Day 44: Pepper Battles

Quote of the Day: “Philip of Macedonia, the father of Alexander the Great, said ‘An army of deer led by a lion is more to be feared than an army of lions led by a deer.’ That may be true, but I’ve come to believe that Philip missed the bigger point: An army of lions led by a lion is to be feared most of all, for it is unstoppable.” - Mark Sanborn

Question of the Day: Where does the term hypotenuse come from? How do we know whether to subtract or add in doing the Pythagorean Theorem (in reference to finding a leg or finding the hypotenuse)?

Regular Math Objective: Given two points on a coordinate plane find the distance between them using the Pythagorean Theorem.

Regular Math Standards: 8.G. 6a. Understand the relationship among the sides of a right triangle. b. Analyze and justify the Pythagorean Theorem and its converse using pictures, diagrams, narratives, or models.

Regular Math Lesson Sequence:

1. My Favorite No. This was really rewarding to teach. I did not give students anything today. I was locked into ask questions and let students prove why mode. The problem I gave was the points (0, 1) and (-2, 1). Too many students right away got four units. 
   
   Exactly like that. No work. No explanation. So I asked how did you get that? Kids came to the board throughout the day and traced over the legs of the triangle. They were missing the fact that you could go directly from one point to another with a straight line. I used the analogy of walking to the trash bucket in the room and it was effective. Then students had the problem of counting the distance diagonally on a square unit as one unit. To confront this, I took a square object in the room and measured it across as well as diagonally. Students saw that diagonally it was longer. At this point on the SMART Board we had two lines tracing the legs and one tracing the hypotenuse. I told students to look at the board for fifteen seconds and not write or say anything. And finally they started writing a formula for the Pythagorean Theorem. 
2. Depending on the results of My Favorite No, we either did one more problem or worked on what would have been the homework if Halloween wasn't a thing. I started the students with problems three and four on the link since they related back to My Favorite No. I also really like problems five and six as standards to revisit because students are not recognizing the difference between approximating and getting exact values for the irrational numbers. 
3. The exit ticket question was a math mistake of a 3, 4, 5 triangle that had a hypotenuse of 25. We were more successful than normal because at this juncture in the unit, students are actually well ahead of the curve on this mistake. It made for easy correcting and a nice ego boost. 

Honors Math Objective: Use function notation to identify graphs and their matching functions

Honors Math Standards: A1.F-IF 2 Use function notation, evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context.

Honors Math Lesson Sequence:

1. The entire class went to the classroom of the other 8th grade math teacher for Pepper Battles. We had students stand one minute at a time and asked them vocabulary and quick theory based questions. Within 8 or 9 minutes we were out of there. It was a great break from the norm. 
2. QSSQ
3. We discussed the various meanings of parenthesis. It ranged from multiplication to an ordered pair to probability to least common multiple. We then introduced f(x). I was quick to point out that this is essentially the same thing as y. 
4. The students did an explore activity from Big Ideas. 
5. We discussed what graphs from the explore activity go with what functions. By the time I handed out the homework I realized that the students were going to be overwhelmed by what they were facing. We'll have to revisit it again tomorrow.