Algebra I
Table of Contents
Unit 1: Understanding Numeric Values, Variability, and Change ................................1
Unit 2: Writing and Solving Proportions and Linear Equations ................................14
Unit 3: Linear Functions and Their Graphs, Rates of Change, and Applications .....25
Unit 4: Linear Equations, Inequalities, and Their Solutions .......................................37
Unit 5: Systems of Equations and Inequalities ..............................................................47
Unit 6: Measurement .......................................................................................................59
Unit 7: Exponents, Exponential Functions, and Nonlinear Graphs ............................73
Unit 8: Data, Chance, and Algebra.................................................................................84
, Louisiana Comprehensive Curriculum, Revised
Course Introduction
The Louisiana Department of Education issued the Comprehensive Curriculum in 2005. The
curriculum has been revised based on teacher feedback, an external review by a team of content
experts from outside the state, and input from course writers. As in the first edition, the
Louisiana Comprehensive Curriculum, revised 2008 is aligned with state content standards, as
defined by Grade-Level Expectations (GLEs), and organized into coherent, time-bound units
with sample activities and classroom assessments to guide teaching and learning. The order of
the units ensures that all GLEs to be tested are addressed prior to the administration of iLEAP
assessments.
District Implementation Guidelines
Local districts are responsible for implementation and monitoring of the Louisiana
Comprehensive Curriculum and have been delegated the responsibility to decide if
• units are to be taught in the order presented
• substitutions of equivalent activities are allowed
• GLES can be adequately addressed using fewer activities than presented
• permitted changes are to be made at the district, school, or teacher level
Districts have been requested to inform teachers of decisions made.
Implementation of Activities in the Classroom
Incorporation of activities into lesson plans is critical to the successful implementation of the
Louisiana Comprehensive Curriculum. Lesson plans should be designed to introduce students to
one or more of the activities, to provide background information and follow-up, and to prepare
students for success in mastering the Grade-Level Expectations associated with the activities.
Lesson plans should address individual needs of students and should include processes for re-
teaching concepts or skills for students who need additional instruction. Appropriate
accommodations must be made for students with disabilities.
New Features
Content Area Literacy Strategies are an integral part of approximately one-third of the activities.
Strategy names are italicized. The link (view literacy strategy descriptions) opens a document
containing detailed descriptions and examples of the literacy strategies. This document can also
be accessed directly at http://www.louisianaschools.net/lde/uploads/11056.doc.
A Materials List is provided for each activity and Blackline Masters (BLMs) are provided to
assist in the delivery of activities or to assess student learning. A separate Blackline Master
document is provided for each course.
The Access Guide to the Comprehensive Curriculum is an online database of
suggested strategies, accommodations, assistive technology, and assessment
options that may provide greater access to the curriculum activities. The Access
Guide will be piloted during the 2008-2009 school year in Grades 4 and 8, with
other grades to be added over time. Click on the Access Guide icon found on the first page of
each unit or by going directly to the url http://mconn.doe.state.la.us/accessguide/default.aspx.
, 1
Algebra I
Unit 1: Understanding Numeric Values, Variability, and Change
Time Frame: Approximately three weeks
Unit Description
This unit examines numbers and number sets including basic operations on rational
numbers, integer exponents, radicals, and scientific notation. It also includes
investigations of situations in which quantities change and the study of the relative nature
of the change through tables, graphs, and numerical relationships. The identification of
independent and dependent variables is emphasized as well as the comparison of linear
and non-linear data.
Unit 1 is a connection between the student’s middle school math courses and the Algebra
I course. Topics previously studied are reviewed as a precursor to the ninth grade GLEs.
Although this first unit does not follow the order of a traditional Algebra I textbook, it is a
necessary unit in order for a student to develop and expand upon the basic knowledge of
numbers and number operations as well as graphical representations of real-life
situations.
Student Understandings
Students focus on developing the notion of a variable. They begin to understand inputs
and outputs and how they reflect the nature of a given relationship. Students recognize
and apply the notions of independent and dependent variables and write expressions
modeling simple linear relationships. They should also come to understand the difference
between linear and non-linear relationships.
Guiding Questions
1. Can students perform basic operations on rational numbers with and without
technology?
2. Can students simplify, add, subtract and multiply radical expressions?
3. Can students evaluate and write expressions using scientific notation and integer
exponents?
