I have taught for 20 years and I still have a lot to learn.

I'm not quite as pure as Dan, so I can offer a new perspective perhaps. Were it my lesson, I'd want to do the contextual setup first. I'd tell them why I'm driving to Houston, maybe have them guess how long it would take, etc. Engage them with the "why?" of what we're doing.Then I would hit them with the four maps (for which, again, many props for the improved image over the course of your anyqs quest). These are ninth graders, so I think it's reasonable to expect every kid to wrestle with what's going in all four maps. I'd want to have them think before computing, though. See if they can make some initial conjectures about what's going on (e.g. is the difference in mileage enough to account for the difference in driving times on the various maps?), and to see whether some of these can be refuted prior to computing exact average speeds.For me, the precise computations are the finale, and they'll be anticlimactic if we haven't argued about these things beforehand.Good luck with the lesson. It sounds like you're in a great position to learn something useful from it no matter how it goes.

This sounds like a really interesting idea. I agree with christoperdanielson that you should spend a bit of time setting up the discussion--I guess that's Act 1 that Meyer refers to. It's great that you have this real life, concrete example of something they have been learning about.It sounds like you have the main idea sorted out in your mind. But what about Act 3? What are you hoping students will learn or conclude? Do you want them to make a driving plan for you with times, speeds, rest stops, overall mileage and so on? Do you want them to give an opinion on which website gives the most accurate directions? Do you want them to plan a journey of their own?I can think of a neat way to share the answers and check them together. Give each small group a piece of paper that they divide into quarters. Then they use the quarters to give their feedback for each website. Then tear the sheets into quarters and make piles for each website. Rearrange the students into four groups and have each group report to the group how well their website was analysed. (Do you know what I mean? I find it a bit hard to explain in words!)

Thanks for your lawnmowing post. It made me wish I had a lawn so I could do some self reflection half as deep as you have... Maybe next time I'm on the trolley I'll put my book down and use that time for some reflection :)What I especially liked was the ways you set out to learn from your experience *and* value the risks you took and the good work you and your students did. Think how much learning would happen if our students had that attitude when they struggled.This lesson plan seems to take a lot of data from your first experiment: you tested the question and worked 'til you had a problem that people naturally converged around. And that you knew your students had the math chops to engage in. It seems like your plan will hook students, and provides a clear task for them to conquer (figuring out what the different average speed assumptions are for each website).It sounded from the comments like "Act 3" is what people are wondering about. I know Dan Meyer likes to have a resolution that comes from real life is possible (no doubt he'd be trying to get the folks at MapQuest on the phone). But you could also have a 2nd trip of exactly the predicted number of miles mapped out that you could test their hypotheses against and see if the time was exactly one hour. I get worried about asking kids to do complicated route planning and accounting for stops, etc. as that turns into one of those questions that people get engineering degrees to measure! But your idea of *brainstorming* what a software engineer might need to take into account and thinking about the best estimate for *their* family's driving habits seems like it could be a nice final discussion.Basically what I'm saying is your planning sounds right-on to me!

Wait, I take that back! The maps probably assume an average speed for the trip based on speed limits and what-not. They probably don't assume the same average speed for every trip! The part of my brain that said don't try to have students come up with the best average speed should have hollered, "Max, the average speed won't be the same for a short trip!"So... short of writing to the companies and confirming that the assumed average speed for a trip from Cleveland to Houston is what your students calculated, I don't think there's a great "reveal" for Act 3. Instead, your students coming up with a way to satisfactorily explain the results (assumed different average speeds) and to say for themselves which would be more accurate for how their family travels (e.g. no long rest stops, never go above speed limit, etc.) can be plenty sufficient.

I like Max's idea better than Max seems to. What about giving students mileage data from one website for a destination of their choice (but not times) and from a search engine of their choice. They predict what each engine will say for time and distance. Then you have a real-world reveal: gather the data from each engine in front of them.

Hi LisaI think if you wanted to use this as part of a larger investigation, I'd probably just throw out the journey and ask students to plan it for you. "What's the easiest, quickest, cheapest way?" "How far?" "How long?" and so on as prompt questions. They do the research online and come back with answers. In that context, you could just present the slide and the question would "pop out".That's more of an eliciting approach, though. I think just presenting the slide, without the set-up, and then seeing what the students come up with is more what Dan had in mind. Either way, I think the slide is a very good prompt, whichever route you decide to go (no pun intended!).Colin

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## 6 comments:

I'm not quite as pure as Dan, so I can offer a new perspective perhaps. Were it my lesson, I'd want to do the contextual setup first. I'd tell them why I'm driving to Houston, maybe have them guess how long it would take, etc. Engage them with the "why?" of what we're doing.

