Playing Around with Pythagoras- Day 4
Lesson 4 of 12
Objective: SWBAT to prove a triangle is right by applying the Pythagorean Theorem and recall from memory the square roots of the first 20 square numbers.
For today's warm up, I have provided two right triangles, one with two legs identified and the other with a leg and the hypotenuse identified. As I take roll and circulate through the classroom, I am taking note of which students struggle with applying the Pythagorean Theorem. For those students, I ask guiding questions to get them started like, "What will you use to find the length of the missing side of the triangle?" The majority of the time, this is enough to jump-start a student to work. For occasions when it is not, I stay and offer additional scaffolded support or recruit a peer tutor to assist.
Today, I provide students the third and final opportunity of this week to show memory recall mastery of the perfect square numbers through 20. I give five minutes of class time to provide students, especially those who lack academic support from home, the opportunity to practice with flash cards with a partner. After five minutes, I distribute the quizzes face down and start the three minute timer. Once the timer sounds, I collect the quizzes.
I provide three opportunities to demonstrate mastery because many of my students face a variety of challenges from homelessness to lack of parent support. I provide any student who wishes their own set of flash cards for independent practice. For students who have already shown mastery, I ask them to focus on continuous improvement by beating their previous time performance. In addition, each time a student scores 100%, I "pay" them $100 in Royal dollars (see my strategy folder for an explanation of my token economy). In this way, I am providing both intrinsic and extrinsic motivation for skill development.
In preparation for today's work time activity, I present the question, "How would I use the Pythagorean Theorem to prove a triangle is right?" I ask table groups (of four students) to discuss the answer for one minute, then I ask for a volunteer to share his/her thinking. I want to make sure students are grasping the idea that both sides of the equation should be equivalent when triangles are indeed right triangles. I instruct students to work through several problems, so they are prepared to complete the day's activity.
I intentionally include both right and non-right triangles so that students can see the result when the theorem is applied. I also include one question with decimals in order to scaffold for several of the more challenging cards in the activity.
Once students have worked through the sample triangles, I distribute envelopes to student partner pairs (of like-ability) that contain nine triangles that must be sorted into "right" and "not right" piles. I ask students to record both their work and their results in their journals so that we can come together at the end of work time and compare results. I then set the timer for 12 minutes and circulate throughout the room to provide support and/or redirection as needed.
When the timer sounds, I verify that all student groups have finished. If the majority have not, I add additional time to the timer. If students have finished, I pull a stick (from a cup with everyone's names) and ask that student to provide his/her group's findings. I then select three others and record those in a table on the SmartBoard. This data typically drives a great discussion as it is rare that all the partner groups agree. I ask dissenting group members to provide evidence in order to convince their classmates of their correct answer. This is a perfect example of Mathematical Practice 3 (construct viable arguments and critique the work of others)!
For closure today, I am interested in seeing individual approaches based on today's learning so I provide the following question for students to respond to on 3 x 5-inch cards that they will hand me on the way out the door:
Dan was given the following triangle (side lengths of .5, 1.2, and 1.3). He decided that it was not a right triangle. Do you agree? Explain your answer.
This quick assessment will tell me whether students are ready to move on to the next lesson or if they need additional practice to build understanding.