As students walk in the room, I hand them a paper with three postulates on it. Students describe the substitution, subtraction and partition postulates in their own words without using their notes.
Although my students usually use their notebooks for the Do Now, today I have them describe the postulates from memory. I want them to try to mentally access knowledge learned in previous lessons. I encourage my students to do their best to write a full description and not just give an example. I also encourage them to supplement their response with an example.
I find that this activity reinforces their understanding of the postulates, and the need to internalize them. After about 5 minutes, we will go over their descriptions.
In a previous lesson, students explored the criteria needed to prove two triangles congruent using the Side-Side-Side Postulate (G.CO.7, G.CO.8). In this lesson, I ask my students to use the write proofs of triangle congruence based on these criteria (G.CO.10).
Before students write 2-column proofs, I have them begin by writing three paragraph proofs. I find that this helps students organize their thinking logically, in order to better write two-column proofs. I use a modified form of think-pair-share, which in practice looks like think-pair-solo(write)-share. For this protocol I give students a few minutes to discuss ideas with a partner, then I ask them to write their paragraphs. After they write, I will call on students to share what they have written
In SSS Activity, students work independently to write two column proofs using the Side-Side-Side postulate. I encourage my students to begin by taking the first few minutes to look at the given statements and label the information on the diagrams. Then, I encourage them to brainstorm about what information they will need to write a proof, step by step with supporting reasons for each step. I make sure that they understand the task as using the information covered in previous lessons as reasons for the steps in writing the proofs. If students have difficulty working independently, I select pairs of students to help each other. I don't want students to get discouraged.
After about 10-12 minutes, I'll call on a student to present his or her proof to the whole class. Then, as a group we will critique the proof and fix any misconceptions or missteps. For these presentations and classroom conversations it is important to be flexible, support students, and differentiate the scaffolding that is provided to my students. For example, sometimes a student may combine or skip steps when writing his/her proof which, depending on the level of the class or the students, may be appropriate or may show that they do not fully understand the structure of the proof.
To summarize the lesson, I have the students create their own proof statement for a problem involving triangles for another student to solve. I ask my students to:
After five minutes, I have my students exchange papers with a partner. Each partner considers and solves the problem by constructing and writing up a proof based on their partners' problem.
As students work, if they are having difficulty I ask them to refer back to the problems covered in class today. They can write a proof based on the proofs from the lesson activity. They can use the same diagram, but provide different given information. Etc.