Day 40: Linear Functions

Quote of the Day: “I don’t have that much self-discipline. But if I’m surrounded by people who are writing articles and giving lectures and working hard, I tend to fall in line. If I’m in a crowd of people doing things a certain way, I follow along.” - Dan Chambliss

Regular Math Objective: Divide exponents that have negative and positive integers; find how many times a number in scientific notation is relative to another number in scientific notation

Regular Math Standards: 8.EE.3 Use numbers expressed in the form of a single digit multiplied by an integer power of 10 to estimate very large or very small quantities, and express how many times as much one is than the other. For example, estimate the population of the United States as 3  108 and the population of the world as 7  109 , and determine that the world population is more than 20 times larger.

8.EE.4 Perform operations with numbers expressed in scientific notation, including problems where both decimal and scientific notation are used. Use scientific notation and choose units of appropriate size for measurements of very large or very small quantities (e.g., use millimeters per year for seafloor spreading). Interpret scientific notation that has been generated by technology.

Regular Math Lesson Sequence:

1. Students got a self-assessment and their quizzes returned to them.
2. Students shared a pathway to get an answer with a partner. This process is painful for me. I tell the kids that all they have to do is put one problem that they got wrong on a marker board by asking a person in their group who got that question correctly. Yet, way too many of the marker boards are left blank. Maybe I need to have it modeled and let all the students see it done. 
3. After the self-assessment and quiz review in groups, I asked if there were any remaining questions and if students thought that they could do better on the quiz at that moment than they had the prior class. All hands went up. 
4. I gave the students two problems to try on the marker board. First I had them simplify ten to the fifth divided by ten to the negative first. Next I had them find how many times greater 6 x 10 to the fourth is than 2 x 10 to the third power. 
5. We discussed a picture that modeled the Pythagorean Theorem although I left out the term 'Pythagorean theorem' intentionally (this pic is Microsoft Word but in color). Then I had the students answer four questions pertaining to the formulas for area of a triangle and area of a square. I did not want to assume anything when it came to their prior knowledge even though I had many of these students in sixth grade and knew that my colleagues and I hammered the formulas into their brains. Not literally. We'd get fired, but we did everything but that. These four questions were passed in as an exit ticket. That way I could see what students wrote, but more importantly they wouldn't lose this sheet between this class and the next class. 

Honors Math Objective: Determine if a function is a linear function;

Honors Math Standards: A1.F-IF A1 Understand that a function from one set (called the domain) to another set (called the range) assigns to each element of the domain exactly one element of the range. If f is a function and x is an element of its domain, then f(x) denotes the output (range) of f corresponding to the input x. The graph of f is the graph of the equation y = f(x).

Honors Math Lesson Sequence:

1. As a jumpstart students found the domain and determined if graphs from the back of the Domain and Range Activity. 
2. I had students do the tables and graphs from the linear functions explore that we did for homework on the board. Assigning an explore for homework was a bad idea and I didn't help myself by giving away every copy I had to students. 
3. We reviewed the exit ticket. Students were having trouble writing the notation for domain and range. They had a stronger grasp on whether it was a function or not. 
4. I passed out the linear functions homework
5. I had them start the Functions and Everyday Situations by making them graph the first four problems from that activity. This was great as I gave them seven minutes to do it, but they wouldn't shut up. "Should we add numbers?" "It's too hard." "How am I supposed to do it?" I told them I wanted them to struggle up front and said that they would be working with a partner on this tomorrow, but they still wouldn't listen. Despite the frustration I did get what I ultimately wanted. I saw what kids thought. And they thought that virtually every graph was continuous and linear. And almost every graph was increasing.