#### 7G.1: The students will acquire number sense and perform operations with rational and real numbers.

7G.1.1: Compute fluently and make reasonable estimates.

7G.1.1.1: Compute fluently with integers, positive decimals, fractions, and percents.

7G.1.1.2: Determine the reasonableness of a solution to a problem after computing its value.

7G.1.3: Identify relationships among whole numbers, fractions (rational numbers), and decimals.

7G.1.3.1: Compare and order whole numbers, fractions (rational numbers), and decimals and find their approximate locations on a number line.

7G.1.3.2: Predict the outcome of operating among fractions, decimals, percents, and integers, e.g., when multiplying a positive number by a number between 0 and 1 the result is a smaller number.

7G.1.4: Solve problems involving rational numbers using addition, subtraction, multiplication, and division.

7G.1.4.1: Solve problems involving rational numbers using factors, multiples, prime factorization, relatively prime numbers, and common divisibility rules.

7G.1.4.2: Simplify computations using the inverse operations of addition and subtraction, multiplication and division, and squaring and finding square roots of perfect squares.

7G.1.4.3: Compute with percents including those greater than 100% and those less than 1%.

7G.1.4.4: Simplify expressions using order of operations.

#### 7G.2: Students will use patterns, relations, and functions to represent and analyze mathematical situations using algebraic symbols.

7G.2.1: Understand patterns, relations, and functions.

7G.2.1.1: Describe a pattern using a mathematical rule or algebraic expression.

7G.2.1.2: Create simple numerical and visual patterns.

7G.2.1.3: Extend simple numerical and visual patterns.

7G.2.2: Represent, solve, and analyze mathematical situations using algebraic symbols.

7G.2.2.2: Translate verbal expressions into symbolic representations, e.g., “increase by three” translates to + 3.

7G.2.2.3: Translate numerical representations into verbal expressions, e.g., 5 – 3 translates to “five subtract three.”

7G.2.2.4: Verify that performing the same operation to both sides of an equation will produce an equivalent equation, e.g., a + 2 = 4 is the same as a = 2 if 2 is subtracted from both sides of the equation.

7G.2.2.6: Solve two-step single variable equations and inequalities.

7G.2.2.7: Use proportional reasoning to solve problems.

7G.2.3: Represent quantitative relationships using mathematical models and symbols.

7G.2.3.1: Model and solve real-world problems using various representations, such as graphs, tables, manipulatives, and pictures.

7G.2.3.3: Use graphs and tables to identify and describe changes in related quantities.

#### 7G.3: Students will use spatial and logical reasoning to recognize, describe, and identify geometric shapes and principles.

7G.3.1: Describe, identify, and analyze characteristics and properties of geometric shapes.

7G.3.1.1: Classify common two- and three-dimensional objects using information about the sides and angles.

7G.3.1.2: Identify similar and congruent figures.

7G.3.1.3: Identify relationships among angles, side lengths, and perimeters of similar objects, e.g., corresponding angles of similar triangles have the same measure and the ratios of the corresponding sides are equal.

7G.3.1.5: Describe and draw parallel and intersecting lines, including perpendicular lines.

7G.3.1.6: Classify angles as acute, obtuse, or right.

7G.3.2: Specify locations and describe spatial relationships using coordinate geometry.

7G.3.2.1: Graph ordered pairs of integers on a rectangular coordinate system.

7G.3.2.2: Identify the coordinates of a point plotted on a rectangular coordinate system.

7G.3.3: Visualize and identify geometric shapes after applying transformations, and identify lines of symmetry.

7G.3.3.1: Identify line(s) of symmetry in plane figures.

7G.3.3.2: Transform geometric shapes using translations (slides), rotations (turns), and reflections (flips).

7G.3.3.3: Recognize a three-dimensional figure from a net.

7G.3.3.4: Draw two-dimensional representations of three-dimensional objects.

#### 7G.4: Students will understand and apply measurement tools, formulas, and techniques.

7G.4.1: Understand measurable attributes of objects and the units, systems, and processes of measurement.

7G.4.1.2: Convert from one unit of measure to another within the same system, e.g., convert miles per hour to feet per second.

7G.4.1.4: Select and use units of appropriate size and type to describe or identify measurements of angles, perimeter, area, volume, and weight.

7G.4.2: Determine measurements using appropriate tools and formulas.

7G.4.2.2: Measure length, area, volume, and angles to appropriate levels of precision.

7G.4.2.3: Develop formulas for the area of parallelograms (including rectangles and squares) and triangles.

7G.4.2.4: Determine perimeters of polygons and circumferences of circles; areas of triangles, parallelograms, and circles; volumes of right rectangular and triangular prisms and cylinders; and surface areas of right rectangular and triangular prisms and cylinders using formulas.

#### 7G.5: Students will draw conclusions using concepts of probability after collecting, organizing, and analyzing a data set.

7G.5.1: Design investigations to reach conclusions using statistical methods to analyze data.

7G.5.1.1: Identify appropriate questions for data collection and then collect, organize, and display responses to the questions.

7G.5.1.2: Collect, organize, and display data using frequency tables, line plots, bar graphs, circle graphs, line graphs, and stem-and-leaf plots.

