Sunday, November 16, 2014

Parallel & Perpendicular Slope

I have always struggled getting students to really understand how to use slope to create parallel and perpendicular lines.  I have tried many things and many different activities over the years.

This year I did the typical investigation about parallel and perpendicular slopes.  It works pretty well for setting up 3 sets of parallel lines and 3 sets of perpendicular lines and asking students to analyze the equations for patterns.  This took 2 days and went pretty well.

Now on the third day I wanted them to put this new found knowledge to use.  So I created the following DESMOS graphing challenge for them.  (feel free to use and change for your use)

The challenge started pretty basic to make sure they correctly recalled the patterns for parallel and perpendicular slopes.

The next couple asked the students to start creating shapes using their patterns.

There were a couple more like this and students overall handled it pretty well.  There were a couple questions about what a parallelogram was, which I totally expected. 

A few students got off to a slow start because they did not recall anything about parallel and perpendicular slopes.  This did allow me to find them quickly and re-teach the concept.  Once they could visualize the graph on DESMOS with the slopes they seemed to do much better.  

A few student got off to a slow start because they did not understand what they were being asked to do.  This was partially because my projector lamp blew up and I had no way to project anything.  It was also because I threw this together quickly and I don't think it was as clear as it should have been.  I will have to tackle that next year.

Overall it worked pretty well.  We will see if this is the year where I can get students to remember perpendicular slopes!


Wednesday, November 5, 2014

Class Debates in Math Continued...

So yesterday we had a debate about math totally go off the rails.  Students kept arguing without really basing anything on logic or facts or even good common sense.  It sometimes sounded like a 24 hour news network where people yell "I''m right because I feel I am right!" and then someone else yells "No, I'm Right, because I'M LOUDER!"  Only 1 section had this, but still I couldn't stop thinking about how badly this went.

So today we started number talks.  Number talks are just a format for discussing interesting math questions that stress reasoning and estimation skills.  Fawn Nguyen is the amazing teacher behind this website.  Her blog is awesome of course.

We started with the first question on the site.

"Are there more seconds in a day, or inches in a mile?"

Before we started, I wasn't sure what to expect.  I wasn't sure the students would be engaged, participate in quiet thinking time or be able to explain their thoughts.  I was worried that students wouldn't even know where to start and give up right away.

So I put together this smartnotebook slide to help keep the class focused.

The timer is clearly displayed as well as the steps.  Also the blue box is a random name generator.  I like having the first name displayed because it gives fair warning to that student that they are going to be expected to speak about this question.  (you can also see I type to fast and have a typo in the question!)

So every section today went extremely well!  Students respected the 2 minutes of initial thinking time.  I could see some students racking their brain for an answer, a way to approach the problem, or just an idea.  Some students looked around like "He is crazy if he thinks I can do this in my head!"

The discussion time was the best.  All students were engaged.  I mean 100% engagement.  Students either could not wait to share their ideas or they could not wait to hear someone give them a clue about the answer.  I heard great discussion all day long about this problem and different and fantastic ways to approach it.  

The sharing part was a little rough in most classes, but all reasons for picking a side were grounded in math and common sense.  There were no 24-hour news channel type arguments, just reasonable debate.  

I told them I plan to do a problem like this 1-2 times a week.  Most were excited.  Some groaned.  However when I asked them why they groaned, they almost all responded about "having to think to hard"  That is just what a math teacher loves to hear!

Tuesday, November 4, 2014

Classroom Debates about Math...

Today the 7th graders were studying integers.  We are getting ready to add and subtract them.  Yesterday we represented adding and simple subtracting on a number line.  Today we went with a chip board, with black chips representing positive numbers, and red chips representing negative numbers.

I told them that we are going over multiple representations of adding and subtracting to get to the best understanding we could about the operations.  I emphasized we are not going to depend on memorized rules, we must strive to understand adding and subtracting.  This was of course met with some blank stares and confusion.  During their previous year in 6th grade the teachers quickly skimmed the service of arithmetic with negative numbers.  Of course they talked about rules like adding two negatives is always negative, multiplying two negatives is always positive and so forth.

Everything was going quite well with the chip board lesson for the first 30 minutes.  Then with 14 minutes left I asked them to solve -4 - -3 and represent the solution on a chip board.  This was the first negative subtracted by a negative problem of the day.  The previous section and last section of the day handled this fine.  They used the methods we had talked about and it resulted in a short discussion.

However in my middle section of 7th graders, most of the students had ended up with -7 as an answer.  The seating arrangement of the class has 6 groups of 4-5 students in each group.  Four of the groups had come to a -7 conclusion.  One of the groups came to a -1 conclusion.  The last group knew the answer was either -7 or -1 but they couldn't decide which way to go.

So we set up a little debate on the topic.  A very loud and confident 7th grader proudly proclaimed a misstated rule from 6th grade and proclaimed -7 to be the answer.  I held back any judgement and most of the students nodded in agreement.  I then called on a student to present their argument for -1.  They went to the smartboard and explained in a perfectly correct way that -4 - -3 was -1.  No mention of rules they remembered they just used the chip board.  When they finished 2 students loudly and confidently recited different rules incorrectly proclaiming -7 to be the answer.

At this point I reminded them how using rules can be confusing and we have to focus on what adding and subtracting means.  This fell on completely deaf ears.  At this point the 4 groups held fast to their wrong -7 answer, but there were now 2 groups solidly in the -1 camp.  We were also down to about 4 minutes left of class.

Now I love student debate, I love discussions in math, I love to hear the thought processes of students, and I whole heartedly believe that mistakes push learning forward.  However, I just couldn't bring myself to let the class leave thinking that -4 - -3 was -7.  So I asked for anybody to argue for the -1 answer, because there were several students still shouting out arguments for -7.  When nobody stepped up I felt I had to make an argument for -1.

So I asked them the questions that I thought would end the debate:
"If you have 4 red things, and you take away 3 red things, how many red things do you have left?"
They all correctly answered 1 red thing.  The 2 groups beamed with delight that -1 was correct.  Most of the other students looked a little confused, and 3 students starting misquoting rules to me about negative numbers to continue arguing for -7.  At this point I told them that -1 was the answer.  I showed them in a similar way to the first student using the chip board that -4 - -3 was -1.  Some students still did not believe me.

