UbD-comments

Writing my lesson plan in this manner was difficult for me to do. Even though I have written many lesson plans, I believe that this took more time and effort than previous lesson plans. Essentially, I thought about every single second of my 42 minute period. I believe it is a great tool to use for a weekly plan, but seems unrealistic to do for every individual lesson plan.

UbD

Understanding By Design Lesson Template

Title of Lesson	Developing Patterns in Linear Equations		Grade Level	8
Curriculum Area	Algebra and Patterns		Time Frame	Five Days
Developed By	Mary Giacomarro
Identify Desired Results (Stage 1)
Content Standards
4.3.2.A.1 Patterns - Recognize describe and extend patterns 4.3.2 B.1 Functions and Relationships -Use concrete and pictorial models of function machines to explore the basic concept of a function. 4.3.3 B. Functions and Relationships 1. Use concrete and pictorial models to explore the basic concept of a function. Input/output tables, T-charts
Understandings			Essential Question(s)
Overarching Understanding			Overarching		Topical
To recognize linear patterns from using square tiles, tables and graphs. To use data patterns to make predictions. To be able to create linear equations			*What are linear equations? *How do you represent linear equations using concrete models?		*How is slope represented concretely across each stage of various patterns? *How is the y-intercept determined once patterns are developed and represented in tables?
Related Misconceptions
Students may not see the pattern initially. A student may find it difficult to make predictions when the constant is changed from a number to a variable. Students may also have trouble with graphing these patterns.
Knowledge Students will know…			Skills Students will be able to…
*What is slope? *What is the y-intercept? *Where do they appear in patterns? What are different ways to represent patterms?			Take a domain and range chart and develop linear equations Compare graphs and understand how the input/output effect the slope and y-intercept of the graph
Assessment Evidence (Stage 2)
Performance Task Description
Goal	SWBAT use patterns to develop linear equations.
Role
Audience	8th grade students
Situation	Period 4 Algebra Class
Product/Performance
Standards
Other Evidence
Read chapter 4.1 Coordinate systems and plotting points on a coordinate plane. Do 2-20 even. Check answers in the back of book.
Learning Plan (Stage 3)
Where are your students headed? Where have they been? How will you make sure the students know where they are going?		Students will be able to develop the ability to examine graphs and explain the relationship to the data provided.
How will you hook students at the beginning of the unit?		Creating the models using square tiles (concrete manipulatives).
What events will help students experience and explore the big idea and questions in the unit? How will you equip them with needed skills and knowledge?		The students will be able to explore and experience a variety of patterns and determine equations from them. After the students have had a chance to use the manipulatives, they will be able to explain what their findings are.
How will you cause students to reflect and rethink? How will you guide them in rehearsing, revising, and refining their work?		The students will have the opportunity to reflect and rethink using a Kagan cooperative learning strategy called “Sage and Scribe.” The students will be set in pairs. One student explains and shows, while the other listens. Then, they switch.
How will you help students to exhibit and self-evaluate their growing skills, knowledge, and understanding throughout the unit?		The students will be able to use “Two Stars and a Wish.” Students will write down two things they learned from the lesson, and one thing they hope to learn during the next lesson.
How will you tailor and otherwise personalize the learning plan to optimize the engagement and effectiveness of ALL students, without compromising the goals of the unit?		During class, I will use communicators in order to be able to keep the students actively engaged. This will enable me to see that ALL students are on task.
How will you organize and sequence the learning activities to optimize the engagement and achievement of ALL students?		All manipulatives are ready on their tables, in baggies. The baggies are located in a box. Each table has a group box, which includes everything that the students will need in order to move from one activity to the next. The box includes pencils, calculators, manipulatives, and communicators .

From: Wiggins, Grant and J. Mc Tighe. (1998). Understanding by Design, Association for Supervision and Curriculum Development

I believe...through the eyes of an eighth grader

I took "I believe" into my classroom of 8th graders. One of my students wrote this in under 10 minutes. Had I not had that extra few minutes in class...I never would have known what this student was capable of. Let's face it, I teach Mathematics...we rarely get to see this side of the students. So, I decided to put it to music and surprise her with a video of her writing. This video was shown to my entire school (grades 6-8) during a school-wide assembly. It will also be shown at our next faculty meeting. I must say that I am pretty excited for my student.

Do You Know?

