Patty Paper - It’s Good For More Than Hamburgers

When I first heard about patty paper, I had no idea what it was (I obviously don’t make my own hamburgers), let alone what it had to do with mathematics. Tracing paper, transparencies, patty paper… they can all be used similarly to help students visualize key geometric ideas. Now that I am acquainted with the multifaceted nature of patty paper, I don’t know how I would teach certain concepts without it! Here are a some examples of how patty paper can be used in the classroom:

Transformations.

For “spatially challenged” people like me (yes, I get lost at the mall), patty paper is invaluable for visualizing transformations - particularly rotations and reflections.  Here is how one teacher uses patty paper to demonstrate a rotation. What are some connections the students would be able to make using this visual model? How would you do it differently?

Constructions

Constructions are typically learned with a compass and straightedge. This is important work which helps develop an understanding of constructions and the geometric reasoning that accompanies them. Patty paper can be a nice compliment to the work with a compass, giving students another avenue to “see” the relationships between various figures and thereby solidifying the understanding they started with the compass and straightedge.

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http://www.cpalms.org/Public/PreviewResourceLesson/Preview/51159

Now that we've seen some of the uses of patty paper, two questions commonly arise - Are we allowed to use patty paper? Does using patty paper lower our expectations for students?

First - Yes, we are allowed to use patty paper. In fact, several standards even call for it:

• 8.G Understand congruence and similarity using physical models, transparencies, or geometry software
• G.CO.2 Represent transformations in the plane using, e.g., transparencies and geometry software; describe transformations as functions that take points in the plane as inputs and give other points as outputs. Compare transformations that preserve distance and angle to those that do not (e.g., translation versus horizontal stretch).
• G.CO.5 Given a geometric figure and a rotation, reflection, or translation, draw the transformed figure using, e.g., graph paper, tracing paper, or geometry software. Specify a sequence of transformations that will carry a given figure onto another
• G.CO.12 Make formal geometric constructions with a variety of tools and methods (compass and straightedge, string, reflective devices, paper folding, dynamic geometric software, etc.).

Second - A tool by itself cannot raise or lower our expectations. How we use the tool defines the cognitive demand of the task. Standard for Mathematical Practice 5 says: “Use Appropriate Tools Strategically.” Patty paper is a tool that, when used strategically, can give many students access to understanding and connections that the students otherwise may have missed. Additionally, students may combine patty paper with other tools and strategies to check their work and to validate their own learning.

How have you used patty paper in your classroom? If it is new to you, are you willing to give it a try?

Gaining Momentum

The estimated reading time for this post is 1 minute.

Merriam-Webster dictionary defines momentum as “the strength or force that allows something to continue or to grow stronger or faster as time passes”.

It turns out, Momentum is also a google extension I added this week.  When I was working with a teacher, he opened a new tab in chrome and it looked something like this:

I admit, initially, I was drawn to the simple greeting, “Good afternoon, Sarah”.  Who wouldn’t like a nice picture and a lovely greeting instead of internet advertisements?

Upon further scrutiny, the question and the immediate blank felt like a slap in the face.  What was my main focus for today?  I wanted to fill the blank line with so many things.  But I soon found out that I could only put ONE thing, my MAIN focus.  What was my main focus?  What was driving me and giving me momentum for that day?

Today marks the 3rd week of classes in RUSD, the honeymoon might be over for some. Now comes the real work.  We are committed to these students for the school year.  As the year progresses, there will be many things to do, but what will give you the strength you need each day?  So I ask, what is your momentum, what is your main focus for today?  What is the strength or force that enables you to continue to grow stronger or faster as time passes?  

In a few weeks when we are knee deep in the semester and school year, we will need to remember our main focus.  Take a moment and find your momentum.

Math is Beautiful, Isn't It?

Disneyland just ended their Forever Fireworks show.  Beyond enjoying the fireworks and projected show, have you ever asked yourself, "What Math is involved in this?"

The first time that I watched the show I was amazed at all of the mathematics necessary for the show.  Stop for a second and think about all of the mathematical factors that go into a place like Disneyland.  When I think about the future "Emagineers" that we are educating today, I wonder what marvel they are going to create for our tomorrow.  How do the Mathematical Practices that we are developing in our students relate to places like Disneyland? Do you wonder like I did, if students would be able to connect their daily learning to the world around them?

Could you highlight and/or find the Mathematical Practices in this video?

