For today's Warm Up, I have selected two problems that continue to provide opportunities for students to build fluency with the Pythagorean Theorem.
The first problem reviews the previous topic of proving a right triangle. I want to reinforce for students the concept of equality when applying the Pythagorean Theorem, since both sides of the equation should be equal if the given triangle is, in fact, right.
The second problem requires students to estimate the square root of 74 using a double-number line (another previously introduced skill). I included this problem to remind students the benefit of using a double-number line to estimate since several problems during today's work time will involve estimation.
Blue, Yellow, Red is the Work Time activity for today in which students work through scaffolded problems involving Pythagorean Theorem. As student pairs work through each color of problem, they trade their cards in for the next level. I explain that I expect all groups to complete the first two levels and record their work in their journals. The 'red' card is optional for students and is provided as a challenge for those who have a strong grasp on the concept.
The first three problems, the "blue" ones are basic application problems where students are simply solving for an unknown side.
The 'yellow' problems are a bit more difficult as students must apply larger numbers or estimate their solutions.
Finally, the 'red' problem is the challenge problem that requires students to not only understand how the Pythagorean Theorem will apply in the situation, but also, how to use the information gathered to solve the problem.
Student pairs have 25 minutes to complete the five (or six) problems. As students work, I circulate through the room and ask various student pairs to record their work on large post-it paper to share with the class at the end of work time.
When the Work Time timer sounds, I ask my pair 'volunteers' to present their poster solutions, one at a time, to the class. After each presentation, I ask for questions or comments (both skills we have practiced previously with student presentations). By providing time for questions and comments, I am helping students to make sense of problems they may not have understood or gotten to during work time. This is especially helpful when the 'red' challenge problem is presented as it models perseverance for those who did not attempt it. Also, it often shows a student-friendly approach that improves a willingness to try on future challenging problems.
For closure, I distribute Learning Scale Surveys to my students for them to complete. Although we are now eight days into the unit, I often have students who need additional time to understand and apply concepts. The Learning Scale Survey requires students to rate their understanding of applying the Pythagorean Theorem to solve problems. Students can rate their learning from 5 (I could teach someone else this concept) to 1 (I don't understand this concept at all). I also ask them to justify their rating with an explanation. This information will assist as I plan interventions for students in order to prepare them for the unit assessment.