Focusing on the M in STEM: Preparing for Math Exams

Most students in the Academy of Aerospace and Engineering are studying for either Algebra I (Honors) or Geometry (Honors) exams to be taken this Wednesday. These mid-term exams will test their knowledge on all the content covered since the start of the school year. While the academy students are in middle school, which does not have exams, because the math classes are for high school credit, they require exams. To prepare for the exams, we have used a thick review guide provided by the math department in each class, and we had IXL strands for each unit. My approach has been to show the students how to break down this review into two or three day units, each of which is checked and covered before we move on to the next unit. The responsibility is mainly on the students, as I post my solutions to each unit of the review and let the students check their work against mine. Today we covered the last unit, and I am very proud of the students’ efforts to keep up with work and do a thorough job of review.

Focusing on math means that our usual approach of integrating all STEM (science, technology, engineering, math) classes has not been as strong as usual. Therefore, I have used this time instead to focus on how to apply what we have done for the math exam review as a model for other, future big projects. Big projects usually can be broken into smaller parts, each of which is easier to tackle and manage than the project as a whole. After we finish exams, I will ask the students to reflect on what they learned throughout this process so that they can get the maximum benefit from the experience. Here are photos of both 7th graders in Algebra and 8th graders in Geometry as they study and review in class:

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Integrated STEM Project: Designing Sundials

The 8th grade students at the Academy of Aerospace and Engineering have just completed an integrated STEM (science, technology, engineering and math) project where each crew (student groups of four to five students) designed a sundial, built a model of it, tested it, and presented it to Mr. Dias, our current Assistant Principal and next year’s Principal at John Wallace Middle School. The requirement given to the students was to design a sundial with an aerospace theme that could be built on the school grounds outside the academy. Mr. Dias saw all the designs presented, then he chose what he believed was the best design that would complement our school. The winning design, by Crew 4, uses a person as the gnomon (the part of the sundial that casts the shadow) and directs the person to stand on different places on the sundial, depending on the time of year, in order to accurately depict the time year-round.

So what makes this an “integrated project?” Integration means applying what is learned in one class to a problem in another class, or connecting concepts across two or more classes. We do this type of learning every day in the academy, and this project was especially integrated. The 8th graders have learned about the Solar System and how the Sun, Moon and planets move across the sky from an Earth observer’s point of view–they applied this knowledge to the sundial since the Sun changes its position in the sky not only hour to hour, but also day to day. The students used astronomy software to plot the Sun’s position every hour from 6:00AM to 6:00PM on both the summer and winter solstices and on the spring and fall equinoxes. They used this information to design the hour lines on their sundials. Drawing these lines required knowledge of circles, which is the unit in geometry we are studying–so students applied their knowledge of central angles and angular motion to design the sundial’s face with its hour lines. Half of the students are also studying air navigation, including latitude and longitude, so they applied that knowledge to the problem of designing the gnomon whose angle depends on latitude. Finally, the students applied what they have learned the past two years in the academy about the engineering design process and presentation skills. All of these connections made this a highly integrated project.

Here are photos of each crew with models of their sundials:

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Crew 1’s design would be on a pillar and is based on the academy logo with the gear as the sundial’s base and the red arrow as  the gnomon.
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Crew 2’s design would be on a pillar and has an aerospace theme with celestial objects marking each hour.
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Crew 3’s design uses the current academy sign, shaped like an aircraft tail, as the gnomon, then rocks in the ground would mark the hour lines.
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WINNING DESIGN – Crew 4’s design would be laid out in the ground with pavers and requires a person to stand as gnomon on the appropriate month to cast a shadow and give the time.
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Crew 5’s design is a large cement slab sundial in the ground with a gnomon shaped like an aircraft wing.
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Crew 6’s design would be on a pillar and has interchangeable disks for each season  so that the sundial is accurate year round.