Playing Around with Pythagoras- Day 3
Lesson 3 of 12
Objective: SWBAT apply the Pythagorean Theorem to find the length of a missing side of a right triangle and recall from memory the square roots of the first 20 square numbers.
Continuing with this week's Warm-Up concept, I provide another linear equation for which they can extend to a table and a graph, this time with a fractional coefficient. As students work, I take the time to record on my clipboard which students struggle with this concept. Fractions typically pose a challenge for students, so this skill will be important to revisit throughout the year. Any struggling student is pulled into my class during advisory period to take advantage of additional support and practice with the skill.
Today, I provide students the second opportunity of three 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.
Although students have already been exposed to the Pythagorean Theorem during the previous two lessons, I intentionally continue to chunk its application to give students plenty of opportunity to use and make sense of the theorem. Today, I want students to leave class with the understanding that the theorem can be applied regardless of which side of the triangle is missing. I do this by first revealing the slide that asks, "Which one is different?". I include three right triangles with legs identified, one of which has been rotated, and a fourth triangle that has one leg and the hypotenuse labeled instead.
Once I show the slide, I ask shoulder partners (pre-selected, similarly-abled students) to discuss which triangle they believe is not like the others. I give student pairs one minute to make a decision, then I randomly select several students to share their choice. Typically, students choose triangle B becuase it is rotated, or triangle D because they recognize that both legs are not identified. Once a student points out that the hypotenuse is given on triangle D, I ask the class how we might use Pythagorean Theorem to find the length of the missing leg. I select a student to guide me as I solve for the missing leg. I then ask students to try solving several problems on their own as I circulate and check for understanding.
For work time, I want students to practice solving for a missing leg of a right triangle with their shoulder partner. Partner A shows his/her work on problems 1 & 3, while partner B shows work on problems 2 & 4. While one partner works, the other is charged with checking the work and suggesting tips as needed. Because the students are paired in similar-ability pairs, this procedure typically works well when students are in the concept devleopment stage.
The first two problems are straight forward with triangles labled. For the second two practice problems, however, I provide students with side lengths only. I am interested to see how students will approach this type of question. I want to see which students must draw the triangle to solve and which ones can approach the solution more abstractly by using the formula. This will provide me valuable insight into each student's developmental level, which I will note on my clipboard for use when planning future lessons.
For closure today, I select a proficient student to summarize the learning for the day. Then, as students are dismissed, they must give a correct answer to one of the "big seven" (13, 14, 15, 16, 17, 18, and 19)perfect square roots that I have written on large flash cards. This will give additional exposure to the perfect squares and aid with retention to build success for the final mastery test that will come the following day.