their reasoning, we worked out a table on the board, starting with 1, 2, 3, 4, 5 weeks, then figuring out the equation for each week. I then gave each group a time frame-1, 2, 3, 5, 10, or 20 years and had them figure out the weekly salary for each option.  The bell rang right in the middle of posting the results, but we still had fun talking about making $10^22!

Today I showed them the graphs in desmos and we talked a bit about them:

(Desmos file here) But I think we FINALLY got the power of the exponential when we put it in table form:

exp 1

I mean, look at how slow both the linear and quadratic are growing. 10^8 after 40 years? That’s not even worth getting up in the morning for! I also wrote out the final numbers on the board while they were working on the next task, using all 87 zeros.

Yup, I think they will say that exponential will win every time now. 🙂

As we were working on it, I thought of a lot more things we could extend with:

  • Figuring out the time to switch by solving a quadratic (option 1 & 2) or by using technology–either Desmos or using Excel?
  • Have them write an actual recommendation of which salary to chose and why.
  • For the first couple of years, students were wondering if making so much at the beginning would make you have more money at the end of the year with the linear. What a perfect way to bring in area under the curve! Especially because they could actually calculate the linear function’s area with just one trapezoid, then I was thinking just to use the integral function on the TI for the other two.
  • Of course it could also be a nice lead-in to logs: when will each salary hit $100,000? $1,000,000? $10,000,000?  (Also nice to look at graphically!)

So this post is serving as my reminder to myself to devote some days to this next year, and try to do some of these extensions. But if any of y’all want to try it out and make it awesome as you are wont to do, please do and report back! I’ll be chillin’ with my cool $10^87.

Desmos Activity Builder Success

This summer I was so excited when Activity Builder was revealed at TMC. About the second week of school, I made a really quick one that involved the students graphing their names with lines. I reserved the mobile laptop cart that our school has just for Math and Science to use, wheeled it into my room, and was ready for the excitement to begin.

Oh, wait, except my classroom is in some sort of wifi blackhole, so it was taking students 10-15 minutes to be able to log in to the computer and open the activity, and even then only about 4 kids got to that step. It was the Friday before Labor Day; I didn’t have any backup plans, so I just threw in the towel and they had a chill day. I, on the other hand was not chill.  I was Over Technology. I was at Unstackable-Cups-Otter level of Not Chill.

stacking-cups

It took me two months to venture into trying it again. This time I reserved the computer lab, where the computers are wired to the Internet. It went much better. Here are the two activity builders that I made:

Algebra II:

Writing Equations of Transformed Parent Functions

We are graphing 5 different functions (lines, absolute value, quadratics, cubics, and square roots) and the students were having a lot of trouble writing equations from given graphs. Enter in Match My Functions Activity Builder!

Match My Functions Activity

Issues: Students still do not know how to find the slope of line. This makes me sad. So they just tried decimals and then were upset because it seemed “like random decimals for the slope.” At least they were trying something, I guess? Also a couple students said it didn’t help them because they could just guess until they got it right. But all in all I would probably do it again; they actually did very well on their test writing the equations and recognizing the functions.  Also, a student who is in two math classes bragged about how fun/cool it was to his other math teacher. 🙂 Plus when it came to study guide day, at least a few students broke out the app on their phone to check their equations!

PreAP Precal

Introduction to Polar Graphs

I had actually done this activity last year as just a regular Desmos file paired with a worksheet that asked them questions about the graphs. It didn’t take too long to create an activity builder based off of it. We had graphed polar points and graphed a couple circles by plugging in values of theta, but they had not seen any other type of polar graph. I set them loose (in pairs) to work on Polar Graph Exploration.

polar exploration

I had them play around with sliders for each graph; then submit “I notice…” and “I wonder…” On the more complex ones, we then looked at each part individually (like the slide above that just focused on the n value). Trying to learn from the feedback from Algebra II, I made a few “quick check” text questions where they couldn’t just guess (although some just went back a screen and played around with the sliders until it matched)

polar exploration 2

The fact that, with no direct instruction, most of them realized there had to be a 3, 6, and sin involved in the graph above is pretty amazing. I really loved the notice/wonder part as well (I’ve actually never used it before in class #MTBoSDirtySecret).  I always had an issue with the petals on a sine rose alternating between positive and negative y-axis. One student noticed that if it is positive, more petals will be above the x-axis. So clever!

