Math in Waʻa: Examples of math in waʻa and navigation

At the site of the Star Compass, begin by attaching kaula to the flag pole using a bowline, making sure the length of the kaula reaches to the end of the outer circle or longer. Keep this kaula attached for the remainder of the lesson.

Using a modern compass (a cell phone with a compass is good), stand at the flagpole and move around the base until you are facing North (ʻĀkau). Ask a student to hold the kaula tight on the ground in the direction of North. Trace over this line with chalk to mark the direction. Repeat the steps for the remaining cardinal directions: East (Hikina), South (Hema), and West (Komohana).

Now that we know East (Hikina) and North (ʻĀkau), ask students what is the next house we locate and why? Ans: We locate Manu because it is halfways between Hikina and ʻĀkau.

In the other days when we practiced building the Star Compass, we just estimated where halfway is, but we need to be precise. How do we find where halfway is between the Hikina and ʻĀkau? Let students discuss. If necessary, use the kaula to connect the part where Hikina intersects the outer circle to the part where ʻĀkau intersects the outer circle.

Now that students see the line, ask how to find halfway on the line? Although using a measuring tape to find the length and dividing that measurement in half does work, a simplier solution would be to fold the kaula in half. Before doing this, trace the line with chalk. Now you can fold the kaula in half to determine the halfway point on the kaula which is the halfway point on the line between Hikina and ʻĀkau. Use chalk to mark this halfway point.

With the kaula that is secured to the flag pole, extend it through this point to the outer circle and trace the line with chalk. This line is the center of the house Manu. You may also erase the chalk line connecting Hikina to ʻĀkau.

The next house to be located is ʻĀina, which is halfway between Hikina and Manu.

Using the method of locating halfway that we used for Manu, we will start by connecting kaula from the point where Hikina intersects with the outer circle to the point where Manu intersects with the outer circle, and using the method of folding the kaula in half, locate the halfway point, marking it with chalk. Note: it is important that you are using the points that intersect the outer circle.

Extend the kaula attached to the flag pole over the point you just marked and to the outer circle. Trace this line with chalk. This is the center of the house ʻĀina. You may erase the chalk line connecting Hikina with Manu.

Using the methods we learned in Lesson 1, Continue this process until the center of all the houses are marked.

You may want to clean up the area and erase the house lines that are between the flag pole and the inner circle.

Now that we found the center of the houses, we are ready to locate the boundaries. To locate the boundary between Hikina and Lā, we use the method of connecting the intersection of Hikina and the outer circle to the intersection of Lā and the outer circle, then find the halfway point, and extend a line from the flag pole, past this point to the outer circle.

Repeat this process of locating the boundaries for all houses.

We now have the outline for each house and can paint over the chalk outlines for the house boundaries.

The outline of the Star Compass is complete. Now you can decorate and color the Star Compass and add the names of the houses and quadrants.

The first step is to draw the circle. Begin by identifying the center of the circle, this is the flagpole.