• Make sense of problems and persevere in solving them
• Reason abstractly and quantitatively
• Construct viable arguments an critique the reasoning of others
• Model with Mathematics
• Use appropriate tools strategically
• Attend to precision
• Look for and make use of structure
• Look for and empress regularity in repeated reasoning 

During the spring of 2016 our sky in Riverside was given a rare display of mathematical brilliance by

the Air Force Thunderbirds.  While I looked in the sky I could not help to think about the hyperbolas, parabolas, circles, ellipse, planes, angles, etc that I was seeing.  The topic that my students were investigating during the time of the show was conics.  Would students find solving a system of conics more interesting if they understood the importance in these planes not intersecting.  As teachers could we provide more meaning to our Teaching Practices if we looked at them through the lens of the crowd drawing shows that we go to each year.  Where is your favorite place to go and what mathematics is necessary for you to enjoy it?

Mathematics Teaching Practices include:

• Establish mathematics goals to focus learning
• Implement tasks that promote reasoning and problem solving
• Use and connect mathematical representations
• Facilitate meaningful mathematical discourse
• Pose purposeful questions
• Build procedural fluency from conceptual understanding
• Support productive struggle in learning mathematics
• Elicit and use evidence of student thinking

In the comment sections, we would LOVE for you to share your thoughts:

Did your students give you insight to the mathematics that they saw in the Forever Fireworks Display or Thunderbirds show?  What mathematics did you uncover in watching these?  What Mathematics Practices or Mathematics Teaching Practices do you see as most necessary for our students to be successful in a future career?

What if you became the "Meaningful Monday Math Teacher"?  What if on Mondays' your warm up was to present a video for students to stop and be marveled by the mathematics that is in the world all around them?  What is you favorite math video?

On Your Mark, Get Set, Go!!!

This summer the 2016 Olympic games were in Rio.  I know that there were many DVRs set to record the events of the Olympics: Opening Ceremonies, Favorite Events, and Closing Ceremonies. Several of the events that took place during the Olympics were races.  Many people around the world watched in anticipation for races to begin.  They watched in anticipation to see who would win. It was amazing to watch the various levels of celebration take place. We were able to watch and see some of the athletes celebrate with a smile from ear to ear because they had made it to: Olympics, final heat, a podium spot, or won a GOLD medal.  The part that we did not see as much were the personal celebrations that people made when they made a personal record, achieved a dream, and/or accomplished their goal.

We have all spent the last week or so taking our mark, getting set, and now we are GOING!

We are running with anticipation, excitement, and eagerness into the 2016-2017 school year.  The closest Olympic event that I can relate the school year to is a Marathon.  The school year is not something that will be over in a quickly, but something that will require work day in and day out.  In my years of running, I have gathered that no matter how fast you are going to run your race, very few people walk across the starting line.  Most of us woke up today and showed up to start the school year running.

Whether you are an experienced teacher or this is your first year, we are all starting the same race,  the 2016-2017 SCHOOL YEAR.  We know that you, just like Olympic athletes, have put in the training, hard work, preparation, and dedication to be a teacher.  Any person training and then competing at something knows that they will hit a wall at some point in time.  Hitting a wall in a race is normal and expected by most.  The size of their wall is different.  When you hit that wall, do not be afraid to look around and see the crowd cheering you on.  You have a crowd of students, parents, administrators, your Math Department, PLC Team, and Staff Developers to cheer you on to keep going through the school year.  Whenever you hit your wall, I encourage and challenge you to look around and see who is there beside you cheering loudest to help you keep going.  

At the end of most races runners earn a medal.  We as teachers will probably not earn a gold medal at the end of year to wear around our neck for everyone to see.  Instead teachers receive other gold medals to hold onto that will be treasured for the rest of our lives. We too can smile from ear to ear when we are able to think about the personal records, student learning, pictures, stories, celebrations, letters, college acceptance letters, and many more things that we have accomplished this school year.  

Take some time and think about what is going to be your Personal Record (PR) for the 2016-2017 SCHOOL YEAR.  As Staff Developers we would love to read your Personal Goals in the comments (do not worry you can comment anonymously if you want to) and then celebrate alongside you when you reach those goals.  

A few messages from “Here Comes the Boom”...

A few messages from “Here Comes the Boom”...

If you haven't seen this movie, let me give you an extremely abridged synopsis: Scott Voss is a burned out former Science Teacher of the Year. Early in the film, the principal announces that, due to budget constraints, they will be cutting the music program and thereby eliminating the position of dedicated Music teacher, Marty Streb. Through a series of events, Voss decides to moonlight at as UFC fighter in order to raise enough money to save the music teacher's job.

