Day 30: Introduction to Ratios

6th Grade Math Standards: 6.RP.1 Understand the concept of a ratio and use ratio language to describe the relationship between two quantities. For example, "The ratio of wings to beaks at the birdhouse in the zoo was 2:1, because for every 2 wings there was one beak." "For every vote candidate A received, candidate C received nearly 3 votes."

The Learning Objective: Write a ratio in three different ways. Differentiate part to part and part to whole ratios. Define ratio. Give a real world example of a ratio.

Quote of the Day: "When kids play video games, they fail 80% of the time. They look at failure there as an opportunity to learn. However students can find school mistakes humiliating." - David Dockterman, Harvard Graduate School of Education

Agenda:

1. Jumpstart with divisibility, listing factors, and prime factorization. As students worked I collected their completed weekly quizzes from the previous class. 
2. Ratio discussion (I listed several ratios and then cold called kids to give me ratio examples)
3. Ratio Notes
4. Three practice problems (I do, we do, you do)
5. An exit ticket that stumped some kids initially
6. Students ripped out their homework at the end of the first class
7. Upon entering for the second part of class we played pepper on the term "ratio" where students gave definitions and examples.
8. Nana's Paint Mix Up
9. Students got started on the homework which was page 25 in the textbook as well as a couple problems on page 26.

The Assessment: The exit ticket went pretty well. Students were given a problem about 4 different items and told to write a ratio of fruit to the total number of items. Most of them were able to do this in the correct order and also simplified the ratio into a unit rate (even though that term wasn't introduced yet). The second question on the exit ticket (there were only 2 questions) involved more thinking than the first as the students had to again find a total in a question that was unnecessarily verbose. Again I was surprised with the success they had - although more students struggled here.

I also was able to assess all weekly quizzes (although this was done somewhat yesterday too) in class and return them to students as the students worked on Nana's Paint Mix Up and also during lunch.

Pepper helped me infiltrate their brains and insert the vocabulary term ratio. I feel like infiltrate is the right word.

Homework: From the math book page 25 and part of page 26. I really liked one question that asked students if 6 out of 24 students in a class had a baseball glove, write the number that have a baseball glove to the ones that don't in the class. Among the papers that I saw as students were working on the homework, more than half were writing the ratio as 6:24.

My Glass Half-Full Take: I had a student say I'm not good at math today. The same student was correctly answering questions in class and tested pretty well on my assessments today. I like that the student can have that attitude, but can come back fighting in class. I told the student it's my mission this year to create confidence in her ability.

Another positive from today was the quote. All three classes cited peer influence and the fear of embarrassment as the most lopsided reason why there is a difference between failure in school and video games. I wholeheartedly agreed that making mistakes can be embarrassing. I shared with them a personal example from a class I took this past summer with about forty other math teachers. The professor saw the work I had (and knew I was close but wrong) and asked me to show my work on the board. It's easy to be embarrassed about this situation and I felt like maybe my peers were judging me. Today I asked my students how many of those forty teachers were thinking about that moment today. The students agreed that none of the teachers were. In fact, I had grown in this moment. I was humbled. I realized for the one billionth time that I need to keep learning and that my status as a teacher doesn't change that in the least. Making a mistake is normal and it is also forgettable.

One Thing to Do Differently: I spoke with a colleague at the end of the day who was arguing that the students do not care as much as they used to. I got the sense that she was not saying this to vent or in frustration, but it was a matter-of-fact position that she had reached. She compared her own childhood to the childhood of the students we have. She said that when she got home from school her siblings and her would do their work "in numbers." Meaning that they would sit around the kitchen table (they had no desks in her home) and their mother wouldn't let them leave until they were done. It was discipline 101. She mentioned how her mother would check their work and even call the Boston Public Library (this is before Google remember) to learn things that they were curious about. She said this same discipline and this same curiosity is rare in the students we teach. Perhaps it has always been the case. Or perhaps we're not letting them find their curiosity as we are teaching right now. This video from Sarah Almeida argues strongly that schools are factories that make it hard to care, be creative, and be curious.

Comparing eras in baseball is always hard because there are so many variables in play. Steroids, the size of the pitchers mound, the strike zone, defensive shifts, situational lefties, etc. I think the same can be said with students today versus when we were their age. Today ADHD is more commonly diagnosed - not necessarily more common. Is this leading to better teaching practices for these students or are these teaching practices being used as a crutch by the students? The internet is essentially making any deep question such as can a number be divided by 0 a quick google type away rather than really investigating. Is having information a positive or is taking away critical thinking a negative? Grades can be seen instantaneously with grade books online. Is this causing the students and parents to view the grades instead of the learning more now than ever or is it a good thing that there instant communication that there is a learning gap or high achievement?

The answers can be debated obviously and I'm not going to be able to answer one way or another. What I do know is this. What I wish I'd done differently is thank my grandmother for instilling my work ethic on homework as a child. How did she do it? Simple. She didn't threaten me by taking away the television if it wasn't done or reward me with cookies if I did problems right. She simply praised my effort. When I was done she complimented me. Occasionally she complimented me in front of my parents. That was it. She didn't even have to ask me to ever take out my homework or check it. The environment of seeing her quiet happiness was the only motivation I needed. Perhaps the same can be said of my colleague's mother's phone calls to the library.

Link of the Day: Tomorrow we are using the Partial Product lesson from Dan Meyer. I'm getting a lot of his lessons right now, and the kids are doing a lot of thinking as a result.