Grade 10 - Math

In addition to the HFCS ‘Āina-based Learning Competencies (click to view), the PK-12 Mathematics Kahua is grounded in the belief that the purpose of math is to search for patterns and relationships in number, shapes and functions, to better appreciate the beauty of math in our world. It is the kuleana of every student to explore mathematics in their daily lives on ‘āina and share mo’olelo of their understanding. End of school year grade level benchmarks were crosswalked with the HFCS Vision of the Graduate (2013), CCSS, Nā Ana Aʻo Hawaiʻi DOE Kula Kaiapuni Content Standards and Benchmarks (Nā Ana ma ka Papa K-12), Student Achievement Partners (SAP) Essential Standards documents K-12, NCTM Catalyzing Change. K-12, Prioritizing Critical Areas In your Math Curriculum K-8 Prerequisites for Success, ALN High Leverage Concepts, CA Digital Learning Integration & Standard Guidance Jo Boaler & Cathy Williams and were prioritized using the following criteria (Reeves, 2004): 1) Endurance, 2) Leverage, 3) Readiness, 4) Assessment Requirements.

I. Sense of Place: ʻĀina Learning Competencies

Overarching goals for ʻāina-based curriculum designed to connect the learner to their cultural, linguistic and physical community

II. Sense of Belonging: Mathematical Practices - http://www.corestandards.org/Math/Practice/

Varieties of expertise students should develop and rest on important processes and proficiencies with longstanding importance in mathematics education.

III. Sense of Belonging: Discovering Shape and Space

Explore triangle congruence including congruence theorems, circle relationships and transformations and geometric models. Use coordinates to prove simple geometric theorems algebraically.

IV. Sense of Community: Taking Wholes Apart, Putting Parts Together

Investigate triangle congruence and transformations.

V. Sense of Community: Exploring Changing Quantities

Explore points & slopes, triangle congruence and problems, circle relationships and engage in trigonometry explorations. Interpret the structure of expressions and create and solve equations and systems of equations that describe numbers or relationships. Interpret, construct and compare linear, exponential, quadratic and exponential functions (models) that arise in applications in terms of the context. Analyze and solve functions using different representations.

VI. Sense of Responsibility: Communicating Stories with Data

Summarize, represent, and interpret data with variables. Understand probability modeling, explore fairness in data and investigate geospatial data.

M.G.1Analyze and cite moʻolelo from a variety of primary and secondary resources (i.e. mele, nūpepa, websites, books, ʻohana) to deepen understanding about the moʻokūauhau of our ʻāina.
M.G.2Utilize kilo in various communities and expand observations through the use of ʻōlelo Hawaiʻi to describe patterns of wahi pana interdependence (i.e. ahupuaʻa, ecosystem, loko iʻa).
M.G.3Discern between and lead appropriate protocol in age/kuleana appropriate ceremonies and protocols.
M.G.4Utilize and mālama wahi pana resources (i.e. pāhonu, limu, salt beds, mala, kupuna, water, kiʻopua) to aloha ʻāina.
M.G.5Understand multiple perspectives to better empathize and collaboratively formulate solutions based on kānaka genealogy of that place (i.e. kupuna, ʻāina partners, state/federal agencies, institutions of higher education, law).

M.G.6Make sense of problems and persevere in solving them.
M.G.7Reason abstractly & quantitatively.
M.G.8Construct viable arguments and critique the reasoning of others.
M.G.9Model with mathematics. ✰Critical emphasis to connect to ‘Āina Learning Concepts
M.G.10Use appropriate tools strategically.
M.G.11Attend to precision.
M.G.12Look for and make use of structure.
M.G.13Look for and express regularity in repeated reasoning.

M.G.14Triangle Congruence: Investigate triangles and their congruence over rigid transformations verifying findings using triangle congruence theorems (ASA, SSS, SAS, AAS, and HL) and other geometric properties, including vertical angles, angles created by transversals across parallel lines, and bisectors.
M.G.15Circle Relationships: Investigate similarity in circles and relationships between angle measures and segments, including inscribed angles, radii, chords, central angles, inscribed angles, circumscribed angles, and tangent lines using dynamic geometric software.
M.G.16Transformations: Understand rotations, reflections, and translations of regular polygons, quadrilaterals, angels, circles, and line segments. Identify transformations, through investigation, that move a figure back onto itself, using that process to prove congruence.

M.G.17Triangle Congruence: Investigate triangles and their congruence over rigid transformations verifying findings using triangle congruence theorems (ASA, SSS, SAS, AAS, and HL) and other geometric properties, including vertical angles, angles created by transversals across parallel lines, and bisectors.
M.G.18Transformations: Understand rotations, reflections, and translations of regular polygons, quadrilaterals, angels, circles, and line segments. Identify transformations, through investigation, that move a figure back onto itself, using that process to prove congruence.
M.G.19Geometric Models: Apply geometric concepts in modeling situations to solve design problems using dynamic geometric software.
- a.Investigate 3-D shapes and their cross sections.
- b.Use volume, area, circumference, and perimeter formulas.
- c.Understand and apply Cavalieri’s principle.
- d.Investigate and apply scale factors for length, area, and volume.

M.G.20Trig Explorations: Investigate properties of right triangle similarity and congruence and the relationships between sine, cosine, and tangent; exploring the relationship between sine and cosine of complementary angles, and apply that knowledge to problem solving situations. Students recognize the role similarity plays in establishing trigonometric functions, and they use trigonometric functions to investigate situations. Using dynamic geometric software students investigate similarity and trigonometric identities to derive the Laws of Sines and Cosines and use the laws to solve problems.
M.G.21Triangle Congruence: Investigate triangles and their congruence over rigid transformations verifying findings using triangle congruence theorems (ASA, SSS, SAS, AAS, and HL) and other geometric properties, including vertical angles, angles created by transversals across parallel lines, and bisectors.
M.G.22Triangle Problems: Understand and use congruence and similarity when solving problems involving triangles, including trigonometric ratios. Use trigonometric ratios and the Pythagorean Theorem to solve right triangles in applied problems using dynamic geometric software.
M.G.23Circle Relationships: Investigate similarity in circles and relationships between angle measures and segments, including inscribed angles, radii, chords, central angles, inscribed angles, circumscribed angles, and tangent lines using dynamic geometric software.
M.G.24Points & Shapes: Solve problems involving geometric shapes in the coordinate plane using dynamic geometric software to apply the distance formula, Pythagorean Theorem, slope, and similarity rules in solving problems.
- a.Investigate equations of circles and how coefficients in the equations correspond to the location and radius of the circles.
- b.Find areas and perimeters of triangles and rectangles in the coordinate plane.