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Course Details:
Course Details:
Grades: 9-12
Length: two semesters
Credit: 1 (0.5 per semester)
Prerequisite: none
Course Description:
Course Description:
Algebra 1 formalizes and extends the mathematics that students learned in middle school. At the heart of Algebra 1 is the study of functions. Throughout the study of specific functions (notably linear, exponential, and quadratic functions), students will be able to see the structures of functions, to make generalizations about all functions, and to describe the uniqueness of specific functions. Within the study of functions, students will apply properties of numbers and equality to carry out operations within different functions, all with the goal of seeing the applicability of mathematics to describe and model a wide range of natural or man-made events.
If students have not taken and passed this course in middle school, this is the first course in their high school math pathway.
Mathematical Topics
Mathematical Topics
(Recommended Order)
Semester 1
Semester 1
Equations and Inequalities
Linear Equations
Relations and Functions
Systems of Equations and Inequalities.
Semester 2
Semester 2
Exponents and Exponential Functions
Polynomials and Factoring
Quadratic Functions
Solving Quadratic Equations
Course/ Grade Competencies
Course/ Grade Competencies
Semester 1
Semester 1
M1.9-12.1: The learner will write, apply, and provide a rationale for a mathematical model representing a given situation.
M1.9-12.2: The learner will interpret and use symbols to express relationships and justify reasoning when solving problems.
M2.9-12.1: The learner will justify how to apply properties of real number systems to variable expressions in a variety of contexts.
M3.9-12.1: The learner will use computational strategies and algorithms and provide rationale for their use.
M3.9-12.2: The learner will reason quantitatively when analyzing, representing, and solving problems.
M3.9-12.3: The learner will compare the effectiveness or logic of two plausible arguments or models.
M5.9-12.1: The learner will apply properties of arithmetic and algebra to simplify and manipulate symbolic expressions or models.
M5.9-12.2: The learner will write and apply algebraic modes to represent and answer questions about a given situation.
M5.9-12.3: The learner will interpret, analyze, and use relations and functions applied in a variety of contexts, including real-world phenomena.
M5.9-12.4: The learner will analyze relations and functions, using multiple representations.
Semester 2
Semester 2
M1.9-12.1: The learner will write, apply, and provide a rationale for a mathematical model representing a given situation.
M1.9-12.2: The learner will interpret and use symbols to express relationships and justify reasoning when solving problems.
M2.9-12.1: The learner will justify how to apply properties of real number systems to variable expressions in a variety of contexts.
M3.9-12.1: The learner will use computational strategies and algorithms and provide rationale for their use.
M3.9-12.2: The learner will reason quantitatively when analyzing, representing, and solving problems.
M3.9-12.3: The learner will compare the effectiveness or logic of two plausible arguments or models.
M5.9-12.1: The learner will apply properties of arithmetic and algebra to simplify and manipulate symbolic expressions or models.
M5.9-12.2: The learner will write and apply algebraic modes to represent and answer questions about a given situation.
M5.9-12.3: The learner will interpret, analyze, and use relations and functions applied in a variety of contexts, including real-world phenomena.
M5.9-12.4: The learner will analyze relations and functions, using multiple representations.
Equations & Inequalities
Equations & Inequalities
Graduate-Level Competency:
Graduate-Level Competency:
M1 – Symbolic Expression: The learner will be able to reason abstractly and utilize symbolic expressions and mathematical models.
M2 – Numbers and Number Systems: The learner will develop an applied knowledge of numbers and number systems to solve problems.
M3 – Reasoning and Strategic Thinking: The learner will use evidence to support authentic application of concepts and support mathematical arguments.
M5 – Algebraic Functions, Patterns and Relations: The learner will utilize patterns, relations, and functions to compare, interpret, and analyze situations.
Course/ Grade Competencies:
Course/ Grade Competencies:
M1.9-12.1
M1.9-12.2
M2.9-12.1
M3.9-12.1
M3.9-12.2
M5.9-12.1
M5.9-12.2
Content Objectives:
Content Objectives:
Must be Covered:
The learner will:
Simplify, then solve equations.
