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Math in the Waʻa:
Lessons in Mathematics and Navigation
Kamuela E. Yong
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Front Matter
Colophon
Preface
I
Lower Elementary
1
ʻUmeke Poi Math
1.1
Materials
1.2
Student Learning Objectives
1.3
Student Learning Outcomes
1.4
Core Standards
1.5
Introduction
1.5.1
Cultural Connection of Poi
1.5.2
Mathematical Context (Teacher Notes)
1.6
Guided-Practice
1.7
Independent Practice
1.8
Reflection
1.9
Extension
II
Upper Elementary and Middle
2
Estimating Speed
2.1
How do we measure speed
2.2
Measuring the speed of a waʻa
2.3
Magic Speed Number
2.4
Classroom Activity
3
Four Quadrants
3.1
Micronesia
3.2
Hawaiʻi
3.3
Direction
3.4
Lesson: Cartesian Plane and Hawaiian Star Compass Symmetry
3.4.1
Objective
3.4.2
Materials
3.4.3
Procedure
3.4.4
Assessment
3.4.5
Homework
4
The Cartersian Coordinate System and the Hawaiian Star Compass
4.1
Student Learning Objectives
4.2
Student Learning Outcomes
4.3
Core Standards
4.4
Introduction
4.5
Classroom Activity
4.6
Extensions
4.7
Exit Ticket
5
Ratios: Anchoring
6
Star Compass
7
Making a Scale Model
7.1
Scale Model
III
High School
8
Trigonometry
8.1
Trigonometry Through Wayfinding and Navigation Across the Pacific
9
Deviation
10
Geometry: Kūmau (North Star)
10.1
Student Learning Objectives
10.2
Student Learning Outcomes
10.3
Core Standards
10.4
Introduction
10.5
Geometry Explained
10.6
Classroom Activity
10.7
Extensions
10.8
Exit Ticket
10.9
Alternate Diagrams
IV
Star-Compass-Construction
11
Lesson 1: Locating the Houses of the Star Compass
11.1
Introduction/Review of the Star Compass (25 mins)
11.2
Discussion on the Physical Properties of the Hawaiian Star Compass (5 mins)
11.3
Understanding the Relationship between Houses and Degrees on the Star Compass (5 mins)
11.4
Constructing One Quadrant on the Board (10 mins)
11.5
Angles on the Star Compass (10 mins)
11.6
Spacing Between Houses (5 mins)
12
Lesson 2: Boundaries of the Star Compass
12.1
Preparation in the Classroom (5 mins)
12.2
Outdoor Activity: Constructing the Star Compass with Students as Houses (20 mins)
12.3
Classroom Review of Outdoor Activity (10 mins)
12.4
Lesson 1 Review and Boundary Claculation (25 mins)
13
Lesson 3: Drawing the Circle
13.1
Classroom: What is a Circle
13.2
Outside: Making a Circle
13.3
The Star Compass Circle
13.4
Summary
13.4.1
What is a Circle
13.4.2
Outside: Making a Circle
13.4.3
The Star Compass Circle
14
Lessons 4 and 5: Installing Star Compass Houses
14.1
Cardinal-Directions
14.2
Finding-Manu
14.3
Finding ʻĀina
14.4
Finding the Center of the Houses
14.5
Locating the Boundary between Hikina and Lā
14.6
Locating House Boundaries
14.7
The Finished Star Compass
Backmatter
Math in the Waʻa:
Lessons in Mathematics and Navigation
Kamuela E. Yong
Math, Natural, and Health Sciences
University of Hawaiʻi - West Oʻahu
October 14, 2025
Colophon
Preface
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