Category Archives: Reflections

#mtboschallenge 1-2-3 Sunday Summary

Going to change up my order a bit so I can start with:

One Totally Awesome Way to Deal with Complex Fractions (complete with poor cell phone visuals)

I don’t know where I picked up this method (I actually want to say it was a textbook and not MTBoS, but that doesn’t sound right, so if it was from you that I got this, let me know) but it is a totally awesome way to deal with complex fractions.  Before, I would simplify the top and bottom, then multiply the numerator by the reciprocal of the denominator.


I was going to use arrows to show the two different ways on the same page but I ran out of room.  It’s not that I don’t think you could follow my steps without them.

Maybe to save time, once I simplified the top and bottom, I’d use “outers over inners” to get the next step, while pretending I didn’t know what this Nix the Tricks thing was all about.

Now here is the totally cool, time-saving, wait-til-you-get-to-cal-to-see-how-awesome-this-is, not-a-trick way instead.

Multiply the top and bottom by the LCD of the “tiny denominators.” 


WHAT???  How amazing is that?  We just have to choose a “convenient one” and all that middle work is taken care of.  Some more examples:

CAM00165I need to set up some sort of royalty system where I get 3 cents every time you use this rule and are completely amazed by it (because I still am amazed after using it for a year).  (I also think all those Shark Tank viewings may be going to my head.)

Two Other Cool Things To Share

1. What reminded me about the cool fraction trick was the fact that we were working with trig identities and double/half angle formulas this week.  Here is a lovely handout (.doc file with “running for a cause” font) for trig identities:

Capture2The order of the identities works out nicely to do 1-6 as a group, 7-12 as individual practice, then the rest as group practice (and yes, 11 and 19 are the same. My laziness strikes again.)  I also tried to disperse the more difficult ones throughout the worksheet instead of all at the end.

2. Mattie B (@stoodle) sent out this plea this week:

Which led to a discussion of Bowman’s Dead Puppy Theorem, which then led to my sharing of this handout, (.doc file with “running for a cause” font) which has all of the ways to save animals.


You’re welcome, I already test drove this and therefore changed save “yourself” to “your grade” to avoid the awkward “don’t kill yourself” statement.

The arrows at the top are a reference for this fabulous way to think about exponents from Sweeney Math

Shoot, Now I Need to Think of Three Other Things to Talk About

1. I tried to go vertical with my group whiteboards this week by having my Precal classes work on their identities.  It was AMAZING!!  I could do a quick scan to see where everyone was, 98% of the kids were engaged, if we had time at the end of class I could say “to the boards!” and they would pick up where they left off the day before.  Then all the whiteboards fell off the wall overnight.  I’m just thankful the one that did fall off during class wasn’t where any students were sitting.  I put in a request to see if someone would mount them for me (or if I would be allowed to mount them), but haven’t heard back yet.

2. Like many of the other MTBoSers, this has not been a very positive year overall for me.  All the grand plans I had at the start of the year have been squashed and now I’m basically back to doing the same things that I’ve always done.  But now with 20% more stress.

3. Have you tried showme? I was introduced to it by a new teacher at my school, and it is pretty cool.  Unlike some of the other ipad whiteboard apps, this one makes and stores the video for you–no need to find a place to upload it or deal with a password-protected site.  The only thing I wish it had would be the ability to import PDFs, but another teacher had the brilliant idea of taking a screenshot of the PDF and importing the picture.  Clever!

Sunday Summary

It’s time for the weekly (ok, technically bi-weekly since I was at the beach last week for a very rejuvenating weekend with the parentals) #mtboschallenge 3-2-1 Sunday Summary!

