I’m going to pose this question to the students to get them thinking about constant speed in our daily lives. “The other day I was traveling to Wisconsin. I set my cruise control for 65 miles/hour. My destination was 130 miles away. How long do you think it will take me to get to my destination”? “Think for a moment about that question and on my say, share with your shoulder partner what you think the ratio means and how long will it take me to get to Wisconsin”. (thinkpairshare) (SMP 1,2,3)
I’m not asking the students to do any calculations on paper, nor am I asking them to make a table, although I will later, I just want them to think logically about this problem because making sense of the problem will help with this concept. I will have the students share whole class after their partner discussion.
I'm anticipating that some students may not get started right away because they are confused. I will read them the question out loud. Then I will ask them "If I travel 65 miles in 1 hour, how many miles do I travel in 2 hours". This prompt should get them moving in the right direction.
I’m going to go through several constant speed problems. I will be modeling with ratio tables and I will be using ratio language to deepen the understanding. I chose these problems because they make sense in real life and connect nicely to the concept of constant speed. I’m also going to be having them graph the speeds on a coordinate plane so they can visualize what happens while something is moving at the same rate. Students should be able to tell you that constant speed results in a flat line because they are moving at the same rate throughout the trip. (SMP 2 and 4)
Students may have difficulty moving from the table to the graph. In order to make this transition easier, I'm going to label my table with an x and y to show them that the points from the table make an ordered pair. This will help with the graphing.
The students will be working in pairs to answer a variety of constant speed problems. Each problem has to do with constant speed and again is connected to real life scenarios. Students will be required to show their work and explain their answers. It is not necessary that they complete all problems. There are enough problems, however, to keep the high performing students busy.
The students will be creating their own constant speed poster to be placed around the room. This will be a good formative assessment piece. Students will be working in pairs to create their own problem about constant speed. Before sharing their problem they must work it out and decide if their answer is reasonable and makes sense. Their poster needs to include a visual, a problem, and space for a solution. If time permits, they make decorate it. Once students have finished their problem, they will partner up with another pair, share and solve their scenario. As students are working on the problems, I will be walking around the room making sure the concept of constant speed is being talked about correctly. I will begin by targeting students that are struggling to be sure they are starting on the right path. Before walking around, I give them a few minutes to get started on their own. They need to find their own starting point before asking me for help.
I’m going to follow up with my opening scenario by asking them another question
“On my trip to Wisconsin, I still had my cruise control set for 65mph. Unfortunately, the Schade kids needed a bathroom break and I had to stop after 30 minutes. How far did I travel?” Show your work and explain how you got your answer.
I’m fine with students coming up with an approximate, reasonable answer. So, if they say that I traveled approximately 30 miles because its half the time, that is acceptable. The actual answer is 32.5 miles.
Students can reflect on this problem in writing. If time permits, have the share their solutions with their tablemates and then discuss as a whole group.