After walking into the classroom, I sit down at a table with another student and wave hello to the young teacher. On the whiteboard are the objectives for the day:

*Geometry*

**Do Intro task now*

**$$$$$$$*

**exit ticket*

Lawrence Teng, wearing chinos and a plaid shirt is a first-year teacher and graduate of the University of Michigan. One semester at MetWest under his belt, he passes out the Introductory task–a slip of paper with three tasks for students to do–as students enter the classroom (LT refers to Learning Target). The 19 sophomores and juniors get immediately to work on the tasks.

A slide on the whiteboard replicates the square with empty space on the slip of paper students begin working on.

The large classroom has a slowly whirling ceiling fan. Tables sitting two to three students each face the whiteboard and the teacher who is working in the front of the room with his laptop and document camera sitting on some cabinets (his desk is in the rear of the room). Lawrence uses the laptop to flash images onto the whiteboard. The room has a clock and phone.

After about five minutes, Lawrence (in this school, students call teachers by their first name) asks the students to stop. He then turns to the question on the slip. “Anyone has any memories from weekend.” One student responds about what his family did. No other responses. Then teacher asks about the squares and how to find answer without counting them. He calls on Bruce who says his answer. Lawrence asks Bruce to come to front of the class to explain his strategy in getting the answer he gave. Bruce tells class each step of his thinking to reach his answer; Lawrence is at whiteboard showing what Bruce said on the grid of squares.

Teacher then says that there are many strategies to solve the problem and Bruce returns to his table. He begins applauding Bruce and a few students join in. He then calls on Maurice and he and Maurice go through the same routine of figuring out that there are 56 squares with eight missing–all without physically counting them (as I did). Lawrence sums up student answers and shows the different strategies of adding, subtracting, and multiplying to get the correct number of missing squares. During this part of the lesson. Wrapping up the opening exercise, Lawrence tells class what assignment is due Friday.

I note that there are two other adults in the room. One is a volunteer (a retired math professor whose son was a staff member at the school) who helps individual students when the class is doing independent work. Another adult is a resource teacher working with individuals who have been identified with special needs.

Then Lawrence turns to the item that was listed on his agenda for the day’s geometry lesson–$$$$$$. He shows a brief video of an art exhibit at the Guggenheim exhibit of paper one-dollar bills pasted the walls and columns of a room. After showing the short clip twice, he stops it at the dollar room.

As I scan the class, students are very attentive to the images of one dollar bills in this museum exhibit. I do not see any students off-task.

He then asks class to write down their questions and turn to partner at table and share questions with one another. Students do so. At one point, he says aloud that he is putting Angel’s and Maurice’s name on the whiteboard for playing around. No response from either student as class works on questions.

Lawrence then asks students to tell him what their questions are and he will divide them into two categories: questions he can and cannot answer. “Can you grab money off the wall?” No, Lawrence replies, it is an art exhibit and there are security guards in room. He calls on students by name and they reply with their questions. He sorts the questions into the two buckets. One student question he pauses over: “How much money is on the walls of the room,” one asks.

With that question, teacher asks students to guess at an answer to the student’s question. Tables erupt into numbers yelled out and much quizzical laughter throughout the class.

Lawrence lists the guesses on the whiteboard:

*$20 thousand dollars

*$1500

*$5500

*$10,000

Teacher then directs students to tell table-mate how they arrived at their guess. Students’ actively engaged with one another as I look around the room.

Lawrence quiets the class and asks:”To get the correct amount of money in the room, what information do you want or need from me?

Students quickly yell out what they want from Lawrence.

*How big is the wall?

*What is size of a dollar bill?

*Are there layers of dollar bills or one each pasted to the wall?

*How many feet across is the wall?

*How tall is the wall?

At the table next to me, I ask the three students what question they came up with. One showed me what they wanted to know: “Figure out area of wall and divide it by area of dollar.”

Lawrence then flashes on the whiteboard close-up photos of the money (students see that there are no layers of dollar bills) and then slides of the dimensions of the columns and walls. He hands out a two page floor plan of the room with the surface area in centimeters of both the columns and the walls. The handout also show a photo of a dollar bill and its dimensions in centimeters. Further information on the handout states that there are 3516 dollar bills on the North Column and the same for the South Column. The dimensions on the floor plan for the width, length, and height of the room are on the floor plan marked in meters and centimeters. He calls on one student to read out dimensions listed on the floor plan. Lawrence asks class: “How do you find the area of one of the walls?” A few students respond by saying to look at the dimensions of the floor plan.

Lawrence then asks students to estimate how much money is on the walls and columns. A few students move to a file box near me and take out calculators and return to their seats. Students at each table (a “team,” Lawrence calls them) get to work. A buzz of noise arises in class as teams work at their tables.

Lawrence quiets the class and before asking them what amount of money they came up with, he asks the class–a choral question–what strategy did each team use in coming up with their answer. In the whole group discussion, a few students reply and list the steps.

Lawrence summarizes the strategies students used: Divide area of walls by area of dollar bills. He goes over steps to find area of rectangle (base multiplied by height). A few students near me comment aloud that their estimates resemble the problem of rectangle of squares with missing ones that they looked at when class began.

A few minutes remain in the class–students look at wall clock–and begin putting notebooks and papers in their backpacks and standing up. Lawrence tells them to fill out Exit Slips. Standing students sit down and write answers to three questions on slip:

**How did you feel during lesson?*

**Did your group work well together?*

**Choose option that best describes you;*

*–I do not know what is going on*

*–I know how to solve problem.*

*–I am done with problem.*

Chimes sound and students drop off slips in box on a table near me as they leave room.

Reblogged this on Eddie's Class and commented:

Reblogged at eddiesclass.com

Thanks for re-blogging post on teaching math.

Good stuff, Larry. I’d love to know what was on the exit slips, and how the teacher typically responds the next day based on the slips.