Mathematics, Algebra I
Student Learning Profile
Within a well-balanced mathematics curriculum, the primary focal points for Algebra I are to continue to build and apply basic understandings developed in K-8, develop symbolic reasoning, understand functions and their relationships with equations, and be able to use a variety of tools and technology to represent functions with multiple representations.
The student will:
· Understand that a function represents a dependence of one quantity on another.
· Understand that a function can be described in a variety of ways.
· Gather and record data, or use data sets, to determine functional relationships between quantities.
· Write equations or inequalities to answer questions arising from functional situations.
· Represent relationships among quantities using concrete models, tables, graphs, diagrams, verbal descriptions, equations, and inequalities.
· Use the properties and attributes of functions.
· Identify and sketch the general forms of linear and quadratic parent functions.
· Identify the mathematical domains and ranges and their reasonableness for situations.
· Interpret situations in terms of graphs.
· Make and interpret scatterplots and models for data to predict and make critical judgements.
· Use symbols to represent unknowns and variables.
· Look for patterns in given situations and express these algebraically.
· Find specific function values, simplify polynomial expressions, transform and solve equations, and factor as necessary for problem situations.
· Translate among and use algebraic, tabular, graphical, or verbal descriptions of linear functions.
· Develop the concept of slope as rate of change and determine slope from various situations.
· Interpret the meaning of slope and intercepts in situations.
· Describe the effects of changes in parameters of linear functions in real-world and mathematical situations (such as intercept changes, slope changes).
· Graph and write equation of lines given characteristics, such as two points, a point and a slope, or a slope and y-intercept.
· Determine the intercepts of linear functions from graphs, tables, and algebraic representations.
· Relate direct variation to linear function and solve problems involving proportional change.
· Formulate equations and inequalities based on linear functions, uses a variety of methods to solve them, and analyze the solution for reasonableness in terms of the situation.
· Formulate systems of linear equations from problem situations, use a variety of methods to solve them, and analyze the solutions in terms of the situation.
· Solve equations, inequalities, and systems of equations using concrete models, graphs, tables, and algebraic methods.
· Determine the domain and range values for which quadratic functions make sense.
· Investigate, describe, and predict the effects of changes on the slope and intercepts of graphs of quadratic equations.
· Solve quadratic equations using concrete models, tables, graphs, and algebraic methods.
· Relate the solutions of quadratic equations to the roots of their functions.
· Use patterns to generate the laws of exponents and apply them in problem-solving situations.
· Analyze data and represent situations involving inverse variation using concrete models, tables, graphs, or algebraic methods.
· Analyze data and represent situations involving exponential growth and decay using concrete models, tables, graphs, or algebraic methods.
· Use tools such as real objects, manipulatives, and technology to solve problems.
· Communicate about mathematics using informal language, objects, words, pictures, numbers, and technology.
· Use logical reasoning to make sense of his or her world and justify why an answer is reasonable.
· Make generalizations from patterns or sets of examples and non-examples.