Day 42: Double Number Line & 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?

Objective: Apply a double number line to solve ratio problems; Create ratio tables to solve problems in which one ratio is given and only one of the other units is given; Use scaling to find equivalent ratios

Agenda:

1. Visual Pattern #18
2. QSSQ 
3. Resuming the double number line gummy bears lesson
4. Double number line guided practice
5. My favorite no. If I mow 8 lawns in 14 hours, at that rate how many lawns could I mow in 49 hours? 
6. Notes
7. Practice/Homework

Assessment: It was a busy day with a lot of content. I mostly circumvented to see how students were doing and gave light instruction at the board, but mostly let them try and fail. Here are a couple of the more common things I saw.

This first picture is from my favorite no. Only about 10 percent of students could do this, so most students required my instruction for how to find equivalent ratios. The student pictured here got much closer than most of the students. They demonstrated the ability to find a unit rate which would lead to an easy solution if they flipped it around to find hours per lawn.

Even during the notes, I was still trying to let them fail a little. Here the student continues to have a flawed definition of what a ratio is by leaving a difference of 10 between the two currencies. The analogy of if I had 10 Canadian dollars being worthless in American dollars goes over their heads so I try to use a wheels to bike analogy to explain away the error. 

This last one is similar to the mistake above. I had students stand and repeat after me. Multiply to find equivalent ratios. Divide to find equivalent ratios. Don't add. Don't add. Don't add. Don't subtract. Don't subtract. Don't subtract. Unfortunately, the students and the co-teacher then bring out the argument that as long as your adding by two wheels on top and one bike on the bottom you can add (or subtract) just not by the same number. Their right. That's so much more complicated to think about though. Let's just call it multiplying.

Glass Half-Full: I had the students complete a Google Form for the homework. First time I've done it all year. It was great for the few students that completed My Favorite No correctly because they got to take a Chromebook and answer these questions in class instead of doing the notes.

Regrets: It was bad for the majority of students who completed the notes because they did not have time to use the Chromebooks in class and I never explained how to do the assignment. Oh well. There was so much going on in one day. Usually I split these lessons into two separate lessons, but with Election Day and Veteran's Day and assembly after assembly I did everything that everyone tells me not to do and rushed it.

Link: Socratic Seminar courtesy of a colleague who I got to see try this today in his 7th Grade ELA class. Always fun to try new things, but more fun when you don't have to be there.