Day 36: Unit Rates

6th Grade Math Standards: 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.”

6.RP.3b 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?

Objective: Define unit rate; describe the relationship between two quantities as a unit rate of each quantity

Agenda:

1. Open Middle - Ratios 
2. QSSQ
3. Pepper
4. Unit Rate Notes
5. Unit Rate HW 

Assessment: I had students stand up when they completed certain sections of the note and then students assessed one another by walking around the room. There was also time left in class to do the homework so I circumvented the room while students worked in partners.

Glass Half-Full: The Open Middle problem was answered by only one out of forty students. I give the hint of "halves" to all classes although that hint is a little misleading since really it's the reciprocal of halves in the answer.

Interleaving with the greatest common factor of 120 and 96 was great because students were forced to plug in their divisibility rules to make it work and about half got a wrong answer among those that attempted it.

Again this year with this lesson I let the students use calculators to check their work. Very good idea as the numbers and the time it takes some students can distract away from the concept of unit rate.

Regrets: The way that students formatted the problems independently was showing division problems when I wanted to see units in many cases. I need to get more emphasis on the setting up a proportion. I also never really introduced the term proportion with the students.

The problem with the ice cream was not done very well by the students. Most students could not show the work effectively and gave up. In my opinion, it was a laziness issue where the homework was mostly done in class, but this problem being the fourth of five, was not done int class. I really like this problem too because it incorporates least common multiple as a method for solving (and probably the most logical way to solve it too).

Link: The author of this Math with Bad Drawings article is basically saying that students subjected to these should have every right to rip up the paper. I don't disagree. If the assignment was changed though to making the drawings make sense as the author did though you may have a very challenging assignment for some students.