Math Models with Applications ~ Unit 3

Transcription

1 Title Graphing and Functions *CISD Safety Net Standards: MMA.2A, MMA.5B, MMA9.A Big Ideas/Enduring Understandings 3 rd Six Weeks 30 Days Guiding Questions Suggested Time Frame Graphs can help us visualize data and their behavior. What is a rectangular coordinate system? Slope and direction are meaningful in predicting future How are points in a plane graphed on the rectangular coordinate outcomes and interpreting data. system? A function is a special kind of relationship between two What are the four regions of a coordinate plane called and how quantities, both linear and non-linear. are they labeled? How can we use the slope of a given line and a point on that line to write it s linear equation? How can we use a set of given points to write the corresponding function of the points? How many different formats can (insert function type) be written in? List all formats. Vertical Alignment Expectations TEA Vertical Alignment Documents Sample Assessment Question COMING SOON.. The resources included here provide teaching examples and/or meaningful learning experiences to address the District Curriculum. In order to address the TEKS to the proper depth and complexity, teachers are encouraged to use resources to the degree that they are congruent with the TEKS and research-based best practices. Teaching using only the suggested resources does not guarantee student mastery of all standards. Teachers must use professional judgment to select among these and/or other resources to teach the district curriculum. Some resources are protected by copyright. A username and password is required to view the copyrighted material. District Specificity and Examples are a product of the Austin Area Math Supervisor s TEKS Clarifying documents as found on the Region XI Mathematics resource page. Updated September 14, 2016 Page 1 of 5

2 Ongoing TEKS MMA.1 Mathematical process standards. The student uses mathematical processes to acquire and demonstrate mathematical understanding. The student is expected to: (A) apply mathematics to problems arising in everyday life, society, and the Focus is on application workplace; (B) use a problem-solving model that incorporates analyzing given information, formulating a plan or strategy, determining a solution, justifying the solution, and evaluating the problem-solving process and the reasonableness of the solution; (C) select tools, including real objects, manipulatives, paper and pencil, and technology as appropriate, and techniques, including mental math, estimation, and number sense as appropriate, to solve problems; Students should assess which tool to apply rather than trying only one or all (D) communicate mathematical ideas, reasoning, and their implications using multiple representations, including symbols, diagrams, graphs, and language as appropriate; (E) create and use representations to organize, record, and communicate mathematical ideas; (F) analyze mathematical relationships to connect and communicate mathematical ideas; and (G) display, explain, and justify mathematical ideas and arguments using precise mathematical language in written or oral communication Students should evaluate the effectiveness of representations to ensure they are communicating mathematical ideas clearly Students are expected to use appropriate mathematical vocabulary and phrasing when communicating ideas Students are expected to form conjectures based on patterns or sets of examples and non-examples Precise mathematical language is expected. Updated September 14, 2016 Page 2 of 5

3 Knowledge and Skills with Student Expectations District Specificity/ Examples Vocabulary Suggested Resources Resources listed and categorized to indicate suggested uses. Any additional resources must be aligned with the TEKS. Ongoing and Embedded Processing Skills: 1ACDEFG 2A 5ABC 9ADF 10B Major Points Coordinate Systems (1.D and 9.A) Graphing Linear Equations (1.G and 9.A) Slope (9.A and 10.B) Writing Equations of Lines (1.A, D and 2.A) Applications and Uses of Graphs (1.A, E, 2.A, 9.A, F, and 10.B) Functions (1.D, E) Function Notation (1.C, D, E, F, G and 2.A) Modeling Linear Functions (1.G) Direct and Inverse Variation (5.A) Modeling Quadratic and Power Functions (1.G and 5.C) Modeling Exponential Functions (5.B and 9.D) X and Y-Axis X and Y Coordinates Origin X and Y-Intercepts Horizontal and Vertical Lines Continuous Discrete Slope Slope-Intercept Form Point-Slope Form Parallel and Perpendicular Lines Dependent and Independent Variables Relation Domain and Range Function Notation Linear Function Constant of Variation Direct Variation Inverse Variation Joint Variation Combined Variation Quadratic Function Roots Solutions Text Resources Mathematical Models and Applications (Timmons/Johnson/McCook) Websites: Khan Academy NCTM Illuminations Region XI: Livebinder Updated September 14, 2016 Page 3 of 5

4 MMA.2 Zeros Maximum Minimum Power Function Exponential Function Exponential Growth and Decay Mathematical modeling in personal finance. The student uses mathematical processes with graphical and numerical techniques to study patterns and analyze data related to personal finance. The student is expected to: 2A use rates and linear functions to solve problems involving personal finance and budgeting, including compensations and deductions MMA.5 Mathematical modeling in science and engineering. The student applies mathematical processes with algebraic techniques to study patterns and analyze data as it applies to science. The student is expected to: 5A use proportionality and inverse variation to describe physical laws such as Hook's Law, Newton's Second Law of Motion, and Boyle's Law; 5B use exponential models available through technology to model growth and decay in areas, including radioactive decay; 5C use quadratic functions to model motion Updated September 14, 2016 Page 4 of 5

5 MMA.9 Mathematical modeling in social sciences. The student applies mathematical processes and mathematical models to analyze data as it applies to social sciences. The student is expected to: 9A interpret information from various graphs, including line graphs, bar graphs, circle graphs, histograms, scatterplots, dot plots, stem-and-leaf plots, and box and whisker plots, to draw conclusions from the data and determine the strengths and weaknesses of conclusions 9D use data from a sample to estimate population mean or population proportion 9F use regression methods available through technology to model linear and exponential functions, interpret correlations, and make predictions MMA.10 Mathematical modeling in social sciences. The student applies mathematical processes to design a study and use graphical, numerical, and analytical techniques to communicate the results of the study. The student is expected to: 10B communicate methods used, analyses conducted, and conclusions drawn for a data-analysis project through the use of one or more of the following: a written report, a visual display, an oral report, or a multi-media presentation Updated September 14, 2016 Page 5 of 5