Day 42 Ratios Test

6th Grade Math Standards: 6.RP.1 Understand the concept of a ratio and use ratio language to describe a ratio relationship between two quantities. For example, “The ratio of wings to beaks in the bird house at the zoo was 2:1, because for every 2 wings there was 1 beak.” “For every vote candidate A received, candidate C received nearly three votes.”
6.RP.2. Understand the concept of a unit rate a/b associated with a ratio a:b with b ≠ 0, and use rate language in the context of a ratio relationship. For example, “This recipe has a ratio of 3 cups of flour to 4 cups of sugar, so there is ¾ cup of flour for each cup of sugar.” “We paid $75 for 15 hamburgers, which is a rate of $5 per hamburger.” 29
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: Write a ratio; find a unit rate; use a tape diagram to solve ratio problems; use a double number line to solve ratio problems; simplify ratios; determine if two ratios are equivalent; compare ratios to see what a better deal is

Quote of the Day: “We go to a higher level when we treat others better than they treat us. When it comes to dealing with others, there are really only three routes we can take:

The low road - Where we treat others worse than they treat us.

The middle road - Where we treat others the same as they treat us.

The high road - Where we treat others better than they treat us.

The low road damages relationships and alienates others from us. The middle road may not drive people away, but it doesn’t attract them either. But the high road creates positive relationships with others and attracts people to us - even in the midst of conflict.” - John Maxwell

Assessment: The ratios test and the weekly quiz were due today, so I was busy grading. The results were mixed and there was not any one question that stood out more than the rest as being a question that students answered incorrectly.

Here a student simplified and then tried to do a unit rate (incorrectly). What's important for me is that they did order the numbers correctly. Obviously the term simplest form and knowing that the smaller number should be on top here are issues that will need to get reviewed when I pass the tests back. 

It was nice to see students write 6.4 packs instead of $6.4. 

Students were choosing to use double number lines (they also used charts, unit rates, and equivalent rates, and divide then multiply). It was great to see a variety of methods.

I had students try this type of problem the day I introduced tape diagrams. Literally nobody could do it in the 3 to 5 minutes that I gave students. This concept was brand new and it was nice to see so many students conquer it like this.

Agenda:

1. Take the test
2. Work on the next weekly quiz

Glass-Half Full: Students are learning. The evidence is there. It's not everyone and it's not every question, but I give them credit for working hard.

Regrets: These are the concepts that are not mastered yet and I think deserve continual attention: simplest form and order of ratios. There is also the issue of comparing prices, but I will leave that to weekly quizzes versus spending class time on it because they can be the type of questions that take a long time.