Portland Community College | Portland, Oregon

Upon successful completion of the course, students should be able to:

1. Manipulate algebraic expressions to create equivalent forms using appropriate strategies.

2. Solve foundational algebraic equations and inequalities both symbolically and graphically.

3. Create algebraic models of real-world situations to generate and interpret meaningful solutions.

4. Analyze and graph linear and quadratic functions to describe their key features.

5. Interpret f(x) notation to identify and explain input-output relationships in numeric, symbolic, graphical, and verbal forms.

6. Reason mathematically to construct, evaluate, and communicate solutions in collaborative and contextual settings.

All activities in this course are grounded in the idea that algebraic definitions and procedures develop through the exploration of meaningful problems. In-class time emphasizes active learning, with a focus on problem solving, multiple representations, and connections between symbolic and graphical reasoning. Activities include a mix of individual work and group collaboration to build both procedural fluency and conceptual understanding.

Technology is an important instructional tool in this course; however, students are also expected to demonstrate conceptual understanding and procedural fluency without reliance on technology for selected content topics.

Students' learning and progress should be assessed regularly throughout the course using a variety of assessment strategies. Their final grade in the course should be a reflection of their content mastery of the learning outcomes:

1. Simplifying linear, polynomial, radical, and rational expressions

2. Solving linear, quadratic, radical, and rational equations in one variable

3. Graphing linear and quadratic equations 

4. Solving linear inequalities in one variable

Formative assessments should be given and feedback provided regularly to inform the student of their progress. They can include but are not limited to: 

• Graded homework

• In-class activities

• Group work

• Writing assignments

• Discussions

Summative assessments should be given at least twice throughout the course and administered in a way to ensure the work is the student's own. One of which should be a comprehensive final exam that assesses each of the course outcomes. Assessments should be primarily free response, include evaluation of the student’s ability to arrive at correct conclusions using proper mathematical procedures and notation, and include application problems that are answered in complete sentences. Summative assessments can include, but are not limited to: 

• Exams 

• Quizzes

• Projects

• Interviews

• Portfolios

• Represent linear relationships numerically, symbolically, verbally, and graphically.

• Interpret slope as a rate of change and identify slopes and intercepts from equations, tables, and graphs.

• Write equations of lines in slope-intercept and point-slope forms.

• Graph linear equations using slope, intercepts, and points.

• Solve linear equations and inequalities symbolically and graphically, with symbolic solutions justified algebraically, and express interval solution sets using interval notation.

• Solve systems of linear equations graphically and symbolically

• Use linear models to represent contextual situations, define variables, interpret units, and communicate conclusions clearly.

• Represent quadratic functions in symbolic, graphical, verbal, and numerical forms.

• Identify and interpret key features of quadratic graphs including vertex, axis of symmetry, and intercepts.

• Solve quadratic equations in one variable using appropriate algebraic methods, including the Square Root Method, the Zero Product Principle (factoring), and the Quadratic Formula; identify when each method is applicable. At least one universal real-number strategy (such as the Quadratic Formula or completing the square) must be taught.

• Factor polynomial expressions in one variable, including factoring out a greatest common factor, factoring trinomials with leading coefficient 1, and factoring differences of squares.

• Analyze the relationship between algebraic form and graph shape, including connections between factored form and x-intercepts.

• Use quadratic models in contextual problems, and interpret maxima/minima and intercepts using appropriate units.

• Simplify rational expressions and complex fractions using appropriate algebraic strategies. 

• Perform operations (addition, subtraction, multiplication, division) on rational expressions. 

• Solve rational equations symbolically, identifying extraneous solutions when they occur.

• Interpret rational expressions and equations in real-world modeling contexts.
   

• Solve equations involving radicals (involving one radical term) using algebraic reasoning, identify extraneous solutions, and justify correctness of solutions.

• Evaluate radicals numerically with and without technology, and apply radical expressions in contextual situations.

• Rewrite and manipulate radical expressions using properties of radicals and exponent rules to simplify expressions effectively.