Day 33 Double Number Line and Ratio Tables

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 part of class: Construct a double number line to estimate the solutions of problems. Second part of class: Find an equivalent ratio through scaling.

Quote of the Day: “Some think it’s their job to change people. Sorry. You can coach, counsel, teach, and guide, but no one changes another person. Change only comes from the inside as a result of decisions made by the individual.” - Jimmy Miller

Agenda:

1. Students worked on a division of decimals jumpstart as I passed back the Weekly Quiz and in one class the progress reports. I also collected Weekly Quiz #5 which I required to have done today. 
2. I cold-called a student to tell me why 1.44 divded by 0.4 was not 0.36. 
3. We did I do, we do, you do of a double number line that served as a way to check Weekly Quiz #4. Really cool way to show students a new topic while also reviewing their homework. 
4. The students tried a couple double number line questions as an exit ticket. 
5. I reviewed the answers to the ticket to leave questions with the students and will do so again tomorrow when I hand the exit tickets back.
6. Before we began looking at ratio tables and more specifically scaling, I had the students try it independently. 
7. We did some tables in notes. First they were problems that were easy to get an equivalent rate, but eventually they involved either decimals or two steps. There were two such problems.

The Assessment: Step 6 of the agenda was a primary assessment for today. "If 14 lawns get mowed in 8 hours, how many lawns can go mowed in 49 hours?" Their pictures are shown below. Many were demonstrating solid ability with the double number line and others were not far away from finding the solution through scaling before we started the activity. None of the three pictures shown actually were able to give an answer, but it let me know students were knocking on the door to this process without any instruction. I also gave the ticket to leave in step 4 and checked the Weekly Quiz in Step 1.

Homework: Page 43-44 in the textbook problems 1-10 and skipping number five.

My Glass Half-Full Take: I was pleasantly surprised at the connection one of my students made as we transitioned to ratio tables. He asked me if ratio tables and the double number line were really two ways of solving the same type of problem. I said there's more than one way to skin a cat (yes).

One Thing to Do Differently: I'm reading Teach Like a Champion right now, and the author uses the analogy of giving students at bats. I don't think students had quite enough at bats with scaling. I think I could have modeled more problems and they could have attempted more. I don't think doing one problem for the class and having them do one independently was enough given that this was my objective for the fifty minute block of time.

Link of the Day: Interesting way to bring students together to communicate about problems in math class. The site/app is called Math Chat and I haven't tried it yet, but I think I'm going to mention it at Parent Conferences this week. Two years ago I'd hesitate and say this won't teach kids anything since they will just be scrounging around for an answer. Today I'd say in our world this is the way in which we add to our knowledge pool and a healthy way to not only learn but have some students teach to demonstrate mastery of a subject.