Grade 6 - 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.6.1Gather manaʻo about moʻokūʻauhau and kūlana through nīnauele (interviews) and oral histories.
M.6.2Use 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.6.3Demonstrate 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.6.4Contribute to community wellness by practicing ola pono (i.e. ʻai pono, laʻau lapaʻau, māla, hoʻoponopono) and building the capacity to connect with ʻāina.
M.6.5Ground our thoughts and actions in kānaka historical and contemporary best practices (i.e. resource management, conservation) and educate others.

M.6.6Make sense of problems and persevere in solving them.
M.6.7Reason abstractly & quantitatively.
M.6.8Construct viable arguments and critique the reasoning of others.
M.6.9Model with mathematics. ✰Critical emphasis to connect to ‘Āina Learning Concepts
M.6.10Use appropriate tools strategically.
M.6.11Attend to precision.
M.6.12Look for and make use of structure.
M.6.13Look for and express regularity in repeated reasoning.

M.6.14Nets and Surface Areas: Build and decompose 3-D figures using nets to find surface area. Represent volume and area as expressions involving whole number exponents.
M.6.15Distance and Direction: Students experience absolute value on numbers lines and relate it to distance, describing relationships such as order between numbers using inequality statements.
M.6.16Graphing Shapes: Use coordinates to represent the vertices of polygons and graph the shapes on the coordinate plane and determine side lengths, perimeter, and area.

M.6.17Model the World: Solve and model real world problems. Add, subtract, multiply, and divide multi-digit numbers and decimals, in real-world and mathematical problems - with sense making and understanding, using visual models and algorithms.
M.6.18Nets and Surface Areas: Build and decompose 3-D figures using nets to find surface area. Represent volume and area as expressions involving whole number exponents.

M.6.19Fraction Relationships: Understand fractions divided by fractions, thinking about them in different ways (EX: how many ⅓ are inside ⅔?), considering the relationship between the numerator and denominator, using different strategies and visuals. Relate fractions to ratios and percentages.
M.6.20Patterns & Numbers: Consider how numbers are made up, exploring factors and multiples, visually and numerically.
M.6.21Generalizing with Multiple Representations: Generalize from growth or decay patterns, leading to an understanding of variables. Understand that a variable can represent a changing quantity or an unknown number. Analyze a mathematical situation that can be seen and solved in different ways and that leads to multiple representations and equivalent expressions. Where appropriate in solving problems, use unit rates.
M.6.22Relationships Between Variables: Use independent and dependent variables to represent how a situation changes over time, recognizing unit rates when it is a linear relationship. Illustrate the relationship using tables, 4 quadrant graphs and equations and understand the relationships between the different representations and what each one communicates.