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Standard Benchmarks and Values CCSS - MP4: Model with mathematics. MP5: Use appropriate tools strategically. NGSS MS-ESS1-1 - Develop and use a model of the Earth-sun-moon system to describe the cyclic patterns of lunar phases, eclipses of the sun and moon, and seasons.
NHMO - #1 ‘Ike Pilina (Relationship Pathway) #6 ‘Ike Na‘auao (Intellectual Pathway) TELLING TIME BY THE LIGHT OF MAHINA
Joél Nathansen
6th - 8th Grade Two classes
How can we use natural clues to perform an essential task (e.g., tell time)? Enduring Understandings Students will… • Define elongation as the measurement • Understand that local time is determined of angular distance (in degrees) between by the position of the sun relative to an a line of sight from an observer on Earth observer’s eye to the sun and a line of sight to any other • Identify by name the phases of the moon celestial object. – waxing crescent, first quarter, waxing • Understand that the phases of the moon gibbous, last quarter, waning crescent, depend on the measurement of the eastern and new. or western elongation of the moon from the sun. Critical Skills and Concepts • Being able to identify the moon • Being able to determine the time of night phases using both scientific and based on the moon. Hawaiian terminology.
Ethnomathematics 2 Authentic Performance Task • Position a student in the front of the classroom with a basketball representing the moon held outward at arm’s length. As the student, who represents Earth, and the “moon” turn slowly in a circle, illuminate them from the back of the classroom with a bright light source representing the sun. Randomly call out the names of various Hawaiian moon phases and ask the student to stop turning when the “moon” demonstrates that phase from the student’s point of view. Have the other students critique the correctness and accuracy of each phase demonstration. • To assess student understanding of the measurement of lunar elongation and its relationship to the phase of the moon, ask the student demonstrator to stop at various elongations, such as 90 degrees west elongation and 135
TASK degrees east elongation. Students should critique this demonstrator’s point of view. Have the demonstrator confirm or correct the class’s phase predictions. Authentic Audience Fellow classmates, friends, and family. Other Evidence Students will be able to… • share the tools created to determine the time using the moon. • identify the mahina according to the Hawaiian Moon Calendar.
Learning Plan Materials: • copies of Worksheets 1 & 2 and Templates publishing/multimedia/apps/mooncalendar/ A, B, C, & D for each student index.html) • Scissors • Online video about lunar phases (www. • Paste and/or tape youtube.com/watch?v=FhokvJZFURg) • Index cards • Mahina book (can be ordered from www. edithkanakaolefoundation.org/shop/ • Online Hawaiian lunar calendar (www. mahina/) kamehamehapublishing.org/_assets/
1. Explain that every culture on this planet has looked toward the heavens to help explain events on Earth. Without a precise calendar based on the apparent motion of celestial bodies through the sky, we would not know when to plant and when to harvest, and a civilization’s chances of survival would be minimal. The annual western calendar is further divided into months, recognizing the 29.5 day period of the moon’s phases. And finally, the days of our lives are marked by the daily rising and setting of the sun.
3 Telling Time by the Light of Mahina As humans learned to navigate this sphere we call Earth, it became necessary to divide the day into 24 hours so that ships at sea could determine the relative local solar time and longitude from that of their home port. Sundials
are simple clocks that help us to determine the approximate hours of the LESSON day while the sun is above the horizon. How can nature help us determine the approximate hour during the nighttime? We use the light of the moon! 2. Share the following mo‘olelo with students about how Hina came to live on the moon. Hina’s husband, Aikanaka was home on her. She was a goddess, but it again. He was not happy. Hina was was useless up here. She fell back happy living alone when her son to earth. Night fell and Hina left Maui came to visit. Aikanaka was a carrying a water calabash and her fearless warrior and a bold hunter, favorite kappa board and beater. but at home he was a teller of tall tales Aikanaka saw her and chased after and hard to please. He would always her. A moon-bow appeared before command to Hina to make new malo Hina and she set foot on it, but for him and he always commanded Aikanaka grabbed her ankle and her to get fresh food and water. One twisted it. Still climbing in pain, day Aikanaka commanded Hina to Hina reached the moon. get him freshwater shrimp. While in She still lives there to this day. the river a rainbow formed in front When thunder rumbles, it is Hina of her. She looked at it longing. She rolling away the stones that keep walked to the foot of the rainbow, her kapa in place. On full moons you took a step, and it held fast. She can still see her resting, with her kept walking, but the sun beat down twisted ankle.
