SWBAT use tangent and inverse tangent functions to solve triangles.
Students will understand the meaning of the tangent function and its inverse.

Student questions are the focus of the lesson as students grade their own homework and prepare for homework quiz.

10 minutes

My goal in this lesson is to encourage students to assess their own learning so far in this unit. The lesson opener asks students what question (or questions) they have about trigonometry. By asking students to choose one question to write on the board as a team, I hope to stimulate discussions within each team that will bring out the questions that most need answering for the class.

As students are entering the classroom, I display the agenda and learning targets (the slide in the presentation) on the white board using the overhead projector. When the bell rings, I display the lesson opener and note the time. Students have 5 minutes to complete the opener.

This sctivity follows the **Team Warmup **routine, which is described in my **Strategy folder**. Instructions are also provided in the slide show. One member of the team writes the question the team agrees upon on the white board at the front of the room.

While students are working on the lesson opener, I complete administrative tasks. These include taking attendance and noting which students have not completed their homework or brought required items to class.

When all teams have finished writing their answers to the lesson opener, I award points by writing a score next to each team’s answer and circling it. I award one point for teamwork, one for accuracy. (Accuracy in this case simply means that the question the team has agreed on is about trigonometry.) Writing the points on the board helps to get students to read the other teams’ questions.

Following the lesson opener, I display the learning goals and agenda for the lesson using the overhead projector and review them briefly with the class.

25 minutes

Homework review begins as a whole-class activity. Using a document camera and overhead projector, I display model solutions to homework problems while students grade their own work. I tell students that looking back at their work is part of the process of understanding the problem (**MP1**). If they did not succeed completely, how much progress were they able to make? If they arrived at the correct answer, can they see the whole process of solution at a glance so that they will be able to reproduce it in the future? Likewise, if students were not able to solve the problem, do they fully understand the model solution I have provided? Could they have solved the problem by a more efficient method? Could they use their method of solution on other problems?

As I read and show the solutions, I point out the errors or omissions that I want students to take care to avoid. For example, students sometimes think that the point of math is to ‘get the correct answer’ rather than to learn ways of thinking. As a result, they may not make an adequate effort when asked to explain or to justify their thinking. I offer model answers to problems that ask students to explain or justify their thinking and ask students to share their own answers if they are different from mine (**MP3**). Where problems require students to write proofs or use geometric notation, I warn students to pay attention to the details that students often miss (**MP6) ** During this time, I encourage students to ask questions that help them to assess their own work. I also answer questions about how to solve a problem, but only if it can be done briefly. If a student asks a question that requires a lengthy answer, I ask them to wait until the class has reviewed all the problems.

Following the homework review, I give students 5 minutes to look over their work so that they can identify the problems on which they need more help. Students write the number of the problems that they want explained in an area of the white board at the front of the classroom. If the number of a problem they want explained is already listed, they make a check mark next to the number. To make the best use of the time available, I will explain the solutions to the problems that most students identified as needing more explanation. During this short period, I circulate through the classroom. I notice which questions most students have questions about and try to answer questions for individual students.

At the end of 5 minutes, I look at the problem numbers students have written on the board to see which problems most students have selected. Based on the time available (ideally, 10 minutes), I then plan the order in which I will explain as many as possible.

10 minutes

To reinforce the expectation that students should learn from their homework, I have them complete a homework quiz at the end of a week’s worth of homework assignments. The quiz consists of a single problem, chosen at random from among the homework problems assigned from the textbook. To discourage copying, students in alternate rows complete different problems. I use a computer program to select two problems at random (SelectorTools by Kagan Publishing and Professional Development, available online at http://www.kaganonline.com ). The application is designed to select students. I enter problem numbers into the roster in place of student names. I allow students to use their homework on the quiz. If they have done a good job checking their work and noting their mistakes, the homework quiz should be easy.

When students complete the homework quiz, they staple it at the front of the homework that is due and turn it in to the box for their section at the resource center. Then, they attend to administrative/ housekeeping tasks, which I display on the front board using the lesson slideshow.

Administrative tasks may include: returning graded work, updating the homework schedule, etc. I have included a slide in the presentation which may be modified. If there are no administrative tasks to be completed (rare), I ask students to begin on their homework.

8 minutes

I display the lesson close question on the front board using the slideshow. I have the students brainstorm in pairs, then in teams, before writing their answers in their learning journals. The purpose of the learning journal is to encourage students to reflect on what they have learned (as well as to provide individual accountability). Time permitting, I also ask one student from each team to write a team answer on the white board. This gives me immediate feedback on what students learned from the lesson.

**Homework for this lesson **is assigned in the unit syllabus. The handout is provided. Students are expected to complete problems 1-2 before the next lesson.