 Mathematics
 805 (Registered)

Credit Value: 1
Anticipated Grade Level(s): 8^{th} and 9^{th}.
Prerequisites: PreAlgebra or equivalent.
Course Description:
The content of Algebra 1 is organized around families of functions, with special emphasis on linear and quadratic functions. As students learn about each family of functions, they will learn to represent them in multiple ways – as verbal descriptions, equations, tables, and graphs. They will also learn to model realworld situations using functions in order to solve problems arising from those situations. In addition to its algebra content, the course includes lessons on probability and data analysis as well as numerous examples and exercises involving geometry.
This is a firstyear algebra course in which you will learn to reason symbolically. The key content involves writing, solving, and graphing linear and quadratic equations, including systems of two linear equations in two unknowns. Quadratic equations are solved by factoring, completing the square, graphically, or by application of the quadratic formula. The course also includes a study of monomial and polynomial expressions, inequalities, exponents, functions, rational expressions, ratio, and proportion. Algebraic skills are applied in a wide variety of problemsolving situations.
Algebra 1 topics include recognizing and developing patterns using tables, graphs, and equations. In addition, students will explore operations on algebraic expressions, apply mathematical properties to algebraic equations. Students will solve problems using equations, graphs, and tables to investigate linear relationships. Technology will be used to introduce and expand upon the areas of study listed above. Use of computers and graphing calculators will be incorporated into each module.
Aims & Goals:
Algebraic thinking is an important lifeskill expected of all school graduates. The course provides a solid foundation for subsequent mathematics courses in the upper school. It also plays an essential role in preparation for standardized tests.
Course Content

Chapter 1: Expressions, Equations, and Functions 0/7

Lecture1.1Evaluate Expressions 06 min

Lecture1.2Apply Order of Operations 15 min

Lecture1.3Write Expressions 15 min

Lecture1.4Write Equations and Inequalities 08 min

Lecture1.5Problem Solving Plan 12 min

Lecture1.6Precision and Measurement

Lecture1.7Represent Functions as Rules, Tables and Graphs 15 min


Chapter 2: Solving Linear Equations 0/8

Lecture2.1Find Square Roots and Compare Real Numbers

Lecture2.2Solve OneStep Equations

Lecture2.3Solve TwoStep Equations

Lecture2.4Solve MultiStep Equations

Lecture2.5Solve Equations with Variables on Both Sides

Lecture2.6Ratios and Proportions

Lecture2.7Solve Proportions Using Cross Products

Lecture2.8Rewrite Equations and Formulas


Chapter 3: Graphing Linear Equations and Functions 0/7

Lecture3.1Plot Points in a Coordinate Plane

Lecture3.2Graph Linear Equations

Lecture3.3Graph Using Intercepts

Lecture3.4Find Slope and Rate of Change

Lecture3.5Graph Using SlopeIntercept Form

Lecture3.6Model Direct Variation

Lecture3.7Graph Linear Functions


Chapter 4: Writing Linear Equations 0/7

Lecture4.1Write Linear Equations in SlopeIntercept Form

Lecture4.2Use Linear Equations in SlopeIntercept Form

Lecture4.3Write Linear Equations in PointSlope Form

Lecture4.4Write Linear Equations in Standard Form

Lecture4.5Write Equations of Parallel and Perpendicular Lines

Lecture4.6Fit a Line to Data

Lecture4.7Predict with Linear Models


Chapter 5: Solving and Graphing Linear Inequalities 0/7

Lecture5.1Solve Inequalities Using Addition and Subtraction

Lecture5.2Solve Inequalities Using Multiplication and Division

Lecture5.3Solve MultiStep Inequalities

Lecture5.4Solve Compound Inequalities

Lecture5.5Solve Absolute Value Equations

Lecture5.6Solve Absolute Value Inequalities

Lecture5.7Graph Linear Inequalities in Two Variables


Chapter 6: Systems of Equations and Inequalities 0/6

Lecture6.1Solve Linear Systems by Graphing

Lecture6.2Solve Linear Systems by Substitution

Lecture6.3Solve Linear Systems by Adding or Subtracting

Lecture6.4Solve Linear Systems by Multiplying First

Lecture6.5Solve Special Types of Linear Systems

Lecture6.6Solve Systems of Linear Inequalities


Chapter 7: Exponents and Exponential Functions 0/5

Lecture7.1Apply Exponent Properties Involving Products

Lecture7.2Apply Exponent Properties Involving Quotients

Lecture7.3Define and Use Zero and Negative Exponents

Lecture7.4Write and Graph Exponential Growth Functions

Lecture7.5Write and Graph Exponential Decay Functions


Chapter 8: Polynomials and Factoring 0/8

Lecture8.1Add and Subtract Polynomials

Lecture8.2Multiply Polynomials

Lecture8.3Find Special Products of Polynomials

Lecture8.4Solve Polynomial Equations in Factored Form

Lecture8.5Factor x^2 + bx + c

Lecture8.6Factor ax^2 + bx + c

Lecture8.7Factor Special Products

Lecture8.8Factor Polynomials Completely


Chapter 9: Quadratic Equations and Functions 0/9

Lecture9.1Graph y = ax^2 + c

Lecture9.2Graph y = ax^2 + bx + c

Lecture9.3Solve Quadratic Equations by Graphing

Lecture9.4Use Square Roots to Solve Quadratic Equations

Lecture9.5Solve Quadratic Equations by Completing the Square

Lecture9.6Solve Quadratic Equations by the Quadratic Formula

Lecture9.7Solve Systems with Quadratic Equations

Lecture9.8Compare Linear, Exponential, and Quadratic Models

Lecture9.9Model Relationships


Chapter 10: Data Analysis and Probability 0/10

Lecture10.1Analyze Surveys and Samples

Lecture10.2Use Measures of Central Tendency and Dispersion

Lecture10.3Analyze Data

Lecture10.4Interpret StemandLeaf Plots and Histograms

Lecture10.5Interpret BoxandWhisker Plots

Lecture10.6Find Probabilities and Odds

Lecture10.7Find Probabilities Using Permutations

Lecture10.8Find Probabilities Using Combinations

Lecture10.9Find Probabilities of Disjoint and Overlapping Events

Lecture10.10Find Probabilities of Independent and Dependent Events

Instructor
David is the professor of mathematics education at David School and a former Associate Professor of Physics at JNTU. He served as a teacher of mathematics and Physics in various international schools in Asia and Europe. His research focuses on social and cultural factors as well as educational policies and practices that facilitate mathematics engagement, learning, and performance, especially for underserved students. David School collaborates with teachers, schools, districts, and organizations to promote mathematics excellence and equity for young people.
0 rating