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Navigating the Hawaiian Canoe Through the Ocean

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Navigating the Hawaiian Canoe Through the Ocean High School: 10th-12th Grade NAVIGATING THE HAWAIIAN CANOE THROUGH THE OCEAN Why does the shape of the Hawaiian Outrigger Canoe varies? How do we differentiate between rounded and “V-shaped” hulls? How do we differentiate between speed and carrying capacity of canoes? by Milena Boritz Standard Benchmarks and Values: Mathematics Common Core State Standards (CCSS): • Geometric Definition of Parabola. • Equations of Parabola. • Analyze Parabola with Vertex at the Origin (0,0). • Differentiate Horizontal and Vertical Axis of Symmetry. • Focus of Parabola; Latus Rectum; Directrix. Nā Honua Mauli Ola (NHMO) Cultural Pathways: • ‘Ike Mauli Lāhui (Cultural Identity Pathway): Perpetuating Native Hawaiian cultural identity through practices that strengthen knowledge of language, culture and genealogical connections to akua, ‘āina and kanaka. • ‘Ike Honua (Sense of Place Pathway): Background/Historical Context: Demonstrating a strong sense of place, including a commitment to preserve the Polynesian voyaging canoes were built delicate balance of life and protect it for centuries ago. The voyaging canoes were generations to come. sailed from Western Polynesia, Samoa, towards Eastern Polynesia, Hawai‘i, between • ‘Ike Na‘auao (Intellectual Pathway): BC 500 – AD 600. The Polynesian voyaging Fostering lifelong learning, curiosity and canoes were designed to last long distances inquiry to nurture an innate desire to share and transport people, food, plants, animals, knowledge and wisdom with others. culture and traditions. • ‘Ike Ola Pono (Wellness Pathway): Caring Canoe designs vary extensively from for the wellbeing of the spirit, na‘au and island to island. Each island group had made body through culturally respectful ways that unique improvements to the canoe design to strengthen one’s mauli and build responsibility meet the challenges of local sailing conditions for healthy lifestyles. and timber resources. Major differences are observed in hull shape, paddle shape, sail • ‘Ike Piko‘u (Personal Connection Pathway): shape, number of hulls, and number of floating Promoting personal growth, development outrigger. The main differences in the shape and self-worth to support a greater sense of of a canoe hull originate from the practical belonging compassion and service toward purpose of the vessel – sailing or paddling. oneself, family and community. Sailing canoes require deeper keel - rounded “V”-shape, to provide a greater carrying Enduring Understandings: capacity and ocean stability for longer • Recognize parabolic shapes in everyday life. voyages, and in various wind conditions. • Identify horizontal or vertical axis of In contrast, paddling canoes are built with symmetry. rounded keels that have less depth than the sailing “V”-shaped hull. Paddling canoes are • Be able to apply equations of parabola. built for greater maneuverability that offers quick and easy turns. • Find the vertex, focus, directrix. Authentic Performance Task: Task #1: The Hawaiian paddling outrigger canoe has parabolic-shape hull (bottom). The waterline of a canoe is at focus, or at 0.125 feet height (waterline-to-bottom). The width at seat level is 1.6 feet. Find the canoe height (in inches) at seat level (seat-to-bottom). Navigating the Hawaiian Canoe Solution: Equation: Vertex: (0,0) Axis of Symmetry: Y-axis Focus: (0,0.125) Parabola: Opens Up Directrix: y = -0.125 Latus Rectum: F (0, 0.125) Width at Seat level: 1.6 feet Height at Waterline: 0.125 feet The height of the canoe is: 1.28 feet = 15.36 inches Task #2: The Hawaiian paddling outrigger canoe has its hull (bottom) shaped in a parabolic form. The waterline of a canoe is at focus, or at 0.1 feet height (waterline-to-bottom). The height of the canoe is (top-to-bottom) is 