Grade 8 - 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

Use shape, number and expressions to explore shapes in the world. Explore distance and directions, 2-D and 3-D connections, scale drawings and investigations and move toward transformational geometry.

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

Search for shapes in the world. Model the world using nets and surface area, 2-D and 3D connections, angle relationships, big and small numbers explorations.

V. Sense of Community: Exploring Changing Quantities

Look for fraction relationships and patterns inside numbers. Generalize with multiple representations and see relationships between variables. Explore unit rates in the world, proportional and graphing relationships and begin to create scale drawings. Find relationships with multiple representations of functions, linear equations, slopes and intercepts.

VI. Sense of Responsibility: Communicating Stories with Data

Explore the variability in data and the shape of distributions. Visualize populations and samples. Use probability models. Engage in data explorations and use various types of graphs and tables to organize data.

M.8.1Gather manaʻo about moʻokūʻauhau and kūlana through nīnauele (interviews) and oral histories.
M.8.2Use ʻōlelo Hawaiʻi inoa ‘āina (traditional place names, mauka/makai) to understand various traditions/histories of a place and to understand my place in different spaces.
M.8.3Demonstrate appropriate lawena when engaging in different cultural protocol (i.e. welcoming, entering, gathering, planting, mahalo, kamaʻāina/malihini) in a variety of settings (i.e. in and out of school).
M.8.4Contribute to community wellness by practicing ola pono (i.e. ʻai pono, laʻau lapaʻau, māla, hoʻoponopono) and building the capacity to connect with ʻāina.
M.8.5Ground our thoughts and actions in kānaka historical and contemporary best practices (i.e. resource management, conservation) and educate others.

M.8.6Make sense of problems and persevere in solving them.
M.8.7Reason abstractly & quantitatively.
M.8.8Construct viable arguments and critique the reasoning of others.
M.8.9Model with mathematics. ✰Critical emphasis to connect to ‘Āina Learning Concepts.
M.8.10Use appropriate tools strategically.
M.8.11Attend to precision.
M.8.12Look for and make use of structure.
M.8.13Look for and express regularity in repeated reasoning.

M.8.14Cylindrical Investigations: Solve real world problems with cylinders, cones, and spheres. Connect volume and surface area solutions to the structure of the figures themselves, (ex: why and how is the area of a circle formula used to find the volume of a cylinder?) Show visual proofs of these relationships, through modeling, building and using computer software.
M.8.15Pythagorean Explorations: Conduct investigations in the coordinate plane with right triangles to show that the areas of the squares of each leg combine to create the square of the hypotenuse and name this as the Pythagorean theorem. Using technology, use the Pythagorean theorem to solve real world problems that include irrational numbers.
M.8.16Shape, Number & Expressions: Compare shapes containing circular measures, to prisms. Note that cubes and squares represent unit measure for volume and surface area. See and use the connection between integer exponents and area volume.
M.8.17Transformational Geometry: Plot two dimensional figures on a coordinate plane, using geometry software, note similarity when dilations are performed and the corresponding angle measures maintain congruence. Perform translations, rotation and reflection and notice when shape maintains congruence.

M.8.18Cylindrical Investigations: Solve real world problems with cylinders, cones, and spheres. Connect volume and surface area solutions to the structure of the figures themselves, (ex: why and how is the area of a circle formula used to find the volume of a cylinder?) Show visual proofs of these relationships, through modeling, building and using computer software.
M.8.19Pythagorean Explorations: Conduct investigations in the coordinate plane with right triangles to show that the areas of the squares of each leg combine to create the square of the hypotenuse and name this as the Pythagorean theorem. Using technology, use the Pythagorean theorem to solve real world problems that include irrational numbers.
M.8.20Big and Small Numbers: Use scientific notation to investigate problems that include measurements of very large and very small numbers. Develop number sense with integer exponents.

M.8.21Interpret Scatter Plots: Construct and interpret data visualization including scatterplots for bivariate measurement data using two-way tables. Describe patterns noting whether the data appear in clusters, are linear or nonlinear, whether there are outliers, and if the association is negative or positive.
M.8.22Linear Equations: Analyze slope and intercepts and solve linear equations including pairs of simultaneous linear equations through graphing and tables and using technology.
M.8.23Multiple Representations of Functions: Move between different representations of linear functions (ex: equation, graph, table and content), sketch and analyze graphs, use similar triangles to visualize slope and rate of change with equations containing rational number coefficients.
M.8.24Slopes & Intercepts: Construct graphs using bivariate data, comparing the meaning of parallel and non-parallel slopes with the same or different y-intercepts using technology.