SWBAT write a geometric proof using a flow-chart or a two-column format. Students will understand how proving triangles congruent can be used in a proof.

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

10 minutes

My goal in this lesson is to encourage students to assess their own learning about triangle congruence, which the focus of the homework problems that will be collected today. The lesson opener asks students to come up with one question they have about proving triangles congruent or about writing flow proofs and two-column proofs. I present the lesson opener using the slideshow for this lesson: ProgressCheckandHomeworkReview2_Slideshow.pptx. Students write their own questions in their learning journals and then share their questions with the other members of their cooperative learning team. One member of each team writes the team’s question on the board.

For more information on how I open lessons, see the article on beginning and ending a lesson in my Strategies folder.

In addition, I have shared my thoughts on using this question for a lesson opener in a video: ProgressReviewandHomeworkReview2_VideoNarrative_LessonBeginning.MP4.

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 appropriateness. (Appropriate in this means any thoughtful question. I only withhold the point for teamwork if I see that members of a team are not participating or not cooperating.)

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

During this lesson, students will review their homework in their cooperative learning teams. Afterwards, I will call the class together to address the most common questions about the assigned homework problems (**MP1**). For more information on how I conduct reviews of homework, see the article on Homework Review in my Strategies Folder:

Before class, I reproduce my solutions to the homework problems, making one packet for each team. I distribute these to the cooperative learning teams (by having one student from each team take a packet from the resource center) and give the class a 10 minute time limit for checking their homework.

While students are checking their homework, I circulate through the classroom answering questions and keeping students on task. In particular, I am looking for the following:

- Students are providing explanations or justification where required.
- Students are writing flow proofs to show that triangles are congruent, when required.
- That students understand the conventions for writing flow proofs, especially the requirement to provide a justification for every statement.

During this time, I look at the problem numbers students have written on the board to see which problems most students have selected.

After 10 minutes, I call the class together and ask students to direct their attention to the front board. I then spend up to 15 minutes addressing the problems that gave the most students trouble. In addition, I point out the errors and omissions I want students to avoid, including any trends I noticed while circulating through the classroom.

For more information on this classroom routine, see the article on Homework Review in my Strategies Folder.

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.

For a demonstration of how I set up the application to choose a homework problem at random, check out the video: *ProgressCheckandHomeworkReview2_VideoNarrative_RandomlySelectingaHomeworkProblem.MP4*.

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.

5 minutes

I display the lesson close question on the front board using the slide show for the lesson. 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 assignments are found in the syllabus, which I provide students at the beginning of the unit. The homework assignment for this lesson is:

Practice 19-2 (Handout), Problems #1, #2