# LEGO Prices vs Marriage Age – Contrasting Activities

I spend a fair amount of my time at Desmos creating activities with the Activity Builder. In my mind, the job becomes more and more interesting over time for at least two key reasons:

• Over time, the toolset expands.
• Over time, our sense of how to use the toolset expands. That is, our pedagogy improves.

These two developments play off one another, and we find ourselves with more and more opportunities to build increasingly interesting things.

One way we push our pedagogy forward is by holding up two activities and asking questions like:

• How are they similar? How are they different?
• What are their strengths? What are their weaknesses?
• In what ways could the Activity Building Code inform these activities? In what ways could these activities inform the building code?

#### Recent Comparison

Earlier this week, we took a close look at two linear modeling activities: LEGO Prices and Are People Waiting to Get Married?

If you’re up for it, I’d love to hear your analysis (similarities/differences, strengths/weakness, relationship to the building code) in the comments.

#### My Thoughts

Each activity has its own strengths, and each activity has the potential to generate interesting class discussion. However, I think LEGO Prices does a much better job with creating problematic activities (Principle #4 if you’re counting).

Are People Waiting to Get Married? nibbles at the edges of a context in a largely disconnected way.

• Students make a prediction, but it never resurfaces.
• Students sketch on a graph, but we’re not told why.
• Students make another prediction, but that too never resurfaces.
• Students write equations. Why? Because we tell them to.

LEGO Prices hits you right out of the gate with a single, overarching question that will drive the rest of the activity: How much did that LEGO set cost?!

• Students make a prediction, and it resurfaces later in order to compare the power of wild guesses with the power of mathematics.
• Students sketch in order to better understand the relationship.
• Students build and then use a model in order to refine their prediction.

The key phrase for me here is in order to. That’s the difference. As much as Are People Waiting… has going for it (and, by the way, I rather love Screen 8), there’s no in order to attached to the tasks we’ve given students. Instead, it’s piecemeal. Screen-by-screen. Asking because we can, not because we must. Questions that serve themselves, rather than a single, coherent pursuit.

LEGO Prices suffers in other ways. For example, I think it does a fairly awful job with Principle #5: “Give students opportunities to be right and wrong in different, interesting ways.” It’s narrow-minded in that sense. There’s really just one way to move through the activity. I’m discouraged by that, and hope to discover creative solutions around that weakness in future activities.

And yet while it struggles with that, it doesn’t struggle with this: clarity of purpose. With the exception of Screen 5 (interpreting parameters), everything students do is done in the service of making the most insightful and accurate price prediction they can.

And that’s something I’ll be trying to infuse in similar tasks in the future.

#### Invitation

What did you see in the activities? What did you think of my analysis? Where did it resonate? Where do you think it’s off base? I’d love to hear your thoughts in the comments.

Cheers!

1. I think it would be interesting to run both activities with a class and have them compare and contrast them.

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3. Scott: In the world of Desmos activities, I’m a fan of these:

The Running Game
LEGO Prices (from the post)
Avi and Benita’s Repair Shop

There’s also another Desmos linear modeling task we’re about to release a new version of. I’ll write about it on the blog soon.

As for non-Desmos activities, it doesn’t get much better than Barbie Bungee.

Fawn’s version – http://fawnnguyen.com/barbie-bungee/
Matt Vaudrey’s version – http://mrvaudrey.com/2012/05/21/the-barbie-bungee/

Hope that helps!

4. Michael and Scott,
Fyi our summer school teachers found barbie bungee + use desmos to analyze and revise prediction was best of all worlds.

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6. First, I absolutely love the Lego Prices activity. Students enjoy it as well because most of them can personally connect to building Lego sets. I’ve often wondered if my students would find the marriage activity interesting just because of lack of experience.

My biggest concern with the marriage activity (and this could absolutely be because I teach 7th graders so this entire activity may not be appropriate for them) is that students are asked to write an equation (slide 5) without the help of a visual of a line aside from the one they sketched on the previous screen. Maybe turning slide 5 into a sketch or have the options to create lines would scaffold that slide a bit.

I’m not sure how you can make Lego Prices better, but I’m excited to see what you come up with! I do like slide 5, though…or something similar to that where students can explain the parts of the graph/equation in context to the problem.

“LEGO Prices suffers in other ways. For example, I think it does a fairly awful job with Principle #5: “Give students opportunities to be right and wrong in different, interesting ways.” It’s narrow-minded in that sense. There’s really just one way to move through the activity. I’m discouraged by that, and hope to discover creative solutions around that weakness in future activities.”

Concerning Principle #5:
I’m trying to wrap my head around why you think Lego Prices does an awful job. I understand that there’s only one way to move through the activity, but I feel like that’s true of most modeling activity builders. I could be absolutely wrong with that, but I remember having the same thought about Charged. It may just be the nature of this style of activity. That being said, I have seen some very interesting ways students have been wrong. In fact, the first time I did this activity, I was sure that this wouldn’t be linear! I thought it would increase at a fairly steady rate for a short time, then start to become curved. I figured the more Legos there were in a kit the less it would cost per Lego…apparently not!

As always, I’m excited to see what you come up with.

7. Elizabeth: Thanks for sharing your insights! As for Principle #5, I think you’ve convinced me that LEGO Prices does a better job here than I originally gave it credit for. That being said, I’m optimistic it still has room to grow on this front. But it’s encouraging to know that we’re heading in the right direction with these modeling tasks. It’s hard to build something truly open ended when the structure of one-screen-after-another invites us so easily to build tasks with strong guidance built in. But I believe there’s room for both approaches (open vs strongly guided).