Mathematics Cumulative Progress Indicators (CPIs) for the end of the designated grade span

Place a "+" for an expectation that represents a strength & a "-" for a weakness

+ or -

STANDARD 4.3     (PATTERNS AND ALGEBRA)     ALL STUDENTS WILL REPRESENT AND ANALYZE RELATIONSHIPS AMONG VARIABLE QUANTITIES  AND SOLVE PROBLEMS INVOLVING PATTERNS, FUNCTIONS, AND ALGEBRAIC CONCEPTS AND PROCESSES.

B.     Functions and Relationships

By the end of Grade 2, students will:

 1.    Use concrete and pictorial models of function machines to explore the basic concept of a function.

Building upon knowledge and skills gained in preceding grades, by the end of Grade 3, students will:

 1.         Use concrete and pictorial models to explore the basic concept of a function.

·        Input/output tables, T-charts

Building upon knowledge and skills gained in preceding grades, by the end of Grade 4, students will:

 1.         Use concrete and pictorial models to explore the basic concept of a function.

·        Input/output tables, T-charts

·        Combining two function machines

·        Reversing a function machine

Building upon knowledge and skills gained in preceding grades, by the end of Grade 5, students will:

 1.         Describe arithmetic operations as functions, including combining operations and reversing them.

 2.         Graph points satisfying a function from T-charts, from verbal rules, and from simple equations.

Building upon knowledge and skills gained in preceding grades, by the end of Grade 6, students will:

 1.         Describe the general behavior of functions given by formulas or verbal rules (e.g., graph to determine whether increasing or decreasing, linear or not).

Building upon knowledge and skills gained in preceding grades, by the end of Grade 7, students will:

 1.         Graph functions, and understand and describe their general behavior.

·        Equations involving two variables

 1.         Graph functions, and understand and describe their general behavior.

·        Equations involving two variables

·        Rates of change (informal notion of slope)

 2.         Recognize and describe the difference between linear and exponential growth, using tables, graphs, and equations.

Building upon knowledge and skills gained in preceding grades, by the end of Grade 12, students will:

 1.       Understand relations and functions and select, convert flexibly among, and use various representations for them, including equations or inequalities, tables, and graphs.

 2.       Analyze and explain the general properties and behavior of functions of one variable, using appropriate graphing technologies.

·        Slope of a line or curve

·        Domain and range

·        Intercepts

·        Continuity

·        Maximum/minimum

·        Estimating roots of equations

·        Intersecting points as solutions of systems of equations

·        Rates of change

 3.       Understand and perform transformations on commonly-used functions.

·        Translations, reflections, dilations

·        Effects on linear and quadratic graphs of parameter changes in equations

·        Using graphing calculators or computers for more complex functions

 4.       Understand and compare the properties of classes of functions, including exponential, polynomial, rational, and trigonometric functions.

·        Linear vs. non-linear

·        Symmetry

·        Increasing/decreasing on an interval