Title Scatterplots and Data Analysis CISD Safety Net Standards: 8.5D Big Ideas/Enduring Understandings The student will understand how patterns are used when comparing two quantities. Suggested Time Frame Time Frame: 4 th Six Weeks Suggested Duration: 13 days Guiding Questions How are patterns used when comparing two quantities? Grade 8 MATH *TEKS one level below* Vertical Alignment Expectations TEA Vertical Alignment 5 th Grade Algebra I *TEKS one level above* 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. Portions of the District Specificity/Examples are a product of the TEKS Clarifying Documents provided by the Austin Area Math Supervisors. Updated November 30, 2016 Page 1 of 12
Ongoing TEKS Grade 8 MATH Math Processing Skills To be embedded and used all year long throughout all concept student expectations. 8.01 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 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 (G) display, explain, and justify mathematical ideas and arguments using precise mathematical language in written or oral communication Precise mathematical language is expected. Updated November 30, 2016 Page 2 of 12
Knowledge and Skills with Student Expectations 8.5 Proportionality. The student applies mathematical process standards to use proportional and nonproportional relationships to develop foundational concepts of functions. The student is expected to: (C) contrast bivariate sets of data that suggest a linear relationship with bivariate sets of data that do not suggest a linear relationship from a graphical representation. District Specificity/ Examples 8.5C Students need to understand that bivariate means two variables or that there are two types of data. Misconceptions: Students may think that if the graph is nonlinear, then there is no relationship. (ie. exponential functions) Examples: Vocabulary Bivariate Graphical representation Linear relationships Sets of data Trend line Suggested Resources Resources listed and categorized to indicate suggested uses. Any additional resources must be aligned with the TEKS. Textbook Resources: McGraw-Hill Chapter 9 Lessons 1-6 (Lessons 3 and 5 are not addressed by 8 th grade TEKS.) Web Resources: Region XI: Livebinder NCTM: Illuminations Khan Academy Examples of non linear relationships Updated November 30, 2016 Page 3 of 12
Updated November 30, 2016 Page 4 of 12
*CISD Safety Net* (D) use a trend line that approximates the linear relationship between bivariate sets of data to make predictions. 8.5D Students need to understand that the trend line closely follows the path of points passing through as many as possible with about half the remaining points above the line and the other half below the line. Student understands that trend line and line of best fit mean the same thing. Misconceptions: Students may think a trend line must connect all the points in the data set. Students may not set up the intervals on the axes correctly. Trend line does not have to start at the origin. Updated November 30, 2016 Page 5 of 12
Examples: Grade 8 MATH Linear models can be represented with a linear equation. Students interpret the slop and y-intercept of the line in the context of the problem. Updated November 30, 2016 Page 6 of 12
8.11 Measurement and Data. The student applies mathematical process standards to use statistical procedures to describe data. The student is expected to: (A) construct a scatterplot and describe the observed data to address questions of association such a linear, non-linear, and no 8.11(A) Represent numerical data on a scatter plot, to examine relationships between variables. Analyze scatter plots to determine if the relationship is linear (positive, negative trend, or no trend) or non-linear. Trend and correlation are interchangeable in reference to scatterplots. Absolute value Data Linear Mean Mean absolute deviation No association Non-linear Population Random samples Scatterplot Simulation Updated November 30, 2016 Page 7 of 12
association between bivariate data. Students represent numerical data on a scatter plot, to examine relationships between variables. Students must understand that in a positive relationship, as one set of data increases, so does the other. The opposite, as one set of data decreases so does the other also represents a positive relationship. Students must understand that in a negative relationship, as one set of data increases the other must decrease and vice versa. Misconceptions: Just because the points are not perfectly lined up does not mean that the data cannot be represented as a linear relationship. Students think that if both numbers in the data are decreasing, then it represents a negative trend. Students think that there is no correlation if the x value is not in numeric order. Grade 8 MATH Updated November 30, 2016 Page 8 of 12
Updated November 30, 2016 Page 9 of 12
(B) determine the mean absolute deviation and use this quantity as a measure of the average distance data are from the mean using a data set of no more than 10 data points. 8.11(B) The mean absolute deviation gives the average variation of the data from the mean. Mean absolute deviation describes the dispersion of spread of data. Student understands that the mean absolute deviation gives the average variation of the data from the mean. Student understands that the mean absolute deviation describes the dispersion or spread of data. The student must be able to find the mean from a given set of data. 1. Calculate the mean of your data set. 2. Subtract the mean from each of the data values and list the positive differences. 3. Calculate the mean of the differences. Updated November 30, 2016 Page 10 of 12
Examples: Grade 8 MATH Updated November 30, 2016 Page 11 of 12
(C) simulate generating random samples of the same size from a population with known characteristics to develop the notion of a random sample being representative of the population from which it was selected. 8.11(C) Know the meaning of random, sample, population, bias and explain why a sample is a good/bad representation of the population. Misconceptions. Sometimes students will confuse the group that is being surveyed (sample space) with the population. Examples: Updated November 30, 2016 Page 12 of 12