Math and Science Discover the Unseen Planets of Trappist-1 – Now That’s Cool!

I am sure by now you have heard about NASA’s discovery of 7 – earth-like planets orbiting the star called Trappist-1 by using the Spitzer Space Telescope. And, apparently 3 of them could possibly be habitable for life. All of this is amazing in itself, but, what is even more amazing is they discovered these planets without really even seeing them.

What?!  How is this possible? How do they know then that there are even planets if they can’t see them? It all comes down to some amazing technology, some data collection, a lot of math, science and analysis. If you are looking for ways to get your students excited about math and science and real-world applications to answer questions, you need look no further.

While listening to a story on NPR, as usual, an astronomer came on to discuss how these planets were in fact discovered. In his discussion, I was just floored by all the applications of geometry and statistics used in this discovery. When he said they couldn’t actually ‘see’ any of the planets, but instead, used the dimming light of the star, Trappist-1, that these planets orbit around as an indication that there were in facts objects/planets orbiting about the star. So – basically,  looking at the stars brightness from the Earth, the amount of starlight that is blocked as each planet passes across the view of the star was used to calculate the size of each planet.  Based on the amount of dimming, they were able to determine the size of the planets, relative to Earth, with the dips in the stars light indicating how fast the individual planets were orbitting the star. This video below explains the process really well:

The star, Trappist-1, is what they call an ultra-cool dwarf star, which is about the size of Jupiter and significantly cooler than our own sun, and is only 39 light years away from us.  That seems far to me, but apparently in ‘space units’ that’s really close! (Here’s a great problem for students – how many miles would 39 light years represent?) Each planets mass was determined by the amount of tug of each planet on the other. Then, using the size and mass calculations, they estimated each planets density, which then allowed them to extrapolate that six of the planets are probably rocky. Another really interesting thing about all the planets is they appear to be tidally locked, which means the same side of the planet always faces its sun, so one half of the planet is always dark, the other always light. This is based on the length of each planets day, or its spin on its axis (determined by watching the planets for a period of days and seeing how often they crossed the star). The shortest day (compared to an earth day) is 1.5 days, the longest is about 20 days (they still have to collect more data for this last one). I found this great chart on the NASA Jet Propulsion site that compares each of the seven planets (with an artist’s rendering of what they might look like…remember, no one can actually ‘see’ these planets yet)

This infographic displays some artist's illustrations of how the seven planets orbiting TRAPPIST-1 might appear — including the possible presence of water oceans — alongside some images of the rocky planets in our Solar System. Information about the size and orbital periods of all the planets is also provided for comparison; the TRAPPIST-1 planets are all approximately Earth-sized.

This infographic displays some artist’s illustrations of how the seven planets orbiting TRAPPIST-1 might appear — including the possible presence of water oceans — alongside some images of the rocky planets in our Solar System. Information about the size and orbital periods of all the planets is also provided for comparison; the TRAPPIST-1 planets are all approximately Earth-sized.

I find the whole process exciting, interesting, and fascinating. I think students would too and there is so much application of mathematics and science going on here. And, as a certified sci-fi geek, just thinking of the possibilities of other life on those ‘M’ class planets (shout out to my fellow Star Trek groupies) is sparking my imagination. Right now, we don’t have the technology to see these seven planets, but who knows? Maybe a student who explores the math and science behind these now might create that next telescope that lets us see the planets, or the space ship that allows us to travel there? Fun to imagine, and fun for students to explore these ‘brave new worlds where no man has gone before….”.

If you are interested in finding out more about this Trappist-1 discovery, here are some more links:


Math, Science, Balloons & Macy’s Thanksgiving Day Parade

ELF ON THE SHELF 2012 Macy'sIt’s that time of year again to do a Thanksgiving themed post. I looked back at what I wrote last year around this time, Engaging in Thanksgiving Data, all about interesting data focused around Thanksgiving (food data for example). Still relevant, if you want to take a look at some of the links to use with students. But obviously I need to do something different for this post.