7G.5.1.3: Display the same set of data utilizing two or more different types of representations.

7G.5.1.4: Compare two similar sets of data using the same type of graph.

7G.5.1.6: Predict basic trends illustrated in a graph.

7G.5.2: Apply basic concepts of probability.

7G.5.2.1: Conduct experiments to approximate the probability of simple events.

7G.5.2.2: Compare individual, small group, and large group results of an experiment.

7G.5.2.3: Write the results of a probability experiment as a ratio, decimal, or percent.

7G.5.2.4: Identify the probability of an event as a number between 0 (cannot happen) and 1 (must happen).

7G.5.2.5: Compute simple probabilities using methods such as lists, tree diagrams, or area models.

7G.5.2.6: Recognize that the sum of the probabilities of all outcomes of an event is 1.

### PA: Pre-Algebra

#### PA.1: Students will acquire number sense and perform operations with rational numbers.

PA.1.1: Compute fluently and make reasonable estimates.

PA.1.1.1: Compute using selected methods from among mental arithmetic, estimation, paper and pencil, and calculator.

PA.1.1.2: Add, subtract, multiply, and divide integers.

PA.1.2: Represent rational numbers in a variety of ways.

PA.1.2.1: Recognize and create equivalent forms of a rational number.

PA.1.2.2: Find an approximate location of a rational number on a number line.

PA.1.2.3: Find a rational number between any two rational numbers.

PA.1.2.4: Choose appropriate and convenient forms of rational numbers for solving problems and representing solutions.

PA.1.3: Identify relationships among rational numbers and operations involving these numbers.

PA.1.3.1: Compare and order rational numbers.

PA.1.3.2: Identify the effects of arithmetic operations among fractions, decimals, percents, and integers; e.g., multiplying or dividing by a number larger or smaller than 1.

PA.1.3.5: Recognize and use the inverse relationships of addition and subtraction, multiplication and division, and perfect square roots and squares.

PA.1.4: Solve problems involving rational numbers using addition, subtraction, multiplication, and division.

PA.1.4.1: Recognize absolute value of a rational number as the value of its distance from zero.

PA.1.4.2: Evaluate numerical and algebraic expressions containing absolute value.

PA.1.4.3: Compute with percents, including those greater than 100% and less than 1%.

PA.1.4.4: Solve problems using simple proportions.

#### PA.2: Students will represent and analyze mathematical situations and properties using patterns, relations, functions, and algebraic symbols.

PA.2.1: Use patterns, relations, and functions to represent mathematical situations.

PA.2.1.1: Represent a variety of relations and functions using tables, graphs, manipulatives, verbal rules, or algebraic rules.

PA.2.1.2: Describe simple patterns using a mathematical rule or algebraic expression.

PA.2.1.3: Create and extend simple numeric and visual patterns, including those that have a recursive nature (e.g., Fibonacci numbers, triangular and square numbers).

PA.2.2: Represent, solve, and analyze mathematical situations and properties using algebraic symbols.

PA.2.2.2: Identify the horizontal and vertical intercepts of a linear relation from a graph or table.

PA.2.2.3: Determine the slope of a linear relation from a graph or ordered pairs.

PA.2.2.4: Solve one- and two-step single-variable equations and inequalities.

PA.2.3: Represent quantitative relationships using mathematical models and symbols.

PA.2.3.1: Create a table, graph, or algebraic expression to represent the relationship between two variables.

PA.2.3.2: Graph ordered pairs of rational numbers on a rectangular coordinate system.

PA.2.3.3: Identify approximate rational coordinates when given the graph of a point on a rectangular coordinate system.

PA.2.3.4: Model real-world problems using various representations, such as graphs, tables, equations, manipulatives, and pictures.

#### PA.3: Students will recognize, describe, and identify geometric shapes, and solve problems using spatial and logical reasoning, applications of geometric principles, and modeling.

PA.3.1: Analyze characteristics and properties of two- and three-dimensional shapes and develop mathematical arguments about geometric relationships.

PA.3.1.1: Identify congruent and similar shapes.

PA.3.1.2: Find missing lengths of similar plane figures using proportions.

PA.3.1.3: Classify two- and three-dimensional objects according to the defining characteristics.

PA.3.1.4: Identify relationships among the angles, side lengths, perimeters, areas, and volumes of similar objects.

PA.3.3: Apply transformations and use symmetry to analyze mathematical situations.

PA.3.3.1: Reflect a geometric shape across a line in a coordinate plane and identify the coordinates of the vertices.

PA.3.3.2: Translate a geometric shape a given distance on a coordinate plane and identify the vertices.

#### PA.4: Students will understand and apply measurement tools, formulas, and techniques.

PA.4.1: Understand measurable attributes of objects and the units, systems, and processes of measurement.

PA.4.1.2: Convert from one unit of measure to an equivalent unit of measure using a given conversion factor, e.g., 60 miles/hour 1 hour/3600 sec 5280 ft/1 mile = 88 ft/sec.

PA.4.1.3: Measure angles, perimeter, area, and volume using the correct size and type of units.

PA.4.2: Determine measurements using appropriate techniques, tools, and formulas.

PA.4.2.2: Solve problems involving scale factors using ratios and proportions.

