Day 32: Double Numberline Graph & Shopping

6th Grade Math Standards: 6.RP.3 Use ratio and rate reasoning to solve real-world and mathematical problems, e.g., by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations.
a. Make tables of equivalent ratios relating quantities with whole-number measurements, find
missing values in the tables, and plot the pairs of values on the coordinate plane. Use tables
to compare ratios.
b. Solve unit rate problems, including those involving unit pricing and constant speed. For
example, if it took 7 hours to mow 4 lawns, then, at that rate, how many lawns could be
mowed in 35 hours? At what rate were lawns being mowed?
c. Find a percent of a quantity as a rate per 100 (e.g., 30% of a quantity means 30/100 times the
quantity); solve problems involving finding the whole, given a part and the percent.
d. Use ratio reasoning to convert measurement units; manipulate and transform units
appropriately when multiplying or dividing quantities
The Learning Objective: First class: Construct a double number line to compare two units. Second Class: Find unit rates of items in a grocery store

Quote of the Day: "At 211 degrees, water is hot. At 212 degrees, it boils. And with boiling water comes steam. And steam can power a locomotive. One extra degree makes all the difference."

Agenda: 

1. Collect all weekly quizzes
2. Check tape diagram and unit rate homework
3. Jumpstart on paperclips and tables
4. Review homework and the jumpstart
5. Estimate too high and too low on how many of the smaller gummy bears can fit in the bigger gummy bears
6. Ask students how we can measure how many gummy bears fit inside a bigger gummy bear
7. Show the students the mass of 10 gummy bears and the mass of a bigger gummy bear.
8. Use a double number line to discover how many gummy bears fit in the larger gummy bear
9. In the second part of class, we discovered the answer for the gummy bear activity
10. The students were given a sheet to go shopping for different items I had placed around the classroom. I explained the directions that I would clap my hands when it was time for the students to switch sections of the classroom and try new problems. As students worked, I circumvented the room. 

The Assessment: Student work on the unit rate and decimal division problems. 

Homework: The students were given Weekly Quiz #5 to do over the weekend for a homework grade.

My Glass Half-Full Take: As students got into their groups, I overheard the conversation of two students. One student was asking another student what his grades were. The student shot back that he did not want to share his grades. He was basically handling it in the exact way that I have been preaching the students to handle that issue.

One Thing to Do Differently: One? How about three today. First of all, I wish the Jets and Patriots game didn't last as it late as it did. I got about ninety minutes less sleep than I usually do and was grumpy at the end of the day.

Second, in the first half of class I really didn't have an assessment. Typically I enjoy Dan Meyer's work, but the numbers were big and intimidating which detracted from putting together the double number line. The numbers we used were the same as the numbers he used. I could have simplified the numbers for the kids by telling them to round. It would shorten the length of time on the activity and not compromise the objective. If I could do this over again, I would probably give the students this as notes and perhaps give them Dan Meyer's problem in the second part of class. As it is I'm doing the linked assignment next class because the students were never assessed. This was a classic case of doing placing the activity ahead of the assessment, and hopefully I don't run into the issue again this year. 

Third, I taught unit rates toward the end of class. We did unit rates the class before, but it would have helped to do this lesson in sync with the other unit rates lesson and would have worked out time wise (we could simply take out the tape diagram lesson and insert it in today's lesson). The activity was a good way to get students out of their seats, but students were doing straight decimal division in many cases in lieu of showing the units and making sense of the real world application of each problem. I think if I either modeled one problem for the students or simply had them recall their notes from the prior class it would have solidified unit rates for them in a deeper way than we did in the last two days of school. 

Link of the Day: 20 minutes well spent. Admiral William H. McCraven's words to the Class of 2014 at the University of Texas at Austin.