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# Two Powerful Shapes

Lesson 1 of 12

## Objective: SWBAT understand that the power structure of this class is better represented by a circle than by a line.

With today's class, I am welcoming students into a math classroom for their first time as high school students. That's a big deal, and there is a lot that I need to (and even more that I want to) tell them about this class. Rather than rushing into all of that, however, I want to develop it as we go. The purpose of today's class is to set the stage for all the structures that I'll share in the next few weeks.

So for today's opener, I show students what this class *will not* be. As they enter, students see the opener projected on the board. It says:

- Sit at a table where you can see the agenda.
- There should be at least 3 students at each table.
- Get an index card.
- Write the name of your table and the full names of all group members on your index card.

I will not tell you where you must sit - but you must be able to see. And the agenda, that's important. In this class, you will not sit alone listening to me - you must sit with people, and I expect you to know their names.

There is certainly some math here: as we begin a unit in which we'll study linear inequalities, the phrase "at least" is going to be important. After a minute in which I welcome kids into the room and tell them to read the opener, I simply ask, "How are we doing with this?" They look around and see if there are "at least 3 students at each table." Maybe they argue a little bit: does that mean 4 is ok?

If we don't quite have it yet, I say, "Is this possible?" If it seems like it was easy, I might informally pose the problem, "Are there any numbers of students for which this is impossible?" just to get them thinking.

The expectation is that I'm not going to tell you exactly what to do, but that I want you to meet certain minimums.

On each of my tables - my class has 8 sets of four desks, each of which I'll call a table - is a sticky note with a Greek letter on it. Some of these, like pi, kids have seen before. Others, like lower-case sigma and phi, are brand new to them. I walk around holding up the sticky notes and naming the letters. I say that these are letters just like the ones in our alphabet, pointing out that Alpha and Beta are the first two, and that's why it's called the alphabet in the first place. I say that Greek letters are often used in algebra, when we run out of our letters as variables. I also throw in, playfully, that if anyone ever wants to join a fraternity or sorority in college, you're going to have to know these letters. It's a silly thing to say, maybe, but I'm also setting the expectation that we're preparing for college within the first few moments of class. And why am I mentioning college? Not because of all that "it's for your future" mumbo-jumbo that 14 year-olds don't want to hear, but because, if you go, you'll have the time of your life.

I give them a few more minutes to get each other's full names, and as I circulate, I say that spelling matters. It matters who you're working with, and it's honorable to know names.

#### Resources

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This is a very conversational class session. There's not much for students to write, and I don't give many notes, but there's a lot to think about. I want to get kids thinking about how hard they're going to have to think in this class.

**Introduction and Framing the Class**

Once everyone has a seat in a group and has written the names of their colleagues, I introduce myself briefly. I point to my name, which is written at the top of today's agenda. I always write the agenda on one of the whiteboards at the front of the room. I tell students that they'll always be able to see the agenda there. I also point to the top of the agenda, where I've written, "Welcome, Class of 2017". I say these words to the class, and I ask them if they've ever thought of themselves like that. Some nod, and some look surprised and excited. It's the first day of school, but I make the point right away of positioning ourselves in relation to the big goal. "In four years, in September 2017, my goal is for each of you to be doing whatever you want," I say. "I promise that if you work hard, this class will help you get there."

**Two Powerful Shapes: Line Up Ice-Breakers**

I point to second item in today's agenda, which is called "Two Powerful Shapes". I ask the class to name the most powerful shapes they can, and my goal is for them to come up with lines and circles. Kids often come to this consensus on their own, pretty quickly. To the class, I reason that these are the most powerful because so many shapes can be made out of lines, and because circles are *not* made of straight lines. It's playful and might tend toward hogwash, but the point is, we're going to talk about lines and circles for a little while today.

I point to the back of the classroom, where there's enough room between the back tables and the wall for everyone to line up. I say that we're going to start by talking about lines, and I give the class their first challenge: "I want you all to line up in order of height. I'm going to time you." I leave it purposefully vague, by not indicating which end of the line is for the shortest person, and which is for tallest. I want to see how they talk about this. "When I say 'go,' I'm going to start the clock, and you should all stand up and get this done as quickly as possible."

