Category Archives: 3-Act

When will I ever use math in life? A true story.

Here’s an answer to the classic question “when will I ever use math in the real world?” There are a lot of assumptions that have to be made, like in many problems involving math in our daily lives. And, perhaps most importantly, my solution to this math problem had a real impact on whether this would go down in my personal history as a good day or a bad day!

Prologue: The Setting

This summer I went down to LA to help watch my nephew Sebastian for 3 days. It was a lot of fun, but being the father of two boys myself I was excited to get back home to my kids in Redwood City. So on Wednesday, I packed my car ahead of time, and then went to pick up my sister after work at UCLA, in her car since she had the right size carseat for her son.

I finally got on the road around rush hour, but was happy to be heading north. Fast forward about an hour and a half later, and I was getting hungry. I stopped right before I-5 and the 99 junction, where I knew I could get the always reliable Chipotle Burrito. So I parked my car and reached for my wallet.

But my wallet was nowhere to be found! It took a few moments of retracing my steps to realize, I could last remember putting it in my sisters car when I drove to pick her up. After a few moments of mild panic, I thought through my options, and realized there were two simple choices. Go back to LA for my wallet or continue driving to Redwood City and have my sister mail me my wallet.

Obviously I didn’t want to turn back, but did I have enough gas? The following is my attempt at turning this adventure into a 3-Act Math lesson.

Act 1:  Go Back to Los Angeles for my Wallet or Continue Home?

Odometer and Gas Meter in Lebec

Above is a picture of my dashboard, I took it right after realizing I forgot my wallet. The last time I had filled up, I reset my trip odometer.

What would you do in this circumstance?

What information would you need to gather to make a decision?

Act 2: Gathering Information

Sitting in my car, I’m hungry and hot (its July in the Central Valley). I talk to my sister on the phone, asking her to double check if my wallet is in her car. She confirms, and I am faced with a dilemma.

I scrounged up all the money I could find in my car, every last coin, but all I could muster is $17.25 cents. Gas was $4.298 per gallon.

So I sat down to calculate whether it was possible to make it home with the money I had available.

Here are a few of the maps I looked at when making my decision.

Distance to Redwood City: 281 miles

 

Screen Shot 2014-10-06 at 4.49.50 PM

Distance to San Jose: 258 miles

Screen Shot 2014-10-06 at 4.50.38 PM

Distance to Gilroy: 227 miles

Screen Shot 2014-10-06 at 4.51.03 PM

Over the years I have gotten in the habit of tracking my mpg, by reseting the odometer each time I fill up my tank. So I knew that my mpg was approximately 22 miles per gallon.

I used that for my estimate, but there are a variety of methods students could use to get an MPG estimate. Here are the first two that come to mind. I wouldn’t just tell students though, as this would rob them of the opportunity to practice making reasonable assumptions, and/or finding relevant and reliable information on the internet.

  1. Google CR-V 2001 Manual Transmission MPG.
  2. The 2001 CR-V has a 15.2 Gallon Tank, and the picture shows I had driven 166 miles with about half a tank.

Summary of Information:

Available Cash: $17.25

Gas Cost: $4.298 per gallon

Approximate CR-V MPG: 22 mpg

Distance to Redwood City: 281 miles

Distance to San Jose: 258 miles

Distance to Gilroy: 227 miles

Act 3: I went for it!

My stomach yearns for the comfort of an oversized burrito, for a moment I consider just buying a burrito and heading back to LA for my wallet. But then I realize that I could use my Starbucks app (which is connected to Paypal) on my phone to buy a sandwich and some snacks, and still fill up my tank with the $17.25.

Here’s how much gas I was able to buy.

Gas Pump in Lebec, Ca

I was worried I wouldn’t quite make it, so I called up my coworker that lived in San Jose and asked if he could be my back up in case I ran out of gas before reaching home. He said he would be ok staying up until midnight, what a pal! I felt pretty sure I could make it at least to Gilroy. So I went for it!

Epilogue: How good were my assumptions?

So I got to Gilroy, before my gas light came on. I gave my coworker a call, and he told me to meet him at a gas station off the 101 in San Jose. He was able to pay for my gas, which I repaid him instantly using Paypal.

Here’s the picture of how much gas I pumped.

What do you wonder?

photo 5

Here’s some of the things I naturally wondered…

Could I have made it to Redwood City?

How far off were my estimates?

How did the assumptions I made create error in my estimates?

Did I really have exactly half a tank of gas before adding 4 gallons?

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Filed under 3-Act, 7.RP, 8.EE, Middle School, MP.1, MP.2, MP.4, MP.6, MP.7, MP.8

Going Solar in 3 Acts

Act One: Ivanpah Solar Electric Generating Facility

Possible Questions:

What percentage of California homes could be powered by this power plant?

How many of these would we need to power a third of California homes?

How about ½, or all?

How much area would that many power plants take up?

Could we fit them in the Mojave?

How much would it cost?

Act Two: What percentage of California homes could be powered by this plant?

