Al.1.1: Evaluate algebraic expressions, including radicals, by applying the order of operations

Al.1.2: Translate word phrases and sentences into expressions, equations, and inequalities, and vice versa

Al.1.3: Apply the laws of (integral) exponents

Al.1.5: Perform polynomial operations (addition, subtraction, multiplication) with and without manipulatives

Al.1.6: Simplify algebraic fractions by factoring

Al.1.8: Simplify radical expressions such as 3/(square root of 7)

Al.1.9: Add, subtract, and multiply simple radical expressions like 3(square root of 20) + 7(square root of 5) and 4(square root of 5) * 2(square root of 3)

Al.2.1: Solve multi-step equations and inequalities with rational coefficients

Al.2.1.a: numerically (from a table or guess and check)

Al.2.1.b: algebraically (including the use of manipulatives)

Al.2.1.c: graphically

Al.2.1.d: technologically

Al.2.2: Solve systems of two linear equations

Al.2.2.a: numerically (from a table or guess and check)

Al.2.2.b: algebraically (including the use of manipulatives)

Al.2.2.c: graphically

Al.2.2.d: technologically

Al.2.3: Solve linear formulas and literal equations for a specified variable

Al.2.4: Solve and graph simple absolute value equations and inequalities

Al.2.5: Solve real world problems that involve a combination of rates, proportions and percents

Al.2.6: Solve problems involving direct variation and indirect (inverse) variation to model rates of change

Al.2.7: Use coordinate geometry to represent and/or solve problems (midpoint, length of a line segment, and Pythagorean Theorem)

Al.2.8: Communicate real world problems graphically, algebraically, numerically and verbally

Al.3.1: Distinguish between functions and non-functions/relations by inspecting graphs, ordered pairs, mapping diagrams and/or tables of data

Al.3.2: Determine domain and range of a relation from an algebraic expression, graphs, set of ordered pairs, or table of data

Al.3.4: Identify independent variables and dependent variables in various representational modes: words, symbols, and/or graphs

Al.3.5: Interpret the rate of change/slope and intercepts within the context of everyday life

Al.3.6: Calculate the slope given

Al.3.6.a: two points

Al.3.6.b: the graph of a line

Al.3.6.c: the equation of a line

Al.3.7: Determine by using slope whether a pair of lines are parallel, perpendicular, or neither

Al.3.8: Write an equation in slope-intercept form given

Al.3.8.a: two points

Al.3.8.b: a point and y-intercept

Al.3.8.c: x-intercept and y-intercept

Al.3.8.d: a point and slope

Al.3.8.e: a table of data

Al.3.8.f: the graph of a line

Al.3.9: Describe the effects of parameter changes, slope and/or y-intercept, on graphs of linear functions and vice versa

### AI: Algebra I

#### AI.4: Students will compare the properties in the family of functions.

AI.4.1: Factoring polynomials

AI.4.1.a: greatest common factor

AI.4.1.b: binomials (difference of squares)

Al.4.2: Determine minimum, maximum, vertex, and zeros, given the graph

Al.4.3: Solve quadratic equations using the appropriate methods with and without technology

Al.4.3.a: factoring

Al.4.3.b: quadratic formula with real number solutions

Al.4.4: Recognize function families and their connections including vertical shift and reflection over the x-axis

Al.4.4.b: absolute value

Al.4.4.c: exponential functions

Al.4.5: Communicate real world problems graphically, algebraically, numerically and verbally

Al.5.1: Construct and use scatter plots and line of best fit to make inferences in real life situations

Al.5.4: Determine the effects of changes in the data set on the measures of central tendency

Al.5.5: Use two or more box-and- whisker plots to compare data sets

Al.5.6: Construct and interpret a cumulative frequency histogram in real life situations

Al.5.7: Recognize linear functions and non-linear functions by using a table or a graph

Al.5.8: Compute simple probability with and without replacement

Al.5.9: Recognize patterns using explicitly defined and recursively defined linear functions

Al.5.10: Communicate real world problems graphically, algebraically, numerically and verbally

### AA: Algebra A

#### AA.1: Students will develop the language of algebra including specialized vocabulary, symbols, and operations.

AA.1.1: Evaluate algebraic expressions, including radicals, by applying the order of operations

AA.1.2: Translate word phrases and sentences into expressions, equations, and inequalities, and vice versa

AA.1.4: Simplify algebraic fractions by factoring

#### AA.2: Students will write, with and without appropriate technology, equivalent forms of equations, inequalities, and systems of equations and solve with fluency.

AA.2.1: Solve multi-step equations and inequalities with rational coefficients

AA.2.1.a: numerically (from a table or guess and check)

AA.2.1.b: algebraically (including the use of manipulatives)

AA.2.1.c: graphically

AA.2.1.d: technologically

AA.2.2: Solve systems of two linear equations

AA.2.2.a: numerically (from a table or guess and check)

AA.2.2.b: algebraically (including the use of manipulatives)

AA.2.2.c: graphically

AA.2.2.d: technologically

AA.2.3: Solve linear formulas and literal equations for a specified variable

AA.2.4: Solve and graph simple absolute value equations and inequalities

AA.2.5: Solve real world problems that involve a combination of rates, proportions and percents

AA.2.6: Solve problems involving direct variation and indirect (inverse) variation to model rates of change

AA.2.7: Use coordinate geometry to represent and/or solve problems (midpoint, length of a line segment, and Theorem)

AA.2.8: Communicate graphically, algebraically, numerically and verbally real world problems

#### AA.3: Students will analyze functions by investigating rates of change, intercepts, and zeros.

AA.3.1: Distinguish between functions and non-functions/relations by inspecting graphs, ordered pairs, mapping diagrams and/or tables of data

