Day 37: Shopping & 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.” 29

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: Apply unit rate in real-world scenarios

Agenda:

1. Estimation 180 with capacity Day 53
2. QSSQ 
3. Review the Unit Rate HW 
4. Shopping Stations in the second class 

Assessment: My chief assessment was getting students to recognize the difference in the quotients of small number divided by large number and large number divided by small number.

Students could recognize for instance that 12 pencils over $3.49 was a ratio. On the bottom of the next ratio in a proportion was $1. They were unsure though if it would be 3.43 pencils for $1 or 0.29 pencils for $1. I sat with groups of four as they came to this station all afternoon and went through what made sense and what did not. Although I was exhausted from this single problem when it was all done, I felt confident that kids could reason that 3.43 pencils per $1 made sense for a number of reasons while 0.29 pencils per $1 did not. We then were able to break into a separate conversation about $0.29 for 1 pencil just before it was time to switch stations.

Glass Half-Full: I accidentally forgot to include Station 5 in the copy machine, but timing wise things worked out just fine as students had enough work to keep them on task. On top of that, I think the variety of questions and ways in which students needed to apply unit rate made for a deeper learning experience. I've used this lesson in the past, but not with this much structure. Groups of three to four were switching every 7 or 8 minutes and for the most part the movement breaks helped students. For full disclosure here are the other pictures used at the various stations:

Regrets: The first station was harder than I meant it to be. The example problem does not appear to be an example or a template for the remaining problems. I would probably just do the problems like Station 2 in the future and revamp Station 2 to ask students if $0.25 per egg makes sense or $2.31 per egg makes more sense and why. That way there is still that variety, but students can take what they learned in Station 1 with me and apply it elsewhere.

I also assigned this as homework. It is probably not necessary because going over it the next day would take a lifetime. Maybe just making one part homework (Pepsi) would be a better use of my time and their time.

Link: I'm not going to do this Halloween task from Yummy Math, but I love the idea of asking students for the questions to consider when planning the most effective route to get their candy. I think it's something that they will actually think back on.