Author Archives: mrmillermath

Taboo – Quadratic Functions

Posted on March 24, 2013 | 3 comments

The Overview

Improve student literacy by focusing in on the math terms surrounding quadratic functions, and then play Taboo using those terms.

IMG_0483

The Description

Warning:  Your students will have a lot of fun with this.

Taboo is a game where you try to get your team members to say the word on your card, but there are a list of restricted words that you cannot use in your descriptions.

I read Fawn Nygun’s Taboo activity and I wanted to do it with my class.  I love how she implemented it by having her students create the cards.  But I decided to control the words in Taboo by creating the cards myself.  This allowed me to scaffold it by first focusing on improving student literacy on the words that I had put into the game.

To scaffold the words that were going into Taboo I decided to use Frayer Models.  I created the packet “My book of Frayer Models” and we did two each day for a week.  It was a warmup activity that they did when they first walked into class, probably took 20 to 30 minutes each day.  Below is an example of one of the pages of a students Frayer Model book.  I would give students the page number where the word could be found in their textbook, and I had them do the model themselves while I did the routines of checking off homework and taking role.

IMG_0487

After I was done checking homework, taking role, I would randomly call on students and get my Frayer Model completed on the whiteboard.  Lastly for each Frayer Model, I would put the word on the whiteboard and ask students for key words that describe it.   This portion of the lesson acted as my substitute for when Fawn’s students wrote out their own taboo cards.  We were essentially writing out a Taboo card as a class, and it allowed me to see what words the students deemed important.

After we finished their book of Frayer Models – It was time for Taboo!

The taboo cards focus on quadratic functions.  I didn’t make them all related to quadratic functions in order to give students the illusion that the game was covering the entire book.  The restricted words were choosen to leave the door open for good mathematical descriptions and not make the game too difficult.  Thus for the word “parabola” I didn’t include “quadratic” as a restricted word.    For me, the restricted words were really meant to try and take away the cheap clues, rather than the good mathematical clues – like for instance with the card “Domain” I restricted “Range” but I did not restrict “x” or “value”.

The rules for Taboo were basically the same as Fawn’s, but here they are:

  1. Class is divided into 2 teams, Team X and Team Y.
  2. Team X goes first: two people from Team X come up to front.
  3. Skipping a word is not allowed.
  4. Team has 1 minute to get as many right as possible.
  5. No hand gestures.

The Keynote slides attached below have a description of how I explained the Taboo game to the students.

For the final round, I was describing each card and giving points to the team that could guess it first.

The Advice:

– I would let one student volunteer to come up and I would randomly select a second student to join them.  I had students who never volunteer for anything, volunteering for this.

– Ultimately if the students knew the goal of Taboo was to work vocabulary of quadratics, then they could just list off all those key words every round.  So it’s important to do the following two things in order to give the students the illusion that any term in the book is possible.

  1. Do not tell the students that they are going to use the terms from the Frayer Models to play Taboo.  Even though every term from the Frayer Models are in the game, the students don’t need to know that.  I even collected the Frayer Models to day before playing Taboo.
  2. Throw in some math terms that do not have to do with quadratics.

– Students liked to say things like “the opposite of” – so if you have a card for maximum, make sure minimum is a restricted word.

– Use the restricted words to keep students from being able to use a non-math description.

– Have your TA cutout the Taboo cards and glue them to playing cards.

The Results:

A high level of engagement.  Definitely an animated class and everyone enjoyed the activity.  Students were shouting out a lot of great vocabulary, and I felt good that the Frayer Models had given them improved math literacy.

The Goods:

BookOfFrayerModels

QuadraticTabooCards  (There are only enough cards here for 2 or 3 one minute rounds if you have two teams)

TabooSlides

3 Comments

Posted in #collaboration, #game, #reasoning

Tagged , ,

You Are Not Your Lesson Plan

Posted on March 17, 2013 | 3 comments

We spend lots of time and energy creating the best possible lessons that we can.  We get excited about them and feel good about them.  Thus many days, armed with well thought-out lessons, we achieve a measure of success in our classes.  But then there are those days when nothing works.  When the lesson we poured our energy into falls flat on the floor.   The kind of day when the lesson is getting disrupted by off-task students, and a carefully scaffolded intro leaves student after student saying “I don’t get it”, “what am I supposed to do?”.  The volume of off-task chatter rises and opens the door to increased behavior problems.  Behavior problems by the way, that are ripe for misintrepretation by the now frustrated teacher.