At this point there is about 1 minute left of class and I am desperate to make sure students know that -4 - -3 is -1.  So I made a last ditch effort and pulled up my smartboard calculator.  I typed in the problem, asked them if it was entered correctly and hit enter.  When -1 popped up as the answer, I actually think there were still students who thought -7 was the answer.

There is no great ending to this story yet.  I have to tackle all the misconceptions tomorrow.  I am pretty sure I completely messed up this lesson and students thinking about integers.  I am not sure what I should have done differently after the debate started.  I made sure in my next 7th grade section to take the subtraction slower and emphasize that subttracting is 'taking away.'  Now I just have to figure out how to right the ship for a group of stubborn 7th graders.

Saturday, November 1, 2014

PLCs, sharing ideas, creating lessons and Statistics

I just want to share how much I love my PLC group.  In our school we do PLCs by content area.  We are a small school so we have 2 math teachers, 2 science teachers, 1 STEM teacher, and a special education teacher.  We meet about every other week for 1.5 hours.  It is always an amazing experience.

2 meetings ago, I went in to develop a lesson on mean and median.  I mentioned how I always struggle with students realizing how an outlier can effect mean much more than median.  Through discussion and brainstorming we came up with a great idea using blocks, a meter stick, and a balance point.  This lesson would have never come together the way it did without my PLC group.

The lesson involved creating sets of data with a mean of 50.  A meter stick was then balanced and blocks were placed at the data points to create a balance.  Students were asked to put on an "outlier" block and recalculate the mean and median.

This activity was also used to visualize missing data point problems with a given mean.  Students placed blocks on the meter stick and saw how it didn't balance.  Then they were asked to place a block so the meter stick would balance at 50 (have a mean of 50).

A quick bare-bones handout can be found here.

Wednesday, October 22, 2014

Estimation 180 & Statistics

I am late to the party here, but the website is amazing.
I have just this year finally started using it during class.

For those not familiar with the site, math teacher Andrew Stadal created some great problems and hooks that require students to use estimation and reasoning skills.  Some very important skills that are getting lost in the standards driven era of school.

For example, this is the first and second problem I had my students think about.

#1)  How many almonds in the 1/4 cup?

#2)  How many almonds in the large container?

The website is called estimation 180 because they recommend one of these problems a day.  I do not use it that way.  I do two problems at a time, once a week.  I use these problems a lot with 7th graders.  In MN many of the standards in 7th grade deal with proportional reasoning.  

So I have them do the first question shown above and ask the students for 3 numbers.  
1. What number is too high?
2. What number is too low?
3  What is your best estimation?  (your "bestimation")

Then I when they have those three numbers, I reveal the answer, drawing the moment out until they are begging for the answer.  After I reveal the answer I immediately throw up the second image as well.  Now I add a question to the mix...

1. What number is too high?
2. What number is too low?
3  What is your best estimation?  (your "bestimation")
4. Explain your reasoning (more than "I guessed")

The more we do these the better the students are getting at thinking with proportionality.  If they know how many almonds are in the 1/4 cup, they use that number to make a good estimation for the large container.  

We are on about our 5th week of this.  The answers I am getting are starting to get better and the reasoning more sound.  When I give them feedback on their answers, I focus solely on the reasoning aspect.  

We started our statistics learning target about a week ago.  This entails measures of center and measures of variability.  So when we did our weekly estimation problem last week, I had them submit their answers and reasoning using a google form.  

The estimation problem was about the large pumpkin below.  
Knowing the weight of the small pumpkin, they had to estimate the large pumpkin's weight.  

Then this week I created a quick PDF with their best estimations sorted by class.  Today their job was to analyze the data (find the mean, median, mode, range quartiles and IQR) for each class.  

Then after they worked to find the answers to those, they took 5-10 minutes to discuss which class had the "best estimations."  I left this vague on purpose.  This led to some great conversations among the students.  It also let me reteach where the meaning of the numbers was missing.  For example some students tried to argue that a class's IQR was close to 14 (weight of large pumpkin), so they were the best.  So it was good to catch those misconceptions early.  

It was really nice that it worked out that one class had the closest mean, another had the closest median, and the other class had the closest mode.  That was a little magical bonus I got with no planning whatsoever.  

The 3 data sets are here if you would like to look at them.  

All in all it was a great day of talking and analyzing statistics.  


Wednesday, September 10, 2014

Algebra & Mathemagic

The 7th graders recently started studying algebraic expressions.  We started with combining like terms with a heavy emphasis on algebra tiles.  This really helps the 7th graders make it visual.  So we spent a couple days playing around with the algebra tiles and combining like terms.  All this sets the stage for


So we started today's class with a little "my favorite mistake" to review expressions.
The students then we told "we are going to have a little contest."

  • Students were asked to pick a number from 0-50.  
  • I told the students they would be asked to perform 5 steps with the number.
  • At the end of the steps, whichever student was closest to the "magic number" would win.
  • The students were instructed to keep their numbers a secret.  
  • The students then performed the following steps.
    • Add 5 to your number
    • Double the result
    • Subtract 4 from the result
    • Divide the result by 2
    • Subtract the number you originally chose
  • The instructions were given slowly, deliberately, and in a way that increases the drama
  • (really the slowness is to make sure students are doing their arithmetic correctly)
  • After the final step, students are instructed to keep their final number a secret
  • The magic number is then revealed by playing this video
Watching the joy cross the faces of the students as they realize their number is the magic number, and then the subsequent confusion is priceless.  They are completely hooked by these magical results.  Every student (no matter what number they picked) ends up with an answer of 3.

I then challenge students to think of a number that will break this trick.  Students vary in their suggestions but the fun ones include super large numbers, decimals, and negative numbers.  Today I had 1,000,000,001 suggested along with -2.51515.  By allowing the students to chose the numbers they are more invested in the process and it really hits home that "any number" ends up with an answer of 3.
After the students realize they can not "break the trick" we break down the trick with algebra tiles.  We walk through each step and perform the operation with algebra tiles.