So, the question then becomes what? If not data about Thanksgiving, what other math/science connections can I make relevant to this particularly U.S.-centric holiday?  The answer – the Macy’s Thanksgiving Day Parade and the large balloons. Thanks to NPR and ScienceFRiday videos/stories, there is already a great video and some interesting math and science that goes on behind and within those large floating balloon animals/creatures that you see in the parade coming up this Thursday.

Did you know? (facts from Francie Diep’s 2014 article in Popular Science, The Science and Engineering of Macy’s Thanksgiving Day Balloons)

  • When staffers come up with a new design for a balloon, they first mold it in clay. Then, to help them calculate how much helium it would take to fill the design, theymacys-parade-2012-pillsbury-doughboy-balloon use good old water displacement.
  • The average balloon requires 12,000 cubic feet of helium. That’s enough to fill about 2,500 bathtubs.
  • The average balloon requires 90 handlers during the parade. Handlers must weigh at least 120 pounds and have no heart, back, or knee problems.
  • The balloons were originally made of rubber. Now, they’re made of fabrics coated in a polyurethane material that’s flexible, durable, and leak-resistant. Polyurethanes are synthetic plastic materials that also commonly show up in couch cushions, insulation, and even in synthetic-fiber clothes.
  • The Pillsbury Dough Boy Balloon pictured above requires 90 handlers, is as high as a 4 story building (so how high is that?), as wide as 7 taxi cabs, and as long as 9 bicycles (so how long??).  And has enough dough to make 4 million crescent rolls….wow!

That’s a lot of math/science going on here: scale modeling, volume, physics, estimation, weight, measurement, and geometry to name a few concepts. Think of the interesting questions that students could ask and then explore! Doing this prior to the actually parade on Thursday would be so much fun, and then having students actually watch the parade and maybe collect some data – i.e. how many balloons, how many people on a specific balloon, what is an average balloon and what would a bigger than average balloon be?

You can even find out about the specific balloons that will be in the parade and other interesting information that you could use to spark some math/science questions prior to the parade. Here are some links that give some facts about balloons and the parade itself:

And finally, here’s a video on the math/science behind the balloons from ScienceFriday

The STEM Around Us

NCTM Innov8, the new team-based conference that NCTM is sponsoring, is going on right now in St. Louis, Missouri. Our team is there of hqdefaultcourse, supporting math teachers with our technology and a great team-building session based on the Wheel of Fortune and the probabilities of winning (session is Friday, November 18 at 10:45 am in Room 265/266). St. Louis brings to mind the very famous St. Louis Gateway Arch, something math teachers attending will probably be exploring and trying to mathematically represent – is it a parabola? (In fact, it is NOT a parabola, but rather a flattened catenary). (Cool 3D mathematical model here).

This idea of looking at real objects and connecting mathematics to them is something math teachers do often. It makes complete sense, and, as I have been teaching a geometry course for Drexel these last several weeks, I have really deepened my appreciation for this idea of looking at our constructed world to find the mathematical connections and relationships. What I think we tend not to do with students, and what we should do much more of, is go beyond the obvious “shape” explorations and function fitting to explore the STEM connections.

What I mean is after we identify the inherent shapes and/or functions in ‘real-world’ objects, start asking questions that get students thinking about the why behind those shapes. The why questions lead to investigation and research by students into science, technology, engineering, and math applications that would take them much deeper into understanding the world around them. And, I wager, this type of questioning will engage students in learning and applying what they learn in a much more relevant and interesting way.  Giving them purpose for learning. And, as a result, we might have more students going into STEM fields.

Some examples:

2016-11-17_15-32-11    download     images

Why, for example, are most buildings polygon shapes, particularly triangles and rectangles? Why don’t we see more circular or cylindrical shapes for buildings, besides the grain silos or water towers? Is there a reason? This is where engineering would come into play – are certain shapes stronger from an engineering perspective?