PA.4.2.3: Solve problems involving rates and derived measures, e.g., miles per hour, kilometers per liter, cubic feet.

PA.4.2.4: Measure inaccessible heights or distances using similar triangles.

PA.4.2.5: Calculate surface area and volume of right prisms and cylinders using appropriate units.

PA.4.2.6: Develop formulas for calculating the circumference of circles and the areas of triangles, parallelograms, and trapezoids.

PA.4.2.7: Calculate the circumference of circles and the areas of triangles, parallelograms, and trapezoids using formulas.

#### PA.5: Students will draw conclusions using concepts of probability after collecting, organizing, and analyzing a data set.

PA.5.1: Formulate and answer questions by collecting, organizing, and analyzing data.

PA.5.1.2: Organize and display data using graphical representations such as line plots, bar graphs, stem-and-leaf plots, histograms, scatter plots, circle graphs, box plots (box-and-whisker plots), and pictographs.

PA.5.1.4: Calculate the mean, median, mode, and range for a data set.

PA.5.1.5: Choose a measure of central tendency most appropriate to analyze a particular set of data.

PA.5.1.6: Describe how an individual data point may affect the measures of central tendency.

PA.5.1.7: Interpret and describe the spread of a set of data, e.g., range, box plot (box-and-whisker).

PA.5.2: Apply basic concepts of probability.

PA.5.2.1: Conduct experiments to approximate the probability of simple events.

PA.5.2.2: Recognize that results of an experiment more closely approximate the actual or theoretical probability of an event as the number of trials increases.

PA.5.2.3: Derive the probability of an event mathematically, e.g., building a table or tree diagram, creating an area model, making a list, or using the basic counting principle.

PA.5.2.4: Represent the probability of an event as a fraction, percent, ratio, or decimal.

### EA: Elementary Algebra

#### EA.1: Students will acquire number sense and perform operations with real numbers.

EA.1.1: Compute fluently and make reasonable estimates.

EA.1.1.2: Compute solutions to problems.

EA.1.2: Represent real numbers in a variety of ways.

EA.1.2.1: Compare and order real numbers.

EA.1.2.2: Choose appropriate and convenient forms of real numbers for solving problems and representing answers, e.g., radical form, multiples of pi, decimal, fraction, or percent.

EA.1.3: Identify relationships among real numbers and operations involving these numbers.

EA.1.3.2: Relate properties and operations of rational numbers to irrational numbers.

EA.1.3.3: Simplify numerical expressions and solve problems using real numbers.

#### EA.2: Students will represent and analyze mathematical situations and properties using patterns, relations, functions, and algebraic symbols.

EA.2.1: Use patterns, relations, and functions to represent mathematical situations.

EA.2.1.1: Write algebraic expressions or equations to generalize visual patterns, numerical patterns, relations, data sets, or scatter plots.

EA.2.1.2: Represent linear equations in slope-intercept form, y = mx + b, or standard form, ax + by = c.

EA.2.1.3: Distinguish between linear and non-linear functions or equations by examining a table, equation, or graph.

EA.2.1.4: Identify the slope of a linear function as an average rate of change in real-world situations.

EA.2.2: Evaluate, solve, and analyze mathematical situations using algebraic properties and symbols.

EA.2.2.1: Solve real-world problems involving constant rates of change, e.g., rates of travel, hourly wages, or rates of interest.

EA.2.2.2: Solve multi-step equations and inequalities:

EA.2.2.2.a: Numerically; e.g., from a table or guess and check.

EA.2.2.2.b: Algebraically, including the use of manipulatives.

EA.2.2.2.c: Graphically.

EA.2.2.2.d: Using technology.

EA.2.2.3: Solve systems of two linear equations or inequalities:

EA.2.2.3.a: Numerically; e.g., from a table or guess and check.

EA.2.2.3.b: Algebraically.

EA.2.2.3.c: Graphically.

EA.2.2.3.d: Using technology.

EA.2.2.5: Evaluate numerical expressions (including exponents and square roots), algebraic expressions, formulas, and equations.

EA.2.2.6: Solve linear formulas and literal equations for a specified variable, e.g., solve for p in I = prt.

EA.2.2.7: Simplify algebraic expressions, including those having integer exponents.

EA.2.2.8: Solve proportions that include algebraic first-degree expressions.

EA.2.3: Represent quantitative relationships using mathematical models and symbols.

EA.2.3.1: Identify the slope of a line when given:

EA.2.3.1.a: A set of two ordered pairs.

EA.2.3.1.b: An equation of a linear function.

EA.2.3.1.c: The graph of a linear function.

EA.2.3.1.d: A table of values.

EA.2.3.2: Write the equation of a line when given:

EA.2.3.2.a: A set of ordered pairs.

EA.2.3.2.b: The slope and a point on the line.

EA.2.3.2.c: The graph of a line.

EA.2.3.3: Identify horizontal and vertical lines given the equations.

EA.2.3.4: Identify the domain and range of a relation or function from a graph, equation, table, or set of ordered pairs.

EA.2.3.5: Determine the effect of parameter changes on the graphs of linear relations.

EA.2.3.7: Determine the x- and y-intercepts from an equation or graph of a line.