Solve equations with variables on both sides.
Solve any linear equation.
Write and solve equations to model situations.
Solve linear inequalities.
Write and solve inequalities to model situations.
Can be Covered:
The learner will:
Solve compound inequalities.
Solve absolute value equations and inequalities.
Standards:
Standards:
AKSS
N-Q.1, N-Q.2,
N-Q.3, A-REI.1,
A-REI.3, A-CED.1,
A-CED.4
Mathematical Practices
All mathematical practices are present in each unit.
Suggested Activities, Materials, and Resources:
Suggested Activities, Materials, and Resources:
enVision Algebra 1 – topic 1
Linear Equations
Linear Equations
Graduate-Level Competency:
Graduate-Level Competency:
M1 – Symbolic Expression: The learner will be able to reason abstractly and utilize symbolic expressions and mathematical models.
M2 – Numbers and Number Systems: The learner will develop an applied knowledge of numbers and number systems to solve problems.
M3 – Reasoning and Strategic Thinking: The learner will use evidence to support authentic application of concepts and support mathematical arguments.
M5 – Algebraic Functions, Patterns and Relations: The learner will utilize patterns, relations, and functions to compare, interpret, and analyze situations.
Course/ Grade Competencies:
Course/ Grade Competencies:
M1.9-12.1
M1.9-12.2
M2.9-12.1
M3.9-12.1
M3.9-12.2
M3.9-12.3
M5.9-12.1
M5.9-12.2
Content Objectives:
Content Objectives:
Must be Covered:
The learner will:
Find and interpret key characteristics (slope, x-intercept, y-intercept) of a linear situation, given a graph, ordered pairs, table, or written description.
Graph a linear equation written in any form.
Model linear situations with equations.
Write a linear equation given information.
Can be Covered:
The learner will:
Graph and find equations of parallel and perpendicular lines.
Recognize and utilize Point-Slope Form.
Standards:
Standards:
AKSS
N-Q.1, N-Q.2,
N-Q.3, F-IF.4,
F-IF.6, F-IF.7,
F-IF.9
Mathematical Practices
All mathematical practices are present in each unit.
Suggested Activities, Materials, and Resources:
Suggested Activities, Materials, and Resources:
enVision Algebra 1 – topic 2
Relations and Functions
Relations and Functions
Graduate-Level Competency:
Graduate-Level Competency:
M1 – Symbolic Expression: The learner will be able to reason abstractly and utilize symbolic expressions and mathematical models.
M2 – Numbers and Number Systems: The learner will develop an applied knowledge of numbers and number systems to solve problems.
M3 – Reasoning and Strategic Thinking: The learner will use evidence to support authentic application of concepts and support mathematical arguments.
M5 – Algebraic Functions, Patterns and Relations: The learner will utilize patterns, relations, and functions to compare, interpret, and analyze situations.
Course/ Grade Competencies:
Course/ Grade Competencies:
M1.9-12.1
M1.9-12.2
M2.9-12.1
M3.9-12.1
M3.9-12.2
M3.9-12.3
M5.9-12.1
M5.9-12.2
M5.9-12.3
M5.9-12.4
Content Objectives:
Content Objectives:
Must be Covered:
The learner will:
Determine whether a relation is a function.
Determine the domain and range of a function, given a table of values, ordered pairs, mapping, or graph.
Determine a reasonable domain for a situation described by a linear function.
Sketch and interpret graphs showing key features given a description of a situation and/or function.
Evaluate functions written in function notation.
Interpret statements in function notation in terms of their context.
Can be Covered:
The learner will:
Use function notation to evaluate functions given a graph.
Compare properties of two functions each expressed in a different way (algebraically, graphically, numerically, in tables, verbal descriptions, etc.).
Write arithmetic sequences both recursively and with an explicit formula.