AA.3.2: Determine domain and range of a relation from an algebraic expression, graphs, set of ordered pairs, or table of data

AA.3.3: Know and/or use function notation, including evaluating functions for given values in their domain

AA.3.4: Identify independent variables and dependent variables in various representational modes: words, symbols, and/or graphs

AA.3.5: Interpret the rate of change/slope and intercepts within the context of everyday life

AA.3.6: Calculate the slope given

AA.3.6.a: two points

AA.3.6.b: the graph of a line

AA.3.6.c: the equation of a line

AA.3.7: Determine by using slope whether a pair of lines are parallel, perpendicular, or neither

AA.3.8: Write an equation in slope-intercept form given

AA.3.8.a: two points

AA.3.8.b: a point and y-intercept

AA.3.8.c: x-intercept and y-intercept

AA.3.8.d: a point and slope

AA.3.8.e: a table of data

AA.3.8.f: the graph of a line

AA.3.9: Describe the effects of parameter changes, slope and/or y-intercept, on graphs of linear functions and vice versa

#### AA.5: Students will compare various methods of reporting data to make inferences or predictions.

AA.5.1: Construct and use scatter plots and line of best fit to make inferences in real life situations

AA.5.4: Use two or more box-and-whisker plots to compare data sets

AA.5.5: Construct and interpret a cumulative frequency histogram in real life situations

AA.5.6: Recognize linear functions and non-linear functions by using a table or graph

AA.5.7: Compute simple probability with and without replacement

AA.5.8: Recognize patterns using explicitly defined and recursively defined linear functions

### AB: Algebra B

#### AB.1: Students will develop the language of algebra including specialized vocabulary, symbols, and operations.

AB.1.1: Evaluate algebraic expressions, including radicals, by applying the order of operations

AB.1.2: Apply the laws of (integral) exponents

AB.1.4: Perform polynomial operations (addition, subtraction, multiplication) with and without manipulatives

AB.1.5: Simplify algebraic fractions by factoring

AB.1.6: Simplify radical expressions such as 3/(square root of 7)

AB.1.7: Add, subtract, and multiply simple radical expressions like 3(square root of 20) + 7(square root of 5) and 4(square root of 5) * 2(square root of 3)

#### AB.2: Students will write, with and without appropriate technology, equivalent forms of equations, inequalities, and systems of equations and solve with fluency.

AB.2.1: Solve systems of two linear equations

AB.2.1.a: numerically (from a table or guess and check)

AB.2.1.b: algebraically (including the use of manipulatives)

AB.2.1.c: graphically

AB.2.1.d: technologically

AB.2.2: Solve and graph simple absolute value equations and inequalities

AB.2.3: Communicate real world problems graphically, algebraically, numerically and verbally

#### AB.3: Students will compare the properties in the family of functions.

AB.3.1: Factoring polynomials

AB.3.1.a: greatest common factor

AB.3.1.b: binomials (difference of squares)

AB.3.1.c: trinomials

AB.3.2: Determine minimum, maximum, vertex, and zeros, given the graph

AB.3.3: Solve quadratic equations using the appropriate methods with and without technology

AB.3.3.a: factoring

AB.3.3.b: quadratic formula with real number solutions

AB.3.4: Recognize function families and their connections including vertical shift and reflection over the x-axis

AB.3.4.b: absolute value

AB.3.4.c: exponential functions

AB.3.5: Communicate real world problems graphically, algebraically, numerically and verbally

#### AB.4: Students will compare various methods of reporting data to make inferences or predictions.

AB.4.1: Determine the effects of changes in the data set on the measures of central tendency

AB.4.2: Use two or more box-and- whisker plots to compare data sets

AB.4.3: Construct and interpret a cumulative frequency histogram in real life situations

AB.4.4: Recognize linear functions and non-linear functions by using a table or a graph

AB.4.5: Compute simple probability with and without replacement

AB.4.6: Recognize patterns using explicitly defined and recursively defined linear functions

AB.4.7: Communicate real world problems graphically, algebraically, numerically and verbally.

### G: Geometry

#### G.1: Students will develop the language of geometry including specialized vocabulary, reasoning, and application of theorems, properties, and postulates.

G.1.1: Define, compare and contrast inductive reasoning and deductive reasoning for making predictions based on real world situations

G.1.1.c: conditional statements (statement, inverse, converse, and contrapositive)

G.1.3: Describe relationships derived from geometric figures or figural patterns

G.1.4: Apply, with and without appropriate technology, definitions, theorems, properties, and postulates related to such topics as complementary, supplementary, vertical angles, linear pairs, and angles formed by perpendicular lines

G.1.5: Explore, with and without appropriate technology, the relationship between angles formed by two lines cut by a transversal to justify when lines are parallel

G.1.6: Give justification for conclusions reached by deductive reasoning

#### G.2: Students will identify and describe types of triangles and their special segments. They will use logic to apply the properties of congruence, similarity, and inequalities. The students will apply the Pythagorean Theorem and trigonometric ratios to solve p

G.2.1: Apply congruence (SSS...) and similarity (AA...) correspondences and properties of figures to find missing parts of geometric figures and provide logical justification

G.2.2: Investigate the measures of segments to determine the existence of triangles (triangle inequality theorem)

G.2.3: Identify and use the special segments of triangles (altitude, median, angle bisector, perpendicular bisector, and midsegment) to solve problems

G.2.4: Apply the Pythagorean Theorem and its converse in solving practical problems

G.2.6: Use trigonometric ratios (sine, cosine, tangent) to determine lengths of sides and measures of angles in right triangles including angles of elevation and angles of depression

#### G.3: Students will measure and compare, while using appropriate formulas, tools, and technology to solve problems dealing with length, perimeter, area and volume.