First thing to remember during these times – You are not your lesson plan.  Thus every student act of ignoring it, failing at it, brushing it aside, sleeping during it, distracting it, or any other negative, is not a personal affront to you.  That took me awhile to realize.  In my own practice, in the midst of my favorite lessons failing it would bring up anger and frustration, often towards the students who were most clearly rejecting me (of course they were not actually rejecting me, but hence the point of this post).

There are an array of reasons a lesson might fail, but you will be unable to properly diagnose any of them if you are angry.  Anything in your teaching practice that creates negative energy towards your students, your profession, or yourself, needs to be analyzed and reconstructed.   These negative emotions commonly end up concluding that the lesson failed because the students are lazy, don’t care or don’t pay attention.  Maybe they were or didn’t, but if that is the primary conclusion then you are overlooking a couple important facts:  First – there is a way to improve the lesson and those students are helping you discover it.  Secondly, deep down you were probably personally offended by the way the students interacted with your lesson, which is intimately connected to your identity as a teacher.  Thus you feel like a failure, and angry at those who exposed you.

Experience doesn’t necessarily help in this situation.  This problem of identifying with our lesson plans actually got worse for me as I became more experienced.  Because often at some point we as teachers, who pour ourselves into teaching, begin to recieve a fair amount of praise from adminstrators and students.  We start to look at ourselves as great teachers, which makes the day when that identity is challenged even more difficult to take.

So bottom line is this:  You aren’t your lesson plan.  Don’t take it personal.  If you have a lesson that collapses into failure don’t get upset, don’t get stressed out, don’t get frustrated.  Stay positve and do whatever you have to do in that moment to teach the best you can.  Afterwards,  I recommend you take a moment to reflect on what went right, what went wrong, and how it could be improved.  Make sure you properly file that reflection so you can use it the next time you plan the lesson.  After that, just finish the day and be done with it.

3 Comments

Posted in classroom management

Tagged ,

Parabola Review Worksheet

Posted on March 13, 2013 | 3 comments

I created the following worksheet to help students review what they learned about identifying the different characteristics of a parabola.

ParabolasCharacteristics

After printing it out I decided that I wanted to make it an error analysis exercise instead, so I filled it out myself and made one or two mistakes for each parabola.   I had students put check marks by the correct answers, circle and fix the wrong answers.  Here’s that worksheet:

MathHustlaError

The Goods:

ParabolasCharacteristics

ParabolaCharacteristicsError

3 Comments

Posted in #error, algebra, worksheets

Tagged , , ,

This Is Too Grand To Be Said

Posted on March 3, 2013 | Leave a comment

In college I had the honor of taking Elliot Aronson’s last Social Psychology class at UCSC.  He had been a professor there for many years and was going to take a position at Stanford.  The large lecture hall was packed for that last day, filled with his current and former students.  He ended the class by reading the final lines of  J.D. Salinger’s “Seymour, An Introduction”.  He got all choked up and started to cry midway through.  The passage itself is a wonderful reflection on life and teaching, and I get why Professor Aronson choose to end his last class with it.  Here is what he read to us that day:

“Nonetheless, I’m done here.  There are one or  two more fragmentary physical-type remarks I’d like to make, but I feel too strongly that my time is up.  Also, it’s twenty to seven, and I have a nine-o’clock class.  There’s just enough time for a half-hour nap, a shave, and maybe a cool, refreshing blood bath.  I have an impulse-more of an old urban reflex than an impulse, thank God- to say something mildly caustic about the twenty-four young ladies, just back from big weekends at Cambridge or Hanover or New Haven, who will be waiting for me in Room 307, but I can’t finish writing a description of Seymour-even a bad description, even one where my ego, my perpetual lust to share top billing with him, is all over the place-without being conscious of the good, the real.  This is too grand to be said (so I’m just the man to say it), but I can’t be my brother’s brother for nothing, and I know-not always, but I know-there is no single thing I do that is more important than going into that awful Room 307.  There isn’t one girl in there, including the Terrible Miss Zabel, who is not as much my sister as Boo Boo or Franny.  They may shine with the misinformation of the ages, but they shine.  This thought manages to stun me:  There’s no place I’d really rather go right now than into Room 307.  Seymour once said that all we do our whole lives is go from one little piece of Holy Ground to the next.  Is he never wrong?