Why are science and medical tubes cylindrical? Is their a scientific reason for these shapes/containers? Why not use a prism shape, so then you could set the vials down on a table versus having to store them in special holders so they don’t roll away? Is the shape somehow connected to the way molecules or blood cells behave – i.e. science factors that might determine the tools used.  2791136-image-of-the-motherboard-without-a-pc-processor-closeup

Look at all the different shapes on a computer motherboard – there are cylinders, rectangles, squares, networks of curves/lines of wires, prisms…so many things going on. Students could ask whether certain shapes provide better conductivity? Or heat control? How does the height of a component impact it (notice the different heights of the cylindrical components). I don’t even know the questions to ask here, but this is a great example of where technology comes into play.

I feel that if we allowed students to explore beyond simple things like fitting a function to a curve or identifying shapes in a picture, and really focused on STEM applications and reasons behind the use of those specific shapes, we would be encouraging students creativity, curiosity, and developing research capabilities in order to find solutions. It would be so engaging and really get students interested in those STEM careers, but more importantly, a better understanding of the STEM around them.


Test-Driving Classroom Technology

45785364I am a huge proponent of using technology in the classroom, particularly in mathematics. If technology is used appropriately, it can do several things: provide visuals for concepts that are often hard for students to grasp; allow for students to explore and test conjectures; provide opportunities to go beyond basic understandings and get into deeper meaning and more complex structures; provide multiple ways to practice and learn; and obviously, foster engagement. These are just some of the benefits.  There is of course a downside to technology – lack of training for teachers often leads to using technology just as a digital replacement of paper and pencil – an electronic worksheet for example – in which case, what’s the point?  That’s NOT a great use. Or using technology when it is NOT the best option or doesn’t really enhance/support the learning goals. Or using the wrong technology. Just because you have technology doesn’t mean it’s a good fit for your learning goals/standards.

In my own research, and in my personal travels around the country working in math classrooms and with math teachers, there is a wide variety of technology available, and more often than not, this technology is NOT being used to enhance and expand learning. Often times this is because technology has been purchased with no real effort to match it to learning goals or standards, and little or no training or support for how to use the technology in the classroom has been provided. Teachers are frustrated, students are frustrated, and the technology becomes just another ‘add on’ versus a true learning tool.


What is often missing in a technology implementation is the most crucial step – planning. With planning, technology aligned to objectives becomes a focus for purchasing technology that actual supports learning goals and needs. Seems obvious – but, having been an administrator, I know that often times ‘funds’ for technology are released and must be spent quickly (i.e. for me, I was told we must put our orders in by this week or we lose the funding), so often times technology is purchased that sounds good, or looks good, but may in fact not be a good fit.

Ideally, technology should support learning goals, which can only happen if you sit down with your subject leaders/teachers, look at your standards and learning goals, and then analyze the various technology options and determine which ones support those goals. And, if possible, test these technologies out BEFORE purchasing, to ensure they do indeed support learning.  This also allows you to plan for training needs of the teachers, infrastructure, curriculum and standards alignment, etc. These are important steps – often left out of the technology implementation process – and often the reason why much of the technology in school is misused and unused.  I bet if you looked around your school you would find a lot of ‘great technology’ gathering dust.


If technology company’s were smart, and if IT and Education leaders really focused on planning for technology, there would be a lot more pilots or test-driving of technology before big purchases are made. (LAUSD and the iPad debacle comes to mind). The ability to try out technology with both teachers and students and really see if it is going to be a good fit to meet your learning goals is something that will  help your school/district make the best technology decisions and purchases. As an example, CASIO Education has a technology loaner program where you can in fact, test-drive our technology before you purchase. It makes sense – if you are thinking of purchasing some graphing calculators, why not test-drive the 9750 GII and the Prizm and see which one fits your algebra or geometry or calculus students and standards the best? Is the FX-55plus a good fit for your elementary and middle school students? These types of questions are what should arise when you plan for technology AHEAD of time and having the ability to test-drive your options before spending the money just makes sense.