This is pretty much the end of day 1.

The next couple days are spent practicing number tricks with algebra tiles and eventually being able to seamlessly manipulate algebraic expressions without algebra tiles.

The lesson is loosely based off of a CPM lesson.


Sunday, September 7, 2014

No Grades for Homework...

We just finished up our third week of school on Friday.  I recently wrote about my first week of school where we talked about the brain, mindset, and multiple intelligences.  During that week I mentioned several times that homework this year will not be a part of the grade.  The first week of school is always a tidal wave of information for students.  Our school is rolling out a 1:1 program this year, so that kind of doubles the first week information.

So I was helping some 8th grade students with their homework this week, which was tough, and a student asked me "what grade do I get for this?"  I said "what do you mean?"  They responded "you know how many points do I get?"  I reminded him that homework does not actually count towards their quarter grade.  Homework is for practice.  I had about 10-15 kids in the room at that time.  About half said "Oh yeah, I remember that."  About a quarter of them said "Really?!"  Then the last group said "What?!?!  Then why am I doing this?!?!?"  One girl even marched out of the room in a hissy fit.  

I noticed that the majority of my 7th graders knew, and my 8th graders had forgotten or never heard that in the first place.  So that day I talked about it again with the 8th grade students.  During 8th grade math I reminded all the students that HW does not count towards your final grade.  Some asked "So do we have to do all of it?"  I fell back on the practice vs game analogy as that is probably the easiest way to explain to students the point that homework is for practice to make yourself better.  The game is what decides the level of our success.  I asked them if they would look at their coach and say "do we have to do this?" or even walk out of practice when it was half done.  They agreed that that would be silly.  

I give one weekly homework assignment.  It is based around basic applications of the ideas we are doing in class.  I always give two choices of problems to do as well, an "A-level" and a 'B-level."  I use class time for the upper end of Bloom's.  I am tracking their scores on HW so I can report to parents.  The scores do show up in their online gradebook with a weight of zero (which probably caused some of the confusion).  

I am wondering what will happen to their scores now that they think "homework doesnt count."  Just how successful will I be in trying to instill an intrinsic motivation to get homework done.  Will some of them ever see that they are doing homework to help make them better?  

Also I am just waiting for the parent wave of questions, comments and complaining.  I do send out a weekly newsletter via email.  I did address it in the newsletter.  I also made a video explaining how grading works in my room and why homework is not counted in the grade.  However after sending out the email to over 100 sets of parents, I got exactly 2 views.  So I need to rethink that strategy.  I did put the video on the front page of my website.  

Sunday, August 24, 2014

First Week in a 1:1 Junior High Math Classroom

I have the pleasure of teaching in a 1:1 classroom this year.  So my usual first week activities were not going to quite cut it this year.  So I incorporated some activities and ideas, with some new 1:1 training into my first week this year.  I liked how it turned out and will use a similar set up next year.

Monday - Day 1
Welcomed them into class with way over the top enthusiasm.  This was followed by, straight out Teaching Like a Pirate by Dave Burgess, a quick summary of classroom expectations with an emphasis on NO MEANNESS.  The new part was that I threw in a quick reference to our iPad expectations.  I showed them the class sign that shows the iPad expectations on one side, and then on the other side says FUN SIDE DOWN.  I then took a minute to model how the sign worked.  I did this with enthusiasm and humor.  The kids laughed, were put at ease and hopefully got the point of FUN SIDE DOWN.  I define "fun side down" with an iPad as screenside down on the desk and off.
I then showed the students a quick Prezi about me in a "by the numbers" style.  For example the number 1 popped up, and then "how many wives I have."  We went through 5-6 of these.  The students then filled out a short google form with the following questions.
Explain the number
What else should I know about you.
How much do you like math 1-5

We then spent the remainder of the class talking to students about their google form submissions in a relaxed way.  I would ask each student 1-2 questions about them and move on.  Overall this worked very well and helped put students at ease while simultaneously modeling the top 2 expectations for the day NO MEANNESS and FUN SIDE DOWN.

Tuesday - Day 2
As the students were seated, before the bell even rang, I pressed play on this video.  (watch here).  This set up a small mathy competition.  The students then filled out a google form with their name, their guess and their explanation of how they got their answer.

Next I gave some students information about their brains.  (prezi here)  We focused on how the brain creates neural connections as needed.  So math talent is not genetic, the only way to get better at math was to practice math.  We then talked about how the brain needs three things to function: fuel, exercise and safety.  This helps me bring up NO MEANNESS for 2 days in a row.

After the brain part of this prezi, we watched this Dan Meyer 3-act problem.  The students did their best in small groups to solve it.  With the brain speech beforehand, the problem helps emphasize that we will be doing difficult problems in math and sometimes we will get things wrong.

Overall it was a busy day, but a productive one.

Wednesday - Day 3
This day started with a fun announcement of the Jolly Rancher contest winners.  This was done with much theatrics and heavy on the dramatics of course.

I then gave part 2 of the prezi speech.  This entailed watching this video on Mindset (based on Carol Dweck's work).  We watched it twice.  First time, we just watched it through.  Second time we paused for each animation and then I expanded on how that particular idea applied to math.

The final part of the day, the students each set up and logged into Google Drive on their iPads.  They each created a math folder and shared it with me.  I am looking forward to using this folder this year!

Thursday - Day 4
On this day we started with the final part of the prezi presentation about Multiple Intelligences.  We talked about how school seems to pick out "smart" kids.  We talked about how these kids are generally good at math, good at reading, sit still, and hand their homework in on time.  I then went on to explain how this wasn't fair to everybody and thank goodness for a man named Howard Gardner and his theory of multiple intelligences.  We then talk about all the different intelligences and their strengths and other famous people with those intelligences.

The second part of the day the students take a short multiple intelligences quiz (here).  When they finish they were instructed to snap a screenshot of their results.  They then were directed to this site to look at possible career choices based on their intelligences.  (here)

The day ended helping any students with tech issues and HW questions (first assignment was due Friday).