I did get a few complaints on the feedback, “why didn’t you teach us?” but I’ve come to expect that.  The other complaint was not being able to know if their work was correct on the quick check. Maybe I should add a screen after that with the graph that says, “check your work” or “how close were you?” (but then I also don’t want to discourage them if they were wrong–I only wanted to see how much they had learned from the activity).  The best part was the last screen where I told them to have fun!  They made so many cool graphs, and then I was able to show them off the next day in class.

Now I know Desmos gets a lot of love around here, but let’s not forget about Geogebra, which is powerful and useful in its own right. For example, this beautiful, awe-inspiring, oh-so-that’s-why file that compares the two versions of a trig equation (made by Mark Fowler):

geogebra activity

(Which I found the morning after we had done the Desmos activity, and now I’m debating if I want the Ss to play with this instead of the Desmos one! Or if Desmos could make this into a split screen activity with sliders that controlled both graphs?!?!) I used it as we talked about each graph, and was able to reference their responses from the day before, “Some of you were wondering what causes the inner loop…”

All in all, a fun week using technology in class. 🙂

Evolution of a Theorem (or How to Save All the Animals)

It all started when Bowman Dickson posted The Dead Puppy Theorem and Its Corollaries. Others joined in on the effort, most notably the additional corollaries developed by Math Curmudgeon   I also joined the cause, making a worksheet that covered the do’s and don’ts of exponents.   Lisa at eatplaymath took that idea and made an a full-page warning worksheet for her Algebra II students.

Lisa posted her worksheet at just the right time as I was about to start one of the more dangerous chapters: Trig Identities and Equations!  EEEEK!  So I made this and we spent about 15-20 minutes discussing the various problems that come up, why they’re illegal and what to do instead.Save the Trig Kittens

(file here) We also added more to the back as we needed them (e.g. can’t cancel sin x in 1/sin x + sin x.)  I really think it worked as the identities section of their quiz was really quite pretty!  Only 4 kittens were harmed in 75 tests!  It really made them think about each step and I got a lot of “Mrs Craig, is this hurting an animal?” or “Mrs Craig, is this legal?” questions when we were working on them, whereas before I think they just did magic and didn’t care.

What are some constant mistakes that you would want to warn your students about?

Life-Size Sine Curve

Last weekend, there was some twitter chatter about making life-size graphs so students could explore points/transformations/what-have-you. That got my wheels turning, and after a quick trip to the dollar store and about an hour’s worth of work I ended up with:

trig graphSteps:

1) Buy four shower curtains at the dollar store. Bonus if they are prelined!

2) Tape together with packing tape. (hint: tape them down to the floor with washi tape to hold them down, then tape the seams on the front. When done with the whole thing, flip over and tape the back)

3) Use duct tape to mark the x-axis. Print labels (file here), cut out, measure your axis, and tape down with packing tape.

4) Apply colored masking tape for 1/2, root 2/2, root 2/3. (see next picture since the masking tape was at school)

Total cost depends on how much tape you have around the house. I used almost 3 full rolls of colored masking tape, but the good news is I bought it from naeir.org. Have you heard of this site? One of the teachers at school shared it with me. Basically companies donate overstock and you get to buy it for the cost of handling. You do have to spend at least $25 and shipping takes about 2-3 weeks, but holy cow, can you get a lot of stuff for $25!  My first shipment I got 8 rolls of patterned/colored masking tape, 2 packs of 12 small post-its pads, 8 post-it pop-up cubes, 12 correction tape thingies, a pack of sharpies, 3 sets of dividers, 2 packs of post-it labels, and I think some other things I’m forgetting. It’s crazy!