I’m filing this post under classroom management because our own personal happiness as teachers is often the most important ingredient to a positive and productive classroom.

Leave a comment

Posted in classroom management, Uncategorized

Tagged ,

Investigator Training

Posted on February 27, 2013 | 15 comments

The Description:

The goal here was to use Dan Meyer’s “Bone Collector” 3Act problem, as the motivation for a series of lessons on scaling.

dollar2foot

The basic premise is as follows:  I show the Bone Collector clip first (see the link above for the clip), tell them we need to figure out the shoe size of the killer because we need to make sure that the killer is not in the room.   Then I concede that I realize they are not trained investigators.  Thus I tell them that over the next couple days we will be doing some investigator training, to get them ready to take on this case.   I help a lot during the first two cases, but I provide little help during the Bone Collector case – and the good news is that they didn’t need much help on it after the investigator training.

CASE 1 “The Drug House”

For their first case, I used a google maps images (see Keynote or PowerPoint file below) of a huge house that I was calling a “known drug” house (It’s actually Michael Jordan’s house).  The goal is for them to calculate the area of the very suspicious large building at the bottom right of the picture, where a lot of cars are located.  I tell them the FBI wants to perform a raid but they do not know how many agents to send, because they don’t know the size of the building.  And they are waiting for our calculations to proceed.

DrugHouseGoogleMaps

I handout the above picture to each student.  Then do a little strategy session where they write down how they are going to calculate the size of the building.  At that point they are given time to solve it with their pair/share partner.

The next day  I come and say that althought the FBI was happy that we correctly calculated the size of the building, unfortunately after performing the raid they learned that this was not a drug house, it was in fact Michael Jordan’s house.  And that big building is a basketball court.

CASE 2 “The Statue Thief”

I use a picture of the Surfer Memorial Statue in Santa Cruz.  Then I show a the same picture but with the statue photoshopped out.  I then tell them that a security camera picked up a very suspecious person who had visited the statue multiple times before night of the theft , and that the FBI needs us to find the height of the suspect in the picture.  This case is very similar to the Bone Collector.

StatueThief3_2

(awesome statue)

StatueThief3

(sadly it was stolen)

StatueThiefSuspect1

(but we have a suspect)

Students get a copy of the image above.  We again do a strategy session, where I require them to write a strategy for finding the suspects height.

The next day I reveal that the suspect was captured and he is 6ft.  Most students calculate something around 6″3′, so we spend some time talking about possible sources of error.

CASE #3 The Bootprint

Here we do the actual Bone Collector problem, delievered in much the same way that is described in Dan’s blog.

The Advice:

– I have students work in groups of two.

– I don’t spend the entire class period on these.  I do investigator training for the first 20 minutes or so, and then move on to something else.  Thus I essentially make this investigator training week.

– I help the students with the strategy sessions for the two practice cases, and then leave it up to them for the Bone Collector problem.

– Definitely play up the investigation aspect of these cases.  I tell them how much investigator make and that they should take these cases to the polic department and interview for a job.  If a couple students complain the quality of the bootprint picture is not very good, respond with “Yeah, I’m not sure why the FBI would provide such a low quality image”.

– That is me in the picture for the “Statue Thief” problem.  That is definitely an added bonus if you can do it.  It allows me to completley deny it’s me, while also saying “Look it’s not enough to just tell the police the suspect is extremely good looking, we have to get them information about his height”.

The Results:

High level of engagement.  Take a listen to student reaction when they hear that the shoe print is a size 10.

