Day 50: Ant and Ladybug Disaster

Quote of the Day: “It can be seen that mental health is based on a certain degree of tension, the tension between what one has already achieved and what one still ought to accomplish, or the gap between what one is and what one should become.” - Victor Frankl

Regular Math Objective: Differentiate between two lines in a graph

Regular Math Standards: 8.EE.5 Graph proportional relationships, interpreting the unit rate as the slope of the graph. Compare two different proportional relationships represented in different ways.

Regular Math Lesson Sequence: This was the resource that was used for the entire agenda.

1. Students discussed what they noticed and wondered when looking at two graphs. It was easily the best part of the lesson. 
2. I had the students first count where the ladybug and the ant were on the number line. The attention to detail was extremely important. If you look closely at the number line, the head of the insects is where to count. I for one was caught off guard. This is excellent for getting students to stop and think. It's a higher level concept inside a higher level concept. We weren't ready for it though. The directions say "constant rate of change." I really had to spell that out for students. 
3. After we looked at each insects distance after a certain amount of time, I had students discuss the ratios. They were not able to articulate what a ratio was. That made it really hard for us to talk about proportions. If I were to do it over again, this is where to begin. It's not as if students do not get ratios and proportions in prior grades. As a former sixth grade teacher for many of my current students, I can personally attest that we talked about ratios at least twice per week. If it doesn't matter to kids though eventually they will forget. And that happens to be the case here. Not for all of them, but for a critical mass of them that forces my hand to pump the brakes. 
4. We answered the four questions about multiple representations. Students had a difficult time placing the graph with the correct bug. There were definitely students that were successful and that learned. It just felt very painful and students didn't show any joy, curiosity or any other positive emotion. It could have been the long weekend, but I also think the background knowledge was not strong enough to do this lesson at this point.

Honors Math Objective: Derive the Pythagorean theorem

Honors Math Standards: 8.G.6 6. a. 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.

Honors Math Lesson Sequence:

1. Pass out self-assessment sheets
2. Review the functions quiz as a whole group
3. Students were given a picture of two different pictures and told to determine why a-squared plus b-squared equals c-squared. The cat was already out of the bag on the formula, so asking that to get the formula would be too easy. Asking them to determine why the formula is what it is was more fun.
4. I had students write for 90 seconds everything they knew from the drawing. I then had them share out what they wrote in groups of three. Finally they shared out to the larger audience. From there we were able to break down the problem with my help. 
5. Kinesthetic learning of what the hypotenuse, legs, and right angle were to the right triangle. 
6. Assign the homework.