I have mixed feelings when watching movies about education. On one hand, I enjoy them because I can relate to the funny, inspiring, or poignant content; on the other, I a tendency to become incredibly irritated since most of these movies have scenes that require a huge suspension of reality. So, for now, let's just choose to let those irritating scenes fade in light of the positive messages we can glean from this (in my opinion) HILARIOUS film:

We can be each other's heroes. Now, I don't believe we need to go so far as to take up UFC fighting, but what about letting a fellow teacher know that what they do inspires us? Our profession, by its very nature, tends to isolate us from each other. We need to remember that we are all part of the same team with the same goal: to educate our students. Sometimes it feels like we've gone a few rounds in a UFC fight. So, if we notice a colleague doing something well, let's acknowledge it.

Photo by Tracy Bennett - © 2012 CTMG

We accomplish more as a team. Being part of a team helps each member achieve more than they could alone. A team provides the support we need when we want to back down. A team provides the forum for generating new and improved ideas. A team provides the momentum necessary for following through with challenging commitments.

Photo by Tracy Bennett - © 2012 CTMG

The movement of one person can affect an entire system.
We don't always have the luxury of being a member of a high functioning team. But we can still move forward with the important work of inspiring our students. If you feel alone in your endeavors, remember, someone is always watching. You may be the catalyst for change right where you are. Keep moving forward, and eventually someone else will join you. It can be a long road, but as long as we're headed in the right direction, it's worth it.

Are you curious?

I surely did not think that this Friday we would be picking up tasks to grade from all of our 7-12 school sites as part of the district final.  However, in December, a team of teachers decided just that for our end of semester assessment!  Teachers at the pull out day agreed they wanted the test to cover key concepts, have a balance of DOK and rigor, and include questions that show student thinking.  The team, through their discussion, boldly took the step to require a task in our semester district assessments to ask questions that would show student thinking.

So, you’ve given the test, now what?  You may have graded the task already on your own, so you feel you already know how your students did.  However, do you want to know how other students at your site did on the task?  Are you curious about  how other students in the district did on the task?  You have the opportunity.  Come be part of the discussion and norm grade exams with us.  We will hold norming sessions from 4-6pm at Miller MS rm. 452.  HS week 1/25-1/29, MS week 2/1-2/5.  You will be compensated with snacks and a timecard.  Come for an hour and see what it’s all about.  We spoke to an RUSD teacher who participated in norm grading sessions in another district.   “It totally changed the way I taught!”  Show up to a norming session and listen to the discussion around student thinking.  While you may not grade your own students’ work, I believe it will change the way you see your own students.

Sticky Collaboration

Recently, I visited a 7th grade SDC (Special Day Class) math class and observed students huddled in groups of four passionately discussing variables.  I was intrigued.  I moved a little closer to one group and heard a student say “No, my post-it should be our group summary.”  Another student in the group responded, “But, your answer doesn’t describe what a variable is; all your answer says is an example of solving for a variable. Your answer doesn’t work for my example on my post-it note, so we can’t just use it.”  The productive discussion lead the group to a response that all were happy with, and so one student wrote their group response in their center of their shared paper.

These students were working on what the teacher described Sticky Note Collaboration.  The idea is for the teacher to pose a question for the students to respond to.  (This works best when the question is more of a generalizing a concept idea rather than a ‘how to’ idea.)  Then, the students independently write their response on their post-it note.  Once students have written their response, they move into groups of four.  Each student reads aloud their post-it note and then sticks it to the corner of the group summary paper.  Once all members of the group has shared their post-it, then the group collectively discusses the commonalities of their responses and creates a group response.  After a short time of the groups working together, each group selects a student to read aloud their group summary.   

What I liked about the activity:

Students were using multiple SMPs in this brief 10-15 minute warm-up activity.  By having the student individually create a response, students were being asked to make sense of the prompt (SMP 1).  The students shared ideas and generated a general response and in order for students to do that, they had to critique the reasoning of others (SMP 3).  The students had to be precise with the vocabulary and language of their answer (SMP 6).  All this was done with the teacher providing one high level cognitive demand prompt and a well executed structure of interaction with students.  At no point did the teacher tell them a response to the question.  Instead, the students did all the thinking, comparing, analyzing and reflecting to determine a well constructed answer to a mathematical question.  

Sample Sticky Note Collaboration (7th Grade Math, SDC)