This stage of the lesson starts with the teacher establishing classroom norms for active listening. The class does a whole-group experiment of the teacher power walking a 5-meter strip. The members of the class are given jobs for collecting data or monitoring time. Then the teacher uses a ratio table to talk about rate and find equivalent rates and unit rates.
6th Grade Math - Rates - Price School
Joe Condon, Lipman Middle School, Brisbane School District, Brisbane, California
00:00 Let's get started. First of all my name is Joe Condon. You guys can call me Mr. C.
00:06 I teach in Brisbane School District. Down near San Francisco. Right next to the Cow Palace.
00:12 We'll talk about one thing before we start and that's active listening. I know that we've moved your desks to make it difficult to actively listen but I ask you…
00:21 If somebody is sharing, to turn towards them. If I am speaking, to turn towards me. So we actively listen with our eyes and our ears. O.K.
00:31 Everybody good with that? Alright.
00:37 We're going to do a little experiment with rate. O.K.?
00:43 I'm going to do the first one and then you guys are going to do some experiments.
00:47 We're going to talk to each other. We're going to talk across our desks with our partners and as a group.
00:54 And in the end I think you guys are going to come away with an excitement about continuing the study of rate and, a little bit, deeper knowledge about what rates are.
01:07 All right. So. I'm going to start. I need this group to time me for ten seconds.
01:17 Up in the front of the room is a five meter tape.
01:21 I'm going to walk this tape as fast as I can.
01:26 I need this group to count how many times I walk back and forth on that five meter tape. All right?
01:35 This group, you guys have to tell me what was my total number of meters, that I walked. Based on the fact that this is a five meter tape.
01:47 You guys back there, when they yell start, you watch the clock for ten seconds and you yell stop.
01:56 Thumbs up everybody understands their job. All right. You guys are going to tell me when to start.
02:02 So, eyes on the clock. Use the second hand up there. Give me a Ready, Set , Go, whenever you are ready. Let's actually have, what is your name?
02:12 Sammie? Why don't you yell it out for us. Tell me when I'm ready to go.
02:33 Stop. Good. Now. O.K. stop.
02:39 Let's go here. How many, back and forths, did I do?
02:45 Everybody agree?
02:47 Total meters?
02:59 Thirty-five meters. All right. Let's put down our first rate.
02:55 I traveled thirty-five meters in ten seconds.
03:08 What I'm going to ask you guys to do is if I double the amount of time. If I double the amount of time to twenty seconds.
03:26 Talk to your group. If I am keeping the exact same pace, talk with your group, about how far I will travel.
03:35 Go ahead. Talk to your group right now.
03:39 Once I see a thumbs up from everybody in a group I will know they all agree.
03:43 All right. Looking around I see some from everybody. Well then on the count of three tell me how many meters I will have traveled. One, two, three.
03:53 All right.
04:01 Same situation. Now I'm going to do that shuttle walk for sixty seconds. How far will I have traveled? Talk with your group.
04:14 Make sure everybody in your group understands how you did it.
04:29 When I see thumbs from your groups I will know we can get an anwer.
04:34 All right on the count of three. One, two, three.
04:38 Two hundred and ten.
04:39 Oh my goodness. Now obviously I would have passed out by then but… we will put his up. That's why we did only ten seconds.
04:48 Hey guys notice what I am doing after each term. Whether it be the meters or the seconds.
04:56 What is this?
04:58 Quiet hand. Anybody know the M and the S represent?
05:04 Meters and seconds.
05:06 Meters and seconds. Super important when you are writing a rate, that it has meaning. O.K.?
05:12 Each of the terms has meaning. All right.
05:17 Let's switch this up. Let's talk about how long it would take, given the pace that we've established here. How long would it take for me to go a hundred meters?
05:30 Go ahead and talk with your group.
05:33 What the heck. Go ahead you guys. Pull out a calculator.
05:40 Had a group over here estimating. Any groups come up with an estimation also?
05:47 O.K. So going this direction you are thinking divide. And in going this direction you are multiplying.
05:54 How many times are you going to multiply thirty-five.
05:59 Two point eight five rounded off.
06:02 So you tell me that it's two point eight five. Good enough.
06:10 How do we use that two point eight five?
06:12 Twenty-eight point five what?
06:17 Agreement? You were right there. Very nice job, this group. Really good job.
06:23 Do you agree also? Is that where you were headed Ryan?
06:26 Excellent. All right. Notice I continued to put the M and the S. All right.
06:36 Last one. Our unit rate. How many meters per second am I walking?
06:44 Make sure your whole group understands it before you put that thumb up.
06:49 We've got a thumbs up, this group. Thumbs up here. Thumbs up back there. Great. On the count of three. Tell me, how many meters per second am I moving. One, two, three.
07:00 Three point five.
07:01 All right. I agree. That's quick. It's fast. All right.
07:08 All right you guys. That was excellent. You guys really, obviously, have a good grasp of rate.
COACH LINDA FISHER: The experiment gives all the students a common experience with the idea of rate. This allows all learners access to the discussion and mathematics of the task. At 6th grade, students will have varied degrees of familiarity with the topic.
The ratio table allows students to think about the idea of scaling up a rate or finding a unit rate. Students can think about and discuss the multiplicative nature of rates. I tried to emphasize the importance of units being attached to numbers. I think quantitative reasoning is central to this mathematical concept.
By giving wait time, most students were able to use the ratio table to find equivalent rates. I think the active context helped students to reason more easily than using an abstract rate. We want students to have several opportunities to experiment with rate, before trying to formalize definitions and procedures. We want to develop and build on their ideas.