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Math in Waʻa: Examples of math in waʻa and navigation

Kamuela E. Yong

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Section 2.2 Lesson 2: Boundaries of the Star Compass

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This lesson will spend some time outside, creating a Star Compass where students are the houses.
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Subsection 2.2.1 Preparation in the Classroom (5 mins)

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Before heading outside, it’s essential to make some preparations. Depending on the number of students, determine whether you will construct one or two quadrants of the Star Compass (Koʻolau and Hoʻolua). If there are fewer than 17 students, you will do just one quadrant, Koʻolau. If you have fewer than 9 students, you will still do Koʻolau, but you will need additional objects to stand in for houses, such as water bottles. If you have 17 or more students, then you will construct the two northern quadrants: Koʻolau and Hoʻolua.
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Assign each student (or water bottle, if needed) to a specific house, specifying the quadrant. If more students are present than houses, consider assigning some as helpers who will determine if students are standing exactly halfway between houses or designating one as the center of the Star Compass. Keep in mind each student’s ability to stand still when assigning houses since students assigned to Hikina, Manu, and ʻĀkau will be standing the longest and those assigned to Lā, Noio, Nālani, and Haka will be standing the shortest.
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Subsection 2.2.2 Outdoor Activity: Constructing the Star Compass with Students as Houses (20 mins)

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  1. Setting Up
    • Head to an open space, preferably with markings like a basketball court for better identification of angles.
    • Designate a center for the Star Compass and have a student stand there.
    • Identify Hikina, either by determining the true East (preferred) or by pretending a direction is East.
    • Walk 10 steps in the direction of Hikina and have the student assigned to Hikina stand there.
    • Return to the center and walk 10 steps in the direction of ʻĀkau, placing the student assigned to ʻĀkau at that spot.
  2. Locating Middle House (Manu)
    • Ask students which house is in the middle between Hikina and ʻĀkau (answer: Manu).
    • Have the student assigned to Manu Koʻolau stand halfway between the students representing Hikina and ʻĀkau.
    • Ensure that the class verifies that this student is precisely halfway or adjust positions if needed.
  3. Continuation for Other Houses
    • Repeat the process for the remaining houses, ensuring each student stands exactly halfway between their neighboring houses.
    • Use water bottles if necessary to mark positions for the next house.
  4. Constructing the Entire Star Compass
    • If constructing two quadrants, repeat the process for the Hoʻolua quadrant.
  5. House Positions
    • Emphasize the concept that each student is standing at the center of their houses.
    • Before students leave their positions, ask them to identify where the boundaries of their houses begin and end. This should be at the halfway point between neighboring houses.
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Remind students that they have constructed their own Star Compass and that the boundaries of their houses extend halfway to the neighboring houses.
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Return to the classroom for further discussion.
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Subsection 2.2.3 Classroom Review of Outdoor Activity (10 mins)

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Back at the board in the classroom, review the outdoor activity.
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  1. Drawing the Blank Quadrant Koʻolau
    • Draw the blank quadrant Koʻolau on the board.
  2. Recapping Steps
    • Have students recap the steps taken outside to find the position of the boundaries for the houses.
    • Steps:
      • Finding the center of the houses by halving the distance between neighboring houses.
      • Once the positions of all houses are found, finding the midpoint between house centers to determine the boundaries of the houses.
  3. Marking House Positions
    • Ask students to mark on the quadrant where the houses and house boundaries are located, based on their outdoor activity.
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Subsection 2.2.4 Lesson 1 Review and Boundary Claculation (25 mins)

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  1. Review of Lesson 1
    • As a review of Lesson 1, give students time to calculate the angle for the center of each house individually.
    • Discuss their methods and review the answers as a class.
  2. Calculating Angles for Boundaries:
    • Prompt a discussion on how to find the angle of the boundaries.
    • Individual Calculations
      • Ask students to first determine the boundary between Hikina and Lā. (answer: 5.625∘)
      • Next, determine the boundary between Lā and ʻĀina. (answer: 16.875∘)
    • Group Discussion
      • Have students share their methods for arriving at the answers.
  3. Determining Boundaries for All of Quadrant Koʻolau
    • Ask students to calculate the boundaries for all houses in quadrant Koʻolau.
      Figure 2.2.1. The quadrant Koʻolau for the Star Compass, with the angles labeled for the center of each house.
    • Discuss the results as a class, allowing students to share their approaches and insights.
  4. Completing the Star Compass
    • Pptions for students to complete the angles for the center and boundaries of houses for the entire Star Compass:
      • Individual completion.
      • Group assignment (assigning specific quadrants or the entire Star Compass).
      • Homework assignment.
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Figure 2.2.2. The Star Compass, with the angles labeled for the center of each house.
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Figure 2.2.3. The Star Compass, with the angles labeled for the center of each house.
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