EA.2.3.8: Graph linear functions:

EA.2.3.8.a: By plotting points.

EA.2.3.8.b: By finding x- and y-intercepts.

EA.2.3.8.c: Using the slope-intercept form of a line.

EA.2.3.8.d: Using the slope and any point on the line.

EA.2.3.9: Graph linear inequalities and identify the boundary line and solution area.

EA.2.3.10: Determine and explain the meaning of intercepts using real-world examples.

EA.2.3.11: Use direct variation to model rates of change, e.g., if income = 40 hours times rate of pay, then increasing the rate of pay increases income.

#### EA.3: Students will solve problems using spatial and logical reasoning, applications of geometric principles, and modeling.

EA.3.2: Specify locations and describe spatial relationships using coordinate geometry.

EA.3.2.1: Find the distance between two given points and find the coordinates of the midpoint between them.

EA.3.2.2: Solve problems using the distance formula.

EA.3.2.3: Solve problems for areas, perimeters, volumes, and surface areas using formulas.

EA.3.3: Solve problems using visualization, spatial reasoning, and geometric modeling.

EA.3.3.1: Solve problems using the Pythagorean Theorem.

EA.3.3.2: Find missing parts of geometric figures using proportional reasoning and geometric relationships.

EA.3.3.3: Illustrate multiplication of polynomials using area models, e.g., (a + b)² , x(x + 2), or (x + a)(x + b).

EA.3.3.4: Factor polynomials using area models:

EA.3.3.4.a: To identify the greatest common monomial factor.

EA.3.3.4.b: Of the form ax squared + bx + c when a = 1.

#### EA.4: Students will understand and apply measurement tools, formulas, and techniques.

EA.4.1: Understand measurable attributes of objects and the units, systems, and processes of measurement.

EA.4.1.2: Express the rate of change as a ratio of two different measures.

EA.4.1.3: Select appropriate units to achieve the desired precision when solving problems.

#### EA.5: Students will draw conclusions using concepts of probability after collecting, organizing, and analyzing a data set.

EA.5.1: Formulate and answer questions by collecting, organizing, and analyzing data.

EA.5.1.1: Collect, record, organize, and display a set of data.

EA.5.1.2: Determine whether the pattern of the data is linear or nonlinear when given in a list, table, or graph.

EA.5.1.3: Interpret the correlation between two variables as being positive, negative, or having no correlation.

EA.5.1.5: Analyze the meaning of the slope and y-intercept of a line of best fit as it relates to the data.

EA.5.2: Apply basic concepts of probability.

EA.5.2.1: Determine and express the probability of an event as a fraction, percent, ratio, or decimal.

EA.5.2.2: Identify the probability of an event as being between zero (event not possible) and one (event certain).

### GE: Geometry

#### GE.2: Students will represent and analyze mathematical situations and properties using patterns, relations, functions, and algebraic symbols.

GE.2.1: Use patterns, relations, and functions to represent mathematical situations.

GE.2.1.1: Identify trigonometric relationships (sine, cosine, and tangent) using right triangles, expressing the relationships as fractions or decimals.

GE.2.1.2: Analyze geometric patterns to develop formulas and communicate how the formulas were derived, e.g., angle measure and number of sides of a polygon, interior and exterior angles, diagonals, and vertices.

GE.2.1.4: Identify the effect on area or volume when changing linear dimensions.

GE.2.2: Evaluate, solve, and analyze mathematical situations using algebraic properties and symbols.

GE.2.2.1: Find the angle measure in degrees given the trigonometric ratio using a calculator.

GE.2.2.2: Find the trigonometric ratio given the angle measure in degrees using a calculator.

GE.2.2.3: Find the missing measures of right triangles.

GE.2.2.5: Write an equation of a line perpendicular or parallel to a line through a given point.

GE.2.2.6: Model and solve geometric situations using algebraic properties.

#### GE.3: Students will solve problems using spatial and logical reasoning, applications of geometric principles, and modeling.

GE.3.1: Analyze characteristics and properties of two- and three-dimensional shapes and develop mathematical arguments about geometric relationships.

GE.3.1.1: Use accepted geometric notations, e.g., congruencies, transformations, similarities.

GE.3.1.2: Write conditional statements, converses, and inverses and determine the truth value of the statements.

GE.3.1.4: Identify angle pairs as adjacent, complementary, supplementary, a linear pair, or vertical angles.

GE.3.1.5: Differentiate between parallel, perpendicular, skew, and intersecting lines.

GE.3.1.6: Classify angle pairs formed by two lines and a transversal, e.g., corresponding, alternate interior, and supplementary angles.

GE.3.1.7: Prove lines parallel or perpendicular using slope or angle relationships.

GE.3.1.8: Prove congruency and similarity of geometric figures.

GE.3.1.9: Identify medians, altitudes, and angle bisectors of a triangle, and the perpendicular bisectors of the sides of a triangle.

GE.3.1.10: Classify a quadrilateral as a parallelogram, trapezoid, rectangle, square, rhombus, kite, or none of the above.

GE.3.1.11: Identify radii, diameters, chords, secants, arcs, sectors, central angles, inscribed angles, and tangents for circles.