G.3.1: Calculate probabilities arising in geometric contexts

G.3.2: Apply, using appropriate units, appropriate formulas (area, perimeter, surface area, volume) to solve application problems involving polygons, prisms, pyramids, cones, cylinders, spheres as well as composite figures, expressing solutions in both exact and

G.3.3: Relate changes in the measurement of one attribute of an object to changes in other attributes

G.3.4: Use (given similar geometric objects) proportional reasoning to solve practical problems (including scale drawings)

G.3.5: Use properties of parallel lines and proportional reasoning to find the lengths of segments

#### G.4: Students will analyze characteristics and properties of two- and three-dimensional geometric shapes and develop mathematical arguments about geometric relationships.

G.4.1: Explore and verify the properties of quadrilaterals

G.4.2: Solve problems using properties of polygons:

G.4.2.a: sum of the measures of the interior angles of a polygon

G.4.2.b: interior and exterior angle measure of a regular polygon or irregular polygon

G.4.2.c: number of sides or angles of a polygon

G.4.5: Investigate and use the properties of angles (central and inscribed) arcs, chords, tangents, and secants to solve problems involving circles

#### G.5: Students will specify locations, apply transformations and describe relationships using coordinate geometry.

G.5.1: Use coordinate geometry to find the distance between two points, the midpoint of a segment, and the slopes of parallel, perpendicular, horizontal, and vertical lines

G.5.2: Write equations of lines in slope-intercept form and use slope to determine parallel and perpendicular lines

G.5.3: Determine, given a set of points, the type of figure based on its properties (parallelogram, isosceles triangle, trapezoid)

G.5.4: Write, in standard form, the equation of a circle given a graph on a coordinate plane or the center and radius of a circle

G.5.5: Draw and interpret the results of transformations and successive transformations on figures in the coordinate plane

G.5.5.a: translations

G.5.5.b: reflections

G.5.5.c: rotations (90°, 180°, clockwise and counterclockwise about the origin)

G.5.5.d: dilations (scale factor)

### GA: Geometry A

#### GA.1: Students will develop the language of geometry including specialized vocabulary, reasoning, and application of theorems, properties, and postulates.

GA.1.1: Define, compare and contrast inductive reasoning and deductive reasoning for making predictions based on real world situations

GA.1.1.b: matrix logic

GA.1.1.c: conditional statements (statement, inverse, converse, and contrapositive)

GA.1.3: Describe relationships derived from geometric figures or figural patterns

GA.1.4: Apply, with and without appropriate technology, definitions, theorems, properties, and postulates related to such topics as complementary, supplementary, vertical angles, linear pairs, and angles formed by perpendicular lines

GA.1.5: Explore, with and without appropriate technology, the relationship between angles formed by two lines cut by a transversal to justify when lines are parallel

GA.1.6: Give justification for conclusions reached by deductive reasoning

#### GA.2: Students will identify and describe types of triangles and their special segments. They will use logic to apply the properties of congruence, similarity, and inequalities. The students will apply the Pythagorean Theorem and trigonometric ratios to solve p

GA.2.1: Apply congruence (SSS...) and similarity (AA...) correspondences and properties of figures to find missing parts of geometric figures and provide logical justification

GA.2.2: Investigate the measures of segments to determine the existence of triangles (triangle inequality theorem)

GA.2.3: Identify and use the special segments of triangles (altitude, median, angle bisector, perpendicular bisector, and midsegment) to solve problems

GA.2.4: Apply the Pythagorean Theorem and its converse in solving practical problems

#### GA.3: Students will analyze characteristics and properties of two- and three- dimensional geometric shapes and develop mathematical arguments about geometric relationships.

GA.3.1: Explore and verify the properties of quadrilaterals

GA.3.2: Solve problems using properties of polygons:

GA.3.2.a: sum of the measures of the interior angles of a polygon

GA.3.2.b: interior and exterior angle measure of a regular polygon or irregular polygon

GA.3.2.c: number of sides or angles of a polygon

GA.3.3: Use orthographic drawings (top, front, side) and isometric drawings (corner) to represent three-dimensional objects

#### GA.4: Students will specify locations, apply transformations and describe relationships using coordinate geometry.

GA.4.1: Use coordinate geometry to find the distance between two points, the midpoint of a segment, and the slopes of parallel, perpendicular, horizontal, and vertical lines

GA.4.2: Write equations of lines in slope-intercept form, and use slope to determine parallel and perpendicular lines

GA.4.3: Determine, given a set of points, the type of figure based on its properties (parallelogram, isosceles triangle, trapezoid)

### GB: Geometry B

#### GB.1: Students will develop the language of geometry including specialized vocabulary, reasoning, and application of theorems, properties, and postulates.

GB.1.1: Define, compare and contrast inductive reasoning and deductive reasoning for making predictions based on real world situations

GB.1.1.b: Matrix Logic

GB.1.1.c: Conditional Statements (statement, inverse, converse, and contrapositive)

GB.1.2: Give justification for conclusions reached by deductive reasoning

#### GB.2: Students will identify and describe types of triangles and their special segments. They will use logic to apply the properties of congruence, similarity, and inequalities. The students will apply the Pythagorean Theorem and trigonometric ratios to solve p

GB.2.1: Apply the Pythagorean Theorem and its converse in solving practical problems

GB.2.3: Using trigonometric ratios(sine, cosine, tangent), determine lengths of sides and measures of angles in right triangles including angles of elevation and angles of depression

#### GB.3: Students will measure and compare, while using appropriate formulas, tools, and technology to solve problems dealing with length, perimeter, area and volume.

