Grade 9 - 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

Investigate data and model with functions. 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.

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

Explore growth and decay in various models. 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.

V. Sense of Community: Exploring Changing Quantities

Understand features of functions and engage in function investigations. Explore systems of investigations.

VI. Sense of Responsibility: Communicating Stories with Data

Investigate data and model with functions. 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.

M.AI.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.AI.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.AI.3Discern between and lead appropriate protocol in age/kuleana appropriate ceremonies and protocols.
M.AI.4Utilize and mālama wahi pana resources (i.e. pāhonu, limu, salt beds, mala, kupuna, water, kiʻopua) to aloha ʻāina.
M.AI.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.AI.6Make sense of problems and persevere in solving them.
M.AI.7Reason abstractly & quantitatively.
M.AI.8Construct viable arguments and critique the reasoning of others.
M.AI.9Model with mathematics. ✰Critical emphasis to connect to ‘Āina Learning Concepts
M.AI.10Use appropriate tools strategically.
M.AI.11Attend to precision.
M.AI.12Look for and make use of structure.
M.AI.13Look for and express regularity in repeated reasoning.

M.AI.14Investigate Data: Represent data from two or more data sets with plots, dot plots, histograms, and box plots, comparing and analyzing the center and spread, using technology, and interpreting the results. Interpret and compare data distributions using center (median, mean) and spread (interquartile range, standard deviation) through the use of technology.
- a.Students have opportunities to explore and research a topic of interest and meaning to them, using the statistical methods, tools, and representations.
- b.Have students consider how different, competing interpretations can be made from different audiences, histories, and perspectives.
- c.Allow students to develop follow-up questions to investigate, spurred by the original data set.
M.AI.15Model with Simple Functions: Investigate data sets by table and graph and using technology; fit and interpret functions** to model the data between two quantities both graphically & algebraically, including square root, cube root,absolute value, and simple inverse functions. Interpret information from the functions, noticing key features* and symmetries. Develop understanding of the meaning of the function and how it represents the data that it is modeling; recognizing possible associations and trends in the data - including consideration of the correlation coefficients of linear models.
- a.Students can disaggregate data by different characteristics of interest (populations for example), and compare slopes to examine questions of fairness and bias among groups.
- b.Students have opportunities to consider how to communicate relevant concerns to stakeholders and/or community members.
- c.Students can identify both extreme values (true outliers) and data errors, and how the inclusion or exclusion of these observations may change the function that would most appropriately model the data.
  - i.*intercepts, slope, increasing or decreasing, positive or negative
  - ii.** functions include linear, quadratic and exponential
Note:Allow students to develop follow-up questions to investigate, spurred by the original data set

M.AI.16Growth & Decay: Investigate situations that involve linear, quadratic, and exponential models, and use these models to solve problems. Recognize linear functions grow by equal differences over equal intervals; exponential functions grow by equal factors over equal intervals, and functions grow or decay by a percentage rate per unit interval. Interpret the inverse of functions, and model the inverse in graphs, tables, and equations.
M.AI.17Symbolic Manipulation of Expressions: Solve problems, such as factoring, distributing, multiplying polynomials, expanding exponential expressions, etc.

M.AI.18Systems of Equations: Students investigate real situations that include data for which systems of 1 or 2 equations or inequalities are helpful, paying attention to units. Investigations include linear, quadratic, and absolute value. Students use technology tools strategically to find their solutions and approximate solutions, constructing viable arguments, interpreting the meaning of the results, and communicating them in multidimensional ways.
M.AI.19Function Investigations: Students investigate data sets by table and graph and using technology; such as earthquake data in the region of the school; they fit and interpret functions to model the data between two quantities and consider the meaning of inverse relationships. Students interpret information from the functions, noticing key features* and symmetries. Students develop understanding of the meaning of the function and how it represents the data that it is modeling; they recognize possible associations and trends in the data - including consideration of the correlation coefficients of linear models.
- a.*one to one correspondence, intercepts, slope, increasing or decreasing, positive or negative
M.AI.20Features of Functions: Students investigate changing situations that are modeled by quadratic and exponential forms of expressions and create equivalent expressions to reveal features* that help understand the meaning of the problem and situation being investigated. (driver of investigation 1, making sense of the world)
- a.Investigate patterns, such as the Fibonacci sequence and other mathematical patterns, that reveal recursive functions.
- b.*Factored form to reveal zeros of a quadratic function, standard form to reveal the y-intercept, vertex form to reveal a maximum or minimum.