Anyway, in class, I handed out dry-erase pockets with a sheet that had an x value in it (0, pi/6, pi/4….2pi) (file here) and told the students to find sin x, 2 sin x, sin 2x, sin1/2x, and cos x. Holy moly. We could have easily spent the day doing that. No, if x = pi/3, sin2x does not equal 2pi/3. Once we got that sorted, we went out into the hall. I had all the students stand on their x-coordinate, then step to the y for the function I called out. It was very easy to find people who made wrong calculations! 🙂  Here’s what cosine looked like:

cosine curveAnd sin 1/2x (with an outlier!)

sin half x

By third time I ran through it, I had worked some of the kinks out:

  1. In my first class, I had more people than x-coordinates, so I gave coordinates that were more than 2pi. This did not go well. They were way far down and we couldn’t really see the pattern continuing. The next class I handed out 2-3 points per group and had them work together to find the values, then as we graphed we substituted people in who hadn’t graphed yet.  (The class shown had just one person extra.)
  2. I only did each graph once. We talked about max/mins, who didn’t move and why, how many cycles fit on the mat, etc. I think it would have been beneficial to do sin, then cos, then switch back and forth faster and faster. Then do the same for 2 sin x and sin x, sin 2x and sin 1/2x, etc. And also positive and negative. The last class we even tried sin x + 2 (“oh, that means we need to all step up 2!”)
  3. Have them write down noticing/wonderings as we are doing it, or a quick sketch of the graph (maybe have some axes printed on the back of their point card?) to help solidify the concepts.

The next day, when we went to graph, I asked them if it helped to visualize what we did yesterday. Only a few raised their hands. I told this to Mr Craig, wondering if I would do it again or if it would be more efficient to just jump into graphing then practice. He said, “Hey, you helped those 5 kids see it better! Plus sometimes it’s about the experience, not about being efficient.”  Sometimes that Mr Craig can be pretty smart. (Don’t tell him I said that, his head is big enough already.)

In other news, this happened on Twitter the other night:

8,006 tweetsDo you think I will hit 1,000 followers or 10,000 tweets first?

Category: Precal, trig | Tags: ,

Trig Addendum: Modified Radian Fraction Cutouts

Read about the awesomeness that is Radian Fraction Cutouts in Shireen’s original post (and my implementation). After using them in Algebra II last year, I made one little modification that made them even better (one of last year’s students that I have again even said so!):

unit circle fraction cutouts dotted

File here.  The secret? Cut only on the dotted lines!!!  So easy to see the whole enchilada (or em”pi”nada as Shireen also says) divided up into sixths, thirds, fourths, etc, then seeing if you add one, take one away from one, or take one away from two.

Comments I heard from the first class I showed it to (the others will see it tomorrow):

“This is so easy!”

“OH THIS ACTUALLY MAKES SENSE NOW!”

“Why did no one teach it this way earlier?”

“These are really great!”

[In response to another Ss question about 7pi/6]: “Use your cutouts!!”

Not one person wanted to convert radians to degrees!  Woot woot!!!!!

Timing wise: In one 53 minute class, we cut them out, made a pocket (fold a half sheet into thirds [like a letter] and tape down the sides to the back of the NTM, leaving the top flap untaped), talked about degrees, talked about radians, and finished the front of this notetakermaker. The back has more practice that they had for homework:

degree radian WSFile here

DO NOT LET THEM LABEL THE UNIT CIRCLE!!!  Otherwise they won’t have to work at any of the rest of the worksheet. 🙂

And since it is the first day all week that I’m finished will all my homework before 9:00, I’m going to go read a real book!  That’s not about math! Or teaching! Take that, SCHOOL!!!!!

First Two Days Reflection

I actually started on the 13th, but am just getting around to blogging about it because I spent all last weekend making lagging, spiraling homework as well as activities that were not worth the effort I put into them (but that’s a topic for another post).  I’m teaching Algebra II w/ Trig and PreAP Precal, but I did the same thing in both classes for the first two days. I’m also adding a rating system from 1 (that sucked) to 10 (that was awesome)

Thursday:

