Math Models with Applications Unit 6 Suggested Time Frame 5th and 6th Six Weeks Probability: 18 Days Statistics: 19 Days Statistics Project: 6 Days
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1 Title Probability and Statistics *CISD Safety Net Standards: MMA.8B, MMA.9A Big Ideas/Enduring Understandings Graphs and tables can help us visualize data and its behavior in order to better predict future outcomes. Manipulating data can change the statistics by obscuring or revealing parts of the truth. Probability, based on statistics, can be used to make predictions. Vertical Alignment Expectations TEA Vertical Alignment Documents Sample Assessment Question Suggested Time Frame 5th and 6th Six Weeks Probability: 18 Days Statistics: 19 Days Statistics Project: 6 Days Guiding Questions What is probability? Compare and contrast theoretical probability and empirical probability, and why do we need both? What is the difference between permutations and combinations and what are they used for? How do we use statistics to predict future outcomes? List and describe tables and graphs used to display statistical data that has been gathered. What is the difference between direct variation and indirect variation? Coming Soon. Updated January 3, 2017 Page 1 of 6
2 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. 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 January 3, 2017 Page 2 of 6
3 Knowledge and Skills with Student Expectations Ongoing and Embedded Processing Skills: 1ACDEFG 8AB 9ABCDF 10B District Specificity/ Examples Major Points Sets and Set Theory What is Probability Theoretical Probability Odds Tree Diagrams Or Problems And Problems The Counting Principle, Permutations, and Combinations Introduction to Statistics Reading and Interpreting Graphical Information Frequency Tables and Histograms Descriptive Statistics Variation Box-and-Whisker Plots and Normal Curves Scatter Diagrams and Linear Regression Statistics Project addition rule combination conditional probability counting principle dependent events disjoint sets elements empirical probability empty set equal equally likely outcomes event experiment factorial finite independent events independent outcome infinite intersection law of large numbers laws of probability multiplication rule mutually exclusive events null sets odds Vocabulary frequency table inferential statistics interquartile range least-squares line line graph linear regression analysis mean average measures of central tendency median midpoint of the class modal class mode negative correlation normal curve normally distributed observational study outlier percentile rank pie graph population prediction equation probability of events qualitative data quantitative data quartile random sampling Suggested Resources Resources listed and categorized to indicate suggested uses. Any additional resources must be aligned with the TEKS. Textbook Resources: Mathematical Models and Applications Chapters 7 & 8 PowerPoints Websites: Khan Academy Illuminations.org Region XI: Livebinder Updated January 3, 2017 Page 3 of 6
4 outcomes permutation Probability random sample space set-builder notation sets set notation subset theoretical probability tree diagram union universal set Venn Diagram area under the normal curve average bell curve best-fit line bias box-and-whisker plot dot plot empirical rule frequency distribution range sample scatter diagram standard deviation standard scores statistics stem-and-leaf display strata stratified sampling survey symmetrical systematic sampling table of areas variation weighted mean z-scores circle graph cluster sampling convenience sampling correlation coefficient (r) data descriptive statistics dispersion MMA.8 Mathematical modeling in social sciences. The student applies mathematical processes to determine the number of elements in a finite sample space and compute the probability of an event. The student is expected to: Updated January 3, 2017 Page 4 of 6
5 8A determine the number of ways an event may occur using combinations, permutations, and the Fundamental Counting Principle; *CISD Safety Net* 8B compare theoretical to empirical probability; 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: *CISD Safety Net* 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 9B analyze numerical data using measures of central tendency (mean, median, and mode) and variability (range, interquartile range or IQR, and standard deviation) in order to make inferences with normal distributions; 9C distinguish the purposes and differences among types of research, including surveys, experiments, and observational studies; 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 Updated January 3, 2017 Page 5 of 6
6 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 January 3, 2017 Page 6 of 6
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