Module 3: Sail Area and Perimeter

Transcription

1 Module 3: Sail Area and Perimeter US Sailing s REACH Program utilizes sailing as an educational platform, challenging youth to embrace education, establish a love of learning and explore productive Science, Technology, Engineering, and Math (STEM) based careers. Combining educators, sailing instructors, engineers, scientists with today s youth to provide them with a one of a kind authentic learning experience, giving students the opportunity to apply classroom learning in a cooperative work environment. Find out more information about US Sailing s Reach program. Purchase a full copy of the 10 module Reach Educator s guide. Register for US Sailing s one-day STEM Educator Course. Contact: Jessica Servis Reach Program Manager US Sailing JessicaServis@ussailing.org For more information visit: Reach.ussailing.org

2 Module 3: sail area and perimeter What shape are sails and why? Learn Sailing Right! Beginner Chapter 2 & Intermediate Chapter 3 Subject Areas Math (Pythagorean Theorem, Algebra, Geometry, Measurement, Conversion, Area and Perimeter) Physical Science Summary Students examine why most sails today are triangular in shape. They will investigate the properties of a right triangle, compute and compare sail area, and perimeter. Duration Lesson Time: Part I: 20 minutes Part II: 40 minutes Part III: 120 minutes Part IV: 40 minutes Skills Measuring, Computing, Collecting and Organizing Data, Estimating Measurements, Calculating Area Sailing Skills Rigging, Know your Boat, Parts of a Sail, Sail Shape and Control of the Boat, Basic Science of How a Sail Works Vocabulary Right Triangle, Hypotenuse, Leg, Pythagorean Theorem, Surface Area, Luff, Leech, Trade Winds, Foot. Standards See Standards Correlation Charts related to the National Standards. Common Core Standards relate to mathematics and the K-12 Framework for Science Education relate to Science. Objectives Students will: u Measure the area of a triangle. u Compute Pythagorean Theorem. u Review the parts of a triangle base, height, and hypotenuse. u Identify the parts of a sail, head, foot, luff, and leech. u Compare the sail area of a main sail and a jib sail. Module 3

3 Sail Area and Perimeter Materials One de-rigged instructional boat. Dinghy Main Sail (1 per group of 3) Dinghy Jib Sail ( 1 per group of 3) One Design Sail (1 per group of 3) Clipboards (1 per group) Measuring tape (1 per group of 3) Students sheets (1 per student) Calculators (1 per group) Sailing Centers Complete Parts I and II on day 1, with a lesson on rigging and de-rigging. Complete Part III on day 2. Students measure and calculate sail area and perimeter and then apply that knowledge to their sailing. The primary goal of this lesson is for students to connect math and sailing with engineering and design. Formal Classroom Settings Complete Parts I on day 1, review the classification of triangles with students. Have them practice solving problems using a square to find the area of a triangle. Complete Part II on day 2. You will need to contact your local sailing center to borrow a few sails. The size of the sail and the condition of the sail does not matter. Omit Part III. Implementent Part IV on day 4 and the Extension Activity on day 5. Career Connection Sail Designers, Marine Surveyors, Architects, Engineers, and even construction workers need to know geometry. Have students interview any of the previously listed professionals. Inviting a marine surveyor to bring in blue prints or CAD drawings they may be working on is a great connection for students. Please see the video links in reference to North Sails in the Resource section of the Module.

4 Module 3 Procedure Part I: Features of Sails Classroom - 20 minutes 1. Place the word sail on the board. Access Prior Knowledge: Ask students, Have you ever seen a sail before, what are they used for? and have a student draw one on the board. Ask students, What are some of the features of sails? When do you see sails? Originally, sails were rectangular in shape in order to use the wind to push boats forward. Sailors used the trade winds to leave from port and to eventually sail home again. Show students an image of an early sailing vessel with rectangular sails. 2. Ask students, What are some limitations of only using the wind to push your boat, downwind sailing? 3. Ask students, What shape are most of the sails we use at the Sailing Center? (triangular) Today we are going to calculate the area and perimeter of a few of our sails? What are some of the reasons we may want to calculate area of our sails? Generate student response: order new sails, to calculate the area of our sails to compare sail area to boat speed, or to identify situations in which sailors would benefit from reducing sail area. Why do certain sized sails go on certain boats? Part II: Measuring Surface Area of Sails Outdoor Classroom - 40 minutes Note: The main sails are not perfect right triangles, and kids may notice this. If they do, explain that you can still use right triangles to measure the existing sail area on the leech. 1. Tell students, Today we are going to learn more about our sails. We will calculate the area of the main sail and jib sail and the main sail of a laser or other sails. (Use sails that are easy to move and measure.) This is one way that we can use math in other parts of our life. 2. Roll out a sail and review the parts of a sail with the class. Relate the parts of a sail to your body, head at the top, foot at the bottom, then luff, leech, tack, and clew. 3. Ask students, How do we measure the perimeter and area of a sail? After students respond, put the formula for Sail area on the board. Area of a triangle = ½ Base (foot) * Height (luff.) Show students a rectangle is made of 2 triangles.