GE.3.1.12: Classify and use the properties of acute, right, scalene, oblique, isosceles, equilateral, or equiangular triangles.

GE.3.1.13: Classify polyhedrons and other three-dimensional figures according to their properties.

GE.3.2: Specify locations and describe spatial relationships using coordinate geometry.

GE.3.2.1: Graph a circle given the equation in the form (x - h)² + (y - k)² = r².

GE.3.2.2: Write the equation of a circle given its graph.

GE.3.2.3: Verify the classifications of geometric figures using coordinate geometry to find lengths and slopes, e.g., verify or prove the diagonals of a rectangle are congruent using the distance formula.

GE.3.2.4: Perform and analyze transformations (translations, rotations, reflections, and dilations) using coordinate geometry.

GE.3.3: Use visualization, spatial reasoning, and geometric modeling to solve problems.

GE.3.3.1: Construct/copy angles and segments, bisect angles and segments, and create perpendicular lines and parallel lines using a compass and straight edge, technology, or other manipulatives.

GE.3.3.2: Define p as the ratio of the circumference to the diameter of a circle.

GE.3.3.3: Identify the relationships between the measures of intercepted arcs and inscribed or central angles.

GE.3.3.4: Solve real-world problems using trigonometric ratios and properties of congruent and similar figures, e.g., “How much paint is needed to paint a room?” or “How can we ensure square corners in a building during construction?”

GE.3.3.5: Sketch cross-sections of geometric solids.

#### GE.4: Students will understand and apply measurement tools, formulas, and techniques.

GE.4.2: Determine measurements using appropriate techniques, tools, and formulas.

GE.4.2.1: Find the area of a regular polygon.

GE.4.2.3: Find the surface area and volume for prisms, cylinders, pyramids, cones, and spheres given the formula.

#### GE.5: Students will draw conclusions using concepts of probability after collecting, organizing, and analyzing a data set.

GE.5.2: Apply basic concepts of probability.

GE.5.2.1: Identify geometric probabilities by performing simulations involving length or area.

GE.5.2.2: Calculate geometric probability.

### IA: Intermediate Algebra

#### IA.1: Students will acquire number sense and perform operations with real and complex numbers.

IA.1.2: Represent complex numbers in a variety of ways.

IA.1.2.1: Extend the number system to include complex numbers in the form a + bi.

IA.1.2.3: Simplify expressions involving radical expressions including square roots of negative numbers.

#### IA.2: Students will represent and analyze mathematical situations and properties using patterns, relations, functions, and algebraic symbols.

IA.2.1: Use patterns, relations, and functions to represent mathematical situations.

IA.2.1.1: Compare and contrast relations and functions.

IA.2.1.2: Identify the domain and range of the absolute value, quadratic, radical, sine, and cosine functions.

IA.2.1.5: Find the inverse of a function by interchanging the values of domain and range, reflecting across the line y = x, or by using algebra.

IA.2.1.6: Relate the sine, cosine, tangent, cosecant, secant, and cotangent to the unit circle.

IA.2.1.7: Express angle measure in degrees or radians when given the trigonometric value.

IA.2.2: Evaluate, solve, and analyze mathematical situations using algebraic properties and symbols.

IA.2.2.4: Solve single-variable quadratic and absolute value inequalities.

IA.2.2.5: Write a quadratic equation when given the rational roots or zeroes of the function.

IA.2.2.6: Solve systems of equations with no more than three variables using technology.

IA.2.2.7: Solve and graph systems of linear inequalities.

IA.2.2.9: Recognize that a to the -nth power is defined as the reciprocal of a to the nth power, i.e., a to the -nth power = 1 over a to the nth power if a is not equal 0.

IA.2.3: Represent quantitative relationships using mathematical models and symbols.

IA.2.3.1: Interpret rates of change by analyzing graphical and numerical data for quadratic and radical functions.

IA.2.3.2: Find the vertex, maximum or minimum values, intercepts, and axis of symmetry of a quadratic or absolute value function, algebraically, graphically, and numerically.

IA.2.3.3: Write the equation of a parabola in the form y = a(x - h)² + k and a circle in the form y = a(x - h)² + (y - k)² = r² by completing the square.

#### IA.3: Students will solve problems using spatial and logical reasoning, applications of geometric principles, and modeling.

IA.3.2: Specify locations and describe spatial relationships using coordinate geometry.

IA.3.2.1: Sketch the graph of a quadratic and absolute value function.

IA.3.2.2: Sketch the solutions of absolute value and quadratic inequalities of one variable on a number line.

IA.3.2.3: Sketch the solutions of absolute value and quadratic inequalities of two variables on a Cartesian coordinate system.

IA.3.2.4: Sketch the graph of a square root function.

IA.3.2.5: Write an equation of a parabola in the form y = a(x -h)² + k when given a graph.

IA.3.2.6: Graph sine and cosine functions.

IA.3.2.7: Perform the transformations of stretching, shifting, and reflecting the graphs of linear, absolute value, quadratic, and radical functions.

IA.3.2.8: Perform transformation on the sine and cosine functions involving amplitude, period, phase shift, vertical shift, and reflections.

IA.3.3: Solve problems using visualization, spatial reasoning, and geometric modeling.

