I’m going to use a previous question and extend it for them in the DO NOW. The original question was as follows:
Michael is shopping for baseball cards. He finds a deal on cards that is on sale for a special rate of 5 packs for 7.50. At this rate, what is the cost of one pack of cards? The students can re-work this problem to make sure they understand how to find the unit rate. Then I’m going to say, that another store is selling these same cards for $.99 each. Where should Michael purchase baseball cards to get the best deal?
Allow students time to think about what the question is asking them. Have them work independently to get started on this problem. Walk around the room to see the strategies that the students are working on. For students that are struggling, ask them what they have to start with for the second scenario (SMP 1). Also, you can ask them how the first and second scenario relate to each other? Remind students to use a strategy for solving to support their solution (SMP 4)
Once students have worked out their solution, have them share with their tablemates to see other strategies that were used. (SMP 3)
During this time, I’m going to show students how to use strategies to find the unit rates which in this case is the unit price By then end of this guided practice, I’m looking for students to understand that when trying to find the better deal, we don’t usually find the per dollar rate, we use the per product rate. According to CCSS, students will need to find both unit rates. For example, If something costs $4 for 2 pounds , one unit rate is $2/lb. This is the type of unit rate we are used to seeing. The other rate would be how many pounds could you get for a dollar. In this case you could get 1/2 lb for a $1. Both of these rates can be useful when finding unit rates because the goal is to compare common parts. The latter example is just something we are unfamilar with. Another example, I can travel 50 miles in 5 hours. The well known unit rate would be 10 miles/hr. The "other" unit rate would be 1/10 of a hour in 1 mile or 6 minutes/mile. I'm going to show students both unit rates as this is a requirement for common core. Some of the problems will lead to not-so-nice numbers. If students can show you the ratio and explain what they need to do, allow them to use calculators to lessen the frustration. (SMP 5) AT this time, I would use question number 3 to show both unit rates.
Barry earns $36.00 for 6 hours. Henry earns $24 for 3 hours. Who has the better hourly rate. In this problem, the students need to know that when we are looking at earning money, the better deal is to earn more money.
The quetions is how much money do they earn per hour?
Barry: $6/hr and Henry $8/hr
If you flip this around you could ask, how many hours do they work to earn $1?
Barry has to work 1/6 of an hour to earn a dollar or 10 minutes/$1
Henry has to work 1/8 of an hour to earn a dollar or approx 7 minutes/$1
Either way, Henry is earning more money!
Teacher note: finding both unit rates requires you to use the reciprocal and simplify. Since we don't show the students to do it that way, have them use a a ratio table and find the "1" for both the bottom and the top measurement.
I am going to ask students if there is ever a time when using the per dollar rate or per mile rate would be useful? I'm hoping to hear, when you only have a $1 in your pocket and you need to how much you could get would be a good time to know this unit rate! Or you could only travel for a mile, how long would it take you. These would all be good examples of the "other" unit rate.
For this section, you will need to collect a variety of store flyers. I start collecting these a few weeks before this lesson. The dates on the paper are not important. If you can find local chain store flyers, they usually have competitive pricing which will be helpful for studnents to comparison shop. If the students can't find same products, they can use comparable products. For example, if one store has Pepsi on sale and the other has Coke, the students can use these for their better deal examples. I'm not concerned about using the exact same product. Doing the math, using real life examples, is key here. Students will have access to use a variety of flyers at their table. This does not have to be a group activity, but I’m going to allow the students to work in groups, pairs, or individually during this time, their choice. Before letting the student go, it would be a good idea to explain to students the layout and vocabulary in the flyer. Some students may not have as much exposure as others when it comes to finding information from the flyer. Choose a couple of flyers that are displayed differently and point out where to look for information and what it means.
I’ve pre-made a spreadsheet for the students to use when discovering their unit rates. The spread sheet is set up so that the students must find a comparable product at another store so they can find the better deal.
I’m going to have the students complete a comprehension menu to assess level of understanding. The comprehension menu has the students answering 4 different learning style questions with different levels of complexity. Students will make a mark by the question they felt most comfortable to answer.
Collect this as evidence of student learning.