GB.3.1: Calculate probabilities arising in geometric contexts

GB.3.2: Apply, using appropriate units, appropriate formulas (area, perimeter, surface area, volume) to solve application problems involving polygons, prisms, pyramids, cones, cylinders, spheres as well as composite figures, expressing solutions in both exact and

GB.3.3: Relate changes in the measurement of one attribute of an object to changes in other attributes

GB.3.4: Use (given similar geometric objects) proportional reasoning to solve practical problems (including scale drawings)

GB.3.5: Use properties of parallel lines and proportional reasoning to find the lengths of segments

#### GB.4: Students will analyze characteristics and properties of two- and three-dimensional geometric shapes and develop mathematical arguments about geometric relationships.

GB.4.3: Investigate and use the properties of angles (central and inscribed) arcs, chords, tangents, and secants to solve problems involving circles

GB.4.5: Use orthographic drawings (top, front, side) and isometric drawings (corner) to represent three-dimensional objects

GB.4.6: Draw, examine, and classify cross-sections of three-dimensional objects

#### GB.5: Students will specify locations, apply transformations and describe relationships using coordinate geometry.

GB.5.1: Write, in standard form, the equation of a circle given a graph on a coordinate plane or the center and radius of a circle

GB.5.2: Draw and interpret the results of transformations and transformations on figures in the coordinate plane

GB.5.2.a: translations

GB.5.2.b: reflections

GB.5.2.c: rotations (90°. 180°, clockwise and counterclockwise about the origin)

GB.5.2.d: dilations (scale factor)

### GI: Investigating Geometry

#### GI.1: Students will develop the language of geometry including specialized vocabulary, reasoning, and application of theorems, properties, and postulates.

GI.1.1: Define, compare and contrast inductive reasoning and deductive reasoning for making predictions based on real world situations

GI.1.1.c: conditional statements (statement, inverse, converse, and contrapositive)

GI.1.3: Describe relationships derived from geometric figures or figural patterns

GI.1.4: Apply, with and without appropriate technology, definitions, theorems, properties, and postulates, related to such topics as complementary, supplementary, vertical angles, linear pairs, and angles formed by perpendicular lines

GI.1.5: Explore, with and without appropriate technology, the relationship between angles formed by two lines cut by a transversal to justify when lines are parallel

GI.1.6: Justify conclusions reached by deductive reasoning

#### GI.2: Students will identify and describe types of triangles and their special segments. They will use logic to apply the properties of congruence, similarity, and inequalities. The students will apply the Pythagorean Theorem and trigonometric ratios to solve p

GI.2.1: Apply congruence (SSS...) and similarity (AA...) correspondences and properties of figures to find missing parts of geometric figures and provide logical justification

GI.2.2: Investigate the measures of segments to determine the existence of triangles (triangle inequality theorem)

GI.2.3: Identify and use the special segments of triangles (altitude, median, angle bisector, perpendicular bisector, and midsegment) to solve problems

GI.2.4: Apply the Pythagorean Theorem and its converse in solving practical problems

GI.2.6: Use trigonometric ratios (sine, cosine, tangent) to determine lengths of sides and measures of angles in right triangles including angles of elevation and angles of depression

#### GI.3: Students will measure and compare while using appropriate formulas, tools, and technology to solve problems dealing with length, perimeter, area and volume.

GI.3.1: Calculate probabilities arising in geometric contexts

GI.3.2: Apply, using appropriate units, appropriate formulas (area, perimeter, surface area, volume) to solve application problems involving polygons, prisms, pyramids, cones, cylinders, spheres as well as composite figures, expressing solutions in both exact and

GI.3.3: Relate changes in the measurement of one attribute of an object to changes in other attributes

GI.3.4: Use proportional reasoning to solve practical problems (including scale drawings) given similar geometric objects

GI.3.5: Use properties of parallel lines and proportional reasoning to find the lengths of segments

#### GI.4: Students will analyze characteristics and properties of two- and three-dimensional geometric shapes and develop mathematical arguments about geometric relationships.

GI.4.1: Explore and verify the properties of quadrilaterals

GI.4.2: Solve problems using properties of polygons

GI.4.2.a: sum of the measures of the interior angles of a polygon

GI.4.2.b: interior and exterior angle measure of a regular polygon or irregular polygon

GI.4.2.c: number of sides or angles of a polygon

GI.4.5: Investigate and use the properties of angles (central and inscribed) arcs, chords, tangents, and secants to solve problems involving circles

GI.4.7: Use orthographic drawings (top, front, side) and isometric drawings (corner) to represent three-dimensional objects

#### GI.5: Students will specify locations, apply transformations and describe relationships using coordinate geometry.

GI.5.1: Use coordinate geometry to find the distance between two points, the midpoint of a segment, and the slopes of parallel, perpendicular, horizontal, and vertical lines

GI.5.2: Write equations of lines in slope-intercept form and use slope to determine parallel and perpendicular lines

GI.5.3: Determine, given a set of points, the type of figure based on its properties (parallelogram, isosceles triangle, trapezoid)

GI.5.4: Write, in standard form, the equation of a circle given a graph on a coordinate plane or the center and radius of a circle

GI.5.5: Draw and interpret the results of transformations and successive transformations on figures in the coordinate plane

GI.5.5.a: translations

GI.5.5.b: reflections

Gi.5.5.c: rotations (90°, 180°, clockwise and counterclockwise about the origin)

GI.5.5.d: dilations (scale factor)

### AC: Algebraic Connections

#### AC.1: Students will evaluate and interpret data, make predictions based on data, and apply basic understanding of probability to solve real-world problems.

AC.1.1: Apply counting techniques to determine the number of outcomes

AC.1.1.a: tree diagram

AC.1.1.c: permutations (with and without repetition)

AC.1.1.d: combinations

AC.1.2: Conduct and interpret simple probability experiments using

AC.1.2.a: manipulatives (spinners, dice, cards, coins)

AC.1.2.b: simulations (using random number tables, graphing calculators, or computer software)

AC.1.3: Compute and display theoretical and experimental probability including the use of Venn diagrams.

