Day 38: Intro to Functions

Quote of the Day: “Treat today as if it were your first day. Ask yourself, ‘If I were just starting this job, what would I do differently?’” – Barry Posner

Question of the Day: Does the order matter in terms of where you put numbers in scientific notation? In other words is 2 x 10 to the third the same as 10 to the third x 2

Regular Math Objective: Write numbers in scientific notation; multiply and divide numbers in scientific notation find cube roots/square roots of negative exponents and perfect cubes/squares

Regular Math Standards: 8.EE.2 Use square root and cube root symbols to represent solutions to equations of the form x 2 = p and x 3 = p, where p is a positive rational number. Evaluate square roots of small perfect squares and cube roots of small perfect cubes. Know that is irrational.

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: This was where it went wrong. I did not really have a sequence going in. I knew the study guide would not consume the whole class. I interspersed QSSQ, reviewing the homework and pepper throughout the lesson. It was bad. Plus the weather was cloudy for the first time ever in New England which had everyone in a slightly worse than normal mood. If I could recreate the day and do it correctly this is what I would have done.

1. The last two problems of the study guide as a warm up.
2. QSSQ including a look back on the exit ticket from yesterday in which kids could not subtract a negative number.
3. Try number six from the study guide which is a division problem since that problem would be fresh in our minds off of QSSQ and yesterday's exit mistakes. 
4. Give six minutes to do problems four and five of the study guide which in my opinion were the hardest on the study guide because they were reading comprehension questions. 
5. Finish the rest of the study guide which students did not really struggle with. 

Honors Math Objective: Analyze if a graph, set of ordered pairs, or t-chart represents a 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: This sequence actually made sense and went better.

1. 100 divided by 0 and 0 divided by 100 were the warm up question. I was surprised at how few students knew this up front. It's really hard to discuss functions without this as a perquisite in my mind. As my colleague and I were previewing what we were about to teach I kept wondering why it was that the vertical line test worked and that each input needed exactly one output. Finally he started to answer and I just blurted out because the slope would be undefined. I haven't been in eighth grade since I was in eighth grade so take it easy on me with the hateful "you didn't know that and you're a math teacher" jibber jabber. 
2. QSSQ 
3. We reviewed the do now and then I asked one more post-warm up question. How do we know a slope? Students mentioned change in y over change in x. 
4. I passed out the vocabulary terms. Students read them for a minute. They then quizzed each other for a minute (I was timing it to the second). Then I asked students do you think it might be good to make flashcards? They agreed. 
5. Review homework and pepper with the vocabulary terms 
6. Students did in explore activity from Big Ideas and ripped out their homework which was seven problems asking about functions, domain, and range.