3 Things I’ve Done Recently That Were Not Half-Bad.

1. Question Brainstorming

I usually try not to reward promoted links on twitter, but this article about students asking questions was too tempting not to click.  I read it Thursday night and then tried it out Friday morning in PreAP Precal where we were preparing for a test on Monday.  I handed each student a piece of scrap paper and let them have 3 minutes to jot down any question they had–it could be general (“how do you write an equation for a tangent graph?”) or specific (“how do you do #11 on the study guide?”).  Then I gave them 6-8 minutes to try to answer the questions in their groups–I saw A LOT of good peer helping at this stage!  Then I collect any remaining unanswered questions and answered them

…Except for “why is -1 used for inverse notation?” (unless you count “because it is” as an answer).  I did a little googling this weekend and all I was able to come up with was if you want to perform f on x, you write it f(x).  If you want to perform it twice, you could write it as f(f(x)), or f²(x).  Following that same notation, undoing f once could then be written as  f‾¹(x).  Anyone have anything better?

2. Using Graphing Calculators to Graph Absolute Value

I found great discovery activity worksheet online and actually used the entire thing with limited modifications (I took out graphing the piecewise lines because we hadn’t discussed piecewise yet and one battle at a time, amirite?)  It went over great!  The kids were enthralled at using their calculator to do this.  (Actually, they were more amazed that it could graph y = |x + 2| than the fact it could give you a line of best fit when given 15 different ordered pairs.)   Hint: Have them turn their grid on (under “format”-the top middle button on TIs) for better transferring of graphs to paper.

3. Linear Modeling in Algebra II

Totally stealing from Mimi’s (@untilnextstop) fabulous worksheet, I made some math libs of my own.

Capture1(doc file here)We did these by hand (well, as in putting equation in point-slope form and then converting to slope-intercept).  Things I need to change: kids have no idea about having to pay a fare just for getting in a taxi nor do they understand #4 at all.  I should throw something in there about having to pay for both AOL and internet service just to complete date myself.  Also it’s best not to have a question about a rod expanding or growing if you’re teaching high school boys.

Then I made another worksheet to use the linear regression on the calculator.

Capture4 Capture3(doc file here) As I said, I did steal the first two questions directly from Mimi.  One thing that I didn’t notice until a kid pointed it out is that the answers to 4D don’t correspond very well to the chart, which led to a great discussion of what the line of best fit can and can’t do for us.

You can’t see it in the picture, but the next problem has the y-scale in billions which was something good to discuss as well.

We then did Mathalicious’s Reel Deal lesson, which was using a scatterplot and line of best fit to determine the movie lengths.  Maybe it was because I was pressed for time, but it did not go over as well as I thought it would.  I think next time I will just add it as another example to discuss in class.

Two Things That Are Not So Great

1. Even after all the work we did with the linear equation mad libs (and we did more work in bellringers and study guides) some students still had trouble telling me what the slope or intercept meant on the quiz.  (As in being able to fill in the blanks: for every _____, the something will increase _____.  At the beginning, there was _____.)  Maybe I should have done Mathalicious’s Domino’s activity instead of Reel Deal.  I also waver back and forth between “they should know this already!” and “they need to know this and they don’t so I need to spend a lot of time on it!”

2. Time is still a huge stress, since we are also nearing the end of the nine weeks and I am struggling to get in 6 major test grades.  Do I just have one test on a single topic to get the required six?  Or cram a lot of material in to have the test cover more than one topic?  Ugh.

One Thing I’m Looking Forward to This Week

Trig Identities!!!!!!!!!!!!!!!!!!!!!  I could do those all day.

Ok, so maybe I just like them for the puns.  🙂

#MTBoS Sunday Summary

My week:

Algebra II w/ Trig

We took our first test, which was a GREAT segue[1] into growth mindset and overcoming setbacks.  Although they didn’t knock it out of the park, I had fewer really low grades than previous years, so that’s a good sign.  This is usually a tough test and I think I need to either (a) break it up into 2 quizzes or (b) actually follow the notes that I leave myself every year that say “DO MORE DAYS OF ____”

Then into functions with this beautiful Note-Taker-Maker[2] that I stole bits and pieces of from everyone, but I think mostly from mathequalslove.

Capture1.doc file here

Friday we did the ever-popular graph stories, but I made it into a worksheet because I do not have time for scissoring.  They worked in groups and I paired groups up as they finished to discuss answers.  Then when everyone was done I brought out the talking dog.

No, it didn’t actually talk. I’ve been having an issue with students not listening to other students talking, so I thought I’d take a cue from GWWG and Mr Healy and start the rule that you can’t talk unless you have the talking dog.