IA.3.3.1: Solve problems involving absolute value and quadratic functions algebraically and graphically.

IA.3.3.2: Solve problems using graphs of sine and cosine functions.

#### IA.4: Students will understand and apply measurement tools, formulas, and techniques.

IA.4.1: Understand measurable attributes of objects and the units, systems, and processes of measurement.

IA.4.1.2: Calculate the exact values of the sine, cosine, and tangent functions for the special angles of the unit circle.

IA.4.2: Determine measurements using appropriate techniques, tools, and formulas.

IA.4.2.2: Find the area of a sector in a circle using radian measure.

#### IA.5: Students will draw conclusions using concepts of probability after collecting, organizing, and analyzing a data set.

IA.5.2: Apply basic concepts of probability.

IA.5.2.1: Identify the difference between a permutation and a combination.

IA.5.2.2: Calculate a probability using the Fundamental Counting Principle.

IA.5.2.3: Calculate simple combinations and permutations of n objects taken r at a time.

### PC: Pre-Calculus

#### PC.1: Students will acquire number sense and perform operations with real and complex numbers.

PC.1.1: Compute fluently and make reasonable estimates.

PC.1.1.1: Add, subtract, multiply, and find the absolute value using complex numbers.

PC.1.1.2: Add, subtract and perform scalar multiplication on vectors using a variety of techniques with or without the use of technology.

PC.1.2: Represent complex numbers and vectors in a variety of ways.

PC.1.2.1: Represent vectors graphically and symbolically.

PC.1.2.2: Represent complex numbers in rectangular and polar form and convert between rectangular and polar form.

PC.1.3: Identify relationships among complex numbers and vectors and operations involving these items.

PC.1.3.1: Analyze properties of vectors and their effects on vector operations.

PC.1.3.2: Analyze properties of complex numbers and their effects on operations in rectangular and polar form.

#### PC.2: Students will represent and analyze mathematical situations and properties using patterns, relations, functions, and algebraic symbols.

PC.2.1: Use patterns, relations, and functions to represent mathematical situations.

PC.2.1.1: Identify the domain, range, and other attributes of families of functions and their inverses, i.e., exponential, polynomial, rational, logarithmic, piece-wise, and trigonometric.

PC.2.1.3: Write functions and relations in parametric form.

PC.2.1.4: Identify vector-valued functions using a variety of approaches, e.g., algebraically or graphically.

PC.2.1.5: Identify and generate arithmetic and geometric sequences and series recursively and explicitly using correct notation.

PC.2.1.6: Identify a geometric series as convergent or divergent.

PC.2.2: Evaluate, solve, and analyze mathematical situations using algebraic properties and symbols.

PC.2.2.1: Solve equations and inequalities involving exponential, logarithmic, power, polynomial, rational, and trigonometric functions, including real-world situations.

PC.2.2.2: Compare logarithmic and exponential functions.

PC.2.2.3: Combine and compose functions using algebraic methods or by using technology when appropriate.

PC.2.2.6: Solve systems of non-linear equations and inequalities.

PC.2.2.7: Find the x- and y-intercepts, zeros (roots), maxima, and minima of functions.

PC.2.2.8: Approximate instantaneous rates of change and find average rates of change using graphical and numerical data.

PC.2.3: Represent quantitative relationships using mathematical models and symbols.

PC.2.3.1: Represent quantitative, real-world situations using exponential, logarithmic, power, polynomial, rational, and trigonometric functions, vector and parametric equations, and sequences and series.

PC.2.3.2: Identify and analyze graphical features of functions such as asymptotes, holes, local, global, and end behavior.

PC.2.3.3: Recognize symmetric properties of even and odd functions.

PC.2.3.4: Relate the graphical representation of discontinuities and end-behavior to the concept of limit.

PC.2.3.5: Identify the effects of changing the parameters in transformations of functions.

PC.2.3.6: Identify a family or families of functions that model real-world relationships.

#### PC.3: Students will solve problems using spatial and logical reasoning, applications of geometric principles, and modeling.

PC.3.1: Analyze characteristics and properties of two- and three-dimensional shapes and develop mathematical arguments about geometric relationships.

PC.3.1.1: Determine and analyze the characteristics of graphs and the related equations of conic sections.

PC.3.1.2: Analyze problems and solutions involving vectors using algebraic and graphical techniques.

PC.3.2: Specify locations and describe spatial relationships using coordinate geometry.

PC.3.2.1: Perform transformations on exponential, power, polynomial, rational, logarithmic, and trigonometric functions.

#### PC.4: Students will understand and apply measurement tools, formulas, and techniques.

PC.4.1: Understand measurable attributes of objects and the units, systems, and processes of measurement.

PC.4.1.1: Select appropriate units and scales for situations involving measurement.

PC.4.1.2: Recognize the changes in magnitude with various measurement scales, e.g., Richter, pH, decibel.

#### PC.5: Students will draw conclusions using concepts of probability after collecting, organizing, and analyzing a data set.

PC.5.1: Formulate and answer questions by collecting, organizing, and analyzing data.

PC.5.1.1: Find regression equation for bivariate data including power, exponential, logarithmic, polynomial, and sinusoidal curves using technology.

