Day 44: Equivalent Ratios

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.

Objective: Determine if two ratios are equivalent

Question of the Day: Would the points on a graph always be connected?

Agenda:

1. Estimation 180 Day 54 & Day 55
2. Quote, Star Students, Question of the Day
3. Review the homework or coordinate plane and ratios
4. Pepper
5. "One chocolate chip recipe makes 48 cookies and call for two cups of flour. A different recipe calls for 3 cups of flour and makes 60 cookies. Are these rates equivalent? Explain why or why not."
6. We looked at student answers to this question
7. Practice using the textbook on page 43 and 45. 
8. Interleaving homework assignment started in partners

Assessment: There was actually a nice question in the textbook that asked students to determine if a rate per day and a rate per week was equivalent. About 90 percent of the class got it wrong, and quickly did the "ohhhh" when the students that got it right explained. I checked homework and the chocolate chip problem.

Glass Half-Full: I really enjoyed walking around the room during the problem that students did on the chocolate chip cookies. In the past, I have just given notes and showed students different methods. The methods were always either scaling or unit rate, but by letting students work they showed me ratio tables, double number lines, and least common multiple as alternatives to solving this problem.

Regrets: I do not think students fully grasp the concept of scaling yet and if they do they are not using the term scaling because I am leaving it out. I think this terms will be helpful to them in years to come. I also think this is the most frequently use way to compare ratios in the real world because it is the easiest. This is partially a flaw of the common core system. There are so many tools in the toolbox, but some tools are only necessary once in a blue moon while others require more wear and tear.

Link: 71 - 58 in the eyes of a second grade. When you listen to them it's a little better than when you look for how you want to do it.