Lesson - Part 5

lesson - part 5

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The teacher has a student share a conjecture with the class: If the rate is seconds per step, Alex wins; if the rate is steps per second, Joe wins. Students talk in groups to try to figure out how she got this conjecture and whether it makes sense. During class discussion a student talks about 20 seconds per step and 20 steps per second. The teacher has two different students demonstrate each rate. A final student concludes that the goals are different for each rate.

lesson - part 5

6th Grade Math - Rates - Lipman School
Joe Condon, Lipman Middle School, Brisbane School District, Brisbane, California

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00:00 Steps per second.

00:03 And if I use a seconds per step, Alex wins.

00:10 Seconds per step. Alex wins.

00:18 So that people will have numbers to work with were you working with these numbers right here?

00:23 Yeah.

00:24 O.K. Two minutes. Talk about her conjecture. Talk about what she believes is true.

00:32 Write down this on your paper. What is the steps per second. What is the seconds per step. Where did she get this idea from?

00:45 I know you want to share out right now. Talk about it.

00:49 Twenty seconds per step then you would be really slow but if you had more steps per second, then you would go faster.

00:57 Because if you had twenty steps in one second, then you would be like way faster.

01:05 I don't really disagree but I thought that Joe wins and that Sarah wins because I multiplied what Sarah got by two.

01:21 So twenty seconds times two is forty seconds and thirty-two steps times two is sixty-four seconds.

01:29 And then with Joe I did ten times for to get to forty seconds. So you had to do sixteen steps times four to get to sixty-four steps so they equaled the same.

01:45 O.K. Alex what did you do?

01:48 Well, the steps per second and the seconds per steps isn't any different

01:56 because for steps per second you are quantifying how many steps you can take per second and for the seconds per step

02:06 you are trying to see how many seconds for one step.

02:11 So if you had a higher seconds per step would you be faster or slower?

02:17 You'd be the same.

02:18 No you'd be slower.

02:19 You'd be the same because you're just switching around.

02:22 O.K. if you had twenty seconds per step then you'd…it would take twenty seconds to take one step.

02:30 If you had twenty steps per second it would be one second and you would walk twenty steps.

02:39 Yeah.

02:44 Don't you think.. do you still think it's the same?

02:48 Yeah if you turn it around. It would take you twenty steps for one second.

02:55 So Carlos what did you get? I already shared. What did you get? I'm just curious.

03:01 Well, how Michael was saying if you get the twenty seconds per step…

03:08 All Right. Let's share this out. Obviously people had ideas right away. Right away. So anybody like to share? Anyone? No one at all?

03:24 I think you wouldn't want to have higher seconds per step because if you had twenty seconds per step then it will take you twenty seconds to go one step.

03:38 Hold on. Hold on.

03:40 Mikey, stand up and show us what twenty seconds per step would look like.

03:56 Would you agree that is close to twenty seconds per step? Aiden, stand up in the back and show us what…

04:03 Twenty steps per second.

04:04 Thank you.

04:11 Twenty steps per second.

04:18 Pretty good. Pretty good. All right.

04:28 Hold on for a second. Go ahead Michael.

04:32 And it would be better to have, if you are in a race, twenty steps per second because you would, obviously, go a lot faster

04:40 and…a lot faster than twenty seconds per step.

04:45 O.K., O.K. What do you think was the confusion here? Aiden?

05:01 I think the confusion was with the idea of if you switch it around it's one hundred percent different.

05:15 I think that was the confusion.

05:18 I'm not sure I understand. How many of you would like Aiden to explain it in a different way? O.K. Try again.

05:25 Well, with the idea if you switch it around the goals become different. I think that was what was confusing.

05:40 I agree with you. I think that's…yeah. Did you want to add something to it.

05:43 No I had something for steps per second.

05:48 Well, I think that Joe didn't just win. That Sarah did too because, what I did was…

05:56 For Joe I did ten…no…for Sarah I did twenty times four…I mean, twenty times two to get forty seconds.

06:10 So Sarah was thirty-two steps in twenty seconds. Uh-huh, and then what did you do?

06:18 And I times twenty seconds times two to get forty seconds. So I had to do the same with thirty-two steps.

06:27 Thirty-two steps times two and I got sixty-four. So it was sixty-four steps in forty seconds.

06:36 So for Joe I did the same. I did ten seconds times four to get forty seconds. So I had to do the same for sixteen steps. Sixteen times four is sixty-four.