AC.1.3.a: simple

AC.1.3.b: complementary

AC.1.3.c: compound (mutually exclusive, inclusive, independent and dependent events)

AC.1.5: Interpret and evaluate, with and without appropriate technology, graphical and tabular data displays for

AC.1.5.a: consistency with the data

AC.1.5.b: appropriateness of type of graph or data display

#### AC.2: Students will analyze linear functions by investigating rates of change, intercepts, and zeros.

AC.2.1: Create, given a graph without an explicit formula, a written or oral interpretation of the relationship between the independent and dependent variables

AC.2.2: Create, given a situation, a graph that models the relationship between the independent and dependent variables

AC.2.3: Determine the independent and dependent variables, domain and range of a relation from an algebraic expression, graph, set of ordered pairs, or table of data

AC.2.4: Interpret the rate of change (slope) and intercepts within the context of everyday life

AC.2.5: Calculate the slope given

AC.2.5.a: two points

AC.2.5.b: a graph of a line

AC.2.5.c: an equation of a line

AC.2.6: Determine, using slope, whether a pair of lines are parallel, perpendicular, or neither

AC.2.7: Write an equation given

AC.2.7.a: two points

AC.2.7.b: a point and y-intercept

AC.2.7.c: an x-intercept and y-intercept

AC.2.7.d: a point and slope

AC.2.7.e: a table of data

AC.2.7.f: the graph of a line

#### AC.3: Students will write and solve, with and without appropriate technology, equations, inequalities, systems of equations and systems of inequalities.

AC.3.1: Solve, with and without appropriate technology, multi-step equations and inequalities with rational coefficients numerically, algebraically and graphically

AC.3.2: Solve, with and without appropriate technology, systems of two linear equations and systems of two inequalities numerically, algebraically and graphically

AC.3.3: Solve linear formulas and literal equations for a specified variable

AC.3.4: Use, with and without appropriate technology, coordinate geometry to represent and solve problems including midpoint, length of a line segment and Pythagorean Theorem

AC.3.5: Determine and describe, with and without appropriate technology, the resulting change in the perimeter, area, and volume when one or more dimensions change (apply this idea in solving real world problems)

AC.3.6: Apply linear, piece-wise and step functions to real world situations that involve a combination of rates, proportions and percents such as sales tax, simple interest, social security, constant depreciation and appreciation, arithmetic sequences, constant

#### AC.4: Students will use algebraic, graphical and numerical methods to analyze, compare, transform, and solve nonlinear equations (absolute value, quadratic, and exponential).

AC.4.1: Factor polynomials

AC.4.1.a: greatest common factor

AC.4.1.b: binominals (difference of squares)

AC.4.1.c: trinomials

AC.4.1.d: combinations of the above

AC.4.3: Solve, with and without appropriate technology, quadratic equations with real number solutions using factoring and the quadratic formula

AC.4.4: Determine the independent and dependent variables, domain and range of a relation from algebraic equations, graphs, sets of ordered pairs, or tables of data

AC.4.5: Identify and apply nonlinear functions to real world situations such as acceleration, area, volume, population, bacteria, compound interest, percent depreciation and appreciation, amortization, geometric sequences, etc.

AC.4.6: Recognize function families including vertical shifts, horizontal shifts and reflections over the x-axis

### AII: Algebra II

#### AII.1: Students will represent and analyze mathematical situations and properties using patterns, relations, functions and algebraic symbols.

AII.1.1: Determine, with or without technology, the domain and range of a relation defined by a graph, a table of values, or a symbolic equation including those with restricted domains and whether a relation is a function

AII.1.2: Evaluate, add, subtract, multiply, divide and compose functions and give appropriate domain and range restrictions

AII.1.4: Analyze and report, with and without appropriate technology, the effect of changing coefficients, exponents, and other parameters on functions and their graphs (linear, quadratic, and higher degree polynomial)

AII.1.5: Determine, with and without appropriate technology, whether a function is even, odd or neither to analyze the behavior of a graph

AII.1.7: Apply the concepts of functions to real world situations

#### AII.2: Students will analyze and apply various methods to model, graph and solve linear and absolute value equations and inequalities.

AII.2.1: Translate linear equations from one form (slope-intercept, point-slope, and standard) to another

AII.2.2: Develop, write, and graph, with and without appropriate technology, equations of lines in slope-intercept, point-slope, and standard forms given

AII.2.2.a: a point and the slope

AII.2.2.b: two points

AII.2.2.c: real world data

AII.2.3: Develop, write and graph (given the point and the slope, two points, or a point and a line) equations of

AII.2.3.a: a parallel line

AII.2.3.b: a perpendicular line

AII.2.3.c: a perpendicular bisector of a segment

AII.2.4: Solve, with and without appropriate technology, absolute value equations and inequalities written in one or two variables, and graph solutions

AII.2.5: Solve, with and without appropriate technology, systems of linear equations and systems of linear inequalities with two or more variables through the use of graphs, tables, matrices, and other algebraic methods

AII.2.7: Apply, with or without technology, the concepts of linear and absolute value equations and inequalities and systems of linear equations and inequalities to model real world situations including linear programming

#### AII.3: Students will use algebraic, graphical, and numerical methods to analyze, compare, translate, and solve quadratic equations.

