Great model of time

http://www.sciencealert.com/watch-this-3-minute-animation-will-change-your-perception-of-time

Chess games

Fantastic Video for scientific notation and exponential growth:

https://www.youtube.com/watch?v=Km024eldY1A

How many students are suspended each year?

Let's make this a math lesson. https://t.co/gVjol6PiI6

— Brian Aspinall (@mraspinall) July 26, 2015

I thought this was a great idea! Here are my draft ideas.

Act 1:

Students walk in and see these questions:

"How many students do you think are suspended each year in the entire United States?"

Write down a reasonable range as an answer. Include your reasoning.

Before we deal with Super Bowl stadiums full of suspended students, I ask them to first think about the total number of suspenions. I want to students to contrast their instinct with the reality. Contrast and conflict tends to leave an impression on the mind. If their instinct is on track, they will have confirmation (which is pretty great as well).

Although students may write a response to the prompt without any assistance. Others will want to ask for more information (which is exactly what I want). If they are making progress, I will let them talk it out. If not, I will stop individual students, groups or even the entire class and ask what they need from to make a reasonable estimate. Some students will ask for the total number of students, which I am willing to give to help them:

Total students: about 49.8 million (I might write 4.98 e 7 to stress scientific notation). 

Once students have decided upon a reasonable range of values, I ask them to write those numbers out on a post-it. One high number and one low. We can post these on the wall to see the full range of guesses and talk about reasonable guesses (something based on their anecdotal experiences) and unreasonable guesses (0 and 49.8 million). 

Once we have talked out our ideas, I show this stat, with a slight omission:

Students can share their observations and questions.  If they have a wide range of questions, I like to type them out on the board as they ask them. There is something wonderful about being quoted in class. Eventually, we settle on the main question, "how many stadiums would they fill?"

To answer the questions, students need to ask for:

1. The seating capacity of the stadium

2. The total number of suspensions

Act 2:

As expected, I found a wide range of Superbowl seating capacities. So I give a few samples:

They also need to know the total number of suspensions:

3.45 out of school suspensions

3.5 in school suspensions

Act 3:

As students consider how to count the suspensions (one type or both), I like to point out the ambiguity of the statistic. Many powerful messages omit the necessary details needed to assess the validity of the message. In this case, we don't know what types of suspensions they were considering and what size stadium they were using.

With the stadiums selected, they might get something like this (this table also shows how many stadiums would hold all students):

When I show the final reveal slide, we will know a bit more about the assumptions the authors of this sign made (Mercedes stadium is by far the closest to 45, if we only consider out of school suspensions).

Although the reveal of "45" may only be somewhat climatic, I image that the discussion afterward could be very rich. We could discuss the following:

• Why did they only include out of school suspensions?
• Why didn't they use a smaller stadium to maximize their number?
• Does this number still seem large if we consider that all students would fill 651 stadiums?
• What percent of students are suspended?
• Is this stat helpful or misleading?

Aside from the powerful social commentary available in this lesson, I would also stress the use of mathematics in modeling the situation. It is always wonderful to give students a chance to critique a model and the assumptions that went into it. In the process, they do something I always want them to do: decide what is reasonable for themselves. 

Sources:

Total school enrollment: http://nces.ed.gov/fastfacts/display.asp?id=372

School suspensions: http://www2.ed.gov/policy/gen/guid/school-discipline/data.html

Video games and Scientific Notation

A world without end, quadrillions of planets to explore, fractal math and of course, scientific notation:

http://www.newyorker.com/magazine/2015/05/18/world-without-end-raffi-khatchadourian

Megaannus and other Units

https://en.wikipedia.org/wiki/Year#SI_prefix_multipliers

funny comment thread: 

https://m.reddit.com/r/todayilearned/comments/2u0ryg/til_that_a_megaannus_is_a_unit_of_time_equal_to_1/


Article to spark conversation:
http://nyti.ms/1Ij7gPR

Online time for Kids

I came across this article and thought it was perfect for the classroom. I am thinking data, scientific notation, percents, ratios, linear and nonlinear modeling...