1.5 feet. Find the canoe width (in inches) on top. Solution: Equation: Vertex: (0,0) Axis of Symmetry: Y-axis Focus: (0,0.1) Parabola: Opens Up Directrix: y = -0.1 Latus Rectum: F (0, 0.1) Width at Top: 1.5 feet √ Height at Waterline: 0.1 feet The canoe width on top is: 2(x), or 2(0.7746) = 1.5492 feet = 18.6 inches. Milena Boritz Task #3: The Hawaiian paddling outrigger canoe has its hull (bottom) shaped in a parabolic form. The width at top of a canoe is 1.34 feet (top-to-bottom). The height of the canoe is (top-to-bottom) is one foot. Find the focus of the parabolic canoe hull (in inches). Solution: Equation: Vertex: (0,0) Axis of Symmetry: Y-axis Focus: (0,a) Parabola: Opens Up Directrix: y = - a Latus Rectum: F (0, a) Width at Top: 1.34 feet Height Top-to-Bottom: 1 foot The focus of a canoe is: 0.11225 feet = 1.3467 inches Task #4: Akela (Happy) and Kahewai (Flowing Water) keep their canoes in the same storage hale. Akela’s canoe is measurements are: width (beam) 1.5 feet and focus at 0.1 feet. Kahewai’s canoe is measurements are: width (beam) 1.6 feet and focus at 0.13 feet. a. If the waterline of Akela’s canoe is at focus, find the distance top-to-bottom of the canoe. Or, what is the depth of the canoe? b. If the waterline of Kahewai’s canoe is at focus, find the distance top-to-bottom of the canoe. Or, what is the depth of the canoe? c. Based on the above information, which of the two canoes has deeper keel and greater carrying capacity for long voyages? A. Solution: Equation: Vertex: (0,0) Axis of Symmetry: Y-axis Focus: (0,0.1) Parabola: Opens Up Directrix: y = - 0.1 Latus Rectum: F (0, 0.1) Width at Top: 1.5 feet Focus: 0.1 feet The depth of Akela’s canoe is 1.4 feet. Navigating the Hawaiian Canoe B. Solution: Equation: Vertex: (0,0) Axis of Symmetry: Y-axis Focus: (0,0.13) Parabola: Opens Up Directrix: y = - 0.13 Latus Rectum: F (0, 0.13) Width at Top: 1.6 feet Focus: 0.13 feet The depth of Kahewai’s canoe is 1.23 feet. C. Solution: Akela’s canoe is 1.4 feet deep; and Kahewai’s canoe is 1.23 feet deep. Evidently, Akela’s canoe is deeper and it has a greater carrying capacity than Kahewai’s canoe. Authentic Audience: Students, parents, and community members. The assigned tasks are designed to familiarize new paddlers with the canoe shape. The background information is designed to educate both students and their ‘ohana. Learning Plan: 1. Students visit a canoe club or a shipyard to 6. Examine the parabolic shape and analyze examine various canoe hulls. Field trip day for the Axis of Symmetry; Origin; Latus Rectum; credit. Directrix. 2. Listen to historical lecture on Hawaiian 7. Draw conclusion of Parabolic Equation voyaging and the cultural impact on the type. Apply Analytic Geometry knowledge Hawaiian people. and skills of Conics (Parabola) to the assigned tasks. 3. Paddle out on a sailing or paddling canoe to experience the outrigger Hawaiian canoe. 8. Visit the Bishop Museum Polynesian and Hawaiian exhibits. 4. Write a reflection about the paddling or sailing experience from the field trip day. 9. Perform research on Polynesian Students share their prior knowledge and skills voyaging canoes and present stories and to reflect the new experience. pictures to the classmates. 5. Draw a parabolic conic shape of a canoe 10. Prepare a group presentation on hull as if canoe body is bisected. popularity of Hawaiian canoes today. Milena Boritz References: Dierking, G. (2007). Building Outrigger Sailing Canoes: Modern Construction Methods for Three Fast, Beautiful Boats. McGraw-Hill Professional Pub. Davis, D. (1997). Build Your Own Canoe. Crowood Press, Ltd. West, S. (2013). Outrigger Canoeing: The Art and skill of Steering. Batini Books Pub. Holmes, T. (1993). The Hawaiian Canoe. Editions Ltd. D’Ambrosio, U. (2001). Ethnomathematics: Link between traditions and Modernity. Amsterdam: Sense Publishers. Navigating the Hawaiian Canoe.
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