AII.3.1.a: simplify radicals with different indices

AII.3.2: Extend the number system to include the complex numbers

AII.3.2.c: rationalize denominators

AII.3.3: Solve quadratic equations with and without appropriate technology by

AII.3.3.a: extracting the square root

AII.3.3.b: graphing

AII.3.3.c: factoring

AII.3.4: Develop and analyze, with and without appropriate technology, quadratic relations

AII.3.4.a: graph a parabolic relationship when given its equation

AII.3.4.b: write an equation when given its roots (zeros or solutions) or graph

AII.3.4.c: determine the nature of the solutions graphically and by evaluating the discriminant

AII.3.4.d: determine the maximum or minimum values and the axis of symmetry both graphically and algebraically

AII.3.4.e: Apply the concepts of quadratic equations and functions to model real world situations by using appropriate technology when needed

#### AII.4: Students will use algebraic, graphical, and numerical methods to analyze, compare, translate, and solve polynomial and rational equations.

AII.4.1: Determine the factors of polynomials by

AII.4.1.a: using factoring techniques including grouping and the sum or difference of two cubes

AII.4.1.b: using long division

AII.4.1.c: using synthetic division

AII.4.2: Develop and analyze, with and without appropriate technology, polynomial functions from their roots, graphs, or equations

AII.4.2.a: write an equation when given its factors or roots (zeros or solutions)

AII.4.2.b: determine the x- and y- intercepts

AII.4.2.c: describe the end behaviors

AII.4.2.d: sketch the graph

AII.4.5: Graph, with and without appropriate technology, rational functions of the form y = 1/x and y = 1/x² and their transformations and identify x- and y- intercepts, domain restrictions, and vertical asymptotes

AII.4.6: Solve, with and without appropriate technology, problems using rational equations, including proportions, rate, and variation (direct, inverse(indirect), or joint) and real world problems

AII.4.7: Establish the relationship between radical expressions and expressions containing rational exponents

AII.4.8: Simplify variable expressions containing rational exponents using the laws of exponents

#### AII.5: Students will graph exponential functions and relate them to logarithms. They will solve real world problems using exponential functions.

AII.5.1: Interpret and graph, with and without appropriate technology, exponential functions

AII.5.3: Establish the relationship between exponential and logarithmic functions

#### AII.6: Students will evaluate and interpret data, make predictions based on data, and apply basic understanding of probability to solve real world problems.

AII.6.1: Interpret and evaluate, with and without appropriate technology, graphical and tabular data displays for

AII.6.1.a: consistency with the data

AII.6.1.b: appropriateness of type of graph or data display

AII.6.2: Calculate, with and without appropriate technology, probabilities of events using the laws of probability

AII.6.2.b: distinguish between and use permutations and combinations

AII.6.2.d: calculate probabilities of mutually exclusive events, independent events, and dependent events

### AIII: Algebra III

#### AIII.1: Students will use algebraic, graphical, and numerical methods to analyze, compare, translate, and solve linear and quadratic equations.

AIII.1.1: Evaluate, add, subtract, multiply, divide and compose functions and determine appropriate domain and range restrictions

AIII.1.2: Develop, write, and graph, with and without appropriate technology, equations of lines in slope-intercept, point-slope, and standard forms given

AIII.1.2.a: a point and the slope

AIII.1.2.b: two points

AIII.1.2.c: real world data

AIII.1.3: Develop, write, and graph, given a point and the slope, two points, or a point and a line, the equation of

AIII.1.3.a: a parallel line

AIII.1.3.b: a perpendicular line

AIII.1.3.c: the perpendicular bisector of a line segment

AIII.1.4.a: simplify radicals with different indices

AIII.1.5: Solve, with and without appropriate technology, quadratic equations by

AIII.1.5.a: extracting the square root

AIII.1.5.b: graphing

AIII.1.5.c: factoring

AIII.1.7: Solve, with and without appropriate technology, systems of linear and quadratic equations and inequalities with two or more variables

AIII.1.8: Apply, with and without appropriate technology the concepts of functions to real world situations including linear programming

#### AIII.2: Students will use algebraic, graphical, and numerical methods to analyze, compare, translate, and solve polynomial and rational equations.

AIII.2.1: Determine the factors of polynomials by

AIII.2.1.a: using factoring techniques including grouping, the difference of two squares, and the sum or difference of two cubes

AIII.2.1.b: using synthetic division

AIII.2.2: Investigate and sketch the graphs of polynomial and rational functions using the characteristics of domain and range, upper and lower bounds, maximum and minimum points, asymptotes and end behavior, zeros, multiplicity of zeros, y-intercepts, and symmetry

AIII.2.4: Describe, with and without appropriate technology, the fundamental characteristics of rational functions: zeros, discontinuities (including vertical asymptotes), and end behavior (including horizontal asymptotes)

AIII.2.5: Establish the relationship between radical expressions and expressions containing rational exponents, and simplify variable expressions containing rational exponents using the laws of exponents

AIII.2.6: Apply, with and without appropriate technology, the concepts of polynomial and rational functions to model real world situations

#### AIII.3: Students will solve real world problems involving logarithmic and exponential functions. They will draw and analyze graphs and find inverse functions.

AIII.3.1: Establish the inverse relationship between exponential and logarithmic functions

AIII.3.4: Find, with and without appropriate technology, the domain, range, intercepts, and asymptotes of logarithmic and exponential functions

AIII.3.5: Draw and analyze, with and without appropriate technology, graphs of logarithmic and exponential functions

#### AIII.4: Students will use sequences and series to represent and analyze mathematical situations.

AIII.4.1: Develop, with and without appropriate technology, a representation of sequences recursively and explicitly

AIII.4.2: Define and discriminate, with and without appropriate technology, between arithmetic and geometric sequences and series

AIII.4.3: Solve, with and without appropriate technology, problems involving the sum (including Sigma notation) of finite and infinite sequences and series

AIII.4.4: Determine, with and without appropriate technology, the nth term of a sequence given a rule or specific terms

#### AIII.5: Students will identify, create, and solve real world problems involving right triangles and oblique triangles.

