Month: April 2023

Indirect Measurement Lab

Probably my second-favorite Algren line. The man knew of what he spoke. (And yes, I know Hammond is not Chicago. But we share a border, and weather, so I’m granting myself poetic license.)

Been planning an indirect measurement lab for my geometry classes that included an outdoor component. Keeping an eye on the long-term forecast, I flip-flopped the lab and our unit quiz to days I felt had a better chance of sunshine, and thus, shadows.

Whiff.

Friday’s effort with two of my classes was a strictly indoor affair, lack of sufficient sunshine calling for Plan B.

So instead we measured student heights in the classroom then went to the stairwell on my side of the building and set our sights on what appeared to be a 20-25 foot high wall.

We used the Measure app on their phones rather than the DIY clinometers that I built a million years ago the first time I taught geometry. If those tools still exist they are buried in a box in my basement. And that definitely made our data a little shaky. Getting angle measurements with the level feature on the Measure app is definitely an inexact science. No one was really close to the actual (18.5 foot) height of the wall. And we didn’t have the similar triangles/proportions results to compare.

It was good enough for a Friday and gave them a chance to dig back in their notes for trig application problem set-up. I also asked them to reflect on possible sources of error.

Walking in this morning I saw abundant sunshine and hoped for outside project time but we got off to a sluggish start taking each others’ height mesurements in my 2nd hour. Not enough time to try to get all the angle and distance measurements done whether outside or inside. We stepped outside again for third hour but there just was not enough sunshine so ducked back inside.

One last class, getting underway at about 12:40. My twitter bio doesn’t say “Stubborn Jackass” for nothing. So back out we went. Just in time to get a sliver of sun, enough to measure a lamppost shadow and student shadows before the sun ducked back behind the clouds. We got what we needed though. Took our angles of elevation and horizontal distance to the lamppost under the cloud cover and headed back in to crunch some numbers.

The experience made an awesome dry run for the quiz next block. I wrote a couple questions that mimic this activity so I’m hopeful that second rep in quick order will spark their memories.

And honestly, just formative-assessing-by-walking-around it was clear we could use the practice on using similar triangles and trigonometry to perform indirect measurement. But that’s literally my job to tease that out.

We’ll take the first half of class to review next time, quiz the second half, and we’ll see if hands-on opportunities make the learning last.

Because it might feel like October out there but next Monday it’s May already and we’ve got 16 blocks left and there’s work to do.

Out Of The Shadows

As a longtime Region guy, I appreciate having four seasons. During the years we lived in Vegas, where there’s 320 days of sunshine a year, I used to pine for just one sorta crappy cloudy day every now and then, just for old times’ sake and for my mental equilibrium.

But perpetual sunshine had its benefits when I was planning outdoor activities in math that required shadows. My mentor teacher turned me on to an indirect measurement lab where his kids determined the height of the streetlamps in the drive in front of our school using similar triangles.

I had my kids outside pairing up and measuring heights and shadows, then we came back in and the math to figure the height of the lamppost was the first question on their quiz. (Surprise!) It worked out super-well.

Fast forward 20 years and here I am hoping to take my geometry kids outside for an indirect measurement lab next week. But sunshine in the Region in April is a dicey proposition at best. Case in point: Last week: 80F and glorious. Bike rides and T-bones on the grill and hanging outside with the puppies.

Dogwwods are in bloom by me.

By Sunday tho? Overnight snow in the forecast.

But I’m willing to risk it. Put together the paperwork for the lab before I left the building Friday (doc here – feel free to copy/remix/improve). Also: I’ll need to be flexible.

We are very large Pixar fans in this house

I originally wanted to quiz Friday-Monday and do the lab Tuesday-Wednesday but it looks like we have a better chance of sun (and thus, shadows) on Friday and Monday. So here we go. Flip-flop the lab and the quiz, right? Honestly I put a couple questions on the quiz that mimic the lab so that’s actually probably better from a measuring learning POV.

They’ll partner up, brainstom objects on campus they could indirectly measure, measure each others’ height (top of head and to eyes), then head outside and measure each others’ shadow length.

They’ll select one of the objects they brainstormed to measure, then determine the length of that object’s shadow, as well as their distance from it.

Having all the data we’ll head back inside and do some calculations, determining the height of their object both by similar triangles and by trigonometry. Then they’ll contrast and compare the results and the process.

I’m hopeful that the chance to apply some of the math they’ve encountered will make the learning more permanent. And any day we can get outside and get hands-on with math is a good day. So whatever day we get sunshine, that’s the plan.

I’ll let you know how it goes.

Oh BTW the way the tortilla soup was fabulous.

Can I Treat This Like A Triangle?

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My Algebra 1A freshmen were very freshman-y today. Retaking a class they hate, last day before a four-day weekend, quiz day. Recipe for disaster. OK maybe “disaster” is a strong word but nobody’s packaging up today’s sixth hour and sending it to the Teaching Hall of Fame. The bell rang to end class and I took a minute to walk the room and straighten desks and pick up left-behind review pages and pencils and snack wrappers, feeling like a not-good teacher.

We’ll try again Tuesday.

But take your minute to sulk (a good playlist helps) and then get your head straight because geometry is coming in like four minutes. I had a singleton Grey Day ahead of the long weekend. We just started our Right Triangles & Trigonometry unit, two sections in, so we had done the Pythagorean Theorem and Special Right Triangles. We had our ups and downs, in about equal measure. What I need for this day is a Three-Act. Taco Cart has been a go-to for years, with the added benefit of being an application of the Pythagorean Theorem. Perfect for my Never-Ending Quest to fill in my students’ pandemic-related foundational holes.

We started off with a Would You Rather rates bellringer since we’re going to be thinking about distance and time.

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Then rolled right into the Desmosified version of the Taco Cart activity.

We did our noticing and wondering, made predictions, asked for more information, then I turned them loose in pairs to math this out. And in my last class of the day, it happened: “Mr. Dull, can I treat this like a triangle? And do that a-2 plus b-2 is c-2 thing?”

Hell yes you can. A right triangle even. Let’s go.

We’ve been kind of hammering away at using the principles of a right triangle to solve problems when we have a vertical and horizontal distance. And she connected the dots. It was epic. It’s super-important to me that we can take the training wheels off and let my kids ride on their own. (Pro-tip that was passed on to me by a wise older dad: take the pedals off your kids’ bike when they are learning to ride without training wheels. They’ll learn balance first, and the next thing you know, we ride at dawn!)

With some nudging many of the students produced solid work. Some quality questions in there too. “Were the tacos worth it?” “Do they really walk slower in sand?” “Don’t they have a car?”

Meet them where they’re at , walk with them to get started, and magic will happen.

So that’s how you recover from a disaster of a sixth-hour class. And how you roll into a long weekend. With singing, obvi.

Oh, and I’m not giving up on the freshmen. Gonna tweak my Algebra II survey/data project a little bit and turn them loose on that this week. Bribe them with a quiz grade. Do some math and give some hope. But that sounds like a whole ‘nother post.