Friday - Day 5
Day 5 was a work day.  The students were asked to start working on a presentation about themselves.  The presentation should include a title slide, a slide for each of their top 2-3 intelligences, and a slide for each of the 2-3 careers they are thinking about, and then one final slide with their title and name on it.

The reason we save their name for the last slide is because over the next month or so, we will show one of these presentations a day.  We show the title slide, strengths and possible careers, and then try to guess who it is.  A nice little activity to help everyone get to know each other a little better.

All in all it was a great week.  I want to make some improvements to the slide presentation.  I am not super happy with the app we used this year to make them.  We used Notability to help them learn how to use the app.  Hopefully Google will come out with their Slides App pretty soon so we can make presentations on the iPad.


Tuesday, May 6, 2014

MCTM Day 2 (the final sessions)

Saturday morning was the third act of the trilogy.  The climax of the action was my own session, mostly because I was so nervous about it.  I have presented on numerous topics to my own school before, but never at a conference of this magnitude.

Session 1: Bag of Math Tricks
I chose this first session because it was in the same room as I was presenting during the next time frame.  I figured this would help ease my nerves about being on time and getting set up and stuff.  It did seem to help, but not as much as a couple words of encouragement from staff from my school who were also in attendance.

The session itself was a very useful.  It was literally a bunch of small activities, tips and tricks for any age elementary classroom.  From getting to know you activities, to making booklets, to fun formative assessments, and brain breaks.  It was fabulous and very well done.  It is everything a session at a conference is supposed to be.  Fun, interactive and then sends you off with numerous activity ideas.

Session 2: My Session "Teach Like a Flippin' Pirate"
I have to admit I was extremely nervous about my session.  This was partly due to the fact that I am not an expert in flipped learning nor teaching like a pirate.  I was only trying to share how I mashed the two together.  My plan to help my nerves was to start with a humorous story about last year's MCTM.  The session was packed and the story drew some laughs and overall it went pretty well.  I had numerous teachers come up afterwards asking lots of questions and saying that it was "awesome."   The slideshow is below.

Session 3: Student Engagement in a Flipped Classroom
It was probably the fact that I has just finished, but this session did not engage me.  Although I am not sure any session would have.  I was just so relieved that my session was over.  The session was mostly about getting students to watch the video through Moodle tricks and class management.  It was mostly geared towards high school and none of the suggestions really applied to my classroom.

Session 4: Math My Pace
I was really excited about this session as it was Carol Mahler's session, who I had seen present 2 years ago about a self paced flipped classroom.  I took a lot of her ideas and ran with them.  So i was pumped to see what she had done to add to her idea.  I felt bad for her as she had some tech issues, but once she got going it was great!  Her ideas and resources are available at  I highly recommend stopping by this site, it is awesome.

Overall the last day was great.  My session went okay, I got some great ideas from other sessions, and I skipped out on the last keynote because my family wanted to grab lunch at a great local restaurant, walk the shores of Lake Superior, and go comic book shopping.  On a side note, free comic book day cost me $60 in comics...  Must be that new math they teach....

Monday, May 5, 2014

MCTM Day 1 PM Sessions

The MCTM (Minnesota Council of Teachers of Mathematics) conference every spring is my PD highlight of the year for face to face sessions.  I always come back with great ideas to use right away and think about for next year.  In fact I usually have so many ideas, I have to take time to organize them so I can actually use them all at some point.  This year I am using this blog to do that.  Here is a quick summary of my afternoon on the first day....

Desmos & Meta Calculator:
This session focused on the online calculators desmos and metacalculator.  The presenter started with a quick summary of metacalculator.  It seems like a great free resource.  It seems like it could almost replace a TI-84 all by itself.

The real focus however was desmos.  The presenter quickly went over the basics and showed us how to do some slider graphs to create animations.  That was pretty cool.  But the real treat was the other activities that desmos has been adding.  Go here to explore some really fun math activities.
Penny Circle, Function Carnival, Desman and Waterline

Flipped JH Math Classroom
This session was called "Even Han Solo had a Wookie."  Its focus was on how this school used a team to determine essential learning targets and align their curriculum with no textbook.  They came from a bigger school and hearing about their meetings with 8-10 teachers trying to agree on "essential standards" sounded like a terrible process.  It made me really appreciate working in a small school where I am the only 7/8 math teacher.  Overall they had some good ideas on flipping and the fact that they presented in a team showed how easily a flipped classroom can be interpreted in different ways.

The Conversation before the Last Session
I got to my last session early and ended up sitting next to a teacher who has presented numerous times.  So as I was getting more nervous about my presentation the next day, I asked him for some advice.  He said some kind words that helped, but then said he was going to present again next year.  He was going to present on his use of this lesson and how he has adapted and expanded it.  It was fascinating.

However the best part was that it created a three-way conversation about the lesson and it could be further expanded.  We came up with some really great ideas involving probability, transformations and inequalities.  This is another great thing I love about MCTM, the side conversations which often are just as fruitful as the session themselves.

Potato Chips & Absolute Value Inequalities
This last session started and the teacher ran one of my favorite kind of sessions.  He basically ran us through a lesson as though we were students, but paused to add commentary from the teacher perspective to help us implement the ideas behind the lesson.

The actual lesson was a brilliant way to give a real world meaning to absolute value inequality.  it made perfect sense, and if I ever taught high school, I would really use this idea.

The main part of the lesson involved starting with a bag of potato chips which says it weighed 42.5 ounces.  Then we talked about how the bag would have to have a range of acceptable weight coming out of the factory.  Then we linked that to the graph and reversed engineered the inequality from the story and then linked it to the graph.  Really good stuff.

At this point I was supposed to go to my district meeting, which I really should go to.  However, my wife and 3 kids were waiting and so we went out on the town in Duluth and had a fabulous night that included supper, live music and toy shopping.

In the next blog:
Bag of Math Tricks
My own session
Engagement in a Flipped Classroom
MathMyPace (self-paced classroom)


Sunday, May 4, 2014

MCTM 2014: Day 1 A.M.

