Kempsville High School

APPLIED GEOMETRY (PBL COURSE)

Alina Dougherty, Chelsea Kimbrough, JENNA FILIPOWICZ

A Project and Problem Based Learning Course

This Geometry team is interested in transforming their traditional geometry classes into a completely project-based course. With the removal of an SOL test, they plan to explore other methods of assessment to engage their students in more meaningful, cross-curricular and authentic tasks. They have outlined several possible tasks and worked with T&L to secure approval. They initially signed up for the innovation squad because they are interested in transforming their classrooms physically. The traditional classroom setting is not conducive to the collaborative style and nature of an authentic project-based course. They prefer the collaborative seating and presentation stations in the Academy's lab spaces and notice a significant difference in student productivity and effectiveness in comparison to their traditional classrooms.

After meeting with this group, we discussed some possibilities for curriculum design including some early ideas for sharing PBL projects virtually. This group is pioneering some asynchronous tasks through Defined Learning where the students work through tasks independently and submit work digitally for feedback from the teacher. The group has a fully developed curriculum and are currently working on flexible plans to implement the projects in the fall based on developing COVID conditions.

Asking students big questions and allowing students time to collaboratively wrestle with them is at the heart of this course. How is origami being used by NASA to deploy space sails and where can we find our basic Geometry vocabulary embedded in this process? Why are quadrilaterals important to automotive engineers and furniture designers and, how can exploring quadrilateral attributes with exploragons help solidify these important principles? What happens to planar Geometry vocabulary terms when they go 3D? Let's build a planetarium out of isosceles triangles to find out. Or, maybe an augmented reality sand table to estimate mountain erosion or glacial melting to explore Surface Area and Volume changes. Which VB High Schools have food deserts? Embed a map in Desmos. Identify all the grocery stores. Label the coordinates and use them to draw circle equations. Voila!

Applied Geometry - Where the process of Problem Solving is more rewarding than knowing the "Right" answer.

Team Building - Use materials in the classroom to lift the cup off of the paper without anyone touching it?
It's OK to be Different - How many triangles, pentagons, hexagons are required to make a ball? Be prepared to explain your process to the class and quantitatively compare your ball with another group's.
Use precise words precisely - How does the radius change as you move around a pine cone spiral? Is the term "radius" exact enough or do we need a new term?
Challenges worth completing are not done in isolation: Make a personal cell phone hologram projector from an old CD case or lamination paper. Task: create four congruent isosceles trapezoids with base lengths of 12mm and 61.5mm and diagonal length of 43mm. Use your knowledge of right triangles, quadrilateral attributes, parallel lines and angles to accomplish this task. Precision is the key to clear images on your projector.

Teamwork doesn't just happen. It must be intentionally curated.

Task: Create a map that redesigns a section of Virginia Beach. Draw it in painter's tape on a white board. Label all lines and angles with accurate vocabulary and measurements. Define roles for each team member. Track roles and results on a DO - DOING - DONE chart that is shareable with the group and your teacher. Finally, create a presentation (and share it with the class) that highlights the Who, What, Where, How, Why and When of your project.

“Student engagement is the product of motivation and active learning. It is a product rather than a sum because it will not occur if either element is missing.”

― Elizabeth F. Barkley

Students will learn about the history, art, and real world applications of origami while learning geometry vocabulary. Each student will fold origami of their choice and find the geometry vocabulary embedded in their art.

Student Choice

Vocabulary in Origami

Student Engagement

Unfold and Discover

There are endless possibilities in mathematics. Our goal is to cultivate sensemaking and out-of-the-box thinking, and inspire the next generation of creative mathematical thinkers.

Connecting the community and mathematics -- Students will use tessellations to design a mural for the "There's Something in the Water Festival" for the main stage. Students may use works of MC Esher for inspiration and follow the theme "i am OTHER... R U?". Explain and justify the mural and its meaning.

Infinite HALLWAY

"I created an infinite school hallway to go with the slogan 'i am OTHER...R U?' I did this because this is where most people get their ideas of what they are going to do in their future because they have their own dream or are trying to become someone else's vision that they see of them. So picture this, you are constantly running down the hallway trying to find the right path and it goes on forever and ever until you finally realize you have been running in the same spot the whole time and you see that your locker is the key to your dreams. Find your true self and express it."

Learning is possible with multiple pathways to demonstrate learning.

Exterior angle sum theorem

INterior angle sum theorem

Exterior and interior Angle Sum theorem

Next project

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