PC.5.2: Apply basic concepts of probability.

PC.5.2.1: Find sample spaces and probability distributions in simple cases.

PC.5.2.2: Differentiate between independent and dependent events and calculate the probability of each.

PC.5.2.4: Calculate the probability of a compound event.

PC.5.2.5: Calculate and interpret the expected value (weighted average) of random variables in simple cases.

#### AM1.1: Students will acquire number sense and perform operations with real numbers.

AM1.1.1: Compute fluently and make reasonable estimates.

AM1.1.1.1: Add, subtract, multiply, and divide real numbers using the order of operations.

AM1.1.2: Represent real numbers in a variety of ways.

AM1.1.2.1: Compare and order real numbers.

AM1.1.3: Identify relationships among real numbers and operations involving these numbers.

AM1.1.3.1: Simplify numerical expressions and solve problems using real numbers.

#### AM1.2: Students will represent and analyze mathematical situations and properties using patterns, relations, functions, and algebraic symbols.

AM1.2.1: Use patterns, relations, and functions to represent mathematical situations.

AM1.2.1.1: Distinguish between linear and non-linear functions when given a table, equation, or graph.

AM1.2.1.2: Represent linear equations in slope-intercept form, y = mx + b, or standard form, ax + by = c.

AM1.2.1.3: Write algebraic expressions describing numerical patterns or relations; e.g., triangular numbers, square numbers, arithmetic sequences, and recursive sequences.

AM1.2.1.4: Determine whether a relation is a function when given a graph or set of ordered pairs.

AM1.2.2: Evaluate, solve, and analyze mathematical situations using algebraic properties and symbols.

AM1.2.2.1: Evaluate numerical and algebraic expressions, formulas, and equations.

AM1.2.2.2: Solve multi-step linear equations and inequalities algebraically and graphically.

AM1.2.2.3: Solve systems of two linear equations and inequalities that have two variables algebraically and graphically.

AM1.2.2.5: Solve proportions that include algebraic first-degree expressions.

AM1.2.2.6: Solve linear formulas and literal equations for a specified variable, e.g., solve for p in I = prt.

AM1.2.2.7: Solve real-world problems involving constant rates of change, e.g., distance, rate and time, hourly wages, rates of interest.

AM1.2.3: Represent quantitative relationships using mathematical models and symbols.

AM1.2.3.1: Write the equation of a line given:

AM1.2.3.1.a: Ordered pairs.

AM1.2.3.1.b: The slope and a point on the line.

AM1.2.3.1.c: The graph of a line.

AM1.2.3.2: Graph linear functions:

AM1.2.3.2.a: By plotting points.

AM1.2.3.2.b: By finding x- and y-intercepts.

AM1.2.3.2.c: Using the slope-intercept form of a line.

AM1.2.3.2.d: Using the slope and any point on the line.

AM1.2.3.3: Identify the domain and range of a relation or function when given a graph, equation, table, or ordered pairs.

AM1.2.3.4: Identify horizontal and vertical lines given their equations.

AM1.2.3.5: Determine the effect of parameter changes on the graphs of linear relations using appropriate technology.

AM1.2.3.6: Identify the x- and y-intercepts when given the equation of a line.

AM1.2.3.7: Determine the slope of a line when given a set of ordered pairs, the graph, or the equation of the line.

AM1.2.3.8: Graph linear inequalities and identify the boundary line and solution area.

AM1.2.3.9: Determine and explain the meaning of intercepts using real-world examples.

AM1.2.3.10: Use direct variation to model rates of change, e.g., if income = 40 hours times rate of pay, then increasing the rate of pay increases income.

#### AM1.3: Students will solve problems using spatial and logical reasoning, applications of geometric principles, and modeling.

AM1.3.1: Analyze characteristics and properties of two- and three-dimensional shapes and develop mathematical arguments about geometric relationships.

AM1.3.1.1: Draw geometric objects when given specified properties, e.g., side lengths or angle measures.

AM1.3.3: Solve problems using visualization, spatial reasoning, and geometric modeling.

AM1.3.3.2: Solve problems involving right triangles using the ratios for the sine, cosine, and tangent.

AM1.3.3.3: Solve problems using the Pythagorean Theorem.

AM1.3.3.4: Find missing parts of geometric figures using proportional reasoning and geometric relationships.

AM1.3.3.5: Solve problems using similar triangles.

AM1.3.3.6: Illustrate multiplication and factoring of polynomials using area models, e.g., (a + b)² or (x + b)(x + a).

AM1.3.3.7: Factor polynomials using area models:

AM1.3.3.7.a: To identify the greatest common monomial factor.

AM1.3.3.7.b: Of the form ax squared + bx + c when a = 1.

#### AM1.4: Students will understand and apply measurement tools, formulas, and techniques.

AM1.4.1: Understand measurable attributes of objects and the units, systems, and processes of measurement.

AM1.4.1.1: Measure lengths of designated sides and calculate area and volume using the correct units.

AM1.4.1.3: Express the rate of change as a ratio of two different measures.

AM1.4.2: Determine measurements using appropriate techniques, tools, and formulas.

AM1.4.2.1: Calculate derived measures using formulas, e.g., areas and velocities.