Bone Collecter student reaction

The students were upset (yes, actually upset) because all their solutions were between size 13.5 and size 16.5 .  They all calculated a larger size because they used the bootprint, rather than the actual size of the foot inside the boot to convert to shoe size.   I ended the lesson with a great back and forth with the students about what happened with their calculations.

One of my lowest performing students asked me if her proportion she setup was correct…  it was.

Using the Bone Collector clip without the associated investigator training works too, but not as well for me.  I really enjoyed these lessons, and I felt like my two initial cases put the students in a place to be successful with the Bone Collector problem.

The Goods:

Dan Meyer – Bone Collector problem

The Drug House Handout

The Statue Thief Handout

Bone Collector Bootprint  (just pick one – my girlfriend and I messed around with the image in photoshop to get the best quality for different printers)

InvestigatorTraining   (Keynote and PowerPoint)  I created this in Keynote, and highly recommend using Keynote.

Update 1:

To see whether or not the students retained any of this, I put the following picture into the chapter test.  The question was:  How tall is the tree?

MrHaysAndTree

The guy in the picture was brave enough to take me on as his student teacher and I am a profoundly better teacher because of it.  His name is Walt Hays.  His height is 6ft.

Update 2: 3/23

Based on Debbie’s comment, I have fixed the typos in the Keynote and Powerpoint files and adjusted the scaling to result in an answer that is consistent with the size of the tennis court next to the basketball court building.

 

 

15 Comments

Posted in #perplexity, algebra, geometry, Uncategorized

Tagged , , ,

This Is What I Was Born To Do

Posted on February 20, 2013 | 5 comments

I don’t watch American Idol looking for inspiration towards the teaching profession.  But I found it the other night.  Contestant Nicholas Mathis went on stage looking very defeated and full of doubt, and his performance was lack luster because of it.  After Mathis finished, Idol judge Keith Urban made the following remark to him about musicians, but I believe it applies even more for teachers:

“There’s a lot that pulls at you in this calling. And somehow we have to compartmentalize that and when we wake up at three a.m. in the morning on a tour bus and we wonder ‘What are we doing here,’ and we just cry, the only answer can ever be ‘This is what I was born to do. This is my calling.'”  –  Keith Urban

Except for teachers instead of 3am, it’s 3pm, and instead of a tour bus it’s a classroom.

The judges voted Mathis off after that appearance, and if we show up to the classroom like Mathis showed up to Idol, then we are likely to be voted off by our students.   We cannot show up to a class looking defeated – your students deserve a teacher who is positive and professional.  So you need to figure out how you are going to intrepret the things that happen in your class in such a way that keeps you positive and happy.  Realizing that you were born to do this, well, that is just one way.

5 Comments

Posted in classroom management

Tagged ,

Factoring Puzzle – Practice Version

Posted on February 18, 2013 | 2 comments

The Overview:

I wrote about a factoring puzzle I found online here.  That puzzle is difficult because it has trinomials with a leading coefficients other than 1, as well as special products.  I wanted to create a puzzle that would be a simple review on factoring trinomials where the leading coefficient is always 1, or could be 1 if the GCF is factored out first.  Thus when they eventually challenge the more difficult puzzle, their questions will be focused on factoring, rather that “I don’t get what to do?”.

I did not create a scrambled version, so obviously you will need have a TA cut out the pieces and put them into envelopes.

FactorPuzzlePractice

FactorPuzzleChallenge

The Goods:

FactorPuzzlePractice

FactorPuzzleChallenge

Update 1:

Thanks to a great comment from John, I have created one that does not have a border, thus allowing us to differentiate for the excelling students.  That puzzle is now included above in the original post.  The puzzle without the border is the exact same on the inside as the puzzle with the border, I will eventually make that different too when I get some time.

2 Comments

Posted in #kinesthetic, algebra

Tagged , , ,

‘Who Am I’ Worksheets

Posted on February 9, 2013 | 1 comment

The Overview

I have been making more of these “Who Am I” style worksheets where the students are given a set of clues and possible answers, and they need to figure out which answer works for which clue.  I would consider this a graphical organizer and a puzzle activity, since all the information is already organized, and the students are making connections between the answers and the clues.