4. Can students identify independent and dependent variables?
5. Can students recognize patterns in and differentiate between linear and non-
linear sequence data?
Algebra I•Unit 1• Understanding Numeric Values, Variability, and Change 1
, 2
Unit 1 Grade-Level Expectations (GLEs)
GLE # GLE Text and Benchmarks
Number and Number Relations
1. Identify and describe differences among natural numbers, whole numbers,
integers, rational numbers, and irrational numbers (N-1-H) (N-2-H) (N-3-H)
2. Evaluate and write numerical expressions involving integer exponents (N-2-H)
3. Apply scientific notation to perform computations, solve problems, and write
representations of numbers (N-2-H)
4. Distinguish between an exact and an approximate answer, and recognize errors
introduced by the use of approximate numbers with technology (N-3-H) (N-4-
H) (N-7-H)
5. Demonstrate computational fluency with all rational numbers (e.g., estimation,
mental math, technology, paper/pencil) (N-5-H)
6. Simplify and perform basic operations on numerical expressions involving
radicals (e.g., 2 3 + 5 3 =7 3 ) (N-5-H)
Algebra
7. Use proportional reasoning to model and solve real-life problems involving
direct and inverse variation (N-6-H)
8. Use order of operations to simplify or rewrite variable expressions (A-1-H) (A-
2-H)
9. Model real-life situations using linear expressions, equations, and inequalities
(A-1-H) (D-2-H) (P-5-H)
10. Identify independent and dependent variables in real-life relationships (A-1-H)
15. Translate among tabular, graphical, and algebraic representations of functions
and real-life situations (A-3-H) (P-1-H) (P-2-H)
Data Analysis, Probability, and Discrete Math
28. Identify trends in data and support conclusions by using distribution
characteristics such as patterns, clusters, and outliers (D-1-H) (D-6-H) (D-7-H)
29. Create a scatter plot from a set of data and determine if the relationship is linear
or nonlinear (D-1-H) (D-6-H) (D-7-H)
34. Follow and interpret processes expressed in flow charts (D-8-H)
Algebra I•Unit 1• Understanding Numeric Values, Variability, and Change 2
Table of Contents
Unit 1: Understanding Numeric Values, Variability, and Change ................................1
Unit 2: Writing and Solving Proportions and Linear Equations ................................14
Unit 3: Linear Functions and Their Graphs, Rates of Change, and Applications .....25
Unit 4: Linear Equations, Inequalities, and Their Solutions .......................................37
Unit 5: Systems of Equations and Inequalities ..............................................................47
Unit 6: Measurement .......................................................................................................59
Unit 7: Exponents, Exponential Functions, and Nonlinear Graphs ............................73
Unit 8: Data, Chance, and Algebra.................................................................................84
, Louisiana Comprehensive Curriculum, Revised
Course Introduction
The Louisiana Department of Education issued the Comprehensive Curriculum in 2005. The
curriculum has been revised based on teacher feedback, an external review by a team of content
experts from outside the state, and input from course writers. As in the first edition, the
Louisiana Comprehensive Curriculum, revised 2008 is aligned with state content standards, as
defined by Grade-Level Expectations (GLEs), and organized into coherent, time-bound units
with sample activities and classroom assessments to guide teaching and learning. The order of
the units ensures that all GLEs to be tested are addressed prior to the administration of iLEAP
assessments.
District Implementation Guidelines
Local districts are responsible for implementation and monitoring of the Louisiana
Comprehensive Curriculum and have been delegated the responsibility to decide if
• units are to be taught in the order presented
• substitutions of equivalent activities are allowed
• GLES can be adequately addressed using fewer activities than presented
• permitted changes are to be made at the district, school, or teacher level
Districts have been requested to inform teachers of decisions made.
Implementation of Activities in the Classroom
Incorporation of activities into lesson plans is critical to the successful implementation of the
Louisiana Comprehensive Curriculum. Lesson plans should be designed to introduce students to
one or more of the activities, to provide background information and follow-up, and to prepare
students for success in mastering the Grade-Level Expectations associated with the activities.
Lesson plans should address individual needs of students and should include processes for re-
teaching concepts or skills for students who need additional instruction. Appropriate
accommodations must be made for students with disabilities.
New Features
Content Area Literacy Strategies are an integral part of approximately one-third of the activities.
