Estimation 180 & Statistics

I am late to the party here, but the website estimation180.com 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.  

thanks!

Chris

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

MATHEMAGIC

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.

Chris

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.  

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.
Name
Grade
Number
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.


Chris

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 http://www.mathmypace.com/  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....

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.
https://www.teachingchannel.org/videos/graphing-linear-equations-lesson

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)

Chris

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.
Traditionally
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.  blog.peerinstruction.net



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.

Chris
@CjSieling34