1. Recognizing the STEM in mathematics Supporting Common Core & Mathematical Practices A Fourth Year Course

2.  A person gathers, discovers or creates knowledge in the course of some purposeful activity set in a meaningful context.  Improve understanding and motivate.

3. Provide meaning to mathematics through activities that have a real purpose- Provide an answer to the question: When am I ever going to use this? Solve problems in a STEM context. Bring meaning through purposeful activities

4. From the Common Core Document under Mathematics: Standards for Mathematical Practice 4. Model with mathematics. “Mathematically proficient students can apply the mathematics they know to solve problems arising in everyday life, society, and the workplace. “

5. “They routinely interpret their mathematical results in the context of the situation and reflect on whether the results make sense, possibly improving the model if it has not served its purpose.”

6. FOCUS LOSS of : Width, Motivation, Applications Loss of: Depth Efficiency Elegance

8.  A Driving Question- drive critical and creative thinking!  Significant Content & Connects to Standards  Meaningful  Mock Scenario  Voice & Choice  21 st Century Skills  Conduct Real Inquiry  Feedback & Revisions

9.  Problem:  Problem: You and your partner are surveyors and are asked to provide an accurate survey of a plot of land of your choosing.  Geometry- Polygons, convex and concave, parallel lines, alternate interior angles.  Orienteering  Using a compass to create the plot and test the region.  Trigonometry  Pythagorean Theorem, Right Triangle Trig, Law of Sines and Cosines, Area and Triangulation.

10. To test their orienteering skills, we go out into the wild! Surveying their plot of land.

11. When am I ever going to use cell phones in class?!

13. A great real-life application of trigonometry.

14. Applying the trig.Reflecting on the results

16. …Oops! There was a big problem with how our course wound up looking. There was a big problem with how our course wound up looking.

17. Spot on! Our Map vs Google Earth Comparison

18. Solving yields the answer 150.2 ft when rounded to the nearest tenth as instructed. Solving yields the answer 150.2 ft when rounded to the nearest tenth as instructed. The process is repeated for the other missing side. The process is repeated for the other missing side. Using Law of Sines 150.2ft

19.  Pythagorean Thm  Alternate int. angles, corresponding angles  Triangle-Angle_Sum Thm  Parallel lines  Soh Cah Toa  Law of Sines  Law of Cosines  Area of triangles  Non right triangles-icky ones too!  Measurement and measuring tools  Dimensional analysis  ?

20.  Problem: Design and build a car so as to determine its acceleration using a variety of methods.  Functions  Constant, Linear, Quadratic. Function notation as it applies to physics.  Technology  Authentic Data Collection, graphing calculators, motion detectors.  Physics  1-Dimensional Kinematics

21. Kelvin.com is a wonderful source for technology and finding cool things to build. You can get great ideas there too! Building the Car

23. It’s a team effort. After data is collected students decide through applying their new skills and knowledge if the data is “good” data. The Set Up

24.  How do you know you have “good” data?  The following are from student reports.

25. Acceleration GraphDistance time graphVelocity time graph Constant graph, as time increases, acceleration remained the same. As time increases on a distance time graph, so does the distance, quadratically. Linear graph, when time increases, velocity does also at a constant rate.

26. D(T)= ½aT^2 + V 0 T + D 0 a (lead coefficient) = acceleration V 0 = initial velocity T = time D 0 = initial distance My Data D(T)= (.31)T^2 + (-.51)T +.62 Acceleration =.62 m/s/s Doubled lead coefficient to find this.

27. V(T) = aT + V 0 a = acceleration V 0 = initial velocity T = time My Data V(T) =.63T + (-.534) Slope =.63 m/s/s Acceleration = change in velocity/change in time

28.  Xbar = ave acceleration  Constant function  Average Acceleration =.62 m/s/s

29.  Look at the next slide carefully…  What do you notice?  What do you think happened?

30. D(T)= -.312T 2 +2.136T-.993 Acceleration = a(2) = -.624 m/s

31.  Modeling Arctic Sea Ice –open questions ◦ When do you think sea ice will be gone? ◦ At what rate is it decreasing? How fast? ◦ What month is most important to study and why? ◦ Is Climate change real? Causes? ◦ Why is it important? ◦ How was it caused? ◦ Weather verses climate? ◦ Cryosphere- where is it ? Why is it important? ◦ World Politics?

32.  Build content knowledge through research ◦ Internet research at several reputable websites  NSIDC, NASA, NOAA ◦ Film : “NOVA: What’s Up with the Weather”  Build mathematical skills through activities and other related data sets ◦ Graphing calculator for small set, Excel for larger ◦ Interpolation, extrapolation, meaning of slope as an average rate of change. ◦ DATA, DATA, DATA and more DATA

35.  Global Temperature Changes ◦ Visual Engagement- What do the graphs show? ◦ What could we ask?

36. Relative Etrema Observations? What about local anomalies? Averaging? How is the data collected? This graph illustrates the change in global surface temperature relative to 1951-1980 average temperatures. The 10 warmest years in the 134-year record all have occurred since 2000, with the exception of 1998. The year 2015 ranks as the warmest on record. (Source: NASA/GISS).NASA/GISS

37. What does the comparison show? Can you determine which graph is closest to the Arctic? Why? Not the same for everyone! Connect to previous images.

38.  Access the data and apply linear regression  NASA Vital Signs makes it easy to download data for analysis  Supports practice for working with large TXT files. Need for Excel. NSIDC data

39.  Apply knowledge to Arctic sea ice open ended question.  What month of data is best to examine and why? How does sea ice change over time? What are the impacts of this change?  Prepare your findings in present to the UN Committee on Climate Change

40.  Questions?  NASA Sources are excellent  Space Math has an entire unit on climate change and sea ice. Most enjoyable course EVER! Please feel free to contact me -