PK–12 Essential Standards and Benchmarks

Kahua Standards and Benchmarks

PK-12 essential standards and benchmarks for Hawaiian-focused education.

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Grade 11 - 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.

  • M.AII.1Create and share capstone projects and hōʻike (i.e. puka kula haʻi ‘ōlelo, research papers, community service, testimonies) to expand the body of knowledge about ʻāina.
  • M.AII.2Synthesize ʻōlelo Hawaiʻi kilo, performance cartographies (i.e. oli, mele, hula, kaulana mahina, hoʻokele), and inoa ʻāina (traditional place names) to make decisions about what ʻāina needs.
  • M.AII.3Perpetuate ʻike kupuna through the creation and use of Hawaiian cultural artifacts (i.e. kīhei, lei, ʻohe kāpala, mea ʻai) in ceremonies and protocols.
  • M.AII.4Contribute knowledge, resources, and practices to enhance the lāhui and world as aloha ʻāina.
  • M.AII.5Take actions to advocate for justice on behalf of kānaka and ʻāina because we are an extension of ʻāina (i.e. testimonies, water rights, civic engagement).

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

  • M.AII.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.AII.15Model with Functions: Investigate data sets by table and graph and using technology; fit and interpret functions** to model the data between two quantities. 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.
    • d.*intercepts, slope, increasing or decreasing, positive or negative
    • e.** functions include linear, quadratic and exponential
  • Note:Allow students to develop follow-up questions to investigate, spurred by the original data set
  • M.AII.16Analyzing Series: calculate the sums of arithmetic and geometric series, including infinites geometric series.

  • M.AII.17Growth & 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.AII.18Application: Use multiple algebraic representations to model and solve problems presented as real world situations or simulations. Use algebra to rewrite complicated algebraic expressions and equations in more useful forms. Rewriting rational expressions and arithmetic operations on polynomials.
  • M.AII.19Complex Numbers: Operate with complex numbers, and solve quadratic equations with complex solutions.
  • M.AII.20Analyzing Series: calculate the sums of arithmetic and geometric series, including infinites geometric series.

  • M.AII.21Systems 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 while recognizing the connections among these multiple representations.
  • M.AII.22Function 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.
  • M.AII.23*one-to-one correspondence, intercepts, slope, increasing or decreasing, positive or negative
  • M.AII.24Trig Explorations: Model periodic phenomena wit trigonometric functions. Solve trigonometric equations and prove trigonometric identities.
  • M.AII.25Features 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.
    • c.Visualize, express, interpret and describe, and graph functions and their inverses in many cases:
      • i.Absolute value, exponential, linear, logarithmic, piecewise-defined, polynomial, quadratic, square root, trigonometric
  • M.AII.26Exploring Logarithms: Understand logarithms and their inverse relationship with exponentials. Use logarithms to solve exponential equations.

  • M.AII.27Investigate 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.AII.28Model with Functions: Investigate data sets by table and graph and using technology; fit and interpret functions** to model the data between two quantities. 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.
    • d.*intercepts, slope, increasing or decreasing, positive or negative
    • e.** functions include linear, quadratic and exponential
  • Note:Allow students to develop follow-up questions to investigate, spurred by the original data set.
  • M.AII.29Exploring and Interpreting Data: Use the concepts of randomness & bias in survey design and interpretations of the results. Use normal distribution to model outcomes and make inferences as appropriate. Use computers to simulate and determine complex probabilities. Use margin of error and sample-to-sample variability to evaluate statistical decisions.