Day 46 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

Objective: Write a ratio three ways in a word problem context; find equivalent ratios by getting a unit rate; solve problems with ratio reasoning; apply a tape diagram to solve for an equivalent ratio; apply a double number line to solve ratio problems; find the least common multiple; compare two different prices

Agenda:

1. Quote, Star Student, Question
2. Take the Test
3. Retake any previous assessments from this year
4. 5, 4, 3, 2, 1 challenge (get to 20 through 30)
5. Read a book

Assessment: The test results were about what I would expect. This was a test that featured many concepts and covered almost all of the ratio common core standards, so there were definitely students with gaps. Class averages were in the high 70s. What will be interesting to see is how these gaps get filled moving forward. In general, ratios do not always correlate with future topics such as algebra and statistics, so I may explore getting these concepts in.

Here is an example of students getting two different answers (bottom is correct, top is incorrect) by doing the problem two different ways. I have used this problem for three years now and like the depth it forces students to use when they solve it multiple ways. 

Glass Half-Full: On part three of the agenda, students were allowed to retake any test or quiz from earlier this year. Students have folders in my room which show me which questions that they have answered wrong on any prior test or quiz we have had at this point in the year. It's not always the most efficient way to differentiate (I would love to rely on software instead), but it does give students the opportunity to increase their grade and me the opportunity to reteach and motivate students to continue learning the skills that they lack. Students were retaking quizzes from September and October (not the exact questions, but similar ones) and answering them well. This was encouraging to me because I do not think there's anyway that these skills can be classified as simply memory activating their brains. They were truly capable of performing the skill and this is a sign of mastery.

Regrets: Many students approach me during a test to sneak an answer out of me. I very rarely will comply. I wonder what research says about providing assistance during tests. My personal view which was influenced by Rick Wormeli is that mastery is not mastery until it is independent.

Link: That quiz was a resource I just heard about on Twitter. Not very fancy, but seems easy to use and a good place for remediation, pre-assessment, and even homework.