5 Sail Area and Perimeter ½ (10 * 5) = ½ ( 50 ) = 25 square feet = Area of the triangle 1. Measurement Review: Tell students, Today we are going to measure to the nearest inch. ½ round up to the nearest inch < ½ round down. Show students how a tape measure works. Remind them to slowly walk the end in and not to let it snap. The ends are sharp and you could get cut or smash your fingers. 2. Draw a triangle on the board and ask two students to help you find the perimeter and area of the triangle. Ask one student to be the recorder: taking down the measurements and the other to hold the end of the tape measurer. You as the instructor will read the measurements of the base and height of the triangle. Have the rest of the class practice rounding your measurements to the nearest inch. 3. Split class into groups of three; a recorder, measuring tape reader, and measuring tape holder. Ask students to measure the sail area of a main sail and jib sail, and one design sail. 4. Once students have measured and calculated the sail area of all three sails ask students to return to their individual clipboards and transfer their measurements. Next, they should calculate the sail perimeter. 5. From the data collected ask students to compare the sail area and perimeter. How does sail area impact our sailing?

6 Module 3 Part III: Sail Area on the Water On the Water minutes Note: This Part has two options. Option 1: Rig two dinghies, one with a reduced area sail (RAD) and one with a full size main. Option 2: Rig two keel boats reef one of the main sails. 1. While rigging review the parts of the sail (leech, luff, head, and foot) with the students. Ask students to predict how the different size sails will affect the boat s speed? 2. Discuss proper sail trim for up and downwind sailing. 3. Once on the water have boats 1 and 2 sail a windward leeward course. Both boats will start at the same time. This visual should show students that a boat with less sail area is slower and a boat with more sail area is faster. 4. While sailing students should help trim sails and possibly help skipper the boats. Once back on shore have students calculate the difference in sail area between the boats. As a challenge calculate the boat speed versus sail area. 5. After students have measured and calculated the difference in sail area ask them if there is ever a benefit to having less sail area. 6. have students make a connection to racing or cruising. For racers, in heavy winds you can not reef a 420 sail, but you can flatten the sail by tightening the vang and the outhaul which reduces the sail area. For cruisers, you can reef the main sail and the jib to depower your sails and still maintain control of the boat in heavy winds. Images: Reefed Main by spinnaker sailing.com Part IV: Pythagorean s Theorem Classroom/Docks - 40 minutes 1. Now that we have calculated the sail area of the sails we have, I have another challenge for you. Pass out Student Sheet US Sailing is designing a new boat. The new boat will need a sail. The sail will need to be 15 feet high and 8 feet long. Find the length of the hypotenuse using Pythagorean s Theorem a² + b²= c² Design and calculate the sail dimensions for the new design. (ANSWER: The hypotenuse is 17) 3. Take some time to review Pythagorean s Theorem and show students how to solve a sample problem. Leg a=2 Leg b=3 2²+3² =c² = c² 10 = c² 10 = c 3.16 =c

7 Sail Area and Perimeter 4. Using Student Sheet 3, explain to the students, their task is to design a main sail and a jib sail for a new sail boat. Please note: There are not any specific requirement for the dimensions of the boat. Using Pythagorean s Theorem, calculate the length of the foot, luff, and leech of the main and jib sails. Once you have the calculations for the production team at North Sails, please provide a rough sketch of the sails for the new boat. 5. When your design is complete please add a short paragraph explaining the benefits of your design and why US Sailing should use it. Resources How It s Made: North Sail One Design- video of how sails are made. ( Math.com area of a polygon ( Sailing Secrets From Larry Leonard - Charleston Race Week Video about adjusting new sails to boats. ( Extension Activities 1. have students research the evolution of sail shape throughout history. Ask students how sailboats affected trade and commerce throughout history?

8 Module 3 Module 3: Student Sheet 1 Sail Area Name: Date: Perimeter of a triangle = base + hypotenuse Area of a right triangle = ½ (base * height) Show all work. Sail 1: Sail 2: Sail 3: Luff Leech Foot Sail Perimeter Sail Area

9 Sail Area and Perimeter Sail Area Name: Module 3: Student Sheet 2 Date: Challenge: US Sailing is designing a new boat. The new boat will need a sail. The sail will need to be 15 feet high and 8 feet long. Find the length of the hypotenuse using Pythagorean s Theorem a² + b²= c². Design and calculate the sail dimensions for the new design.

10 Module 3 Sail Area Name: Module 3: Student Sheet 3 Date: Challenge: US Sailing is working with North Sails to develop a new boat design with new sails. Your task is to design a main sail and a jib sail for their new sail boat. Using Pythagorean s Theorem, calculate the length of the foot, luff, and leech of the main and jib sails. Once you have the calculations for the production team at North Sails, please provide a rough sketch of the sails for the new boat. When your design is complete please add a short paragraph explaining the benefits of your design and why US Sailing should use it. Please note: There are not any specific requirement for the dimensions of the boat.