Trash Sculptures

This sculpture shows one hour of trash build up in NYC:

http://www.thisiscolossal.com/2014/07/a-sculptural-cloud-of-plastic-bottles-to-illustrate-one-hour-of-trash-in-nyc/

G(Math) Individualized Exams

This is exciting:

http://www.gmath.guru/quick-quiz-creator/#/quizninja-for-individualized-forms/

Classroom Robot

From Harvard: 

http://www.wired.com/2014/11/10-dollar-education-robot/

OER Report

In the dismal landscape of corporate education reform, OER offers a glimpse of hope: 

https://stateof.creativecommons.org/report/

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

Van Gogh, Turbulence and Mathematics

My colleague found this interesting analysis of Van Gogh's Starry Night:



Along with this article: http://www.upworthy.com/in-125-years-millions-of-people-have-looked-at-this-painting-no-one-really-saw-it-until-now?c=ufb1

Art and the Powers of 10

My colleague found this great art/scientific notation video.

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

Invisible Cloaks and Functional Thinking

To make an image invisible, they much use a sequence of lenses to bend the light around a given object. In this way they need to think of the path for light as a function of the position of each lens.

http://www.rochester.edu/newscenter/watch-rochester-cloak-uses-ordinary-lenses-to-hide-objects-across-continuous-range-of-angles-70592/

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

Nametags can be a great first day activity

http://purpleprontopups.wordpress.com/2013/08/07/day-one/

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/

Raw = Great data tool

All I have to say here is wow: http://raw.densitydesign.org/

Water Facts

Here are stunning water facts that can be integrated into many math units. I will use them for percents, ratios, scientific notation and part of my divergent homework series:

http://water.org/water-crisis/water-facts/water/

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.

Convincing Students to Collaborate

How can we convince our students to collaborate with each other?

I am always looking for resources on collaboration. Today, I found one:

Perfect for the first week of class!



Article Link

Brainwriting vs Brainstorming

I often give students a 1-2 minute window to write out their own thoughts before sharing with their partner, group or class. Everyone needs a few minutes of safe time to process their ideas (or at least I know I do). I am starting to realize that this writing time is critical and is needed before the collaboration brain storming phase.

Professor Leigh Thompson makes this distinction by defining brain writing as the simultaneous written generation of ideas and brain storming as the simultaneous oral generation of ideas.

Using the writing first prevents what she calls "the doom cycle," in which one or two people dominate the brain storming process, perpetuating their own ideas as others step back.

I realize that I see this with students all the time!

In contrast, writing is safe.

Thompson mentions that two things need to happen during brain writing:

1. No one can interrupt you
2. No one can block your thoughts

This video sums up the research as to why this is so important:




Here is a great article for further reading:

http://www.fastcompany.com/3033567/agendas/brainstorming-doesnt-work-try-this-technique-instead?partner=rss

I am implementing these protocols into my class.

Also, here is an app developed around these protocols: http://usecandor.com/users/sign_up

Counterfeit Money Problem

I came across this great problem and am thinking of using it to demonstrate the power of using a physical model in solving a math problem:

http://www.nctm.org/publications/blog/blog.aspx?id=42693&blogid=599514

and the answer:

http://www.nctm.org/publications/blog/blog.aspx?id=42820&blogid=599514

Rethinking Learning Projections in Mathematics

I often wonder if we limit ourselves by teaching mathematics in a prescribed progression. Dr. Maria Droujkova posted an interesting photo of an anonymous user on Khan Academy. Notice the non-linear nature of their progress, with 13% mastered of Early Math topics and higher percentages of mastery on "higher level" topics, like 62% mastered on Pre-Algebra.

My first question is, "did this person attempt 100% of each topic?" I know that I move away from topics that I find tedious. Especially at the early math levels. 

I am curious to see who this mystery user is.

Using a name to predict someone's age

I enjoy reading the FiveThirtyEight blog and always mine it for great math content. I came across this article and thought it was perfect for a box and whisker plot lesson:

Source: http://fivethirtyeight.com/features/how-to-tell-someones-age-when-all-you-know-is-her-name/

I will post more once I develop the lesson.