Standards:
Standards:
AKSS
N-Q.2, F-IF.1,
F-IF.2, F-IF.4,
F-IF.5, F-LE.5,
F-IF.9, F-BF.1
Mathematical Practices
All mathematical practices are present in each unit.
Suggested Activities, Materials, and Resources:
Suggested Activities, Materials, and Resources:
enVision Algebra 1 – topic 3 (focus on 3-1).
Systems of Equations and Inequalities
Systems of Equations and Inequalities
Graduate-Level Competency:
Graduate-Level Competency:
M1 – Symbolic Expression: The learner will be able to reason abstractly and utilize symbolic expressions and mathematical models.
M2 – Numbers and Number Systems: The learner will develop an applied knowledge of numbers and number systems to solve problems.
M3 – Reasoning and Strategic Thinking: The learner will use evidence to support authentic application of concepts and support mathematical arguments.
M5 – Algebraic Functions, Patterns and Relations: The learner will utilize patterns, relations, and functions to compare, interpret, and analyze situations.
Course/ Grade Competencies:
Course/ Grade Competencies:
M1.9-12.1
M1.9-12.2
M2.9-12.1
M3.9-12.1
M3.9-12.2
M3.9-12.3
M5.9-12.1
M5.9-12.2
Content Objectives:
Content Objectives:
Must be Covered:
The learner will:
Solve systems of equations by graphing.
Solve systems of equations using substitution.
Solve systems of equations using elimination.
Model situations with linear systems of equations.
Can be Covered:
The learner will:
Determine solutions to linear inequalities and systems of linear inequalities.
Model situations with inequalities, representing constraints with equations or inequalities and interpreting solutions as viable or non-viable.
Standards:
Standards:
AKSS
A-REI.5, A-REI.6,
A-REI.10, A-REI.11,
A-REI.12, A-CED.2,
A-CED.3
Mathematical Practices
All mathematical practices are present in each unit.
Suggested Activities, Materials, and Resources:
Suggested Activities, Materials, and Resources:
enVision Algebra 1 – topic 4
Exponents and Exponential Functions
Exponents and Exponential Functions
Graduate-Level Competency:
Graduate-Level Competency:
M1 – Symbolic Expression: The learner will be able to reason abstractly and utilize symbolic expressions and mathematical models.
M2 – Numbers and Number Systems: The learner will develop an applied knowledge of numbers and number systems to solve problems.
M3 – Reasoning and Strategic Thinking: The learner will use evidence to support authentic application of concepts and support mathematical arguments.
M5 – Algebraic Functions, Patterns and Relations: The learner will utilize patterns, relations, and functions to compare, interpret, and analyze situations.
Course/ Grade Competencies:
Course/ Grade Competencies:
M1.9-12.1
M1.9-12.2
M2.9-12.1
M3.9-12.1
M3.9-12.2
M5.9-12.1
M5.9-12.2
M5.9-12.3
Content Objectives:
Content Objectives:
Must be Covered:
The learner will:
Simplify and evaluate expressions containing integer exponents.
Rewrite expressions involving radicals and rational exponents using the properties of exponents.
Solve equations with rational exponents using the properties of exponents.
Graph simple exponential functions (no vertical or horizontal translations).
Construct simple exponential functions from graphs, tables of values, or a description.
Distinguish between situations that can be modeled with linear functions and with exponential functions.
Can be Covered:
The learner will:
Write geometric sequences both recursively and with an explicit formula.
Simplify radical expressions.
Standards:
Standards:
AKSS
N-RN.1, N-RN.2,
F-LE.1, F-LE.2,
F-LE.5, A-SSE.3,
F-IF.3, F-IF.8,
F-IF.9, F-BF.2
Mathematical Practices
All mathematical practices are present in each unit.
Suggested Activities, Materials, and Resources:
Suggested Activities, Materials, and Resources:
enVision Algebra 1 – topic 6
Polynomials and Factoring
Polynomials and Factoring
Graduate-Level Competency:
Graduate-Level Competency:
M2 – Numbers and Number Systems: The learner will develop an applied knowledge of numbers and number systems to solve problems.