MCTM (Minnesota Council of Teachers of Mathematics)

Just got back from the conference late last night.  It is always a rejuvenating experience.  I come back with great ideas for next year as well as ideas for tomorrow.  I also presented this year, and that went pretty well.  I will post on that later.  Below is a summary of the fabulous sessions I experienced on the morning of day 1.

Day 1 Morning Sessions

Keynote: Cathy Seeley
Overall, the keynote format is tough, but she was good and it was a good reminder of how to get students thinking, and the ways we unintentionally shut down their thinking.  She also talked about the I-We-You model, vs the You-We-I model of teaching.
I will show you.
We will practice
You will do it.

This is compared to
You will try it.
We will discuss it.
I will bring out the math summary.

I thought this was a good and simple way to remember students need to think and discuss mathematics.

Session #1: Peer Instruction Troy & Rob from Byron
Troy and Rob are part of Byron's award winning flipped math classroom.  They discussed how they use peer instruction in class to extend the learning beyond the videos.  I love peer instruction but am kind of a novice at it.  They had some great tips and examples to help me implement this in my classroom better.

Session #2: Sara VanDerWerf talking about Math Pictures
Sara is always a fun and engaging speaker.  She spoke about using pictures to help students engage, discuss  and learn math in a deeper way.  The quote she stressed was "“He who does the most talking, does the most learning.”  She had some great examples of using pictures to get discussion going.  She said phrasing is important to students when looking at a picture and trying to get them to ask questions.  
Phrases she highly recommended:
"How would a mathematician describe this picture?"
"What words would a mathematician use?"
"What do you wonder about this picture?"

She mentioned this amazing video by Annie Fetter.  It is short, and amazing.  She demonstrates simple strategies to get students wondering, thinking, and discussing mathematics.  

The afternoon of Day 1 will come later:
Desmos & MetaCalculator
Flipping a Junior High Math Classroom
Potato Chips & Absolute Value Inequalities
How the small conversations before and after sessions can be just as amazing as the sessions themselves.


Monday, April 28, 2014

The train ride of learning

State testing season is well under way.  As scores come back I always start to question choices.  Was genius hour really worth it?  Did I push students hard enough in the self paced curriculum?

The big question was genius hour.  I knew it would cause us to go slower, but in theory it would be worth it.  Letting students follow, develop and share their passions should be a main goal of classrooms.  I knew it would lower test scores, but in terms of "eternal significance" passion should always outweigh test scores right?  It reminded me of an analogy for learning I wrote about during my masters program. 

In today's testing environment learning seems to be a train ride.  There are tracks that predetermine where students go and there is no deviation from the path.  Not only are students on the same path, they are transported in the same cars on the train.  Meanwhile the train speeds by the beauty of the landscape and students can only catch glimpses as it passes by.  

My argument is that the train not only needs to allow various speeds, but encourage stops along the way.  Students need to be able to get out and wander the land.  We need to allow students to stop and smell the roses of learning.  We need to let them explore the land to develop or find their interests.

This will in the end slow the trip down.  Not all students will reach the end destination.  However all students will travel significant distances during the year.  They will hopefully end the year with a passion, some great experiences, and a love of learning.  


Sunday, March 30, 2014

Flipped Classroom (the first 10 minutes of class)

I am really experimenting with the first 10 minutes of class lately.  It is my 10 minutes of whole group time.  On Mondays, we play "the White Board Game" for state test review and to keep something consistent.  Any other day is up for grabs.  

With my first ten minutes I am trying to accomplish a couple tasks.  First, general review of a learning target.  Second, practice and feedback for every student on a learning target.  Third, exposure to all the types of problems on a learning target.  

Students can work different "levels" of a learning target in my room.  So a 7th grader may practice most of their time working on circumference of a circle, but never practice finding the "arc length" of a sector of a circle.  So I at least want all students to have exposure to that type of problem.  

One of my favorite activities to open class with is My Favorite No.  If you have never seen the video on Teaching Channel, you should watch it.  Pretty cool stuff.  (Here)

So I have expanded "my favorite no" to include student choice.  I started with posting 2 problems instead of 1.  The problems were on different "levels."  The students were asked to answer at least 1 of the problems.  

An 8th grade example would be two Pythagorean theorem questions.  1 question was about finding a missing leg of a right triangle.  The second question was solving a distance formula problem from 2 coordinate points.  When I did this with the 8th grade students, most students answered 1 question only.  It led to two quick discussions of each problem.  The best positive out of this was that the "level 2" students, saw a level 3 problem, and some thought that it didn't look that hard and were inspired to go try level 3 stuff.  

Last week with the 7th grade I expanded it even further.  I posted 3 questions.  1 from each of the Levels (2, 3 and 4).  I asked students to try 2 of the questions.  It was on Circumference of a circle.  

Level 2:  Find the circumference given the radius.
Level 3: Find the radius given the circumference.  
Level 4:  Find the arc length of a sector.  

The good news was that most students answered 2 questions, and some answered all three.  All students were exposed to the arc length problem.  Some students even used notes from the My Favorite No to skip the video, and go right into the level 4 practice.  I am okay with this as long as they write down their notes and get the practice done with some feedback.  The goal is learning right?

So I am at a point now where I am trying to plan the progression of my first ten minutes to lead students through all 4 levels of the learning target.  Sometimes this is difficult with students going at different paces.  However, in the end it seems to be a good review for some, exposure for the others, and good practice for the rest.  

So my first ten minutes of class are taken up by:
     White Board Game
     My Favorite No
     Daily Algebra Challenge (
     Number Talks
     Peer Instruction (also leveled)
     Other Various quick games

So a progression through all levels of a learning target could stretch over a 1-2 weeks.  Using the various activities above to slowly progress through all the levels of a learning target.  

Now if I could just make my last 5 minutes of class as productive...

Thursday, March 27, 2014

Exponential Relationships & Mythbusters

Every year around this time, I get to tell the famous rice on the checkerboard story for exponential growth.  Every year I love it, but I always feel I need to do more to bring home how quickly exponential growth can happen.  

This year I plan to try to put together two ideas into one amazing or mess of a lesson.  

