# Get Your Model On: Mathematical Modeling in the Elementary Classroom

## Graham Fletcher and Mike Wiernicki

• 3–5 Session

**Thursday, November 19, 2015 | 9:30-10:30 a.m.**

** Room: Broadway Ballroom F (Omni Nashville)**

Is it a noun or a verb? The term model is frequently misinterpreted as hands-on, but manipulatives in isolation do not satisfy the expectation of SMP #4. In this session, participants will explore the progression of mathematical modeling, what it means, and how it can be achieved through purposeful task design before students get to sixth grade.

**Resources:**

**Description: ***Is it a noun or a verb? The term model is frequently misinterpreted as hands-on, but manipulatives in isolation do not satisfy the expectation of SMP #4. In this session, participants will explore the progression of mathematical modeling, what it means, and how it can be achieved through purposeful task design before students get to sixth grade.*

**Slides: NCTM Nashville (Mike and Graham)**

**3-Act Tasks:**

- 3-Act Recording Sheet
- Graham’s 3-Acts website link
- Mike’s 3-Acts website link

**Student Work:**

**My Go-To Resources**

Can’t wait to see Graham’s presentations! He is a MUST see speaker for any elementary teacher attending the conference.

Both Mike and I are looking forward to continuing the conference experience through this page and beyond. If you have any questions or just want to share, leave us a comment or reach out to us through Twitter. @mikewiernicki @gfletchy

All of us are smarter than one of us!

Dear Graham and Mike,

Thanks for the presentation and to NCTM for making the video available! I’m in Bangkok, so the NCTM events are a bit too far to stretch in person. Really great to have it all online.

I wrote up some quick notes from watching it with my older 2 kids (8 and 6): Skittles and Middles.

Though it didn’t make it as a highlight on this page or my notes, I agree that the idea from the opening 4 minutes is really striking. Seems a really powerful way to launch a conversation. Also, I wonder if there are many teachers who would be brave enough to abandon the pre-planned question underneath if something better came up from the kids’ ideas?

Thanks for the comment Joshua. There is definitely a level anxiety that comes with abandoning pre-planned questions when students’ thinking goes in a different direction. But for us, and those teachers we’ve worked with who have begun to drink this Kool-aide, we’d never go back! Thanks again.

I hadn’t seen this! Great to hear you to talk! Joshua just sent me here in a comment on my post:

http://followinglearning.blogspot.fr/2015/12/making-sense.html

I love the message of this talk, and it’s so good it’s online.

I’m not at all sure about what you and your audience’s estimates of the midpoint. I don’t usually like quibbling, but as this one is quite interesting, I’ll quibble.

I estimated about 220.

The reason I chose such a low number is because this is an estimation line. What I mean is, if we’re estimating something where the answer is five, and we say six (we’re just one out), that’s pretty good. But if we’re estimating something where the actual answer is 500 and we estimate 501 (out by one again), this time it’s impressive (if a little poor on the rounding side)! The number is bigger, so we expect the estimate to not be so close.

So the line should reflect that – it should grow in a multiplying kind of way, not an adding way. There should be two jumps where we’re multiplying by the same number for both jumps, not adding.

4 and a bit does the job. 50 x 4 and a bit = 220. 220 x 4 and a bit =1000. It’s a geometric mean not an arithmetic one.

I often get things wrong, so I’d be interested in what other people have to say about this.

But anyway, the main thing is how much I loved the talk guys!

I wish it was possible to edit comments! I always read them too late and spot the grammatical glitches!

What you have in mind is that estimate lines should be on a log scale. This will mean that, roughly, the same percentage differences in the values correspond to the same linear distance on the line. I say “roughly” because logs are symmetrical (ln(a/b) = -ln(b/a)) while percentage differences have a convexity adjustment (a/b -1 is not the same as -(b/a-1)).

I agree that this is a good way to show estimates. Would be interesting to have this conversation with elementary school students. Certainly a good discussion with high school kids.

There is another idea related to your point about 500 vs 501: significant digits. Making an estimate of 501 gives the impression that we are confident to the ones place, e.g., we’ve chosen 501 instead of 500 or 502. On the other hand, 500 doesn’t show nearly so much confidence. In this case, because they are asked for an interval of estimates, there is an alternative source of information about confidence, so significant digits aren’t so critical.

Putting the two together, what we have lurking is the notion of a probability distribution. A great extra extension to talk about when a linear vs log scale does a better job of capturing the probability distribution around our estimates.