Students are asked to name some familiar or common rates. Students then try to give their own definition of rate after looking at these examples. Finally students are given a ratio with no words and asked what it could mean.
00:00 So what I want to do now is I want to find out some rates from you. So I'm going to ask you again to talk with your group. Let's just put up mine first.
00:12 Three point five meters per second. Can you think of any other common rates that we use every day? When going shopping, when driving down the road. Anything.
00:28 Fourteen made. Or fourteen sold. I'm sorry.
00:34 Yeah, fourteen sold.
00:35 All right. How about another one? Go ahead.
00:39 You use slips, like, when you go to dinner. If it costs like forty-eight dollars and you wanted to give fifteen percent, you'd multiply forty eight times one point five you'd get the tip which is seven point two.
00:54 O.K. so the dollars per percent tip. I'm not certain if I'm…is that covering what you are saying?
01:13 How about another one. How about when mom is speeding down the freeway? What do we see flying by us? Yeah.
01:22 Miles per hour.
01:23 Miles per hour.
01:29 Great. These are great ones. Let me ask you a question. How do we define rate. Anybody have an idea of what a rate is? Based on our examples
01:42 Based on the shuttle run. Based on some of these, what do you think rate is? Go ahead.
01:48 Like the beat. Like if you are going really fast it's like…..
01:51 A beat. I'm going to put that on as an example of a great rate. That's great. What kind of beat?
01:57 Like if you are going really slow it's a slow beat and if you are going like…
02:03 Beats. Like music?
02:06 What else beats?
02:07 Your heart.
02:08 Yeah. Your heart beats. Good. What about that definition? Any idea what a rate is?
02:15 Like a fraction? Like when you are multiplying a fraction, if you simplify it, it will always go back down to the same number.
02:25 O.K., a fraction simplified. The gentleman in the back here had his hand up. Did you want to share something?
02:34 Something occurs. Great. Last one.
02:44 A rate is how fast a person runs or how fast a car drives like fifty miles per hour or something.
02:55 How fast something is. Nice. All right.
03:06 Tell me guys. Talk with your group right now. What is this rate? What is this rate? Now I don't need you to use your calculator. I want you to describe this rate to me.
03:21 What is each term representing? Just talk. What is it?
03:30 All right, I want to hear some. Ryan, I heard you say a couple things, give me one.
03:36 All right. You think six hundred… I like your reducing. Really nice. Nice simplifying. Six hundred meters in fifteen seconds. Anybody else?
03:55 Come on now. I heard a lot of good discussion. Go ahead.
03:59 Six hundred made, fifteen sold.
04:03 Six hundred made, fifteen sold. Yep.
04:12 Six hundred dollars and fifteen tip.
04:16 Six hundred dollars with fifteen dollars as tips. Is that what you were saying?
04:26 Fifteen dollars as tips. Anything else?
04:35 O.K. Which one is right? Sinally? Did I pronounce that right?
04:47 Which one's right?
04:48 All of them.
04:49 All of them. O.K. Any other ideas? Yes.
04:57 I think it's the first one.
04: 58 You think it's the first one. Why? Six hundred meters in fifteen seconds.
05:04 Do we know? Can we tell? Give me a thumbs up if you think, "Yep we can tell which one is right."
05:10 Give me a thumbs down if you are like, "Naw, we can't tell." Why not?
05:16 We're missing units. We're missing words, right? O.K. you guys want to know what it is? Six hundred students taught in fifteen years. That's how long I've been teaching.
05:39 That's how many students I've taught. Very important part of rates. Are those words. It means nothing or as…I can't remember who said it but it was absolutely…
05:51 Was it Jordan? It means nothing or it can mean anything. Anything you want it to mean. So until you put terms down…Sonali, sorry.
06:01 Until you put terms down. Until you put words near your rates. It means nothing. O.K.? All right.
COACH LINDA FISHER: I was surprised with some of the examples of rates given by students, such as cost of meal and tip. Students did not seem to be as familiar with rates as I might have expected. After some coaxing, they were able to think about miles per hour.
Students struggled with defining rate. When we trialed the lesson, there was more time available to tease out their thinking. Because of the short class period, the teacher had to move through this part faster than desired.
Finally, the teacher gave students naked numbers (600/15) and asked them what it could mean. They gave answers such as 600 meters in 15 sec, or 600 burgers made and 15 sold. When asked which one was right, we heard lots of ahas. It got through to them that the rates had to have words or quantities to be a rate.