Any time there's a challenge like this, the debrief is the most important part. When students are successfully lined up by height, we debrief. I ask what went well. I say the time that it took the class to line up, and I ask if they could do better. If anyone says they could improve, I ask how. I ask for someone to explain how everyone decided which end was low and which was high. If someone emerged as a clear leader, I ask if it's helpful to have a strong leader.

Then I say that I've got another challenge. "This time," I say, "you have to line up by your birthday, and you're not allowed to talk." I give them a moment to groan and to ask how that's possible, then I ask if anyone has any clarifying questions about the challenge. If they continue to wonder how that's possible, I simply say, "You can all work together to figure this out." I say I'm going to time them again, and again I say "go!" and start the clock.

When they say they're done, I stop the clock, then I go down the line, and ask each student to say their birth date. We're checking for errors. In my experience, it's rare for a group of brand new 9th graders to do this perfectly, so I count errors. It's also rare for them to be completely silent. When we debrief I say how long it took to complete the challenge and how many errors there were.

Usually, these results disappoint some of the kids, which gives me the chance to introduce the grading policy in this class. I tell students that they'll be graded based on *mastery* in this class, and that grades will be on the scale from 0 to 4. If any students are particularly disappointed in their performance on this challenge, I'll point to them and ask, "Was this a complete failure -- would you say that you all had a 0 on this challenge?" Everyone is quick to agree that the performance was not a 0. "So maybe it wasn't perfect either, but do you all think you could improve it?" It's clear, on a challenge like this, that a little practice could really improve our outcomes. I tell students that this is how I'll want them to think in this class.

**Where's the Power in a Line?**

"There's one more thing that I'd like you all to see about lines," I say. "This is the only time I'm going to ask you to do this: stand with your back and your head against the wall, so you can only move your eyes." I demonstrate what I'm asking for by facing the class on the opposite wall. "How many of your classmates can you see?" If they try really hard, they might be able to see three classmates on each side. "How many of you can see me?" I ask. They all agree that I'm easy to see, and that I can see all of them. "Keep this in mind," I say.

**Circle Up**

Next, I say we're going to "circle up". I walk around the room to show students where the circle will fit, and I explain what I mean when I say to "circle up". It means that everyone is standing, in a big circle around the room. We make the circle, and I gently coach everyone to find a spot - there's no double-parking allowed.

When the circle is made, I ask the question again: "How many people can you see now?" Everyone agrees that now it's pretty easy to see everyone else. I explain that this is how the power will be distributed in this class. "When you were all lined up, I had the power," I say, "because I was the only person who could see everyone else, and you all had to look at me. Now, who has the power?" We talk about how a circle distributes the power in the group, and that everyone has an equal position. I point out that desks are arranged in small circles, because that's how the power will be distributed in this class.

Finally, we do one more initiative. I say that we're going to go around the circle, and everyone will introduce themselves by saying their full name, and the name of one person who they think is powerful. No one has to explain their choice of who they name, they just have say the name of someone powerful.

**What Makes Someone Powerful?**

After we go around the circle, I recite a selection of the names I heard: celebrities, presidents, family members, super heroes, historical figures, kids who named themselves. I ask what it is that all powerful people have in common, and I open the floor to this conversation. Some kids share their ideas with the circle. When everyone who wants to speak has had a chance, I say my theory: **I think that powerful people get to choose what they do, and that when they have ideas, they can act on them. **

#### Resources

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#### Syllabus Distribution

*7 min*

While we're still in a circle, I pass around the class syllabus, which begins with the purpose statement:

**The purpose of this class is to give you a powerful background in Algebra. At the end of this class, you will know concepts and ways of thinking that will enable you to put ideas into action.**

I ask for a volunteer to read this statement, and then I offer anyone the opportunity to chime in with their thoughts. Usually, with all the rest that's going on with the first day schedule, I don't have time to run through the entire syllabus. If there is time, I might run through a few of the parts of the syllabus, but it's most likely that the bell will ring right about now.

I show students the bottom of the page, and I ask them to bring it home and read it with their folks. "If anyone at home has questions about this class, they can write them in this box," I say, and point to the bottom of the page. "Then, you and a parent should sign this, so I know that you've read it together. We'll finish reading through tomorrow."

A more complete reading of the syllabus will be on the agenda tomorrow.