So the dog was passed around as we explained and discussed our answers to each graph.  And what do you know?  It worked!!  Not 100% of the time, but they were listening a lot more than before. Some of the kids had great explanations, too, including “we first thought it was this graph, but then when we met with another group, we realized….”  Win!

PreAP Precal

Holy moly, definitely some ups and downs this week with discovery learning.  All of the kids are working super hard at trying to figure out what I throw at them, but they are lacking in (a) math skills and (b) seeing math connections.

We spent about 1.25 days on translating linear equations to discover our “new” point-slope form: y = m(x – h) + k.  Worksheet here.  It went really well and was a good lead-in to piecewise (“isn’t it so much easier to write the equation of this guy using point-slope since we don’t know the y-intercept?”)

We also spent 2 days on average rate of change, worksheet here. (I’m pretty sure I stole this from someone, too–I really need to work on documenting my sources!)  The first side of it went great, but I need to reword it so they understand we’re doing the exact same thing on the back!  Just calling it a different name!  Really!  That’s it!  Then I wonder to myself, would they have made better connections within the same time frame if I had lectured for 20 minutes on AROC, definition, formulas, etc, then let them work with applications of it for 1.5 days?

So even though it may get me kicked out of the MTBoS, I think I’m going to stick with introducing a topic as a class first, then letting them loose on going deeper, rather than letting them loose to discover the topic but running out of time to go deeper.  Plus, I think based on this: zone(poster available here) I’ve been in the panic zone as a teacher way too much this year and need to scale it back to be in the learning zone.  I need to keep reminding myself I don’t have to try everything that I learned at TMC during the first month of school!

[1] I’m not going to lie to you; I just found out last year this is word that people are using when they say “segway” as in, “Using (person, birthday) as a function example allowed me to segway into mentioning I don’t like Starbucks.”

[2] Notetakermakers (or “NTMs”) are what I call my graphic organizers.  Yes, I make one for each section.  Yes, I do use a lot of paper.[3]

[3] Dude, I don’t know why the superscript is showing up as just tinier script.  I’m using “sup” and everything.  Here’s a subscript example: [1] which looks to me exactly like the superscript.  Sometimes I hate everything about wordpress except for the fact that I get to use “”

Many Questions, Few Answers

So in trying to be a better teacher this year, I have a few questions that I would LOVE LOVE LOVE LOVE LOVE LOVE like, seriously, LOVE if you could add your input either here or on twitter (@mathymeg07)

1) I’m really trying to “you, y’all, us.”  But Y’ALL is soooooo slow.  I hear them having great conversations on example three for 10 minutes, but I want them to see example four before they leave, too!  How do you not worry about time?  Or how can I better plan or pace my class time?  I am trying to book it through bellringers, homework questions, discussion/lecture/practice and definitely not having enough time to finish or even squeeze in a quick formative assessment (other than me going around and looking at their work in groups).  And I don’t want this “oh, the learners will learn at their own pace and just take as many days as you need” because I have approximately 217 objectives to cover in Algebra II.  (FYI, we switch between 47 and 52 minute classes every other day).

2) The class is finally rocking and rolling and 25/26 have the correct answer.  What do I do with the one kid who doesn’t get it?  Move on and tell them I’ll help at the end, but I won’t really because I’ll run out of time?  Tell them to come back later, but they won’t?  Have someone (or me) explain the problem even though 25 of them have it solved correctly?

3) Also, what about the one kid that is always finished first?  I have one kid that has already finished the application practice we’re going to work on tomorrow.  I don’t mind that he has because I’m also the type of person that will work through something you give me until I am done, whether or not it is assigned.  I would just like to make class time more worthwhile for him.

4) What do you do with the kid that answers every. single. question?  Or, I guess to describe it better, the kid who thinks out loud.  Loudly.

5) I tried whiteboarding mistakes and I really liked it for the groups that were making the mistakes.  However, some students complained that it confused them when we went over them.  How can I make whiteboarding beneficial for the students that got it and for the students that are still struggling with the concept being whiteboarded?  (side question: could we come up with a better name than “whiteboarding” so it doesn’t seem like I’m using questionable spy tactics with my students?)