3. Tell your students that in this activity they will be learning the phases of the moon. They will also learn how they can use the moon’s position relative to the horizon and to the sun to determine the approximate hour of the night. Students will create a “flip book” of photographs showing various stages of the lunar phases. a. Print out the 26 lunar phases on Worksheet 1: “Lunar Phase Flip Book.” b. Cut out each picture and paste it to the edge of an index card. Arrange the 26 cards in order and staple them together at the top of the cards. As the students flip and view the animation, have them make a distinction between that part of the phase cycle characterized as “waxing” and that part characterized as “waning.” Using the cards, have the students identify the phases as new, waxing crescent, first quarter, waxing gibbous, full, waning gibbous, last quarter, and waning crescent. With either the book Mahina or a Hawaiian Lunar Calendar, have students identify and record the Hawaiian name to each of the phases. c. The phase of the moon in dependent on the angular distance between it and the sun (which illuminates the moon). Depending on whether the moon is to the east or the west of the sun, this angular distance is called the eastern elongation or western elongation. For example, when the moon is in the first quarter phase, it is at 90 degrees eastern elongation from the sun. d. Watch a video to review the causes of lunar phases with your students, and then try Worksheet 2: “Lunar Phases and Elongation from the Sun.”
Ethnomathematics 4 4. By observing and naming the current phase of the moon, the elongation from the sun can be estimated. This elongation estimate will help to locate the position of the sun somewhere below the horizon. Since it is the position of the sun that determines the local time in hours, we can estimate the hour of the night without actually “seeing” the sun.
a. Print out Template A: Telling Time with Phases of the Moon. b. Print out Template B: Telling Time with Phases of the Moon. c. Follow the instructions on each template and assemble them. Place a thumbtack through the center dots so that Template B can rotate on top of Template A. Use the completed construction to review the meaning of local solar time. Local solar time is determined by the position of the sun. Whenever the sun is located, above or below the horizon, determines the approximate local solar time.
LESSON 5. Once the students become comfortable with determining the local solar time with the device constructed in part 4, pass out Template C: Telling Time with Phases of the Moon and add it to the previous assembly. The final assembly should look like this:
Note All three templates may be printed onto pieces of overhead transparency film that are suitable for use with an ink-jet or laser printer. If this is possible, the teacher may find it more convenient to instruct students on how to use the device to determine the local solar time with the aid of an overhead projector.
Image from Discovery Education
6. This devise can also be used for determining the hour of the night by observing and naming the current lunar phase. Find the identified phase on your template circle using the lunar phase images. Turn the lunar phase template until the correct lunar phase image is roughly over the horizon template in the same was as it appears over the real horizon. Determine the elongation from the sun for this phase, and rotate the sun template carefully (without rotating the moon phase template) until it is at the determined elongation. Read the hour of the night from the clock printed on the horizon template.
5 Telling Time by the Light of Mahina Example Imagine that you are viewing a waxing gibbous moon located directly above the southern point on your horizon. Place the image of the waxing gibbous moon on the lunar phase template directly over the southern point on the horizon template. When the moon is waxing gibbous, it has a 135-degree eastern elongation from the sun. Taking care not to move the moon image template, rotate the sun template approximately 135 degrees away from the image of the waxing gibbous moon so that the moon will be properly placed at 135 degrees east of the sun. Read the hour of the night shown next to the sun. If you have carefully followed these instructions, the time should read 9:00 p.m.
7. As an extension, print out Template D: The Hawaiian Star Compass. Students can add the Compass to determine which house the moon is. References • Kamehameha Schools. (n.d.). Mahina. Retrieved from http://kms.kapalama.ksbe.edu/ projects/ahupuaa/kaneohe/kan/kan20mahina/index.html. • Latham, T. (2014). Telling time by the light of the moon. Retrieved from http://www. discoveryeducation.com/teachers/free-lesson-plans/telling-time-by-the-light-of-the- moon.cfm. • Thompson, N. (n.d.). Star compass. Retrieved from http://pvs.kcc.hawaii.edu/images/ navigation_and_weather/star_compass_plain.gif.
Ethnomathematics 6 http://school.discoveryeducation.com/lessonplans/worksheets/lightofthemoon/worksheet1.html 7 Telling Time by the Light of Mahina http://school.discoveryeducation.com/lessonplans/worksheets/lightofthemoon/worksheet2.html Ethnomathematics 8 http://school.discoveryeducation.com/lessonplans/worksheets/lightofthemoon/worksheet3.html 9 Telling Time by the Light of Mahina http://school.discoveryeducation.com/lessonplans/worksheets/lightofthemoon/worksheet4.html Ethnomathematics 10 http://school.discoveryeducation.com/lessonplans/worksheets/lightofthemoon/worksheet5.html 11 Telling Time by the Light of Mahina Telling Time by the Light of Mahina HAWAIIAN STAR COMPASS BY NAINOA THOMPSON Template D
http://pvs.kcc.hawaii.edu/images/navigation_and_weather/star_compass_plain.gif Ethnomathematics 12