A Story of Ratios

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NYS COMMON CORE MATHE MATICS CURRI CULUM A Story of Ratios

A Story of RatiosGrade 8 – Module 6

Linear Functions


N YS CO MM O N CO R E M AT H E MAT I C S C U R R I C ULU M A Story of Ratios

Session Objectives1. Discuss the key ideas of what students learn in the module

Linear Functions.

2. Examine sample lessons to become familiar with the main objectives of the module



AgendaIntroduction to the ModuleConcept DevelopmentModule Review



Curriculum Overview of A Story of Ratios



Module topicsTopic A: Linear Functions

5 Lessons8.F.B.4 and 8.F.B.5

Topic B: Bivariate Numerical Data 4 lessons8.SP.A.1 and 8.SP.A.2

Mid-Module Assessment



Module topicsTopic C: Linear and Nonlinear Models

3 Lessons8.SP.A.1 and 8.SP.A.2 and 8.SP.A.3

Topic D: Bivariate Categorical Data 2 lessons8.SP.A.4

End of -Module Assessment



Module’s FoundationConnection between the Function and Statistics and Probability DomainsFocus Standards:

Functions Domain8.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



G8-M6: Vocabulary and Representations



G8-M6: Vocabulary and Representations



AgendaIntroduction to the ModuleConcept Development – Topic AModule Review



Topic A: Linear Functions



Topic A: Linear FunctionsIn 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.



Topic A: Linear FunctionsIn 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.



Key Idea from Lessons 1, 2 and 3Lesson 1 Modeling Linear RelationshipsStudents 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 ValueStudents interpret the rate of change and initial value of a line in context.

Given the equation of a line – interpret the slope in context



Lesson 3: Representations of a LineOutcomes:• 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.

Lesson 3



Lesson 4: Increasing and Decreasing FunctionsStudent 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.



Lesson 4 and 5: Increasing and Decreasing FunctionsOrganize 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.



AgendaIntroduction to the ModuleConcept Development – Topic BModule Review



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




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.




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



Big Ideas in Lessons 6 and 7

Lesson 6 Scatter plotsStudents construct scatter plots and investigate relationships.

Lesson7 Patterns in Scatter plotsStudents describe positive and negative trends in a scatter plot.



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.



Determining the Equation of a Line Fit to DataOrganize 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.

Lesson 9



Exit Ticket for Lesson 8



Mid- Module Assessment



AgendaIntroduction to the ModuleConcept Development – Topic CModule Review



Topic C: Linear and Nonlinear ModelsLesson 10: Linear Models

Lesson 11: Using Linear Models in a Data Context

Lesson 12: Nonlinear Models in a Data Context (Optional lesson)



Topic C: Linear and Nonlinear ModelsIn 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.



Student Outcomes in Lessons 10Student 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.



Lesson 10: Linear ModelsOrganize 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

Lesson 10



Lesson 11: Using Linear Models in a Data Context

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.

Lesson 11



Determining the Equation of a Line Fit to DataOrganize 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.

Lesson 11



AgendaIntroduction to the ModuleConcept Development – Topic DModule Review



Topic D: Bivariate Categorical DataLesson 13: Summarizing Bivariate Categorical Data in a Two-Way

Table

Lesson 14: Association between Categorical Variables



Topic D: Bivariate Categorical DataIn 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.



Lesson 13: Summarizing Bivariate Categorical Data in a Two-Way Table

Student Outcomes• Students organize bivariate categorical data into a two-way

table.• Students calculate row and column relative frequencies and

interpret them in context.

Lesson 13



Summarizing Bivariate Categorical Data in a Two-Way TableOrganize 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.

Lesson 11



AgendaIntroduction to the ModuleConcept DevelopmentModule Review



End of Module Assessment



Module Summary: Key IdeasGrade 8 Module 6 is a key. More use of functions and preparation for Grade 9

Algebra and Functions Conceptual Categories.Big theme is ASSOCIATIONKey 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



Final Comments and/or Questions

A Story of Ratios

Documents

module overview

module linear functions

midmodule assessment

end of module assessment

minutes materials

story of ratiosgrade

network team institutegrade

addition students