The worksheet for graphing slope intercept has exactly one right answer for each clue.  The one for classifying polynomials has a couple right answers for some of the clues.  I think my next “Who Am I” worksheet will have some answers that do not fit any of the clues, which will take away any process of elimination technique the students may be using.

WhoAmIClassifyingPolynomials

The Goods

WhoAmI_SlopeIntercept

WhoAmI_ClassifyingPolynomials

1 Comment

Posted in #graphic organizer, algebra, worksheets

Tagged , , , , , , ,

Say All Their Names… Twice (at least)

Posted on January 19, 2013 | Leave a comment

I say every one of my students name at least twice a day, and I am very intentional about it.   The reason I do it is because saying a students name is a simple way to make students feel welcomed and appreciated.  My method for saying each name allows me to ensure that I do not miss a single student.  Ultimately I may end up saying every name lots of times, but this is my built-in strategy to make sure that on any given day, I acknowledge each student at least twice.

The first time I say each students name is before class when I greet them at the door.   I am never robotic about my greetings – meaning I never say “hello _______ (insert name)” to every student.  I throw out a lot of non-sequiturs “Juan how was 3rd period?” “Beautiful day, right Alicia?” “Welcome to Algebra Josh”.  It’s more fun and sincere that way.  If a group of students show up at the same time I will catch them all in the same greeting  “Thomas, Cinthia, Linda, welcome to class”.

The second time I say each name is when I check off homework.  Right when the bell rings I have all my classes work on warm-up problems while I circulate the aisles and check off the previous days classwork.  Here I once again use each students name, “excellent Leisi”, “you da man Chris”.  I will randomly choose a few students to engage in quick discussions with a simple “How was your weekend Bryce?”.

Thus I guarentee that I acknowledge the existent of each of my students at least twice a day, everyday.  It’s not much, but I believe it to goes a long way in making the students feel like welcomed and appreciated members of the classroom.

Leave a comment

Posted in classroom management

Tagged ,

Algebra Remix – The First 20 Days.

Posted on January 8, 2013 | Leave a comment

One of my goals for 2013 is to rework the first 20 days of algebra to tightly connect it to algebra standards – specifically linear functions.  First semester algebra should begin by setting the goal of understanding linear functions, and everything we do from that point on is in support of that goal.  Currently algebra begins with a basic review of 6th grade standards – adding / subtracting, substitution, order of operations.   I think we should still practice all those skills, but only in service of linear functions.

We currently review those skills in a vacuum, without making connections to algebra standards, such as slope-intercept form, slope, y-intercept, and graphing.   I think we should make sure that when students are practicing their fundamentals, that they are also learning about algebra fundamentals.  For example – practice subtracting negative numbers by first introducing the slope equation, and then asking them to find the slope given two points.  That way they are still practicing subtraction, but they are doing it in service of linear functions.

I believe that after the first 20 days of algebra students should:

  1. be able to graph an equation by plugging in two points.
  2. be able to graph using slope-intercept equation.
  3. understand the difference between discete and continous graphs.
  4. understand how to find slope from a graph
  5. be able to solve for slope using the slope formula.
  6. review skills of multiplying, subtracting negative numbers.
  7. write slope-intercept equation from a graph.
  8. determine if graphs are increasing, decreasing, and connect that concept to positive / negative slopes.
  9. indentify slope and y-intercept from the slope-intercept form of an equation.
  10. determine if a relation is a function.
  11. practice order of operations.
  12. understand domain and range.
  13. be familiar with the concept of an input and an output.
  14. be able to solve a basic two step equation.
  15. solve word problems where the solution takes the form of y=mx+b.

I currently putting this 20 day learning segment together and proposing it to my district.  As it gets completed, I will post it.

Update 1

My principal likes this idea some much he gave me a one day pullout to work with our district curriculeum and instructional specialist on this idea.   We currently have 25 days of remix going, so I should change the name of this post.  I am very excited about the work we got accomplished, and with another pullout day scheduled after star testing, I thinking we will have this well put together by the end of the school year.

The instructional specialist is wanted to make sure our final product works for common core, so that was an added dimension to all this.

Leave a comment

Posted in algebra

Tagged