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! ! Pomona Unified Math News th Domain: 8 Grade Statistics and Probability (SP) 8.SP.3: Use the equation of a linear model to solve problems in the context of bivariate measurement data, interpreting the slope and intercept. For example, in a linear model for a biology experiment, interpret a slope of 1.5 cm/hr as meaning that an additional hour of sunlight each day is associated with an additional 1.5 cm in mature plant height. 1 Suggested Standards for Mathematical Practice (MP): MP 2 Reason abstractly and quantitatively. MP.4 Model with mathematics. MP.5 Use appropriate tools strategically. MP.6 Attend to precision. MP.7 Look for and make use of structure. Number of Absences 3 5 1 1 3 6 5 3 0 7 8 2 9 0 6 6 2 0 5 7 9 1 Explained in 8.SP.1 Vocabulary: (Note: vocabulary will be taught in the context of the lesson, not before or separate from the lesson.) Correlation/association: See 8.SP.1 Bivariate data: See 8.SP.1 Scatter plot: See 8.SP.1 Outlier: See 8.SP.1 Linearity: See 8.SP.1 Line of best fit: See 8.SP.2 Explanations and Examples: Example 1: Given data from studentsโ math scores and absences, make a scatterplot to see if there may be a relationship between the two. Math Scores 65 50 95 85 80 34 70 56 100 24 45 71 30 95 55 42 90 92 60 50 10 80 Example 2: ! 1 Adapted from Georgia Math Grade 8 flip book and www.mathisfun.com Draw a line of best fit, paying attention to the closeness of the data points on either side of the line. Solution: ! ! Pomona Unified Math News th Domain: 8 Grade Statistics and Probability (SP) 8.SP.3: Use the equation of a linear model to solve problems in the context of bivariate measurement data, interpreting the slope and intercept. For example, in a linear model for a biology experiment, interpret a slope of 1.5 cm/hr as meaning that an additional hour of sunlight each day is associated with an additional 1.5 cm in mature plant height. this relates to the graph. Students informally draw a line of best fit for a scatter plot and informally measure the strength of fit. Discussion should include โWhat does it mean to be above the line, below the line?โ From the line of best fit, determine an approximate linear equation that models the given data. Solution: ๐ = โ ๐๐ ๐ ๐ + ๐๐ Students should recognize that 95 represents the y intercept (where the line of best fit crosses the y axis) and โ25/3 represents the slope of the line. (This can be determined by finding the slope between any two points) The slope can vary slightly. Students can use this linear model to solve problems. For example, through substitution, they can use the equation to determine that a student with 4 absences should expect to receive a math score of about 62. They can then compare this value to their line. The study of the line of best fit ties directly to the algebraic study of slope and intercept. Students interpret the slope and intercept of the line of best fit in the context of the data. Then students can make predictions based on the line of best fit. Common Misconceptions: See standard 8.SP.1 Web Help Links (Use a QR scanner to take you directly to the website) https://learnzillion.com/resources/51621 https://learnzillion.com/resources/51624 Instructional Strategies: Scatter plots are the most common form of displaying bivariate data in Grade 8. Students should be provided scatter plots and have studentโs practice informally finding the line of best fit. Students should create and interpret scatter plots, focusing on outliers, positive or negative association, linearity or curvature. By changing the data slightly, students can have a rich discussion about the effects of the change on the graph. Students should have use of a graphing calculator to determine a linear regression and discuss how https://learnzillion.com/resources/51166