When Math Happens

I am super impressed with this teacher's work: http://whenmathhappens.com/

Open Middle - A Collection of Challenging Problems

Just found this great site today and plan on incorporating it into my problem library. It has a fresh approach:

http://www.openmiddle.com/

Here is their explanation of the site, listed under the "about" link:

Dan Meyer introduced us to the idea of “open middle” problems during his presentation on “Video Games & Making Math More Like Things Students Like” by explaining what makes them unique:

• they have a “closed beginning” meaning that they all start with the same initial problem.
• they have a “closed end” meaning that they all end with the same answer.
• they have an “open middle” meaning that there are multiple ways to approach and ultimately solve the problem.

Open middle problems require a higher depth of knowledge than most problems that assess procedural and conceptual understanding.   They support the Common Core State Standards and  provide students with opportunities for discussing their thinking.

Some additional characteristics of open middle problems include:

• They often have multiple ways of solving them as opposed to a problem where you are told to solve it using a specific method. Example
• They may involve optimization such that it is easy to get an answer but more challenging to get the best or optimal answer. Example
• They may appear to be simple and procedural in nature but turn out to be more challenging and complex when you start to solve it. Example
• They are generally not as complex as a performance task which may require significant background context to complete. Example

Bike Riding versus driving

There has got to be a three act in this:

#cycling vs #driving pic.twitter.com/ZjRqWfh0jB
— SCPHRP (@SCPHRP) June 3, 2014

Itunes Vs. Amazon, Linear versus exponential fit

great linear versus exponential fit:
https://twitter.com/mjfenton/status/460984209922732033

Female Named Hurricanes Kill More than Male Named Hurricanes

I heard this story yesterday morning on WNYC morning edition and thought it was perfect for a lesson on causation versus correlation. Essentially the data shows a strong correlation between fatalities and the gender of a hurricane name. Essentially they found that female named hurricanes are much more deadly then male named hurricanes. We can present this to our students with the obvious question, "does that mean that the names are causing higher fatalities?" The goal is to get students to recognize how absurd it would be if we thought this was causal. That would mean that we could simply make a hurricane safer (or more deadly) by changing its name. So this gives students a clear distinction between correlated and causal.

So what is happening? What is a possible cause? If you review the story, articles and data below, you can see that people respond differently to a storm based on its name. It is this response that seems to be causing the difference in results. If we are more afraid of a female named storm, we might take more precautions, etc.

This still leads to more questions and class discussion, why do we respond differently? Why do we give names to storms at all?

Here is the radio story:
http://www.npr.org/2014/06/03/318414845/research-americans-less-fearful-of-storms-with-female-names

You can also find this story on their site:
http://www.wnyc.org/story/research-americans-less-fearful-of-storms-with-female-names/

http://www.wnyc.org/story/study-americans-less-fearful-of-storms-named-after-women/


Article on WNYC: http://www.wnyc.org/story/do-female-named-hurricanes-need-to-lean-in/

Article on the Washington Post:
http://www.washingtonpost.com/blogs/capital-weather-gang/wp/2014/06/02/female-named-hurricanes-kill-more-than-male-because-people-dont-respect-them-study-finds/

Original Study:
http://www.pnas.org/content/early/2014/05/29/1402786111.abstract

Download Data from Original Study:
http://www.pnas.org/content/suppl/2014/05/30/1402786111.DCSupplemental

You can also find the data key here:
https://drive.google.com/file/d/0B5FTxsu-S1CoQ1ZSM2VSR3Yxc3c/edit?usp=sharing