Shift Happens

What was your initial reaction to the video?
I must admit that my initial response to the video was fear. Not crazy over the top fear, but a slow churning gut feeling of fear. I am not sure if I felt this way more for myself or more because I have two small children. What will their future be like? My son (who is almost six) has an I-Pod, knows what a podcast is (because we watch space related podcasts), and hears me talking about my blog. He already plays on the computer on occasion and he is very aware of Google. My daughter (who is almost 3) knows that if I press a few keys, we can get “Dora” to help us with our ABC’s. It’s amazing what they know already. On the flip side, both of my children enjoy “reading” and the library. Neither of them have video games or a tv’s in their rooms. A parent is usually split on this decision. One day research says video games are bad, then the next you hear hat it is great for their hand-eye coordination. Which is correct? Let’s face it, technology is not going away. It is everywhere. It is incorporated in classrooms via blogging, podcasts, wikis, calculators, computers, “Elmo’s”, etc. Therefore, my fear is not necessarily of the fact that the world will not be as it is now, but fear of the unknown. What will it be like for our children? Will they be happy? Will their need for immediate gratification alter the way our society reacts to each other? Will our interpersonal skills come to a screeching halt because we are attached to texting and not talking? Is this flat world going to create such a place where children are almost communicating robotically?

What challenges must we overcome as we move forward?
The challenges we must overcome are far too numerous to state them all. However, I believe that the first step towards teaching the 21st century student is to be aware. Be aware of what new technology is out there. Be aware of the latest technologies that interest your students. Be aware when it is all too much. There will be times when a student is tired of looking at a power-point. There will be times when a student wants more interaction with humans. Be aware of when that is. Be aware of that they are not learning the way the way students did when we were younger.


Is it possible for a teacher to be an excellent teacher if he/she doesn’t use technology?
Well, I don’t really know the right or wrong answer to this. I know of an excellent teacher who barely integrates technology at all. She teaches World History. She incorporates a variety of classroom management techniques. She uses differentiated instruction…name the catch phrase of the week, she does it. She brings in artifacts from around the world, because she is a world traveler herself. She is passionate about her content area (and has visited most of the countries herself). However, she barely uses email. She barely goes on the internet. She doesn’t get her facts about the Mayan civilization from “Google”, she got it from visiting Central America. Yes, a teacher can be amazing without using technology.

Symphony

Picture this...I (as many of us did) had the day off of work today. My children did not. So, I had the television on, and I was listening to the news. Yes, listening, because I was multi-tasking, as many of us are doing these days. (This was actually a treat for me as I do not watch much of anything when my children are home.) I was listening to Mr. Obama speak about what he would potentially do for our country. He began to speak about education. Naturally, I began to focus a little more on what he was saying. He spoke about not teaching to the test, getting and keeping the best educators out there...and then he said (along with many other things) that he would keep art in our schools. He made a clear point to say that our future depends on developing the whole child. I then began thinking about what Pink wrote and how he said that symphony is about seeing relationships. At that moment, I connected what I read in Pink's book to Mr. Obama...and decided...

I couldn't agree more.

Unfortunately, as a math person, I am most likely considered a left-brainer. Although, I understand the importance of putting the pieces together, people would probably assume that I am more logical than anything else. However, even as a "left-brainer" I still believe that symphony should play a role in everyones classroom. Yes, it is the ability to see the "big picture." This ability goes way beyond an art classroom. In my classroom, students have the ability to share their thoughts on the content I am teaching. I have students telling me they learned the same material in different ways...others tell me that they have never seen it all. (Mind you, they are coming from the same classes!) However, when I take the math lingo out of the conversation, that is when they understand it most. I had students not understand what variables were...then I changed the variables for objects and magically they understood. Some of the students did not welcome the symbolism, they wanted more. When they have the opportunity to have manipulatives in hand, or figure out for themselves what I am asking from them...all of a sudden, they make a connection. They are able to see the relationships to real life situations, and why the "stuff" I am teaching is actually worth something! SYMPHONY! Math is not just about numbers and signs! If you allow it, math can be like music. There can be many different steps necessary to get to that end result, but we don't have to all dance the same way to get there. My students know that they do not have to do it my way, as long as it's mathematically legitimate. I encourage them to see the big picture. Telling them stories and relating them to math. Allowing them to draw and explain their answers...I do not try to squash that right brain...I encourage it!

I have a student who is a true artist. She is constantly drawing. She takes my notes in artistic form. It is amazing to see her write notes (that only she usually understands)! Most of her notes are sketches, but she understands her relation to what I am teaching. She can write a logical two-column proof with pictures. Many of her teachers complain about her doodling...I tell them that I allow it. They, in turn, think I am completely wrong. This student just took one of the most difficult tests that I will give in this marking period, and she got every question correct! She is artistic, why would I squander that? As long as she is listening and contributing, and understands what I am trying to teach...I have no problem with her "doodling." The mere fact that she has the ability to work with both sides of her brain and excel should be applauded.