Then I would hit them with the four maps (for which, again, many props for the improved image over the course of your anyqs quest). These are ninth graders, so I think it's reasonable to expect every kid to wrestle with what's going in all four maps. I'd want to have them think before computing, though. See if they can make some initial conjectures about what's going on (e.g. is the difference in mileage enough to account for the difference in driving times on the various maps?), and to see whether some of these can be refuted

priorto computing exact average speeds.For me, the precise computations are the finale, and they'll be anticlimactic if we haven't argued about these things beforehand.

Good luck with the lesson. It sounds like you're in a great position to learn something useful from it no matter how it goes.

This sounds like a really interesting idea. I agree with christoperdanielson that you should spend a bit of time setting up the discussion--I guess that's Act 1 that Meyer refers to. It's great that you have this real life, concrete example of something they have been learning about.

It sounds like you have the main idea sorted out in your mind. But what about Act 3? What are you hoping students will learn or conclude? Do you want them to make a driving plan for you with times, speeds, rest stops, overall mileage and so on? Do you want them to give an opinion on which website gives the most accurate directions? Do you want them to plan a journey of their own?

I can think of a neat way to share the answers and check them together. Give each small group a piece of paper that they divide into quarters. Then they use the quarters to give their feedback for each website. Then tear the sheets into quarters and make piles for each website. Rearrange the students into four groups and have each group report to the group how well their website was analysed. (Do you know what I mean? I find it a bit hard to explain in words!)

Thanks for your lawnmowing post. It made me wish I had a lawn so I could do some self reflection half as deep as you have... Maybe next time I'm on the trolley I'll put my book down and use that time for some reflection :)

What I especially liked was the ways you set out to learn from your experience *and* value the risks you took and the good work you and your students did. Think how much learning would happen if our students had that attitude when they struggled.

This lesson plan seems to take a lot of data from your first experiment: you tested the question and worked 'til you had a problem that people naturally converged around. And that you knew your students had the math chops to engage in. It seems like your plan will hook students, and provides a clear task for them to conquer (figuring out what the different average speed assumptions are for each website).

It sounded from the comments like "Act 3" is what people are wondering about. I know Dan Meyer likes to have a resolution that comes from real life is possible (no doubt he'd be trying to get the folks at MapQuest on the phone). But you could also have a 2nd trip of exactly the predicted number of miles mapped out that you could test their hypotheses against and see if the time was exactly one hour. I get worried about asking kids to do complicated route planning and accounting for stops, etc. as that turns into one of those questions that people get engineering degrees to measure! But your idea of *brainstorming* what a software engineer might need to take into account and thinking about the best estimate for *their* family's driving habits seems like it could be a nice final discussion.

Basically what I'm saying is your planning sounds right-on to me!

Wait, I take that back! The maps probably assume an average speed for the trip based on speed limits and what-not. They probably don't assume the same average speed for every trip! The part of my brain that said don't try to have students come up with the best average speed should have hollered, "Max, the average speed won't be the same for a short trip!"

So... short of writing to the companies and confirming that the assumed average speed for a trip from Cleveland to Houston is what your students calculated, I don't think there's a great "reveal" for Act 3. Instead, your students coming up with a way to satisfactorily explain the results (assumed different average speeds) and to say for themselves which would be more accurate for how their family travels (e.g. no long rest stops, never go above speed limit, etc.) can be plenty sufficient.

I like Max's idea better than Max seems to. What about giving students mileage data from one website for a destination of their choice (but not times) and from a search engine of their choice. They predict what each engine will say for time and distance. Then you have a real-world reveal: gather the data from each engine in front of them.

Hi Lisa

I think if you wanted to use this as part of a larger investigation, I'd probably just throw out the journey and ask students to plan it for you. "What's the easiest, quickest, cheapest way?" "How far?" "How long?" and so on as prompt questions. They do the research online and come back with answers. In that context, you could just present the slide and the question would "pop out".

That's more of an eliciting approach, though. I think just presenting the slide, without the set-up, and then seeing what the students come up with is more what Dan had in mind. Either way, I think the slide is a very good prompt, whichever route you decide to go (no pun intended!).

Colin

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