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*Responding to Teri Shearer*

Thanks Teri, glad I could help! Your question has been at the center of my own PD for years, both as a guide for my own learning, and in conversations with colleagues. It's an impossibly big question to fully answer here, but here are the cliff notes: 1) The ideal is to have a rubric for every learning target. Creating those is hard, iterative work, and it's still in process. When I do have a rubric, I share it with students (most often on projects), and I'll revise a rubric after seeing how kids interact with it. 2) Content and Mathematical Practices are different in nature, are therefore assessed differently, and their rubrics differ accordingly. 3) It's ok - no, it's awesome and liberating - to grade holistically rather than by "% right". If I give students a quiz with 5 equations to solve, for example, I don't have to count how many they solved perfectly. Instead, I can look to see how much they understand. I can also include some really challenging examples, without worrying about the fairness factor of including such problems. // I hope that these thoughts help, and would be happy to continue our conversation in the future. Good luck in September!

| 2 years ago | Reply

What rubric do you use to determine how to score students' level of mastery for each learning target? How does a student earn a 1, 2, 3, or 4? Do you share these rubrics with your students?

As an elementary teacher turned secondary math teacher, your lessons are a life saver! Thank you so much for sharing your incredible talents.

| 2 years ago | Reply

Kay, that is so cool!! Thanks for sharing. I'm just now realizing that I missed your question of a week ago (school started last week!). For quizzes, I try to keep the pressure very low. Kids remain in their groups, and as you've seen, they can use their notes. Sometimes I give different versions of a quiz to each student at a table, and other times I tell them that they can work as a group. The key is that in my mind, quizzes are a chance to help kids learn something: they're not a chance to "get" kids or to bring them down, they're a chance to help kids feel good about what they know, and to recognize what they don't. (Check out this NYT article: http://www.nytimes.com/2014/07/20/opinion/sunday/how-tests-make-us-smarter.html?_r=0.) Exams are the only time that I rearrange the seats from tables of 4 to rows, but even then, the main purpose of this is that I know my kids are going to have to take serious exams at some point, so I want to give them the practice.

| 3 years ago | Reply

Mr. Dunseith, thank you again for the lesson! Today I felt goose bumps of excitement as I carried out the lesson with my students. What a thoughtfully designed lesson!

| 3 years ago | Reply

One question for you, Mr. Dunseith. I am aware that your students are allowed to use notebooks for quizzes. How about seating during exams? Do they continue to sit in a group of four during quizzes/exams? Happy School Year to you as well!

| 3 years ago | Reply

Kay, thanks for the note! If you have the time, I'd love to hear a bit about your favorite tweaks to and adaptations of this lesson. In the long term, I hope that one outcome of this site is that we teachers have a chance to compare notes on the different ways we enact all or part of these lessons.

Happy school year to you!

| 3 years ago | Reply

Thank you for sharing your well-thought out lesson based on a long-term vision for the students. From this lesson I will incorporate many insightful ideas into my own lesson. Thanks again!

| 3 years ago | Reply

This message is so important for kids, especially freshmen- "the power to succeed (or fail) is in your hands, and I will do whatever I can to help you be successful." I love it!

| 3 years ago | Reply*expand comments*

- UNIT 1: Number Tricks, Patterns, and Abstractions
- UNIT 2: The Number Line Project
- UNIT 3: Solving Linear Equations
- UNIT 4: Creating Linear Equations
- UNIT 5: Statistics
- UNIT 6: Mini Unit: Patterns, Programs, and Math Without Words
- UNIT 7: Lines
- UNIT 8: Linear and Exponential Functions
- UNIT 9: Systems of Equations
- UNIT 10: Quadratic Functions
- UNIT 11: Functions and Modeling

- LESSON 1: Two Powerful Shapes
- LESSON 2: Number Tricks, Patterns, and How to Succeed in This Class
- LESSON 3: How Can an Abstraction Show Me How Things Work?
- LESSON 4: Words and Abstractions
- LESSON 5: Patterns and Abstractions
- LESSON 6: How to Write a Pattern Rule
- LESSON 7: How to Write a Number Trick
- LESSON 8: Work Period: Patterns and The Number Trick Project
- LESSON 9: Patterns Quiz and Project Work Time
- LESSON 10: What's Wrong With PEMDAS?
- LESSON 11: Problem Set: Number Lines
- LESSON 12: The Parentheses Challenge