Day 43: Coordinate Plane & Pythagorean Theorem

Quote of the Day: “Playfulness and humor improve the quality of a person’s ideas and creativity, not to mention a person’s health...Studies have shown that laughter reduces stress hormones and increases the level of mood - and health-enhancing chemicals such as endorphins and dopamine.” - Greg Bell

Question of the Day: How can a graph be linear and continuous? If the legs of a right triangle are the same is the hypotenuse always irrational?

Regular Math Objective: Apply the Pythagorean theorem in the coordinate plane

Regular Math Standards: 8.G.8 Apply the Pythagorean Theorem to find the distance between two points in a coordinate system.

Regular Math Lesson Sequence:

1. Student choice either weekly quiz or 11 squared through 20 squared as a warm up as I passed back exit tickets 
2. QSSQ 
3. Exit ticket review. I found the students tuning me out as I was reviewing so I periodically had them get out of their seat and kinesthetically show me where the legs and hypotenuse of a right triangle were. By the last class I just made students stare at my work for 15 seconds and ask a question. Only two kids volunteered questions, but they were good. "Why did you get 7 instead of 49? How did hypotenuse get its name?" 
4. Homework review and pepper. The pepper topics today centered on coordinate plane, right triangles, and rational numbers 
5. Pythagorean and coordinate plane exploration. It was really a great example to go by for exploration, but I completely left off connecting the hypotenuse in the directions. Here is the document. I would add a question nine about connecting the points to create the hypotenuse before students declare that they have just created a right triangle. 

Honors Math Objective: Derive an equation of a graph

Honors Math Standards: A1.F-BF 1 Write linear, quadratic, and exponential functions that describe a relationship between two quantities.

Honors Math Lesson Sequence:

1. 4 minutes of Pepper
2. Review of the graphs and equations from yesterday
3. I passed out four new situations and had the students take 5 minutes to graph them independently. It takes about 2 and a half minutes per graph, so this was not enough time but at some point we need to move forward. 
4. I gave students 8 minutes to debrief in groups.
5. I went over the problems on the board. Students were really angry when they saw the step function that described the first problem. "Is this going to be on the test?" I don't know. It's going to be in this class though right now in this moment. I thought it would be fascinating to discuss if this problem were a function. The kids were still hung up on the chaos of the whole thing compared to what they thought this situation might be (see the picture below). In their defense, this stuff is definitely hard. I think it's really fun though. 
6. I had students match equations to the graphs. 
7. QSSQ