Tomorrow this is the plan.

1. Introduce the Myth of trying to fold a piece of paper more than 7 times.  We will discuss this problem and probably have a couple students try to do it.  Hopefully we will get to the point that students realize that every time you fold the paper, the next fold is twice as hard.  

2.  We will introduce the Mythbusters clip about the paper folding myth.  The paper size will be given to the students and they will calculate the area of the paper.  The students will be asked to answer the following questions:
    How many times will they be able to fold the paper?
    What will the area of the paper be when they are done?

3. We will then watch the paper folding clip on Mythbusters.   

4. We will discuss the results and the students' answers.
At this point I don't expect students to come up with any kind of equation, although some might.  I just hope they get how fast exponential decay happens.  

5.  We will then turn the discussion to how the paper grows in height when it is folded.  We will watch the first part of this TED ED video.  It talks about how paper grows in height as it is repeatedly folded. 

6. I will ask students to answer the following question:
    How tall will the paper be after it is folded 30 times.  

7. We will then watch the rest of the video.  Again, I don't expect students to come up with an equation at this point.  I just hope they realize the idea of exponential growth.  

I am not sure this will be more effective than rice on a checkerboard, but I hope it will get the students thinking.  I think the problems and videos relate nicely to each other and show both the idea of exponential decay and exponential growth.  

Friday, March 21, 2014

Teach Like a Flippin' Pirate Update

I just got my confirmation that I will be presenting at MCTM (MN math teachers' conference in Duluth).  That is pretty exciting and nerve racking.  I will be presenting on how I am implementing a flipped/self-paced classroom.  So with that, I thought a little update and reflection would be good.

I have just switched my 7th grade sections over to a flipped/self-paced style of classroom.  I made a couple changes and tweeks to the system as I re-launched with this group.  I made a new video to introduce the ideas to parents.  Here if you would like to watch.

The system still puts emphasis on differentiation according to difficulty and student choice.  The students work their way through different learning targets

The class generally is split up into 3 segments.
1. Whole Class Introduction
2. Learning Target Work Time
3. Reflection

Learning Target Work Time
Step 1
Each learning target starts off with a short 5 question pre-quiz using the Schoology LMS.  The students are then directed to either Level 2, Level 3 or Level 4 according to their PRE-quiz results. 

Level 2 is the basic knowledge of the learning target.  
Level 3 is the meeting the standard of the learning target. 
Level 4 is exceeding standard of the learning target.  

Step 2
Students watch a video.  There are 3 videos made for each learning target, one for each level.  The students watch the proper video, take notes, and then fill out a google form summarizing their notes.  I created a page using Google Sites that contain links to all the videos and the google form to fill out.  Everything is centralized to try to make things easier for the students.  

Step 3
Students complete 2 practice activities out of 4 choices.  The choices are usually either web based practice (IXL, buzzmath, etc...), a worksheet, an activity, and/or creating some evidence of their learning.  Students have made movies, posters, websites, etc...

Step 4
When the students have completed their practice they take another 5 question post quiz, also on Schoology.  They must get 4 or 5 right to pass the quiz.  If they pass, the level is completed.  If they fail to pass, then they must complete another practice activity and correct their quiz mistakes.  This is done with a lot of remediation from me.  When this is done, their level is completed.  

These steps encompass the "Learning Target Work Time" of the class.  This takes up about 30 minutes of each day. 

I have found this really puts the learning in the hands of the students and I am really the guide on the side.  

Classes are exhausting as I bounce around the room meeting with small groups and individuals helping them further their understanding.  I do try to connect with every student every day.  I don't always succeed, but I am getting better at this.  

This is just the basic set up.  I have also made changes to:
   a. How class begins as a whole group
   b. Grading 
   c. Tracking progress

However, this has gotten to long already.  As I get my google presentation together, maybe I will post that as well.  


Tuesday, March 18, 2014

Kids trying algebra again and again...

Last Friday I was at a small but spectacular tech conference.  One of the sessions was by a local math teacher and how he uses tech in his room.  He had a lot of great tips and resources, but the one I used today in class was the website

The website has various math, science, vocab, geography and foreign language questions.  All topics can be controlled for length and difficulty.  I have seen the website before but was never sure how to use it effectively.  On Friday, a math teacher shared his amazing approach with this website...

So today I started class with the "Daily Algebra Challenge."  I chose the skill of simplifying like termed expressions and set up a ten question quiz.  The quiz then gives a hyperlink so the kids can get right to the quiz with the parameters you chose.  

I took the quiz 1 time, got 100% right in 29 seconds and left the score open in a tab in my browser.  

So when the students came in for class I introduced the new idea of a "daily algebra challenge."  I told them where to find the link, and anyone that can tie or beat my time wins the challenge that day.  

I have never seen the effort or determination from some of the students like I saw today.  Students trying, failing, and eagerly trying again to defeat the challenge.  It was amazing to see.  Of course some students won the challenge in the first 4-5 tries, but other students played 10, 20, or more times.  Some students accomplished the challenge and some did not, but all students got a lot of algebra practice.

Of course some students tried to cheat and change the settings to make their time faster, but they were easy to spot.  

The greatest thing about this website is the ease of it to use.  There were no usernames, no logins and no hassle.  I just found a quiz I liked, clicked "make url" and then posted the URL on my website. 

Super easy, super engaging, and super fun stuff!

Tuesday, March 4, 2014

Marshmallows, Scatterplots, & Line of Best Fit

Marshmallow Challenge & Scatterplots

I recently watched this YouTube video about the famous Marshmallow Challenge

It got me wondering how I could use this challenge for a math problem beyond the problem solving, team building skills that are naturally in the challenge. 

Here is my plan for 8th graders studying scatterplots, correlation and line of best fit.  

Day 1: 
Each team gets the normal materials from the challenge.
1 yard of tape
1 yard of string
1 marshmallow
20 sticks of pasta 
The teams build the structure and measure the height.  
Data is tracked for all teams.   

Day 2:
We repeat the marshmallow challenge, only the team gets to choose a "power up".  The team can get more tape, string  and/or sticks of pasta.  I was thinking of letting them pick 2 more items from 1 yard of string, 1 yard of tape, and 20 sticks of pasta.  We will then repeat the challenge.  