And the original data here:

https://drive.google.com/file/d/0B5FTxsu-S1CoQVJIVzl4SV9yb0k/edit?usp=sharing

Military Deaths in US by war

If we give students the diameter of one circle, they can predict the diameter of another circle (likewise with circumference, radius, area, etc):

source: http://imgur.com/mxdjRlk

Zombie Films

Bar graph on Zombie movies over time:

source: http://imgur.com/a/xkPrW

Military Expenditure

Great pie chart for comparing military expenditure rates by country:

source: https://i.imgur.com/zqUbcvp.png

An Eye for An Eye

Great graphic comparing death penalty executions versus murder rates:

http://www.washingtonpost.com/wp-srv/special/outlook/death-penalty/

Income Inequality through Data

Great pdf source:
http://siteresources.worldbank.org/INTPROSPECTS/Resources/334934-1327948020811/8401693-1397074077765/Prosperity_for_All_Final_2014.pdf

Player Sizes Scatter Plots

Great sports visualization using scatter plots:

Source (you can zoom in): http://sportchart.wordpress.com/2014/05/27/professional-athlete-size-comparison/

Execution Chart Comparisons

Start with this graph, which shows executions per million people:

Then contrast it to this graph, which shows the total number of executions:

You could also start with the first chart, and ask, "which country has the highest number of executions?" And then follow with "what would we need to know in order to figure this out?" Students could then use population counts from each country to sort out the data for themselves. 

Although the data is about death and a potentially difficult subject, students will be using mathematics to make sense of a complex issue which they might feel very strongly about. 

source: http://imgur.com/a/SYIwN

Cell Phone Percentages by Carrier

I think this is a great image for discussion around pie charts:

source: http://www.counterpointresearch.com/wp-content/uploads/2014/05/Q1-2014-USA-Carrier-Market-Share.png

Violent Crimes

I would like to contrast total violent crimes versus violent crimes per 100,000 inhabitants. The following table would be key in that discussion:

source: http://graphzoo.tumblr.com/image/84646626862

Quandl = Free Data Source (yay!)

Free data that you can easily import into spreadsheets? Not a problem with Quandl!

Their promo video says it all:


I will be using this throughout the year: http://www.quandl.com/

Central Tendency and Pay Scale

This simple graph is built around median incomes and sets the stage for the discussion around central tendency:

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

States and Passports

Not only does this site have an interactive map to look at the level of passport holders in each state, but if has this great graph which lends itself nicely to a line of best fit.

I can display this graph and ask, "how many passports will be given out in 2014?" Or I can blur out a point or two and see how close they can get to the actual numbers. So I could blur out 2013 and see how the actual numbers compare to their predictions.

The Baby Name Predictor

You can display trends and predictions in name popularity for up to six names at a time:

Get started by looking at the one thing that everyone wants to see, how their names have done and might do in the future. This would be a great low inference entry into trends. Then try some of the names and trends suggested in the article and bring up correlation and causation. For example, they mention that popularity in the name Adele correlates to her popularity as a singer. Ask the class if they accept the implication that this also a causal relationship. Then have fun debating the merits of why this may or may not be the case. 

source: http://time.com/93911/baby-name-predictor/

Pedestrian and Bicycle Injuries

Another great graph for class on correlation and causation. Show the graph and maybe read the article. Ask students about the reasons why certain areas are dangerous and the compare their answers to the causes listed in the article: http://nyti.ms/1kxRqkx

2Pac - Dear Mama Stats

Post this for your class and ask them, "why the spikes?"

The answer: Mothers Day

Then ask, "is this causal? correlated? both?"

Greenhouse Gas Emissions

The data on this map will certainly connect to many standards on statistics in the common core curriculum, but I especially like how the context sets the stage for a classroom discussion on Global Warming.

