## [Misleading Graph] Peyton Manning vs. Russell Wilson

Does the graph create the impression that Peyton Manning has aboutÂ 10 times as many pass attempts as Russell Wilson?

What can you do with this?

One approach would be to show students the graph and ask how this visual representation could be misleading. Point to the sizes of the circles.

A different approach could be to remove information (and add perplexity). Show them this:

Have students estimate Peyton Manning’s career pass attempts. I’m anticating many students will compare the sizes of the circles. They’ll think about how many green circles could fit in the orange circle. They may not think 100, but I’m confident they’ll think much more than 10. They may have other strategies. Have students share them.

Give students rulers (and the formula A = Ï€rÂ² if they ask for it). Ask them if they’d like to revise their estimate.

Reveal this:

Were students misled? I’m anticipating some will compare the diameters. Take advantage of that. If not, challenge them to find out why the circles are the sizes they are.

Given Manning’s circle, have students draw Wilson’s circle to the correct size. Again, have students share strategies.

(I’ve created this applet in GeoGebra. Not sure what, if anything, it gets me.)

Allowing students to possibly be misled by a misleading graphâ€¦ should’ve thought of that earlier.

I don’t think @ESPNStatsInfo is trying to suggest a much wider experience gap. Seahawks fans may disagree, but the tweet backs me up. This is accidental: the result of focussing on graphic, not info, in infographic.

“I couldn’t help but admire your large triangular prism,” I wrote. Sadly, this is not the strangest way I have begun an email to a colleague.

“Are you talking about the giant Toblerone-shaped thing? You math guys are weird,” she replied.

act one

• About how many regular size Toblerone chocolate bars fit inside the giant Toblerone-shaped thing?
• Give an answer that’s too big.
• Give an answer that’s too small.

act two

• What information would be useful to know?

act three

63. Relax. The video is coming soon.

sequel

• If 72 regular size Toblerone chocolate bars fit inside a mega Toblerone-shaped thing, how large would it be?
• If 112 regular size Toblerone chocolate bars fit inside a mega Toblerone-shaped thing, how large would it be?

better stillâ€¦

• AÂ mega Toblerone-shaped thing is a little bigger than a giant Toblerone-shaped thing.Â What could its dimensions be?
• How many regular size Toblerone chocolate bars would fit inside?

I like the phrase “a little bigger.” Probably “borrowed” from Marian Small. The ambiguity here allows for multiple solutions. Students could increase the length of the prism or the size of the triangle base. Which has the greater effect?

Also, there’s something interesting happening here with the sum of consecutive odd numbers.

Oh yeahâ€¦ a shout-out goes to Andrew Stadel for his Couch CoinsÂ task.

## Math Picture Book Post #2: Calvin Can’t Fly

In my first math picture book post, I suggested these may fall into three categories. In this post, I’ll take a look at a book from the third category.Â Calvin Can’t FlyÂ by Jennifer BerneÂ is the story of a young starling who reads while his brothers, sisters, and cousins learn to fly. Calvin uses his aquired knowledge to save his migrating family from a hurricane.Â Calvin Can’t Fly is about a love of books (and libraries!). It’s about being different. It’s not about math. That is, the author did not intend to write a book about mathematics. Nonetheless, we can find math if we look for itâ€¦

How many starlings are there in the picture below? Take a guess. It’s free!

It helps students to use a referentâ€“a group whose quantity they knowâ€“to estimate the quantity in a larger group. A group of ten can be used (see below). Students can visualize the number of starlings in terms of groups of ten. Making groups of ten helps students countâ€“ it’s a place value thing. There are several other pages where students could be asked to estimate the number of starlings.

Do you want to change your estimate?

One of the problems with my three categories is that it requires guessing the author’s intent. I am arguing that Jennifer Berne did not write “the story of a bookworm birdie” with referents in mind. Of course, I may be wrong. If I ever interview Jennifer Berne, she may insist that there is hidden meaning in her artâ€“ kinda like some sort of children’s literature anti-Dylan.

Watch the first 40 seconds of the video below for more estimation fun. Also, you have to watch uber-intense hair hat guy as he asks Dylan about the hidden meaning in the t-shirt he wears on the cover of Highway 61 Revisited.

Note:Â Great EstimationsÂ &Â Greater EstimationsÂ by Bruce Goldstone provide more opportunities for students to practice using referents to estimate. And check out Andrew Stadel’s new blog,Â Estimation 180.Â Day 7Â nicely uses a referent established onÂ Day 6.

Ain’t that somethin’?