These lessons link the understanding of concepts in chemistry to skills learned in algebra II. Using systems of equations in solving problems, students are utilizing matrices to balance chemical reactions and direct and inverse variations. This fresh approach reinforces students’ understanding of the relationship between two disciplines that have traditionally been taught separately.

CK-12 Foundation's Algebra FlexBook is an introduction to algebraic concepts for the high school student. Topics include: Equations & Functions, Real Numbers, Equations of Lines, Solving Systems of Equations & Quadratic Equations.

These lecture guides will aid students as they progress through the first semester of College Algebra.  They highlight key concepts, allow for note-taking and problem examples to be recorded, and serve to improve student engagement with the material during instruction.

This research-oriented course will focus on algebraic and computational techniques for optimization problems involving polynomial equations and inequalities with particular emphasis on the connections with semidefinite optimization. The course will develop in a parallel fashion several algebraic and numerical approaches to polynomial systems, with a view towards methods that simultaneously incorporate both elements. We will study both the complex and real cases, developing techniques of general applicability, and stressing convexity-based ideas, complexity results, and efficient implementations. Although we will use examples from several engineering areas, particular emphasis will be given to those arising from systems and control applications.

This is a web-based, interactive, introductory linear algebra text. Interactive elements include auto-graded exercises, built-in GeoGebra activities, and Octave code. Topics include vectors and matrices, linear systems, vector spaces (R^n and abstract), linear transformations, eigenvalues, orthogonality, and determinants. Strong emphasis is placed on geometry and visualization. Several applications are included, and links to numerous applications are provided. To access the text directly, use https://ximera.osu.edu/oerlinalg/LinearAlgebra

Algebraic Reasoning

Type of Unit: Concept

Prior Knowledge

Students should be able to:

Add, subtract, multiply, and divide rational numbers.
Evaluate expressions for a value of a variable.
Use the distributive property to generate equivalent expressions including combining like terms.
Understand solving an equation or inequality as a process of answering a question: which values from a specified set, if any, make the equation or inequality true?
Write and solve equations of the form x+p=q and px=q for cases in which p, q, and x are non-negative rational numbers.
Understand and graph solutions to inequalities x<c or x>c.
Use equations, tables, and graphs to represent the relationship between two variables.
Relate fractions, decimals, and percents.
Solve percent problems included those involving percent of increase or percent of decrease.

Lesson Flow

This unit covers all of the Common Core State Standards for Expressions and Equations in Grade 7. Students extend what they learned in Grade 6 about evaluating expressions and using properties to write equivalent expressions. They write, evaluate, and simplify expressions that now contain both positive and negative rational numbers. They write algebraic expressions for problem situations and discuss how different equivalent expressions can be used to represent different ways of solving the same problem. They make connections between various forms of rational numbers. Students apply what they learned in Grade 6 about solving equations such as x+2=6 or 3x=12 to solving equations such as 3x+6=12 and 3(x−2)=12. Students solve these equations using formal algebraic methods. The numbers in these equations can now be rational numbers. They use estimation and mental math to estimate solutions. They learn how solving linear inequalities differs from solving linear equations and then they solve and graph linear inequalities such as −3x+4<12. Students use inequalities to solve real-world problems, solving the problem first by arithmetic and then by writing and solving an inequality. They see that the solution of the algebraic inequality may differ from the solution to the problem.

CK-12 Algebra Explorations is a hands-on series of activities that guides students from Pre-K to Grade 7 through algebraic concepts.

CK-12 Foundation's Basic Algebra FlexBook is an introduction to the algebraic topics of functions, equations, and graphs for middle-school and high-school students.

Students can access the textbook as needed to study and work on homework.

This 23-minute video lesson looks at Rowspace and Left Nullspace. [Linear Algebra playlist: Lesson 97 of 143]

Mathematics instructors at Scottsdale Community College in Scottsdale, Arizona originally created this workbook. Faculty from Housatonic Community College and Middlesex Community College collaborated and edited the book to fit Connecticut’s Intermediate Algebra outcomes. The included content is designed to lead students through Intermediate Algebra, from a functions modeling approach, and to develop a deep understanding of the concepts associated with functions,
data and change. The included curriculum is broken into eleven lessons. Each lesson includes the following components:

MINI-LESSON
• The Mini-Lesson is the main instructional component for each lesson.
• Ideas are introduced with practical applications.
• Worked Examples are provided for each topic in the Mini-Lesson. Read through these examples carefully. Use these as a guide for completing similar problems.
• Media Examples can be worked by watching online videos and taking notes/writing down the problem as written by the instructor. Video links can be found within the MyOpenMath (MOM) Online Homework Assessment System.
• You-Try problems help reinforce Lesson concepts and should be worked in the order they appear showing as much work as possible.

National Board Certified teacher Marlo Warburton introduces a fresh approach to teaching the notoriously difficult "mixture" word problems for Algebra I. Using an in-class demonstration and incorporating basic physics principles of weight and distance, Ms. Warburton helps her students visualize, solve -- and even enjoy! -- these challenging problems.

Students explore the relationship between input and output values and learn to use algebraic expressions and equations.

In June 2009 the Operator Algebras and Applications International Summer School was held in Lisbon. Dr Joel Feinstein taught one of the four courses available on Regularity conditions for Banach function algebras. He delivered four 90 minute lectures on and this learning object contains the slides, handouts, annotated slides and audio podcasts from each session.

Banach function algebras are complete normed algebras of bounded, continuous, complex-valued functions defined on topological spaces.

Students are introduced to algebraic expressions that use more than one variable and have multiple solutions. They figure out combinations of two items at different costs, with each combination adding up to 100.