Perhaps students could turn this data into a bar graph and discuss measures of dispersion and then compare those values to the same map per capita (which will also deepen the mathematical discussion):

source: http://www.mylife.com/blog/us-greenhouse-gas-emissions-by-state/

Cellular Subscribers (per 100 population)

As I mine through the data is beautiful sub reddit, I found this beautiful bar graph:

http://i.imgur.com/o7pHflX.png

It will be great for discussion about the context of the graph and can also be used to discuss the algorithm for calculating their statistics (which is included on the bottom of the graph)

Great Visualization of Citibike Data

Not only does this site capture a tremendous amount of data into a beautiful visual, but it also uses scientific notation. This will find its way into my curriculum next year:

Colbert, Causation and Correlation

Interesting problems on correlation and causation are not easy to find. Perhaps I am not looking in the right places, but when I start to search, this is what I find:

Source: http://www.regentsprep.org/regents/math/algebra/practicetests/MCTest1.htm

This problem offers a nice contrast between causation and correlation, but it feels manufactured. There is nothing compelling about it. Nothing that shows why the causation-correlation contrast is worth thinking about. When we discuss the answer, students understand that the rooster doesn't cause the sun to rise. They know this is ridiculous and wonder, "why are we talking about this? No one thinks that a rooster causes the sun to rise." 

And this is where I am struggling. I want to use examples that show a meaningful contrast between correlation and causation, because I know I can find problems that reflect common assumptions about causation and thus spark a class debate. 

How many times do people assume that a correlation means causation? I know there are endless examples of this, but I need to start compiling them.  

I was watching Colbert this week and found one of my first examples. With some major editing, I am going to show this as my opening:

This clip captures answers a lot of the "so what" question as well as a hilarious example of correlation and causation:

I am now going to think about how to turn the autism and vaccine connection into a investigable lesson.

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

Bullets and Math

Found this on reddit: http://www.reddit.com/tb/23m702

I am wondering how many bullets on in this photo and think there might be a lesson in it.  I might never use the lesson (not sure that I am comfortable estimating something like bullets), but it certainly presents an interesting question. 

So I posted it onto 101 questions. See what other people are asking. 

Martial Arts and Math

Is mathematics useful?

Of course!

Do I expect all of my students to leave class and use the quadratic formula on their way home?

Certainly not!

That is because the quadratic formula, just like all of the other content we teach in mathematics, has value that goes beyond its application (even though its application is fantastic). I want society to stop placing value on the mathematics we learn and teach simply because we will or will not "use" an exact topic outside of the classroom. Instead, I hope we look more towards the habits of mind, which pretty sums up the reasons I teach mathematics.

Mathematics is more than the sum of its content, just as martial arts is more than a collection of kicks and punches:

Math Meme

I am hanging this in my classroom next year.

You can't say that you don't know how to solve a problem until you have tried something. Problem solving isn't just about what you know, its about what you do.

source:
http://img.pandawhale.com/82307-weve-tried-nothing-and-were-al-9vbA.png

Numbers Only on Google Forms

I am currently working on a version of Mean Paper Airplanes that I found on Julie Reulbach's blog and came across her comment to Dan Meyer about Google Form Functionality:

I was excited to find that Google has added this feature in its most significant form overhaul for education: data validation. Forms also now have the ability to post images and video, which is awesome (I am going to make interactive modules with videos and images of tables, graphs and patterns for questions). 

I wanted to show how Google Forms can be set to fix her issue.  

When writing the question, notice the "advanced settings" tab at the bottom:

Click "data validation" and selected the "number" option and specify "is number" so that only numbers can be entered. Then I select an error message to pop up if students type in something else, like the units of measurement. The message I chose was, "only enter the number of inches."

From the student's perspective, they would see this if they typed in units:

There is so much more that can be done with data validation. I can't wait to play around with it more this summer.

Thanks Julie for finding that lesson, it has been really fun so far!  (I will post my extensions to it as it is amazing and fits nicely with the 8th and 9th grade CCSS curriculum as well) 

If the Moon were only One Pixel

A student of mine found this site: http://joshworth.com/dev/pixelspace/pixelspace_solarsystem.html

This just screams proportional reasoning. I will be using it next year.

The Growth Mindset on WNYC

I heard this on the radio this week and was excited to see the Growth Mindset spreading around:

https://www.wnyc.org/story/does-teaching-kids-to-get-gritty-help-them-get-ahead/

Listen to the story here