I am so thankful for the amazing teachers I have the honor of planning, sharing and commiserating with.  It sure is a lot more fun working together. 

I am also incredibly thankful for the gifted and inspiring teachers in my life, specifically my dad, David Giltner, and my high school senior English teacher, Sally Boeschesnstien, both of whom still inspire me with their mastery of this trait:

• I am so thankful to have the opportunity to teach math through discovery and investigation this year.
• I love having loud, dynamic classes of kids who are excited and inspired.  
  
• I love the adventure of never knowing exactly what to expect, but allowing essential learning targets to provide guidance. 
• I'm amazed at what I'm learning when students are on fire to find answers to questions they have by doing their own investigations.
  
• I love witnessing kids making connections to what they already know, often in ways I never considered.
  
• It gives me hope for our future when I witness 11 and 12 year old students participating in remarkably mature mathematical discourse.
  

For years, I've had a quote from Mike Klavon, our ISD math specialist about "teachers working harder than the students" in the back of my mind.  It was a very poignant moment when he shared that observation with our math department. Mike was absolutely right then, and the same "teachers working harder than (most) students" is true now... except in my pre-Algebra classes. 
 
Learning is hard work.  That does not mean that it has to be boring, laborious, or tedious.  On the contrary, I believe it's more likely to happen when lessons are engaging, challenging and dare I say it, fun.  Hard work can be fun, to the point where it's no longer hard.  

Possibly for the first time in my career, I think I have a sense of what it feels like to be teaching important, meaningful math that involves problem solving and real-deal learning.  This is all true while the students are working harder at their learning than I am.  Even in the traditional note taking powerpoint scenario, I'm good at what I do. However, for the first time, I feel like what I'm doing will have far-reaching effects. I hope so, anyway. 

The true litmus test: I would love for my own children to be in a class like this. I want them to be inspired to investigate, question, and make connections.  I want them to be problem solvers and life-long learners and know the joy of learning along side others that help them see different approaches and views.  I can't say for sure, but I feel that is what is happening for my 7th graders this year.

Notes:

• Groups chose the question they wanted to answer.  Every group either looked for the area of the tree or the area of the triangles (found in the negative space).
• In both classes 3 groups found nearly exact answers, 2 groups were significantly far from the target and 2 were somewhere in the middle
• Methods used: building scale models, measuring from the projected image, and finding that the largest leg created an area 64% of the hypotenuse area, and the smaller leg created a square 36% of the area.
• Only one student used Pythagorean Theorem to solve the problem
• Next year, I will teach the Pythagorean directly before this PT.  This year, after direct instruction, we will revisit this PT by creating a Pythagorean Tree Fractal for a bulletin board.

1) Students work in teams to finalize the main question to answer from the 3 Act Task from Friday called Pythagorean Tree.

2) I asked each group to report what they had decided on for their main question. The photo below shows the results from my first hour:

3) Each team had to finalize their choice for the main question and then complete the estimation section of Act 1.  

4) After teams had a head start on figuring out what additional information was required (Act 2), I showed the Act 2 video and WILD PANDEMONIUM broke out.  Kids were looking for other resources such as dot paper, extra scissors, smaller grid paper, etc. It's always the performance task that seems the most mysterious that totally sucks them in.  Below are photos from both classes and videos to try to capture the excitement.  A few groups came close to finding the answer to their question, but more time will be needed tomorrow.

2) Viewing of third video showing the solution to the Taco Cart PT.  Note: both classes were absolutely drawn into this and even the solution produced additional teachable moments such as subtracting time measures using minutes and seconds.

3) PT (spotlight task): Pythagorean Relationships

• I demonstrated how to use graph paper to find the area of the square made from the hypotenuse with two different examples (hints: use the largest leg on the bottom, create a "pinwheel" of rectangles for the hypotenuse square.)
• Each student team was assigned 4 to discover on their own (generally, one for each student)
• After about 15 minutes, helping a few students, teams reported out while I kept track of the reports of the areas of the squares of each leg compared to the area of the hypotenuse square.
• In both classes, students were able to see the relationship that the sum of the ares of the squares of the two legs was equal to that of the hypotenuse.  Some students are starting to connect that the Pythagorean Thm.

4) Assignment: make a nice version of the right triangle with squares formed from each side to be used in your ISN

Bummer. Today was supposed to be my formal observation and the lesson would have been a great one for showing the changes we're making to our curriculum.  Alas, nature is in control, not me.

So, instead, I'll share a fantastic moment from yesterday's second hour.  I didn't post learning targets that the Taco PT focused on because it was such a mysterious and weird video, I didn't want to give any ideas about how to solve it. Instead, I had kids look over their brand new Learning Target sheet (there are MANY this unit, see yesterday's post) and have them decide what the main themes were going to be.   Clearly, they had not heard about the Pythagorean Theorem before.  Many attempts were made to say both words, with no one coming close.  When I explained it was a theorem based on the teachings of a man named Pythagorus, they completely lost it and broke out in loud guffaws.  It simply never occurred to me that they wouldn't know who that was.  Cool! I get to see them figure it all out over the next week.

1) Tests returned

2) Folder clean-out, recycle everything except ISN

3) Get new learning targets

4) 3-Act task, Taco Cart

• 3-Act tasks are strange and mysterious, and result in sucking kids into the math
• Students are encouraged to ask questions, make estimates, ask for information and device conclusions.
• This particular task is summarized here: Taco Cart Task

1) Warm-up: Self checking puzzles for scientific notation
2) Quizzes Returned
3) GiantBurger PT graded in class

• As a class, we went over what was required to solve the problem (both classes identified all three parts)
• Students were given their own copy of the rubric and identified their own score
• Class discussion both hours about the reasoning of 6.6667 % vs. 7%

4) Assignment: Unit 2 Practice Test (handout from class)

Samples of student work for Giantburger PT

Student self scored a 4/10.  Notice corrections in red.                    Student self scored 10/10