Day 39: Equivalent Ratios

6th Grade Math Standards: 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: Determine if two rates are equivalent or not.

Quote of the Day: "“Joanne came up with a big idea in 1990, but within six months her mother suddenly passed away. She was living in England at the time, and decided to accept a teaching job in Portugal to try and escape the grief.

Shortly after moving to Portugal she falls in love and gets married. Less than three years after being married her husband abandons her with their three year-old daughter. She moved to Scotland to be closer to her sister. Joanne was living on welfare and had hit rock bottom.

She started writing the story that was birthed back in 1990. Eventually she gets a publishing deal and is given a three thousand dollar writing advance. The publisher didn’t think much of the work and only published a limited number of books. They also asked Joanne to create a pseudonym to write under to disguise her identity as a female writer, and hopefully attract male readers. Joanne doesn’t have a middle name, but her mother’s name was Katherine, so she wrote under the name J.K. Rowling. You are probably familiar with her work. That first book she wrote was Harry Potter. ‘I was set free because my greatest fear had been realized and I still had a daughter that I adored, and I had an old typewriter and a big idea. And so rock bottom became a solid foundation on which I rebuilt my life,’ she said.” – Joshua Medcalf
Question from Yesterday (as always from a student): How many mini bears would fit inside a super bear?

Assessment: Circumventing the room during the notes

Agenda:

1. Jumpstart with double number lines
2. Return Weekly Quizzes
3. Notes on equivalent ratios
4. Using ratio table practice
5. Equivalent ratio practice out of the textbook

Glass-Half Full: I wrote an email to parents regarding how solid attendance has been this year, the effort of students to retake quizzes and tests, and homework. I had students at lunch and after school today. It's very rewarding to see students want to work hard and to play a small part in giving them that motivation.

Regrets: I'm just going to type and make no deleting as I go. It's frustrating to be on a treadmill like it felt today. There was so much to cover and not enough time to cover it. Ratio tables, double number lines, and equivalent ratios are all cousins, but they also could be done on three separate days (double number lines was given the Friday class). There were too many note problems. Too many homework problems. There should have been less questions and more thinking. I should have been more enthusiastic about the challenges. A problem in the book changed units on students without any big flashing lights and I should have had students work on that problem for fifteen minutes and discuss the intricacies of it. We are getting away from the weekly pepper, visual patterns, and estimation that helped students enjoy my class for the first 30 days. I want to slow things down and do math that let's them think.

Link of the Day: Visual math focuses on a different part of the brain than simply making numerical calculations and research indicates that when visual math and the numerical side of math are in sync, the strongest connections and learning is taking place.