Day 37 Dividing Scientific Notation (Again)

Quote of the Day: “Babies need to learn almost everything from experience. If babies didn’t have a strong drive for novelty, they wouldn’t learn as much, and that would make it less likely they’d survive. ‘So, interest - the desire to learn new things, to explore the world, to seek novelty, to be on the lookout for change and variety - it’s a basic drive.” - Angela Duckworth

Question of the Day: Why is scientific notation listed from the numbers 1 to 10?

Regular Math Objective: Divide and multiply numbers in scientific notation

Regular Math Standards: 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. I took ten problems from this LearnZillion practice sheet and immediately had students get to work in groups of three. The problem I typically chose was the first one since these problems got progressively more complex. Each group had a mini marker board. The rules required that whoever had the marker could not speak and could only write what he/she was told to write by the other two group members. After the group got the hang of the first one, I put a second problem up on the board. I intentionally hid all the problems from view so that I could have students compete. 
2. I intentionally skipped to a problem (#6) that required students to divide a dividend and divisor that were the exact same number. Despite the fact that this exact problem was there exit ticket in the previous class and that I was handing back that very exit ticket as they worked this problem out, many students continued to make the same error they had the previous class. I showed them all of their errors on the exit ticket after students had an opportunity to work this particular problem through.
3. We did one more problem and then looked at the QSSQ for this day. 
4. We did another problem, but this one finally became more complicated. It was problem eight which forced students to subtract with negatives. After all groups thoroughly struggled with this, we moved onto the next part of our agenda to help strengthen this weakness.
5. I created a really basic PowerPoint of nine or ten one digit integer problems in subtraction and addition. We did a pepper type of format with me asking four to six students stand at a time and answer about twenty questions in total before moving onto the next group. As a side note, for the amount of time that I know students spend on this topic in seventh grade, none of it sticks. Developmentally these students either are not interested in this topic or it just is that hard because I know the teachers spend a great deal of time trying to teach this standard. In any event, without mastery of this it is impossible to ask students to put division problems into scientific notation with proficiency. 
6. The students did problems six, eight, nine, and ten as an exit ticket. The interesting answers are shown below. 

I consider both of these interesting because I think there is a narrative here. Both the coefficients and the exponents are wrong. The mistakes are obvious in both cases. The top student did 2.5 divided by 2 and the other student multiplied (probably because it was something that could be done mentally) instead of dividing. The exponents were added instead of subtracted.

I think what is telling is that there is no work here. No effort to divide each part up individually. The top student tries something, but does not even want me to see. This could be because I have been saying to students do not do too much math in an effort to persuade them away from writing out the numbers in standard form. I need to reallocate our goals to do math, but recognize what is necessary and what is not. Here the students are clearly guessing and do not have logical proof to show why what they are doing makes actual sense. 

Honors Math Objective: Find the domain and range of a graph

Honors Math Standards: A1-F-A1Understand 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. QSSQ
2. Recap of Ketchup Day. 
3. I explained to students how pictionary would work. Since I have twenty-six students in this class, I grouped students according to a deck of cards (ace through king). One card was red and one was black. Ideally I would have had the kids with the red card do half of the graphs and the ones with the black cards do the other half. That was not what I did unfortunately, but confusion was only temporary. 
4. The students and I began to do Pictionary (credit to John Scammel). They used a great deal of vocabulary and it served as a nice refresher in a topic that they probably have not visited since June at the earliest. 
5. Afterwards we broke down this vocabulary and I mentioned for the first time words like translation and domain and range. 
6. I assigned students to work out the domain and range of six different graphs for homework. It would have been helpful to get students to use colored pencils, but I was time-crunched at the end of the lesson.