It is a great article: http://www.nytimes.com/2010/01/20/education/20wired.html

Art and the Powers of 10

My colleague found this great art/scientific notation video.

Enjoy: http://gbaacademy.com/watch?id=IIZ0Nt4JDTk

Do all the Ants Weigh as Much as All the Humans?

Great article for scientific notation:

http://www.bbc.com/news/magazine-29281253

Steven Strogatz on Scientific Notation

Great Article: http://nyti.ms/1cWQ9CL

The Distance to Mars

Great for a lesson on scale and perhaps time, distance and speed (linear modeling):

http://www.distancetomars.com/

Great source for Scientific Notation measurements

This site has an extensive list of measurements in scientific notation.

Thought this might help: http://www.falstad.com/scale/

Deconstructing the top 1%

How is the wealth of the top 1% distributed by occupation? Find out with the clever interactive graph:

http://www.nytimes.com/packages/html/newsgraphics/2012/0115-one-percent-occupations/index.html?ref=business

This is another go to for my scientific notation unit.

What percent are you?

In the United States, it is interesting to see where you stand based on your income. Here is a great interactive graphic to help: http://www.nytimes.com/interactive/2012/01/15/business/one-percent-map.html

I see it as a resource for my scientific notation unit.

Buying Basketball Courts

How many could buy for 1 million?

What does a court cost?

What could you buy for a billion? a trillion?

How many times more expensive is the price of a court in one state over an another?

This infographic creates a great platform for discussion around large numbers, rate, ratio, scale and so much more:

Source: http://i.imgur.com/w0WK72P.png

Enceladus Moon: Volume, Rate and Scientific Notation

It turns out that there might be a large volume of water beneath the Surface of Saturn's Enceladus Moon, about equal in volume to Lake Superior and 245 times the volume of Lake Garda in Italy.

I am going to use this next year in conjunction with Scientific Notation. We can analyze what it means to be "about equal" in volume or "245 times the volume" of Lake Garda.

As an extension we will analyze a question that utilizes the context of the scenario. Using different types of models, we can attempt to answer the question: "is it worth it to extract the water?"

Students can start with simple calculations: how long might the water last us? how many bottles would it fill? Then they can progress to bigger questions: based on current technology, how much would it take to get there and extract the water.

Comparing these costs and gains might make for a nice debate (we will also include the typical Neil deGrasse Tyson argument on the connection between space exploration and the future of the economy).


Article Link: http://www.bbc.com/news/science-environment-26872184

Adding Context to Scientific Notation

The world of the small is a great place to introduce scientific notation. This FEI gallery is fantastic and often includes the measurements in the photos: http://flic.kr/ps/DDQp3  I am going to use a bunch of these in my lessons. We could do a daily activity, asking "how many meters is that?"

Fabulous Fab

With the SEC finally prosecuting and winning a case against someone behind the financial crisis, we need to ask ourselves "Is this a meaningful victory for the SEC?"

This is something that students might usually debate in humanities, but I think that these types of debates come to life in math class. It is the numbers that really help us make meaning of the trial of Fabulous Fab, Fabrice Tourre. In this video clip, Stephen Colbert brings light on the situation in a way that is guaranteed to get the attention of your class. He points out that the SEC prosecuted someone responsible for 1 billion of the 22 trillion lost in the financial crisis. Then he breaks out a calculator and tries to figure out how much this actually "matters." He stops in the process saying that his calculator can't fit those numbers. My thinking is that this is a perfect opportunity to discuss large numbers on the calculator, scientific notation and the number sense surrounding very large numbers (especially since you don't need a calculator to realize that 1 billion/22 trillion = 1/22000). It might be a great time to discuss the relationship between billions, trillions and other fabulously large numbers.

Here is the clip:


Here is the link to the clip: http://on.cc.com/17z7smc

A Quadrillion Yen

I just came across this article and thought it might be a great way to discuss large numbers and scale. I might print out the article with some missing numbers and have students fill in the blanks. Here is a link to the article.