You don’t buy a new car without a test drive, so why buy technology without one? Especially when making large school/district purchases.

Here’s the link to CASIO’s loaner program – check it out and go for a drive!

Mathematics and History – Cross-curricular Learning

Obviously with it being February and Black-history month and Presidents Day, a lot of teachers are trying to find ways to bring some of that history into their classrooms, no matter the subject. The sad thing here is that we should be doing these types of cross-curricular learning regularly, not just when there is a designated day, or week, or month. In math and science in particular, there are so many historical events and people that have impacted the study of these subjects, therefore bringing in history, writing, and art really shouldn’t be that much of a stretch. And, vice versa – if you are a history teacher or an English teacher or an art teacher, there are mathematical and science connections that you can be using regularly.  Heck – the Common Core ELA standards actually have a huge focus on students reading in social studies, science and technical subject areas. Cross-curricular learning helps students make connections to not only where these subjects they are learning came from and who helped develop them, but how they work together and apply to life and future skills.

During my middle-school teaching years, it was easy to focus on cross-curricular learning because I was part of a cross-curricular team where we made a concerted effort to focus the learning on themes.  So maybe if we were learning about astronomy in science, then in math we were talking about planetary distances and gravitational forces, and in history they may have been learning the history of space travel and writing about it in English.  As I moved into high school and teaching, where there was more isolation of subjects, I still created opportunities for my students to connect history, science, art, and writing to mathematics. Some of my favorite resources were the AIMS Historical Connections in Mathematics books, which had summaries of various historical mathematicians, some sample problems related to their discoveries or work, and provided connections and timelines.  These were great starting points, often with hands-on activities, that helped support student projects or investigations.

What is probably of most importance, is to try to find historical figures or artistic applications of the math/science your students will be learning so that they see relevance to either a) what they are learning and where it came from; or b) why they are learning it and what they can use it for in the future. Learning is so much more interesting if there is a reason why or and understanding of how the math/science contributed to some point in time, some event, etc.

So – in light of the fact that it is February and Black-history month, I thought I would share a few influential mathematicians/scientists, with some links to what they did to maybe get you or your students thinking and connecting. Let’s write.  Let’s research.  Let’s connect math/science to other subjects so that learning is not an isolated topic but an interconnected experience.

  1. Benjamin Banneker (1731-1806) – mathematician, astronomer, writer of Almanacs
  2. David Harold Blackwell (1919-2010) – mathematician, first African-American inducted into the National Academy of Sciences
  3. Kelly Miller (1863-1939) – mathematician, first African-american to attend Johns Hopkins University
  4. J. Ernest Wilkins, Jr. (1923-2011) – nuclear scientist, chemical engineer, mathematician; contributed to The Manhattan Project; the youngest ever student to enter The University of Chicago (at age 13)
  5. Elbert Frank Cox (1895-1969) – first African-American to earn a Ph.D. in Mathematics
  6. Marjorie Lee Browne (1914-1979) – noted mathematics educator
  7. Charles L. Reason (1818-1893) – mathematician, linguist, educator; first African-American professor to teach at a predominantly white U.S. college
  8. Katherine Johnson (1918 – ) – physicist, space scientist, mathematician; early application of digital electronics as part of NASA space program

This is just my first posting trying to connect mathematics/science to other subject areas. Each month I will share some historical mathematics/scientists to help provide some resources for those of you who wish to incorporate cross-curricular learning.





The snow piled high up the back door….

For those of you in the east coast, particularly from Virginia up through New York, you probably are still digging out from the crazy blizzard that was Jonas. I had about 30 inches at my house, which was wild.  My poor dog took one look and refused to go out – considering the snow is higher than him, you can’t blame him!  I had to dig a tunnel in the back yard, which was no easy task.

