Algebra, Functions, and Data Analysis

1 MATHEMATICS STANDARDS OF LEARNING ENHANCED SCOPE AND SEQUENCE algebra , functions , and data Analysis Commonwealth of Virginia Department of Education Richmond, Virginia 2008 i Copyright 2008 by the Virginia Department of Education Box 2120 Richmond, Virginia 23218-2120 All rights reserved. Reproduction of materials contained herein for instructional purposes in Virginia classrooms is permitted. Superintendent of Public Instruction Billy K. Cannaday, Jr. Chief Deputy Superintendent of Public Instruction Patricia I.

2 Wright Assistant Superintendent for Instruction Linda M. Wallinger Office of Middle and High School Instructional Services Felicia D. Dyke, Director Deborah Kiger Bliss, Mathematics Coordinator NOTICE TO THE READER In accordance with the requirements of the Civil Rights Act and other federal and state laws and regulations, this document has been reviewed to ensure that it does not reflect stereotypes based on sex, race, or national origin. The Virginia Department of Education does not unlawfully discriminate on the basis of sex, race, age, color, religion, handicapping conditions, or national origin in employment or in its educational programs and activities.

3 The content contained in this document is supported in whole or in part by the Department of Education. However, the opinions expressed herein do not necessarily reflect the position or policy of the Department of Education, and no official endorsement by the Department of Education should be inferred. ii Introduction The Mathematics Standards of Learning Enhanced Scope and Sequence is a resource intended to help teachers align their classroom instruction with the Mathematics Standards of Learning that were adopted by the Board of Education in October 2001 (January 2008 for algebra , functions , and data Analysis ).

4 The Mathematics Enhanced Scope and Sequence is organized by topics from and includes the content of the Standards of Learning and the essential knowledge and skills from the Curriculum Framework. In addition, the Enhanced Scope and Sequence provides teachers with sample lesson plans that are aligned with the essential knowledge and skills in the Curriculum Framework. School divisions and teachers can use the Enhanced Scope and Sequence as a resource for developing sound curricular and instructional programs.

5 These materials are intended as examples of how the knowledge and skills might be presented to students in a sequence of lessons that has been aligned with the Standards of Learning. Teachers who use the Enhanced Scope and Sequence should correlate the essential knowledge and skills with available instructional resources as noted in the materials and determine the pacing of instruction as appropriate. This resource is not a complete curriculum and is neither required nor prescriptive, but it can be a valuable instructional tool.

6 The Enhanced Scope and Sequence contains the following: Essential knowledge and skills from the Mathematics Standards of Learning Curriculum Framework Related Standards of Learning Sample lesson plans containing instructional activities; follow-up/extensions; and related resources. iii Acknowledgments The Virginia Department of Education wishes to thank the following individuals for their contributions to this document. J. Patrick Lintner Harrisonburg City Schools Jason Yoder Rupp Harrisonburg City Schools Pamela Bailey Spotsylvania County Schools Nathan Frey Spotsylvania County Schools 4 Organizing Topic: Linear Modeling Mathematical Goals: Students will model linear relationships using a CBR (Calculator Based Ranger).

7 Students will explore positive, negative and zero slopes as rates of change. Students will make predictions using the line (curve) of best fit for the modeled data as well as evaluating the mathematical model for specific values in the domain of the data . Standards Addressed: ; ; ; data Used: data obtained using the CBR , Internet Web sites, surveys, experiments and data provided in tables. Materials: CBR Applications: EasyData and Transformation Application Graphing calculator and links Handout Up to Speed Handout Investigating Slope, Equations, and Tables using the CBR Handout See Starbuck Run Handout White Water Rafting on Silly Creek May also need graph paper Instructional Activities: I.

8 Introduction--Up to Speed Students will acknowledge the average rate of change by discussing speed as miles per hour. If a car is set on cruise control, how far will it travel in 1 hour, 2 hours, 5 hours? Concepts covered include: domain and range; scatter plots; continuity; function; evaluation of a function for domain values; independent and dependent variables; rate of change (slope); slope-intercept form of an equation; linear regression; transformations; and direct variation.

9 5 II. Investigating Slope, Equations, and Tables using the CBR Students will physically model positive and negative lines by using the CBR and walking toward or away from the CBR . Extension to the activity would be to model horizontal lines and have students attempt to model vertical lines. Concepts covered include: scatter plots; domain and range; continuity; function; evaluation of a function for domain values; independent and dependent variables; rate of change (slope); slope-intercept form of an equation; linear regression; transformations; and direct variation.

10 III. See Starbuck Run Students will be given data in a table that represent the results recorded as a horse runs. The data represent a positive rate of change but do not have a correlation coefficient of 1. Concepts covered include: scatter plots; domain and range; continuity; function; evaluation of a function for domain values; independent and dependent variables; rate of change (slope); slope-intercept form of an equation; linear regression; transformations; and direct variation.