Day 3:
Students will then combine the data and plot it on various scatterplots.  
Height vs tape used
Height vs string used
Height vs sticks of pasta used

We will then analyze the scatterplots for correlation and line of best fit.  The students will then have a determine which "power up" had the most effect on the height of the structure.  

I am not sure what to expect out of this little experiment.  I hope the students stay engaged over this entire week dealing with the same type of problem.  

I am thinking of having them make a prediction from the scatterplot about what would happen with more supplies.  Maybe they should look at the three scatterplots and try to figure out which supply makes the most difference.  Then they can make a prediction of what happens when that supply is increased.  

We will see what happens...


Friday, February 28, 2014

Standards-Based Grading, Levels, & Percentages

Standards-Based Grading

Grading is always a tricky subject to discuss.  I have developed my grading system over the last 4 years shifting from points based, to standards based.  I really like how I grade and feel that it reflects exactly what a grade should, student learning.  

Being called out twice on twitter by Ken O'Connor, grading guru, really got me reflecting about how I grade.  It made me question what I am doing and whether it is really good for the students and parents.  

Here is what I do.  Anybody can do this, regardless of whether your district is doing standards-based grading or not.  This method was developed because I am the only teacher in our secondary school doing standards-based grading.  

So 4 years ago I wanted to move away from grading on points and start grading on learning.  I tossed out my curriculum, read a lot of Dan Meyer,  went to some trainings, and went at it.  I developed a list of learning targets (concepts) for 7th and 8th grade.  The only scores in the gradebook were based on assessments of those learning targets.  My gradebook is set up like this...

1. Algebraic Patterns
2. Algebraic Equations
3. Algebraic Properties

There are no "assignments, quizzes, daily points, or tests", listed.  I
Where I get in trouble from Ken O'Connor is that each learning target in the gradebook has a percentage to show how much the student has learned.  This percentage can change depending on how the student progresses during the quarter.  

The percentages are based on numerous and varied assessments of the student's knowledge.  The percentages come from a conversion chart.  The students are given feedback on a 1-4 basis.  The following picture (that I got from someone on twitter) perfectly summarizes the 4 point scale.  

I try to assess students at least 2 times before anything gets entered into the gradebook.  I do however allow unlimited re-assessments from the students.  They are required to study or remediate somehow before they are allowed to retest.  Students of course will try to just take it hoping for a miracle, but I find a quick conversation with the student quickly exposes the student as ready or not for a re-take.  

If you have doubts about re-takes, or redos take 8 min and watch this video.  Life-changing...

I emphasize the words "master" the learning target during class.  Students are taught that 2 scores of 3 or higher mean "mastery."  We even have a wall of mastery in class to celebrate students mastering a skill.  There are different levels of mastery, but I feel if a student can score two 3s, they know the standard to a sufficient level.  

Here is my conversion chart from the 1-4 to a percentage.
This is the part that gets SBG purists going.

4,4 = A = 100%
4,3 = A- = 95%
3,3 = B = 90%
3,2 = C+ = 85%
2,2 = C = 80%
1,2 = D = 70%
1,1 = F = 60%

Of course there are more combinations than this, but these are the basics that I build off of.  

Last time I got called out by Ken O'Connor it was that 90% represented mastery.  He told me to go read an article in Ed Leadership by Thomas Guskey.  So I read the article.  The article made a great point, that percentage (Based on points) is not a good reference for mastery.  The article said that 90% or 80% or any percentage cut off was not a good way to define mastery.  I totally agree with this.  Percentages, when based on points say very little about what a student knows and doesn't know.  I agree.

This is not what I do.  I convert to percentages from a 4 point rubric for 2 reasons.  

1. Our school is not a SBG school.  
I am not even sure I want our school to be an SBG school, top-down mandates like this never seem to go well.  I just wish more teachers graded more on learning and less on points.

2. Parents understand percentages.  
It is way easier to communicate to parents that 90% means mastery, than to try to explain the 1-4 rubric, and they need two scores of 3 or higher, and so on.  Parents of junior high students are busy.  They want to know how their students are doing in a quick and efficient manner.  The percent makes this possible.  

I feel standards-based grading's main emphasis is to shift the focus on learning, instead of points.  My grading system does this.  This is the first step in creating a learning-centered, student-centered classroom.

The arguments about grades, percentages, rubrics, etc... really is only about communication with parents.  To me this is a secondary argument that doesn't mean nearly as much to my classroom, my students, or the school, as truly making sure the class is focused on learning. 

This got way to long.  I really just had to think this out to convince myself that I want to keep implementing my grading system.  I have at least convinced myself.  Now if I could just convince my grading hero that keeps telling me I am wrong....



Wednesday, February 12, 2014

Flappy Birds Math Lesson

I have to admit that I got caught up in the Flappy Bird craze for a couple days.  It was a fun, infuriating and addicting game.  The whole time I was playing I was wondering how I could turn this into a math lesson.  Ideas I came up with were minimal.  They involved measures of center and variability, as students would play a couple times and then find a bunch of one-variable stats and see how outliers can effect some of the different measures.

However this week we are introducing percent of change.  I thought this was also a great opportunity to give this a shot.  So here is what happened...

1. As students came in I had on my mirroring program and on 1 side of the screen was the day's schedule and on the other side was the iPad showing Flappy bird.  As students came in I sat and played a couple games.  Students came in excited and hooked right away.

2. We talked about Flappy Bird a little bit and shared high scores.  We then transitioned to percent change and how it can be used to measure improvement.

3. We went through 2 examples on the board of how to use a graphic organizer to solve a percent of change word problem.  The students took notes and listened, anxious to get to the Flappy Bird part.  I then asked students to solve a word problem on their own using the graphic organizer.

4. After each group proved capable we finally get to the Flappy Bird tie-in.  I made sure each group of 3-4 students had at least 2 devices with the game.  Students were instructed to play 1 time and write down that score.