Naturally, during the storm there was a lot of news-watching to see what the snow accumulation predictions would be. Also, on Facebook, there were a lot of people posting time-lapsed videos of the snow accumulation from various parts of the country.  My favorite one is posted below – it was posted by Ed Piotrowski of WPDE and shows 40 seconds of snow accumulation of 40″ taken over 27 hours with pictures shot every 2 minutes from a guy named Wayne Bennett’s camera.  Here is the clip:

Of course my first thoughts – wouldn’t this make a great math investigation for students.  How much snow is falling each minute? How does12540761_10208896719685904_6604353696648335492_n it change over time? There are a lot of these time-lapse videos out there, some with actual rulers, where students could actually collect numerical data.  And, now that the storm is over, how long is it going to take for this much snow to melt? Have students look at weather temperatures over the next few days and try to determine melting rates and how long this much snow will take to get rid of. How does rain (predicted in my area tomorrow) impact this? If the snow were rain, how much water is that?  There are a lot of interesting questions and predictions that could be made. Heck – just calculating how many frames were needed to capture the time-lapse would be an interesting math problem.

As I continue to dig out from the storm, I just wanted to share my mathematical thoughts. It’s pretty simple to find real-world math and that sure does make learning math a lot more fun.d


Math in the Movies – Let’s go to Mars

Last night I watched the movie The Martianstarring Matt Damon and directed by Ridley Scott. I really enjoyed it because I am a sci-fi fan, but even more so when I realized how much math and science was in the movie. I mean – it’s all about the math really. (I would like to say, for the record, that it is NOT a comedy, even though Matt Damon won best actor in a comedy at the Golden Globes.  Funny moments, yes, comedy?No)

If you have not seen the movie, do so. I am going to be sharing some links that will definitely have spoiler alerts in them and I will probably even share some spoiler alerts myself, so I suggest not reading if you have not seen the movie.  

As I said, the movie is all about math and science – to survive, to communicate, to pull of a dramatic rescue. It reminded me at times of another great sci-fi space movie, Apollo 13, which also involved a space rescue. As in Apollo 13, there are scenes in the Martian where scientists/mathematicians on earth are testing out theories and calculations on replicas on earth so Matt Damon’s character, Mark Watney, can then perform the same things on the real equipment on Mars. There are also numerous mathematical and science calculations and experiments that Mark Watney does during his long time alone on Mars to try to survive – many of which go horribly wrong, but that’s what makes it so realistic and such a great example for students, because if you mess up, you try again and try a new approach.  And sometimes the obvious solutions aren’t the best solutions.

I am not going to go into all the math and science in the movie, because other people have done a great job of that already. What I am going to encourage is that math and science teachers use the math and science from The Martian in your classroom. Bring the movies into your classroom and see the fun students will have applying mathematics and science in an engaging way with something that is of interest to students. When Apollo 13 came out in 1995, I was teaching 6th grade mathematics on a collaborative team. We did a ‘field trip’, taking students to see Apollo 13 and then doing a lot of math/science/english/history activities to bring what they saw back to the classroom to connect to what they learned. One activity I specifically remember is having students work with partners. One partner had to build a structure (we used Legos) and write down what they did, and then read the directions to the other person and see if the other person could make a replica of what they’d built. The idea here was to emphasize the importance of good instructions, logical sequence, etc. But – it simulated the scene in the movie where the scientists on earth had to basically make a square peg fit into a round hole and create a structure that would clean the air in the module so the astronauts would live.  And they had to tell the astronauts what to do clearly and quickly or they would die, and only through their voice – so good descriptions and logical steps. We did a lot of other activities, but what I remember most is how engaged and excited students were to be using their writing, their math, their science, their history, to expand on and understand the movie.

Here are several of the articles and links I have found related to the math/science in The Martian.  Choose a couple and explore with your students and see how much fun you and they have!

  1. Math of “The Martian”: How It Adds Up, Sarah Lewin
  2. “The Martian” is Full of Math Word Problems, Says Author Andy Weir, by Liana Heitin
  3. Do the Math: How to Survive in “The Martian”, by Kari Tate
  4. The Science of “The Martian”: 5 TED-Ed Lessons to Help You Understand the Film, by Laura McClure