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A Story of Ratios

A Story of Ratios. Grade 8 – Module 6 Linear Functions. Session Objectives. Discuss the key ideas of what students learn in the module Linear Functions. Examine sample lessons to become familiar with the main objectives of the module. Agenda. Introduction to the Module Concept Development

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A Story of Ratios

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  1. A Story of Ratios Grade 8 – Module 6 Linear Functions

  2. Session Objectives • Discuss the key ideas of what students learn in the module Linear Functions. • Examine sample lessons to become familiar with the main objectives of the module

  3. Agenda Introduction to the Module Concept Development Module Review

  4. Curriculum Overview of A Story of Ratios

  5. Module topics Topic A: Linear Functions 5 Lessons 8.F.B.4 and 8.F.B.5 Topic B: Bivariate Numerical Data 4 lessons 8.SP.A.1 and 8.SP.A.2 Mid-Module Assessment

  6. Module topics Topic C: Linear and Nonlinear Models 3 Lessons 8.SP.A.1 and 8.SP.A.2 and 8.SP.A.3 Topic D: Bivariate Categorical Data 2 lessons 8.SP.A.4 End of -Module Assessment

  7. Module’s Foundation • Connection between the Function and Statistics and Probability Domains • Focus Standards: • Functions Domain • 8.F.B.4 Rate of Change • 8.F.B 5 Describe functional relationship • Statistics and Probability • 8.SP.A.1 Construct scatter plots • 8.SP.A..2 Informally fit a line to data • 8.SP.A.3 Equation of a line • 8.SP.A.4 Patterns of Association

  8. G8-M6: Vocabulary and Representations

  9. G8-M6: Vocabulary and Representations

  10. Agenda Introduction to the Module Concept Development – Topic A Module Review

  11. Topic A: Linear Functions

  12. Topic A: Linear Functions • In Lesson 1, students are given a verbal description of a linear relationship between two variables, and then must describe a linear model. Students graph linear functions using a table of values and by plotting points. They recognize a linear function given in terms of the slope and initial value or y-intercept. • In Lesson 2, students interpret the rate of change and the y-intercept, or initial value, in the context of the problem. They interpret the sign of the rate of change as indicating that a linear function is increasing or decreasing and as indicating the steepness of a line.

  13. Topic A: Linear Functions • In Lesson 3, students graph the line of a given linear function. They express the equation of a linear function as y=mx+b or an equivalent form when given the initial value and slope. • In Lessons 4 and 5, students describe and interpret a linear function given two points or its graph.

  14. Key Idea from Lessons 1, 2 and 3 Lesson 1 Modeling Linear Relationships Students determine a linear function given a verbal description of a linear relationship between two quantities. Rate of change and initial value are emphasized Lesson 2 Interpreting Rate of Change and Initial Value Students interpret the rate of change and initial value of a line in context. Given the equation of a line – interpret the slope in context

  15. Lesson 3: Representations of a Line Lesson 3 • Outcomes: • • Students graph a line specified by a linear function. • • Students graph a line specified by an initial value and rate of change of a function and construct the linear function by interpreting the graph. • • Students graph a line specified by two points of a linear relationship and provide the linear function.

  16. Lesson 4: Increasing and Decreasing Functions Student Outcomes • Students describe qualitatively the functional relationship between two types of quantities by analyzing a graph. • Students sketch a graph that exhibits the qualitative features of a function based on a verbal description.

  17. Lesson 4 and 5: Increasing and Decreasing Functions • Organize in small groups. • Read through Lesson 4 of this module starting on page 19 of the student edition. Answer questions 2 to 4. • After you have completed the problems, we will discuss the solutions and student expectations.

  18. Agenda Introduction to the Module Concept Development – Topic B Module Review

  19. Topic B: Bivariate Numerical Data Lesson 6 Scatter Plots Lesson 7 Patterns in Scatter Plots Lesson 8 Informally Fitting a Line Lesson 9 Determining the Equation of a Line Fit to Data

  20. Topic B: Bivariate Numerical Data In Lesson 6, students construct scatter plots and focus on identifying linear versus non-linear patterns. In Lesson 7 students distinguish positive linear association and negative linear association based on the scatter plot. Students describe trends in the scatter plot, along with clusters, and outliers (points that do not fit the pattern). In Lesson 8, students informally fit a straight line to data displayed in a scatter plot by judging the closeness of the data points to the line.

