Students will use mathematical analysis, scientific inquiry, and engineering design, as appropriate, to pose questions, seek answers, and develop solutions. Students will use mathematical analysis, scientific inquiry, and engineering design, as appropriate, to pose questions, seek answers, and develop solutions.

Pattern

Students use patterns and functions to develop mathematical power, appreciate the true beauty of mathematics, and construct generalizations that describe patterns simply and efficiently.

Elementary

• recognize, describe, extend, and create a wide variety of patterns

• represent and describe mathematical relationships

• explore and express relationships using variables and open sentences

• solve for an unknown using manipulative materials

• use a variety of manipulative materials and technologies to explore patterns

• interpret graphs

• explore and develop relationships among two- and three-dimensional geometric shapes

• discover patterns in nature, art, music, and literature

Intermediate

• recognize, describe, and generalize a wide variety of patterns and functions

• describe and represent patterns and functional relationships using tables, charts and graphs, algebraic expressions, rules, and verbal descriptions

• develop methods to solve basic linear and quadratic equations

• develop an understanding of functions and functional relationships: that a change in one quantity (variable) results in change in another

• verify results of substituting variables

• apply the concept of similarity in relevant situations

• use properties of polygons to classify them

• explore relationships involving points, lines, angles, and planes

• develop and apply the Pythagorean principle in the solution of problems

• explore and develop basic concepts of right triangle trigonometry

• use patterns and functions to represent and solve problems

Math A

• represent and analyze functions using verbal descriptions, tables, equations, and graphs

• apply linear, exponential, and quadratic functions in the solution of problems

• translate among the verbal descriptions, tables, equations and graphic forms of functions

• model real-world situations with the appropriate function

• analyze the effect of parametric changes on the graphs of functions

Math B

• use function vocabulary and notation

• represent and analyze functions using verbal descriptions, tables, equations, and graphs

• translate among the verbal descriptions, tables, equations and graphic forms of functions

• analyze the effect of parametric changes on the graphs of functions

• apply linear, exponential, and quadratic functions in the solution of problems

• apply and interpret transformations to functions

• model real-world situations with the appropriate function

• apply axiomatic structure to algebra and geometry

• solve equations with complex roots, using a variety of algebraic and graphical methods with appropriate tools

• evaluate and form the composition of functions

• solve equations, using fractions, absolute values, and radicals

• use basic transformations to demonstrate similarity and congruence of figures

• identify and differentiate between direct and indirect isometrics

• analyze inverse functions, using transformations

• apply the ideas of symmetries in sketching and analyzing graphs of functions

• use the normal curve to answer questions about data

• develop methods of solve trigonometric equations and verify trigonometric functions