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Course Details:
Course Details:
Grades: 9-12
Length: four semesters
Credit: 2 (0.5 per semester)
1.0 credit of math elective will be earned for successful completion of Fundamentals and 1.1.
1.0 credit of Algebra 1 will be earned for successful completion of 1.2 & 1.3.
Prerequisite: none
Placement recommendation: Student scored below the 20th percentile on the most recent MAP test and more than one grade level below their current grade level on iReady. Complete the “Decision Point” form.
Course Description:
Course Description:
Algebra 1 formalizes and extends the mathematics that students learned in the 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.
The first semester (Fundamentals) of the two-year Algebra 1 program provides a review of middle school Algebra math standards, with individualized attention to students’ specific skill deficits. The second semester (1.1) begins instruction in Algebra 1. Over three semesters (1.1, 1.2, and 1.3), students receive the Algebra 1 curriculum. Successful completion of the third and fourth semesters (Algebra 1.2 and 1.3) is required to fulfill the Algebra 1 graduation requirement.
Expectations of Two Year Program
Expectations of Two Year Program
Expectations of how the two-year Algebra 1 program will be taught:
This is a student-centered course that maximizes time for teacher-student interaction. Teachers will focus on student engagement and minimize lecture time.
This course will help to build mathematical identity and agency for students. Teachers will validate student thinking and encourage positive connections with mathematics.
Student learning and practice needs to occur in the classroom; assignments completed outside the classroom will have minimal impact on students’ grades.
Shorter, more frequent targeted assessments will be utilized.
It is recommended another educator be present in the classroom, as staffing allows, to assist with teacher-student interaction.
Mathematical Topics
Mathematical Topics
(Recommended Order)
Semester 1
Semester 1
(Algebra Fundamentals)
Topics covered in this semester can include any from the Math 8 curriculum, with the goal of the semester to prepare students for success in the Algebra 1 series. Some suggested areas of focus are listed below.
Order of Operations and Integer Operations
Solving Equations
Linear Equations
Semester 2
Semester 2
(Algebra 1.1)
Equations and Inequalities
Linear Equations
Relations and Functions
Semester 3
Semester 3
(Algebra 1.2)
Systems of Equations and Inequalities
Exponents and Exponential Functions
Statistics
Semester 4
Semester 4
(Algebra 1.3)
Polynomials and Factoring
Quadratic Functions
Solving Quadratic Equations
Course/ Grade Competencies
Course/ Grade Competencies
Semester 1
Semester 1
(Algebra Fundamentals)
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.
5.9-12.2: The learner will write and apply algebraic modes to represent and answer questions about a given situation.
Semester 2
Semester 2
(Algebra 1.1)
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 3
Semester 3
(Algebra 1.2)
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.
M7.9-12.3: The learner will summarize data using appropriate statistics.
M7.9-12.4: The learner will select appropriate graphical and numerical methods, and use these methods to represent the data in a way that supports interpretation.
M7.9-12.5: The learner will interpret descriptive statistics and linear models within the context of the data and the original question.
Semester 4
Semester 4
(Algebra 1.3)
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 1: Algebra Fundamentals
Semester 1: Algebra Fundamentals
Order of Operations & Integers
Order of Operations & Integers
Graduate-Level Competency:
Graduate-Level Competency:
M1 – Symbolic Expression: The learner will be able to reason abstractly and utilize symbolic expressions and mathematical models.
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
M5.9-12.1
M5.9-12.2
Content Objectives:
Content Objectives:
Must be Covered:
The learner will:
Add, subtract, multiply and divide integer values.
Use order of operations to simplify numerical expressions.
Use order of operations to simplify algebraic expressions.
Model situations with algebraic expressions.
Standards:
Standards:
AKSS
7.NS.2, 7.NS.3,
7.EE.1, 7.EE.3,
7.EE.4
Mathematical Practices
All mathematical practices are present in each unit.
Solving Equations
Solving 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:
M1.9-12.2
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:
Solve one-step equations.
Solve two-step equations.
Simplify and then solve equations with variables on one side.
Standards:
Standards:
AKSS
8.EE7
Mathematical Practices
All mathematical practices are present in each unit.
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.
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
M3.9-12.1
M3.9-12.2
M3.9-12.3
M5.9-12.2
Content Objectives:
Content Objectives:
Must be Covered:
The learner will:
Find and interpret the slope of a linear situation given a graph, ordered pairs, table, or written description.
Use a table of values to graph a linear equation written in slope-intercept form.
Use slope and y-intercept to graph a linear equation written in slope-intercept form.
Standards:
Standards:
AKSS
8.F.4, 8.F.5
Mathematical Practices
All mathematical practices are present in each unit.
Semester 2: Algebra 1.1
Semester 2: Algebra 1.1
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 (include literal equations).
Solve equations with variables on both sides.
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, and 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 & Functions
Relations & 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)
Semester 3: Algebra 1.2
Semester 3: Algebra 1.2
Systems of Equations & Inequalities
Systems of 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
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 & Exponential Functions
Exponents & 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:
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
Statistics
Statistics
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.
M7 – Data, Analysis, Probability, and Statistics: The learner will apply statistical methods to summarize, represent, analyze, and interpret data.
Course/ Grade Competencies:
Course/ Grade Competencies:
M1.9-12.1
M3.9-12.1
M3.9-12.2
M7.9-12.3
M7.9-12.4
M7.9-12.5
Content Objectives:
Content Objectives:
Must be Covered:
The learner will:
Represent data on a dot plot, box plot, or histogram.
Use statistics to describe the center and spread of a data set.
Interpret the effect of outliers on a data set.
Represent data on a scatter plot and describe how the two variables are related.
Create linear models from scatter plots (linear regression).
Can be Covered:
The learner will:
Use technology to compute and then interpret the correlation coefficient.
Distinguish between correlation and causation.
Standards:
Standards:
AKSS
S-ID.1, S-ID.2,
S-ID.3, S-ID.6,
S-ID.7, S-ID.8,
S-ID.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 11
Semester 4: Algebra 1.3
Semester 4: Algebra 1.3
Polynomials & Factoring
Polynomials & 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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