Today’s lesson opener asks students to prove that two segments of a figure are congruent. This problem reviews the strategy of proving triangles congruent to analyze or prove the properties of a figure. It also allows me to assess whether students are ready for today’s quiz and to clarify minor points of confusion.
I present the lesson opener using the slideshow for this lesson: TriangleCongruenceUnitQuiz_Slideshow.pptx. Students write their proofs in their learning journals and then share them with the other members of their cooperative learning team. One member of each team writes the team’s answer on the board.
For more information on how I open lessons, see the article on beginning and ending a lesson in my Strategies folder.
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 giving a correct proof (no more than one error). (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.
During this part of the lesson, I review two handouts which were assigned as homework with the class: Geometry_Practice19-1.docx and Geometry_Practice19-2.docx. I design quizzes to assess whether students understand vocabulary, concepts, simple skills, and complex procedures related to the topic of the unit, not to see whether they can persevere in solving a novel problem. For this reason, I assign homework that reviews the types of multiple choice questions and free-response problems students will see on the quiz. Although this might reduce the level of rigor of the quiz, it also helps to reduce the likelihood that a student who knows the material will lose points by failing to read the problem or that students will be confused by a poorly worded problem.
As students complete their Unit 19 Quiz, I bring them the pre-test for Unit 20. Students know that this pre-test does not count as a grade. I ask them to make an effort, answer every problem and make educated guesses where they do not know the answers. I tell them that the pre-test tells me what they already know about the new topic, and it gives them an advance look at the sort of questions they should be able to answer at the end of the new unit. Students generally complete the pre-test in 5-10 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.