AIII.5.1: Define sine, cosine, and tangent as ratios of sides of right triangles

AIII.5.4: Solve, with and without appropriate technology, real world problems involving applications of

AIII.5.4.a: trigonometric functions

AIII.5.4.d: area of oblique triangles

### TM: Transition to College Mathematics

#### TM.1: Students will extend their knowledge of linear equations by using student-generated data to represent constant rates of change. Appropriate technology is essential.

TM.1.1: Identify a linear relationship represented by a table, by a graph, and by symbolic forms

TM.1.2: Determine the initial condition and the rate of change in real-world situations described by y= mx + b

TM.1.3: Make inferences and predictions using

TM.1.3.a: recursion on the table

TM.1.3.b: inspection on the graph

TM.1.3.c: algebraic manipulation on the model

#### TM.2: Students will enhance their knowledge of exponential functions by exploring the nature of multiplicative change.

TM.2.1: Identify exponential growth or decay by creating tables, graphs, and mathematical models

TM.2.2: Compare exponential models

TM.2.3: Compare and contrast linear and exponential models

TM.2.4: Make inferences and predictions using

TM.2.4.a: recursion on the table

TM.2.4.b: inspection of the graph

TM.2.4.c: algebraic manipulation on the model

TM.2.6: Explain, conjecture, summarize, and defend results orally, in writing, and through the use of appropriate technology

#### TM.3: Students will expand their use of mathematical models to describe continuous, discontinuous, and discrete phenomena.

TM.3.1: Establish connections between tables and graphs and the symbolic form using geometric and algebraic models (quadratic, rational, etc.)

TM.3.3: Make inferences and predictions using

TM.3.3.a: recursion on the table

TM.3.3.c: algebraic manipulation on the model

TM.3.4: Explain, conjecture, summarize, and defend results orally, in writing, and through the use of appropriate technology

#### TM.4: Students will develop strategies that will enable them to make decisions based upon appropriate analysis of data.

TM.4.1: Formulate questions that can be addressed with data and, with appropriate technology, collect, organize, and display relevant data to answer the questions

TM.4.2: Describe and summarize data numerically using central tendency variation, position statistics, and distributions

TM.4.3: Use counting methods, permutations, and combinations to evaluate the likelihood of events occurring

TM.4.4: Make inferences and predictions using

TM.4.4.a: recursion on the table

TM.4.4.b: inspection of the graph

### PCT: Pre-Calculus including Trigonometry

#### PCT.1: Students will analyze polynomial and rational functions graphically and algebraically.

PCT.1.1: Investigate and sketch, with and without appropriate technology, the graphs of polynomial and rational functions using the characteristics of domain and range, upper and lower bounds, maximum and minimum points, asymptotes and end behavior, zeros, multipl

PCT.1.3: Describe, with and without appropriate technology, the fundamental characteristics of rational functions: zeros, discontinuities (including vertical asymptotes), and end behavior (including horizontal asymptotes)

PCT.1.4: Apply the concepts of polynomial and rational functions to model real world situations using appropriate technology when needed

#### PCT.2: Students will solve real world problems involving logarithmic and exponential functions. Draw and analyze graphs and find inverse functions.

PCT.2.1: Establish the inverse relationship between exponential and logarithmic functions

PCT.2.2: Develop and apply the laws of logarithms and the change-of-base formula to simplify and evaluate expressions

PCT.2.4: Find, with and without appropriate technology, the domain, range, intercepts, and asymptotes of logarithmic and exponential functions

PCT.2.5: Draw and analyze, with and without appropriate technology, graphs of logarithmic and exponential functions

#### PCT.3: Students will identify, analyze and sketch the graphs of the conic sections and relate their equations and graphs.

PCT.3.1: Identify, graph, write, and analyze equations of conic sections, using properties such as symmetry, intercepts, foci, asymptotes, and eccentricity, and when appropriate, use technology

PCT.3.2: Solve, with and without appropriate technology, systems of equations and inequalities involving conics and other types of equations

PCT.3.3: Solve, with and without appropriate technology, real world problems involving conic sections

#### PCT.4: Students will use sequences and series to represent, analyze, and solve real world problems and mathematical situations.

PCT.4.1: Develop, with and without appropriate technology, a representation of sequences recursively

PCT.4.2: Define and discriminate between arithmetic and geometric sequences and series and use appropriate technology when needed

PCT.4.3: Solve, with and without appropriate technology, problems involving the sum (including Sigma notation) of finite and infinite sequences and series

PCT.4.4: Determine the nth term of a sequence given a rule or specific terms and use appropriate technology when needed

#### PCT.5: Students will use different perspectives to develop and apply the definitions of the six trigonometric functions. They will sketch and analyze graphs, find inverse functions, and solve real world problems.

PCT.5.1: Define the six trigonometric functions as

PCT.5.1.a: circular functions

PCT.5.1.b: ratios of sides of right triangles

PCT.5.3: Sketch an angle in standard position and determine the reference angle and coterminal angles

PCT.5.4: Find the values of the trigonometric functions given the value of one trigonometric function and an additional piece of qualifying information or given the coordinates of a point on the terminal side of an angle

PCT.5.5: Develop and become fluent in the recall of the exact values of the trigonometric functions for special angles

PCT.5.6: Solve, with and without appropriate technology, real world problems involving applications of trigonometric functions

PCT.5.7: Graph the six trigonometric functions, identify domain, range, intercepts, period, amplitude, and asymptotes as applicable and use symmetry to determine whether the function is even or odd through appropriate technology when needed

PCT.5.8: Determine, with and without appropriate technology, the amplitude, period, phase shift, and vertical shift, and sketch the graph of transformations of the trigonometric functions