  21. Topic B: Bivariate Numerical Data In Lesson 9, students interpret and determine the equation of the line they fit to the data and use the equation to make predictions and to evaluate possible association of the variables. Based on these predictions, students address the need for a “best-fit” line, which is formally introduced in Grade 9

  22. Big Ideas in Lessons 6 and 7 Lesson 6 Scatter plots Students construct scatter plots and investigate relationships. Lesson7 Patterns in Scatter plots Students describe positive and negative trends in a scatter plot.

  23. Lesson 8 Student Outcomes • Students informally fit a straight line to data displayed in a scatter plot. • Students make predictions based on the graph of a line that has been fit to data.

  24. Determining the Equation of a Line Fit to Data Lesson 9 • Organize in small groups. • Discuss and complete problems 1 to 6 from Lesson 8 of this module. (S60) • After you have completed the problems, we will discuss the idea of development of informally fitting a line.

  25. Exit Ticket for Lesson 8

  26. Mid- Module Assessment

  27. Agenda Introduction to the Module Concept Development – Topic C Module Review

  28. Topic C: Linear and Nonlinear Models Lesson 10: Linear Models Lesson 11: Using Linear Models in a Data Context Lesson 12: Nonlinear Models in a Data Context (Optional lesson)

  29. Topic C: Linear and Nonlinear Models In Lesson 10, students identify applications in which a linear function models the relationship between two numerical variables. In Lesson 11, students use a linear model to answer questions about the relationship between two numerical variables by interpreting the context of a data set. Students use graphs and the patterns of linear association to answer questions about the relationship of the data. In Lesson 12, students also examine patterns and graphs that describe nonlinear associations of data.

  30. Student Outcomes in Lessons 10 Student Outcomes • Students identify situations where it is reasonable to use a linear function to model the relationship between two numerical variables. • Students interpret slope and the initial value in a data context.

  31. Lesson 10: Linear Models Lesson 10 • Organize in small groups. • Discuss and complete problems 1 and 2 (S81)and problem 11 (S86) from Lesson 10 of this module. • After you have completed the problems, we will discuss the answers

  32. Lesson 11: Using Linear Models in a Data Context Lesson 11 Student Outcomes • Students recognize and justify that a linear model can be used to fit data. • Students interpret the slope of a linear model to answer questions or to solve a problem.

  33. Determining the Equation of a Line Fit to Data Lesson 11 • Organize in small groups. • Discuss and complete exercise 2 from Lesson 11 (S91)of this module. • After you have completed the problems, we will go through the solutions.

  34. Agenda Introduction to the Module Concept Development – Topic D Module Review

  35. Topic D: Bivariate Categorical Data Lesson 13: Summarizing Bivariate Categorical Data in a Two-Way Table Lesson 14: Association between Categorical Variables

  36. Topic D: Bivariate Categorical Data In Lesson 13, students organize bivariate categorical data into a two-way table. They calculate row and column relative frequencies and interpret them in the context of a problem. In Lesson 14, students informally decide if there is an association between two categorical variables by examining the differences of row or column relative frequencies. They interpret association between two categorical variables as meaning that knowing the value of one of the variables provides information about the likelihood of the different possible values of the other variable.

  37. Lesson 13: Summarizing Bivariate Categorical Data in a Two-Way Table Lesson 13 Student Outcomes • Students organize bivariate categorical data into a two-way table. • Students calculate row and column relative frequencies and interpret them in context.

  38. Summarizing Bivariate Categorical Data in a Two-Way Table Lesson 11 • Organize in small groups. • Discuss and complete exercises 11 to 22 from Lesson 13 of this module. (S106) • After you have completed the problems, we will discuss the set up of the two-way table and the vocabulary.

  39. Agenda Introduction to the Module Concept Development Module Review

  40. End of Module Assessment

  41. Module Summary: Key Ideas Grade 8 Module 6 is a key. More use of functions and preparation for Grade 9 Algebra and Functions Conceptual Categories. Big theme is ASSOCIATION Key ideas: •Patterns in Scatter plots (Association between two numerical variables) • Equation of a line • Fitting a line to data • Analyzing categorical data from two-way frequency tables. • Association between two categorical variables

  42. Final Comments and/or Questions

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