    • High-fived all students and checked off names/got nicknames as they walked in. Rating: 9 due to difficulty in multitasking, also weird looks from students
    • Had them fill out google survey. Besides name, nickname, class period, these questions are also on there: Google Student Info Survey Rating: 8 I thought these kids could text fast, but it always takes sooooo long.
    • Told them a bit about myself. Rating: 10 because I’m awesome.
    • Hit the high points of the syllabus, showed them how to get to my google doc that will have links to everything we do in class SO DON’T ASK ME WHAT YOU MISSED. Rating: 5 I mean, it’s a syllabus.
    • Played the first day video from youcubed’s week of inspirational math. Rating: 7 Couldn’t get much discussion out of them after it, but it was first day.
    • Continued with youcubed’s day one activity of writing group norms. Now I just need to make them into a poster. Rating: 8 Got everyone involved and talking. Got some good descriptors: “Open-mindedness” “Listening” “Optimistic”
    • Spent the rest of the day with the Four Fours activity, also from youcubed’s suggested first day. Basic idea: use four fours and any math operation(s)/symbol(s) to make all the numbers from 1-20. Rating: 10 Almost 100% participation the whole time. This would also be a great starting activity for order of operations. Two classes had enough time to get all 20!
    • Homework was reading the Make It Stick handout and also having parent fill out google survey, here’s the good part of it:Google Parent SurveyRating: 7 Only about 75% of parents have filled it out as of yesterday. On the other hand, one parent actually wrote in the additional comments section, “Thank you for a great and innovative syllabus experience.” The “I’m proud of my child because” question is great to refer to in parent meetings.

Friday:

  • High-fived everyone again. Rating: 10 Pro tip: If you’re setting stuff up between classes as kids are coming in, just go around the room quickly and high-five them before you stand outside the door.
  • Bellringer was 3 things you learned from the reading, 2 questions you still have, and one interesting fact.  After they finished writing, I gave them 1 minute to share interesting fact with group. Then I gave them 2 minutes to try to answer each other’s questions, then asked each group to share questions they still had and I answered them. I gave them another 2 minutes to decide their favorite key idea as a group, had each group share, then I elaborated with more information from the book. Rating: 9 Good discussions in each class!  Especially when I brought up the fact about re-reading not being helpful and “illusions of mastery.” My favorite moment: I was discussing lagging homework and asked, “so have you ever been in a class where the teacher says, ‘uh-oh, I have two minutes to finish this problem that you need to know in order to do the homework?’ Well, now we can hold off until the next day since your homework won’t apply to today’s lesson!” Then one girl replied, “Or we could try it as homework as generation for the next day!”  I think I may have cheered when she said that.
  • I had them fill out their math goal and find accountability buddies. Rating: 3 Almost every single student just wrote “make an A.” I also haven’t had time for them to check in with their accountability buddies. Would not do again, or maybe wait until a few weeks into class.
  • Up next was paper folding from youcubed.org.  Rating: 2  I would not do this activity again. After the quick success of the first two (fold a square into a square that is 1/4 of the original; fold a square into a triangle that is 1/4 of the original), the next ones amp up the difficulty by quite a bit (fold a triangle that is 1/4 of original square but not congruent to first triangle; fold 2 different squares that are 1/2 of the original). Also, when students thought they got it, instead of convincing their partner, they would call me over and ask me if it was right. Quite a few students embraced the challenge and kept on folding, but for many of them, the frustration (and maybe pointless-ness?) was just too great and they quit. I’d be interested to hear if those teaching younger students have more success. And I still don’t know how to do the second square oriented differently from the first that has 1/2 the area of the original. I thought quite a few of them had it but upon trying to convince me, they didn’t.

I hope to back soon with a recap of the first real week of teaching, but after working on math for the last two weeks straight I need an afternoon of not thinking. At all.

My thing: It has been a while since I share a favorite thing, so today I’m going to absolutely amaze you with CamelCamelCamel.  This is a price tracker for Amazon and works in three different ways: 1) Connect it to your Amazon wishlist. It will automatically alert you via email when the price of something you want has gone down. You can also add individual items on the website (great for tracking stuff from other people’s wishlists for gifts) 2) Use the browser plug-in or copy the amazon URL into its webpage to see the price history. Great to know if that $40 price is just a high mark, or if it’s been $40 for the last three months, or if it wavers between $30 and $50. 3) Browse their list of popular products for “good deals” and “best prices.” Two things it doesn’t do: it does not alert you to lightening deals (but I usually get an alert if its a an-day daily deal) and it also cannot track kindle book prices. But I still think it’s a great tool!  And you could probably do something really mathy with the historic price charts, too.