M3 – Reasoning and Strategic Thinking: The learner will use evidence to support authentic application of concepts and support mathematical arguments.
M5 – Algebraic Functions, Patterns and Relations: The learner will utilize patterns, relations, and functions to compare, interpret, and analyze situations.
Course/ Grade Competencies:
Course/ Grade Competencies:
M2.9-12.1
M3.9-12.1
M3.9-12.2
M5.9-12.1
Content Objectives:
Content Objectives:
Must be Covered:
The learner will:
Interpret the structure of polynomial expressions using language such as terms, factors, and coefficients.
Add, subtract, and multiply polynomials.
Factor polynomials using the greatest common factor.
Factor trinomials.
Factor a difference of squares.
Standards:
Standards:
AKSS
A-SSE.1, A-SSE.2,
A-SSE.3, A-APR.1
Mathematical Practices
All mathematical practices are present in each unit.
Suggested Activities, Materials, and Resources:
Suggested Activities, Materials, and Resources:
enVision Algebra 1 – topic 7
Quadratic Functions
Quadratic Functions
Graduate-Level Competency:
Graduate-Level Competency:
M1 – Symbolic Expression: The learner will be able to reason abstractly and utilize symbolic expressions and mathematical models.
M2 – Numbers and Number Systems: The learner will develop an applied knowledge of numbers and number systems to solve problems.
M3 – Reasoning and Strategic Thinking: The learner will use evidence to support authentic application of concepts and support mathematical arguments.
M5 – Algebraic Functions, Patterns and Relations: The learner will utilize patterns, relations, and functions to compare, interpret, and analyze situations.
Course/ Grade Competencies:
Course/ Grade Competencies:
M1.9-12.1
M1.9-12.2
M2.9-12.1
M3.9-12.1
M3.9-12.2
M3.9-12.3
M5.9-12.1
M5.9-12.2
M5.9-12.3
M5.9-12.4
Content Objectives:
Content Objectives:
Must be Covered:
The learner will:
Interpret key features (zeros, maximum/minimum, intercepts) of a parabola in terms of a context.
Graph simple quadratics written in standard form (factorable).
Can be Covered:
The learner will:
Graph quadratics in vertex form.
Compare linear, exponential, and quadratic models.
Standards:
Standards:
AKSS
F-IF.4, F-IF.5,
F-IF.7, F-IF.8,
F-IF.9
Mathematical Practices
All mathematical practices are present in each unit.
Suggested Activities, Materials, and Resources:
Suggested Activities, Materials, and Resources:
enVision Algebra 1 – topic 8
Solving Quadratic Equations
Solving Quadratic Equations
Graduate-Level Competency:
Graduate-Level Competency:
M1 – Symbolic Expression: The learner will be able to reason abstractly and utilize symbolic expressions and mathematical models.
M2 – Numbers and Number Systems: The learner will develop an applied knowledge of numbers and number systems to solve problems.
M3 – Reasoning and Strategic Thinking: The learner will use evidence to support authentic application of concepts and support mathematical arguments.
M5 – Algebraic Functions, Patterns and Relations: The learner will utilize patterns, relations, and functions to compare, interpret, and analyze situations.
Course/ Grade Competencies:
Course/ Grade Competencies:
M1.9-12.1
M1.9-12.2
M2.9-12.1
M3.9-12.1
M3.9-12.2
M5.9-12.1
M5.9-12.2
M5.9-12.3
Content Objectives:
Content Objectives:
Must be Covered:
The learner will:
Solve quadratic equations by factoring.
Solve quadratic equations using square roots.
Solve quadratic equations using the quadratic formula.
Can be Covered:
The learner will:
Solve quadratic equations by completing the square.
Write solutions as simplified exact values rather than decimal approximations.
Standards:
Standards:
AKSS
A-REI.4
Mathematical Practices
All mathematical practices are present in each unit.
Suggested Activities, Materials, and Resources:
Suggested Activities, Materials, and Resources:
enVision Algebra 1 – topic 9
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