5. Students were then given 10 minutes to practice their Flappy Bird skills.  

6. Students were then asked to put down their devices and listen.  They surprisingly complied very quickly and quietly.  I did mention that non-compliance would be grounds for being thrown out of the "Flappy Bird Olympics."  

7. I then told students they get 1 trial to get their final score and they should write down that score and then calculate their percent of change.  

8.  Students then helped each other as they worked in groups to use the graphic organizer to calculate percent of change.  I walked around the room helping students who really struggled.  

9.  While I walked around I kept note of some interesting examples to show to the class.  We then spent the last 10 minutes of class discussing examples.  

Example 1:
A pretty typical percent of change example with a small increase and a percent change above 0% and below 100%.

Example 2:
A pretty typical example of percent decrease, with a small decrease between 0% and 100%.

Example 3:
An example with the first and last score being the same.  

Example 4:
An example with over 100% increase. 

Example 5:
I tried to pick Example 4 as the highest percent increase in the room.  For the next part of the discussion I picked the highest initial score in the room.  We then calculated what that student's new score would have had to have been for them to beat the highest percent increase.  In one class we figured that a student's initial score of 133, would have had to increase to 646 for them to have won.  

Example 6:
An example where the first score was zero.  This led to a very interesting discussion where we talked about how to get an answer.  Using the graphic organizer and proportions we would have had to divide by zero to get the percent change.  We then studied what happens as the divisor gets smaller.  It led to a very interesting discussion!  

Surprisingly all these examples happened in both classes of 7th graders.  It turned out to be a very exciting and productive day.  We will see tomorrow about how much they remember about percent change.  


Saturday, February 8, 2014

I am the Lorax, I Read with a Wheez

February is I love to Read month, or so they tell me.  Our school decided that every Friday morning their would be a mystery reader after the morning announcements.  This is the first year they have done this and I was very excited when they asked me to be the first reader.  My excitement kept "biggering and biggering and biggering" when I found out I would be reading a selection from The Lorax, my favorite Dr. Seuss book.  

I love reading this book to my kids and get very dramatic about the whole thing.  I was excited to share my overdramatic side with the entire school.  Keep in mind we are a Pre-K-12 building, so my voice was going to be heard by students age 3-18.  

Fast forward to Friday morning.  My lovely wife had to go into work super early leaving me to get all 3 kids ready for school, ages 5, 8 and 11, and be on time for our Friday morning meeting.  We made it on time but there was some 11 year old drama that day as she lost some of her homework.  Then came the staff meeting, always a good time.  Then I got caught up in a conversation with another math teacher about class offerings for next year.  This is where the fun begins...

I was supposed to be in the office to read at 8:15.  The bell rings to start homeroom, at 8:15, and I am still in the middle of my conversation in my room with the other math teacher.  Nothing is registering yet in my brain about where I am supposed to be at this time.  

Then at 8:16 the speakers crackle and the principal begins his weekly Friday morning message.  In the middle of a sentence, I stop what I was saying, yell out "Oh no!" and in one motion grab my paper with the reading and head out my door.  

Now running in school is generally frowned upon, but I had a very short time to get to the office.  So I ran from my door all the way to the office.  Now keep in mind, I am not at my peak physical shape and I am a pretty big dude.  Even in my younger days, running was not my strong suite despite being a 3 sport athlete.  

I learned later that my principal, while reading the morning announcement had his eye on the cameras and saw me sprinting through the hallways trying to make my reading on time.  He slowed down his reading to try to give me time to make it to the office.  

Just as I reached his room where I was supposed to read, the principal was finishing up the last couple sentences.  However, there was a problem...breath.  

He handed me the phone to do the reading and I hadn't even gotten close to catching my breath.  So instead of a great dramatic reading of the Lorax, hundreds of students, ages 3-18, plus my fellow colleagues,  heard lines from the Lorax a couple words at a time and then a middle aged math teacher gasping and wheezing, and then a couple more words.  I tried to pass it off as dramatic, but I think that just made it worse.  

"From the ... (deep breath) ... rippulous pond ... (wheez)
came the ... (gasp) ... comfortable sound ... (long pause)

This went on for about 15 more line until thankfully it ended.  As I left the office and ran into students, they all yelled out a mixture of "I knew it was you, because we saw you running" and "Are you okay?"  All in all a total failure.  

I think I am ordering a treadmill on Monday.


Sunday, February 2, 2014

Twitter: Light Side vs Dark Side

Twitter Wisdom

I scavenge Twitter for many ideas and resources to help me with teaching.  I often come across things that I think are pretty cool or could be useful to teachers that are not me.  I often send these links and ideas on to colleagues in the building.  I am sure they get sick of this, so I try to limit it, but I do send out ideas quite a bit.  

Yesterday I sent out back to back emails to elementary teachers.  The first tweet quickly explained that I found this resources on twitter and that elementary math teachers might find it useful.  I forgot that I had come across another idea aimed at elementary teachers.  I think it was an app for practicing basic skills that looked pretty fun.  (I think it was Math Slicer)  The subject line of this email was "i spend too much time on twitter."  Trying to poke fun at myself for sending back to back emails to the elementary about ideas that I found on twitter.  

After sending this email out I got a response back from 1 teacher, asking about some drama going on in the Twitter world involving our students.  She asked me what I knew about the drama.  My response to her was that I try to "avoid the dark side of twitter" and I knew nothing.  

The use of the phrase "Dark side" got me thinking.  Star Wars often talks about the Dark and Light side of "The Force."  Twitter can be viewed in a similar way.  

It is the Jedi's choices that put them on the dark or light side of the force, the same is true for twitter users.  

Twitter connects the world just like the Force flows through and connects all of us.  

A Jedi's light saber color symbolizes a lot about the Jedi themselves, much like the twitter user's profile pictures and cover picture.  

A Jedi can move objects using the force with just their mind.  My autocorrect is almost that good as I type things on my phone.  

So all these similarities inspired me to seek out advice from the wise master Yoda.  He gives great advice throughout the Star Wars films and surprisingly a lot of it can be applied to use of Twitter.  So I made the graphic below to remind myself, and my students of choices, consequences, and digital citizenship.