6) How can I get over the feeling that I am letting some kids flounder by pushing so much of their learning onto groups and away from directed teaching?

Again, I would appreciate ANY AND ALL COMMENTS, SUGGESTIONS, OR MAGIC POTIONS!!  Thank you!

Category: Reflections | Tags: ,

Desmos, Giving up Control, & Pretty Happy Things

Mishmash of stuff going through my mind this week:

Desmos Function Carnival

Confession: I had not been to the computer lab at school for 10 years because the last time I went nothing worked.  The second day of school is normally picture day, so I  thought I might venture into the lab again, since it was already a wasted day.  (Of course, they rescheduled picture day.) I tried out the Function Carnival with PreAP Precal and Algebra II w/ Trig.  I think both classes had much success and enjoyed it as a nice way to ease back into math. I have 52 minute classes and some finished with 15 minutes left, many with 5-10 minutes left, and a few were working until the bell.  Since we ran out of time for class reflection, I wish I had made a worksheet (or google form) for them to do about what they noticed/wondered and, maybe for Precal, describing what type of graphs they had seen.  If you’re trying it for the first time, I would definitely recommend having a tablet device of some kind.  I brought in my own iPad, so I could use the teacher dashboard and monitor as I went to talk to kids.  Once they got to the final screen, I could also quickly check their graphs and have them work on ones that could be better (or congratulate them for being very precise).  I think this Friday (the for-real picture day) I will be trying another one–maybe the penny lab?

Giving Up Control

I’ve been tweeting with the group work guru herself, Ms. @CheesemonkeySF, about doing talking points tomorrow.  I asked if I should monitor the “NO COMMENT” rule and she replied:

Capture SF

She went on to say, “So many…don’t delegate this authority and, as a result, they don’t actually gain the benefits of the group work they believe they are using.  If you want kids to go deep you have to set up a structure in which to trust them.  And you can’t test trust cautiously!”

AAHHH.  But it’s scary to give up my authority.  I like feeling like I’m shepherding these little lost sheep to safety.  I don’t know if I can trust them because I’ve been both surprised and disappointed at what they can do when left to their own devices. What if they just stand out in the rain with their mouths open and drown?  And if they can be trusted, how does that change my role as their teacher?

Also going through my mind is a tweet from this week about how we need to build relationships with our students so that they will do anything we ask just to please us (or something to that effect, maybe it was walk through fire just because we asked?).  I do not have this type of relationship with my students.  Yes, most of them come in and do their work and I don’t have many behavior issues, but I don’t see this ever happening in my class.

Is that ok?  If it’s not ok, what can I do to change it? Is there some code word like “BaaRamEwe” I need to use like Babe?

Pretty Happy Things

Man, things are getting a bit deep around here.  Let’s look at some pretty things for Made4Math.  Some of you may have seen my notebook at TMC14:

02-party binderI made it using my Silhouette machine.  It’s like a Cricut, but instead of using cartridges you design things using its software.  That means it can cut ANY font, and a lot of other cool stuff, too.  If your school/district has a teacher resource center, you may want to talk them into buying one.  It can cut paper, cardstock, vinyl, heat transfer, stickers, all sorts of things.  For the notebook, I cut it out of pink vinyl and applied it to a black notebook.  Some other people wanted to get in on the action, here is Susan Craig’s (no relation)

Capture nb

BTW, how can you nicely insert tweets into posts, besides this horrible attempt at screenshotting?

I also have this one from last year:

03-FNL binderAnd as a special offer for reading this far, I will send a notebook-size (or clipboard-sized) vinyl cutout to the first three (3) people to leave a comment.  You can choose from above (I also have “Whenever I’m sad, I stop being sad and start being awesome instead.”) or if you have a favorite quote, I would be glad to make a new one!

Inspired by my FNL notebook, let’s end this post with a little Coach Taylor motivation:

Listen to me. I said you need to strive to be better than everybody else. I didn’t say you need to be better, but you gotta try. That’s what character is. It’s in the trying.