AM1.4.2.3: Select and use an appropriate tool to measure a given attribute.

#### AM1.5: Students will draw conclusions using concepts of probability, after collecting, organizing, and analyzing a data set.

AM1.5.1: Formulate and answer questions by collecting, organizing, and analyzing data.

AM1.5.1.1: Collect, record, organize, and display a set of data.

AM1.5.1.2: Make predictions using a box plot, scatter plot, or histogram for a given set of data.

AM1.5.1.4: Interpret the correlation between two variables as positive, negative, or having no correlation.

AM1.5.1.5: Find mean, median, mode, and range for a data set.

AM1.5.2: Apply basic concepts of probability.

AM1.5.2.1: Determine and express the probability of an event as a fraction, percent, ratio, or decimal.

AM1.5.2.2: Determine the odds of an event when given the probability, and determine the probability of an event when given the odds.

AM1.5.2.4: Compute simple probabilities using the Fundamental Counting Principle or a tree diagram.

AM1.5.2.5: Identify the probability of an event as being between zero (event not possible) and one (event certain).

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

#### 2.1: Use patterns, relations, and functions to represent mathematical situations.

2.1.1: Identify the trigonometric relationships (sine, cosine, tangent) using right triangles and express them as fractions or decimals.

2.1.4: Recognize the relationship between the length of a side of a triangle and the size of the angle opposite the side.

2.1.5: Identify the effect on area or volume when changing linear dimensions.

#### 2.2: Evaluate, solve, and analyze mathematical situations using algebraic properties and symbols.

2.2.1: Find the angle measure in degrees given the trigonometric ratio using a calculator.

2.2.2: Find the trigonometric ratio given the angle measure in degrees using a calculator.

2.2.3: Find missing parts of right triangles using the Pythagorean Theorem.

2.2.4: Find missing parts of right triangles using sine, cosine, and tangent functions and their inverses.

2.2.5: Solve for corresponding sides of similar figures using proportions.

2.2.7: Develop and graph equations using two variables to represent real-world situations, e.g., the volume of an open box made by cutting the corners from a rectangular sheet.

### 3: Students will solve problems using spatial and logical reasoning, applications of geometric principles, and modeling.

#### 3.1: Analyze characteristics and properties of two- and three-dimensional shapes and develop mathematical arguments about geometric relationships.

3.1.1: Write a conditional statement and its converse, then determine the truth value of each statement.

3.1.3: Identify angle pairs as adjacent, complementary, supplementary, a linear pair, or vertical angles.

3.1.4: Identify the medians, altitudes, and angle bisectors of a triangle and the perpendicular bisectors of the sides of a triangle.

3.1.5: Identify radius, diameter, chord, secant, arc, sector, central angle, inscribed angle, and tangent for a circle.

3.1.6: Differentiate between skew and parallel lines.

3.1.7: Prove lines parallel or perpendicular using slope or angle relationships.

3.1.8: Prove congruency and similarity of triangles.

3.1.9: Identify the geometric mean formed by the altitude to the hypotenuse.

3.1.10: Classify polygons by their distinguishing characteristics.

3.1.12: Draw three-dimensional objects from different perspectives using nets, cross-sections, and two-dimensional views.

#### 3.2: Specify locations and describe spatial relationships using coordinate geometry.

3.2.2: Solve problems using the distance formula.

3.2.3: Write an equation of a line perpendicular or parallel to a line through a given point.

3.2.4: Verify the classifications of geometric figures using coordinate geometry to find lengths and slopes.

#### 3.3: Use visualization, spatial reasoning, and geometric modeling to solve problems.

3.3.2: Determine whether coplanar lines are parallel or perpendicular.

3.3.3: Construct/copy angles and segments, bisect angles and segments, and create perpendicular lines and parallel lines using a compass and straight edge, technology, or other manipulatives.

3.3.4: Identify and perform transformations, i.e., translations, rotations, reflections, and dilations, on geometric objects.

3.3.5: Tessellate a plane using reflections, translations, and rotations.

3.3.6: Solve problems using geometric modeling, e.g., similar figures, diagrams, and symbolic notation.

### 4: Students will understand and apply measurement tools, formulas, and techniques.

#### 4.1: Understand measurable attributes of objects and the units, systems, and processes of measurement.

4.1.1: Represent vector quantities with correct notation.

4.1.2: Define sums and differences of vector quantities.

#### 4.2: Determine measurements using appropriate techniques, tools, and formulas.

4.2.2: Determine perimeter, area, surface area, lateral area, and volume for a variety of geometric shapes and objects.

4.2.3: Find the length of an arc and the area of a sector.

### 5: Students will draw conclusions using concepts of probability, after collecting, organizing, and analyzing a data set.

#### 5.1: Formulate and answer questions by collecting, organizing, and analyzing data.

5.1.1: Collect, organize, and display a data set using technology or other methods.

5.1.2: Display data using a box plot, circle graph, or scatter plot.

#### 5.2: Apply basic concepts of probability.

5.2.1: Identify geometric probabilities by performing simulations involving length or area.

5.2.2: Solve problems using geometric probabilities.

Correlation last revised: 10/24/2008

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