#### PCT.6: Students will identify, create, and solve real world problems involving oblique triangles and vectors.

PCT.6.3: Determine the area of an oblique triangle by using an appropriate formula and appropriate technology when needed

PCT.6.4: Use vectors to solve problems and describe addition of vectors and multiplication of a vector by a scalar, both symbolically and geometrically

PCT.6.5: Use vectors to model situations defined by magnitude and direction and analyze and solve real world problems by using appropriate technology when needed

#### PCT.7: Students will verify trigonometric identities and solve trigonometric equations.

PCT.7.1: Develop the Pythagorean Identities and use to verify other identities and simplify expressions

PCT.7.2: Develop and use trigonometric formulas including sum and difference formulas and multiple-angle formulas

#### PCT.8: Students will define polar coordinates and relate them to rectangular coordinates.

PCT.8.1: Convert polar coordinates to rectangular coordinates and rectangular coordinates to polar coordinates

PCT.8.2: Represent equations given in rectangular coordinates in terms of polar coordinates

PCT.8.4: Apply polar coordinates to real world situations and use appropriate technology when needed

### S: Statistics

#### S.1: Students will create, compare, and evaluate data displays using such methods as histograms, cumulative distribution functions, and scatter plots. For these data, they calculate measures of central tendency (various kinds of means, the median, and the mode

S.1.1: Create, compare, and evaluate different graphic displays of the same data, using histograms, frequency polygons, cumulative distribution functions, pie charts, scatter plots, stem-and-leaf plots, and box-and-whisker plots and draw these by hand or use a c

S.1.2: Compute and use mean, mode, weighted mean, geometric mean, harmonic mean, range, quartiles, variance, and standard deviation

#### S.2: Students will describe the method of data collection in a census, sample survey, experiment, and observational study, and identify an appropriate method of solution for a given familiar or unfamiliar contextual problem. Students will plan and conduct a su

S.2.2: Compare and contrast population and sample, and parameter and statistic

S.2.3: Identify biased sampling methods

S.2.4: Describe simple random sampling

S.2.6: Investigate and describe sampling techniques, such as simple random sampling, stratified sampling, and cluster sampling

#### S.3: Students will construct and interpret display of data to solve problems.

S.3.4: Apply concepts of probability to solve familiar and unfamiliar contextual problems

S.3.5: Use simulations to develop an understanding of the Central Limit Theorem and its importance in confidence intervals and tests of significance

#### S.4: Students will collect and analyze data to solve problems

S.4.1: Summarize distributions of univariate data by determining and interpreting measures of center, spread, position, boxplot, and effects of changing units on summary measures.

S.4.3: Construct and interpret graphical display of data

S.4.4: Compare distributions among sets of data.

#### S.5: Students will use statistical models to describe and analyze sets of data.

S.5.1: Investigate and solve relevant problems, using technology to collect, organize, display, and analyze data in tabular, graphical, and symbolic forms

S.5.4: Identify possible correlations between variables in a data set

S.5.5: Develop, use, and explain application and limitations of linear models and line of best fit (linear regression) in a variety of contexts

S.5.7: Determine and use measures of central tendency and dispersion to describe and compare sets of data

S.5.8: Design, conduct, interpret, and justify the results of a probability experiment, sample, or statistical simulation

#### S.6: Students will compute and distinguish between permutations and combinations and use technology for application.

S.6.1: Understand the counting principle, permutations and combinations and use them to solve problems

S.6.2: Compare and contrast permutations and combinations

S.6.3: Calculate the number of permutations of n objects taken r at a time

S.6.4: Calculate the number of combinations of n objects taken r at a time

S.6.6: Find conditional probabilities for dependent, independent, and mutually exclusive events

#### S.7: Students will identify random variables as independent or dependent and find mean and standard deviations for sums and differences of independent random variables.

S.7.1: Compare and contrast independent and dependent random variables

#### S.8: Students will find probabilities, including conditional probabilities for events that are either dependent or independent, by applying the law of large numbers, the addition rule, and the multiplication rule.

S.8.2: Understand and use the multiplication rule to calculate probabilities for independent and dependent events

S.8.3: Develop the binomial distribution within a real world context

S.8.4: Calculate the mean and standard deviation for a binomial variable

S.8.5: Use the binomial distribution to calculate probabilities associated with experiments for which there are only two possible outcomes

#### S.9: Students will develop, interpret, and apply the binomial probability distribution for discrete random variable, including computing the mean and standard deviation for the binomial variable.

S.9.1: Design and conduct an experiment that simulates a binomial distribution.

S.9.2: Design and conduct an experiment that simulates a geometric distribution.

S.9.3: Simulate probability distributions, including binomial and geometric.

#### S.11: Students will use confidence intervals and hypothesis tests, fit curves to data, and calculate correlation coefficients.

S.11.2: Understand hypothesis tests of means and differences between means and use them to reach a conclusion

S.11.4: Calculate and interpret the correlation coefficient of a set of data

### CM: Computer Mathematics

#### CM.1: The student will develop and apply logical reasoning skills to solve real-world problems through the development of mathematical models.

CM.1.1: Analyze and interpret graphs, charts, and tables in the design and implementation of a computer program.

#### CM.2: The student will design a step-by-step plan to solve a given problem.

CM.2.2: Implement conditional statements that include if/then, if/then/else, case statements, and Boolean logic.

CM.2.6: Develop recursive relationships from mathematical models (e.g. arithmetic and geometric sequences).

#### CM.4: The student will use the programming tool to create programs using a programmable calculator.

CM.4.3: Create, edit, and execute programs to calculate mathematical formulas, such as the quadratic formula, and volume of a simple solid.

Correlation last revised: 10/24/2009

This correlation lists the recommended Gizmos for this state's curriculum standards. Click any Gizmo title below for more information.