What information do we need?

Homes powered by Ivanpah: 140,000

California Homes: 13,720,462 housing units

(source: Census 2010)

Extension question:

What percentage of US homes could this power?

US Housing Units: 132,312,404 (Census 2010)

Act Three: The Percentage of California Homes powered by Ivanpah

I allow students to choose to use the 2010 housing data, or estimate the number of housing units as 14,000,000. The Calculations would look like one of these:

140,000/13,720,462= 1.02 %

140,000/14,000,000= 1%

This usually leads naturally into several sequel questions. Below I have listed some of my favorites with the necessary information.

Sequel: The Implications


1. How many would we need to power all California homes?


2. How much land would we need to build that many Solar Facility?

Ivanpah area: 3500 acres or 5.469 square miles


3. How much would it cost to build that many Solar Facilities?

Cost of Ivanpah: $2.2 billion (One might expect price to go down as you scale up, so you could ask students to model the price going down in some way over time.)


4. If you were to place these side by side, what would a few possible rectangular dimensions for the facility be? What would the dimension of a square with that area be?


5. Is there enough space in the Mojave for such a facility?

I had the students look on google earth to find an area that is big enough for all those Heliostats. Here is a shot from google earth of the actual Ivanpah Facility. As a hint, I told them to start there, and look nearby.

Screen Shot 2013-12-03 at 10.04.27 PM

6. Approximately what percent of California’s total electricity requirements will this supply?

Ivanpah projected to generate: 1,079,232 Megawatt-hour(MGh) per year or 1,079.232 gigawatt-hours (source: NREL)

In 2012, Total System Power for California: 302,000 gigawatt-hours (GWh)”

(Source: California Energy Commission)

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Filed under 3-Act, 6.RP, 7.G, 7.RP, Middle School

How Safe is a Tesla?

Act One: Tesla Fire

What is more likely, a fire in a conventional gasoline car or a Tesla?

Act Two: Car Fire Numbers

Conventional Gasoline Car Fires:

  • 150,000 Car Fires per year
  • 3 trillion miles driven by American’s per year

Tesla Fires:

  • 1 Tesla Fire
  • 100 million miles driven by Tesla cars

Act Three: Elon’s Response

Elon Musk Claims the following in this Blog post.

“The nationwide driving statistics make this very clear: there are 150,000 car fires per year according to the National Fire Protection Association, and Americans drive about 3 trillion miles per year according to the Department of Transportation. That equates to 1 vehicle fire for every 20 million miles driven, compared to 1 fire in over 100 million miles for Tesla. This means you are 5 times more likely to experience a fire in a conventional gasoline car than a Tesla!”

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Filed under 3-Act, 7.RP, 8.EE, Middle School

Brewster’s Millions Beta

I’m going to try this today, as a sequel to A Billion Nickels. I’m considering it in Beta, and hoping my awesome students can help concretize and enrich the task.

Act 1: $30 million in 30 Days

Possible Questions:

How much does he need to spend per day?

How do you spend money without building Assets?

Does he do it?

Can it be done?

What would 30 million 1985 dollars be be adjusted for inflation?

Act 2: Take the Wimp Clause, or go for the $300 Million?

Students work in groups to figure out how they could spend $30 million in 30 days without accumulating assets. Using the internet and recording their plan on google spreadsheet.

Act 3: What does he do, does he win the $300 million?

“He Mailed It!”

Sequel:

Changemaker Twist

Since our school aims to educate “change makers”, I wanted to put a twist on this plot line and ask students to think about how they could use $30 million to help people.

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Filed under 3-Act, Middle School

High Fives in Three Acts

This is my first attempt at publishing a “3-Act Math Lesson.” So it’s not quite polished yet, but it worked really well on the first day of school. Lots of different directions to take it at the end, including paths into rates and design thinking.

Prologue

Act One: High Fives All Around

Students share whatever questions they have about this clip with their neighbor.

Possible Questions

Why is he doing that?

How many people are in the circle?

How long is he doing that for?

How many high fives does he give?

Why would you have a world record for high fives?

(students are really surprised at first)

Act Two: How many high fives did he give?

Students work with their neighbor to come up with an estimate.

Take another look at the video, are there any clues?

Notice that in the clip there is a man keeping time, can you estimate how many times he makes it around the circle in a minute from these clues?

What do we need to know?

-Times around the circle

-Number of people in the circle

I make a table on the board with their estimates for revolutions, people in circle, and total high fives.

Act Three: Watch The Whole Clip

59 people in the circle

4 revolutions

How many high fives is that?

What is the average rate of high fives per second?

Is that more or less than you expected?

Sequel:

Do you think you could beat that record?

How could you better design the attempt to get more high fives?

What’s the upper limit for most high fives in 60 seconds?

Who would be able to high five more people Usain Bolt or LaShawn Merritt (400m World Champion)?

What if we each gave a high five to every student in the class, how many high fives would be given in total?

So many more directions you could go with this!

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Filed under 3-Act, Middle School