Strategy names are italicized. The link (view literacy strategy descriptions) opens a document
containing detailed descriptions and examples of the literacy strategies. This document can also
be accessed directly at http://www.louisianaschools.net/lde/uploads/11056.doc.
A Materials List is provided for each activity and Blackline Masters (BLMs) are provided to
assist in the delivery of activities or to assess student learning. A separate Blackline Master
document is provided for each course.
The Access Guide to the Comprehensive Curriculum is an online database of
suggested strategies, accommodations, assistive technology, and assessment
options that may provide greater access to the curriculum activities. The Access
Guide will be piloted during the 2008-2009 school year in Grades 4 and 8, with
other grades to be added over time. Click on the Access Guide icon found on the first page of
each unit or by going directly to the url http://mconn.doe.state.la.us/accessguide/default.aspx.
, 1
Algebra I
Unit 1: Understanding Numeric Values, Variability, and Change
Time Frame: Approximately three weeks
Unit Description
This unit examines numbers and number sets including basic operations on rational
numbers, integer exponents, radicals, and scientific notation. It also includes
investigations of situations in which quantities change and the study of the relative nature
of the change through tables, graphs, and numerical relationships. The identification of
independent and dependent variables is emphasized as well as the comparison of linear
and non-linear data.
Unit 1 is a connection between the student’s middle school math courses and the Algebra
I course. Topics previously studied are reviewed as a precursor to the ninth grade GLEs.
Although this first unit does not follow the order of a traditional Algebra I textbook, it is a
necessary unit in order for a student to develop and expand upon the basic knowledge of
numbers and number operations as well as graphical representations of real-life
situations.
Student Understandings
Students focus on developing the notion of a variable. They begin to understand inputs
and outputs and how they reflect the nature of a given relationship. Students recognize
and apply the notions of independent and dependent variables and write expressions
modeling simple linear relationships. They should also come to understand the difference
between linear and non-linear relationships.
Guiding Questions
1. Can students perform basic operations on rational numbers with and without
technology?
2. Can students simplify, add, subtract and multiply radical expressions?
3. Can students evaluate and write expressions using scientific notation and integer
exponents?
4. Can students identify independent and dependent variables?
5. Can students recognize patterns in and differentiate between linear and non-
linear sequence data?
Algebra I•Unit 1• Understanding Numeric Values, Variability, and Change 1
, 2
Unit 1 Grade-Level Expectations (GLEs)
GLE # GLE Text and Benchmarks
Number and Number Relations
1. Identify and describe differences among natural numbers, whole numbers,
integers, rational numbers, and irrational numbers (N-1-H) (N-2-H) (N-3-H)
2. Evaluate and write numerical expressions involving integer exponents (N-2-H)
3. Apply scientific notation to perform computations, solve problems, and write
representations of numbers (N-2-H)
4. Distinguish between an exact and an approximate answer, and recognize errors
introduced by the use of approximate numbers with technology (N-3-H) (N-4-
H) (N-7-H)
5. Demonstrate computational fluency with all rational numbers (e.g., estimation,
mental math, technology, paper/pencil) (N-5-H)
6. Simplify and perform basic operations on numerical expressions involving
radicals (e.g., 2 3 + 5 3 =7 3 ) (N-5-H)
Algebra
7. Use proportional reasoning to model and solve real-life problems involving
direct and inverse variation (N-6-H)
8. Use order of operations to simplify or rewrite variable expressions (A-1-H) (A-
2-H)
9. Model real-life situations using linear expressions, equations, and inequalities
(A-1-H) (D-2-H) (P-5-H)
10. Identify independent and dependent variables in real-life relationships (A-1-H)
15. Translate among tabular, graphical, and algebraic representations of functions
and real-life situations (A-3-H) (P-1-H) (P-2-H)
Data Analysis, Probability, and Discrete Math
28. Identify trends in data and support conclusions by using distribution
characteristics such as patterns, clusters, and outliers (D-1-H) (D-6-H) (D-7-H)
29. Create a scatter plot from a set of data and determine if the relationship is linear
or nonlinear (D-1-H) (D-6-H) (D-7-H)
34. Follow and interpret processes expressed in flow charts (D-8-H)
Algebra I•Unit 1• Understanding Numeric Values, Variability, and Change 2
