Care for a slice of pie? How about FOUR slices of pi from the Jet Propulsion Laboratory (JPL)? And a dollop of Next Generation Science Standards (NGSS) on top? Certainly! In honor of pi and Pi Day (March 14) and even Rounded Pi Day (March 14, 2016… 3.1416… get it?), JPL serves up its third round of pi-based math problems. These beautifully illustrated exercises highlight NASA science, technology, engineering, and math (STEM) to show us all how pi is utilized in the real world. For teachers, these are engaging for students and connected to standards–but more about that later. So, hope you’re hungry… here we go…
Our first serving takes us to Mars. As the Mars Reconnaissance Orbiter (MRO) traces a nearly circular nearly polar orbit around the Red Planet, scientists back on Earth would like to know when it overflies certain locations on the surface. How far does the MRO travel in one orbit? How long does an orbit take? How many orbits in one Earth day? Interesting questions [and, BTW, the answers are coming on March 16], but let’s take it further. Let’s make it a bit more 3-D and see how the NGSS come into play. 3-D learning brings the NGSS’ disciplinary core ideas (DCIs), crosscutting concepts (CCs), and science and engineering practices (SEPs) together, intertwining like strands in a rope. Usually, a performance expectation (PE) pulls all three together. For example, for this slice of pie we could look at this NGSS PE:
Students who demonstrate understanding can use mathematical or computational representations to predict the motion of orbiting objects in the solar system. (HS-ESS1-4)
This PE integrates an SEP (mathematical and computational thinking), a DCI (Kepler’s laws of planetary motion), and a CC (scale, proportion, and quantity). Now, depending on your own curriculum, your students, and probably many other things, you may need to tweak one or more parts of the PE. And if you’re a parent or an informal educator, you may not want to worry about specific PEs at all! However, the important thing is to focus on the three dimensions of SEPs, CCs, and DCIs: 3-D learning. Now, on to Slice 2.
Welcome to Titan! Saturn’s moon is covered with a hazy atmosphere, but scientists still hope to learn more about its surface. Now we need to use pi to calculate the percentage of Titan’s haze by volume, plus figure out the amount of surface area that a spacecraft would map. Like before, there’s mathematical and computational thinking (SEP) and perhaps some scale, proportion, and quantity (CC). For the DCI, how about solar system moons and atmospheres? What do your students want to know about Titan? Just remember to keep integrating the three dimensions of SEP, DCI, and CC. Ok, last two slices…
For our 3rd slice of pi, we backtrack a bit to Jupiter. The spacecraft Juno is on its way to our solar system’s largest planet, but it will need to slow down a bit to get into orbit. How much will Juno need to change its velocity? This gets kind of tricky, but we have an equation to use and our answer only needs to be an approximation. Whew! Mathematical and computational thinking? Yep. Scale, proportion, quantity? Got it. A DCI? How about gravity and its role in orbiting bodies? This is just one possible way to highlight this activity’s three dimensions.
Finally, we find ourselves back on Earth but gazing fondly towards the Sun… wearing proper eye protection, of course… us, not the Sun… Anyway, sometimes we can see Mercury or Venus cross the face of the Sun–a transit. When this happens, the amount of energy we receive from the sun drops slightly. But how much? During a transit of Mercury, how many fewer watts of solar energy get to Earth? This is another tricky one, but again we have an equation to use so we confidently forge ahead. We’re getting really good at this mathematical and computational thinking stuff. Same with scale, proportion, and quantity. This time, the DCI could be solar energy, but there are other possibilities, too.
So, if you’re in the classroom, get your students thinking with some NGSS 3-D (or today, 3.14159-D) learning! If you’re not in the classroom, sit down with your own kids (or just be selfish and have fun with these yourself) and enjoy some pi.
Slice of pi? Sure! I’ll take mine with ice cream and coffee…
For more on how NASA scientists use pi, and to download these four problems, read the JPL blogpost.
More on 3-D learning: What is Three-Dimensional Learning?