Skills available for
Nebraska high school math standards
Standards
are in bold, followed by a list of the IXL math
skills that are aligned to that
standard.
Students can practice
these skills
online at www.ixl.com.
Standards: Nebraska's College and Career Ready Standards (2009)
9-12.1 Students will communicate number sense concepts using multiple representations to reason, solve problems, and make connections within mathematics and across disciplines.
9-12.1.1 Students will represent and show relationships among complex numbers.
9-12.1.1.a Demonstrate multiple equivalent forms of irrational numbers (e.g., square root of 8 = 8 to the 1/2 power = 2 square root of 2)
9-12.1.1.b Compare, contrast and apply the properties of numbers and the real number system, including rational, irrational, imaginary, and complex numbers
Classify numbers (A1-A.1)
Compare and order rational numbers (A1-A.2)
Convert between decimals and fractions (A1-A.5)
Convert between percents, fractions, and decimals (A1-D.1)
Ratios and proportions (G-A.1)
Properties of exponents (G-A.3)
Lengths of segments on number lines (G-B.2)
Additive property of length (G-B.3)
Midpoints (G-B.4)
Introduction to complex numbers (A2-H.1)
Add and subtract complex numbers (A2-H.2)
Multiply complex numbers (A2-H.4)
Divide complex numbers (A2-H.5)
Add, subtract, multiply, and divide complex numbers (A2-H.6)
Absolute values of complex numbers (PC-R.5)
Introduction to the complex plane (PC-S.1)
Graph complex numbers (PC-S.2)
Absolute value in the complex plane (PC-S.6)
9-12.1.2 Students will demonstrate the meaning and effects of arithmetic operations with real numbers.
9-12.1.2.a Use drawings, words, and symbols to explain the effects of such operations as multiplication and division, and computing positive powers and roots on the magnitude of quantities (e.g., if you take the square root of a number, will the result always be smaller than the original number? (e.g., square root of 1/4 = 1/2))
Properties of exponents (G-A.3)
Simplify radical expressions (G-A.4)
Roots of rational numbers (A2-L.2)
9-12.1.2.b Use drawings, words, and symbols to explain that the distance between two numbers on the number line is the absolute value of their difference
Lengths of segments on number lines (G-B.2)
9-12.1.3 Students will compute fluently and accurately using appropriate strategies and tools.
9-12.1.3.a Compute accurately with real numbers
Add, subtract, multiply, and divide integers (A1-B.1)
9-12.1.3.c Multiply and divide numbers using scientific notation
Convert between standard and scientific notation (A1-W.1)
Compare numbers written in scientific notation (A1-W.2)
Multiply numbers written in scientific notation (A1-W.3)
Divide numbers written in scientific notation (A1-W.4)
9-12.1.3.d Select, apply, and explain the method of computation when problem solving using real numbers (e.g., models, mental computation, paper-pencil, or technology)
9-12.1.4 Students will estimate and check reasonableness of answers using appropriate strategies and tools.
9-12.1.4.a Use estimation methods to check the reasonableness of real number computations and decide if the problem calls for an approximation or an exact number (e.g., 10 "pi" (pi) is approximately 3.14, square and cube roots)
Convert between repeating decimals and fractions (A1-A.6)
Write a repeating decimal as a fraction (A2-BB.19)
Find roots using a calculator (PC-H.3)
Nth roots (PC-H.7)
Write a repeating decimal as a fraction (PC-W.18)
9-12.1.4.b Distinguish relevant from irrelevant information, identify missing information and either find what is needed or make appropriate estimates
9-12.2 Students will communicate geometric concepts and measurement concepts using multiple representations to reason, solve problems, and make connections within mathematics and across disciplines.
9-12.2.1 Students will analyze characteristics, properties, and relationships among geometric shapes and objects.
9-12.2.1.a Identify and explain the necessity of and give examples of definitions and theorems
9-12.2.1.b Analyze properties and relationships among classes of two and three dimensional geometric objects using inductive reasoning and counterexamples
Classify triangles (G-F.1)
Polygon vocabulary (G-G.1)
Interior angles of polygons (G-G.2)
Exterior angles of polygons (G-G.3)
Review: interior and exterior angles of polygons (G-G.4)
Three-dimensional figure vocabulary (G-H.1)
Parts of three-dimensional figures (G-H.2)
Nets and drawings of three-dimensional figures (G-H.3)
Classify quadrilaterals (G-N.1)
Properties of parallelograms (G-N.2)
Proving a quadrilateral is a parallelogram (G-N.3)
Properties of rhombuses (G-N.4)
Properties of squares and rectangles (G-N.5)
Properties of trapezoids (G-N.6)
Properties of kites (G-N.7)
Review: properties of quadrilaterals (G-N.8)
Perimeter (G-S.1)
Area of rectangles and squares (G-S.2)
Area of parallelograms and triangles (G-S.3)
Area of trapezoids (G-S.4)
Area and perimeter in the coordinate plane I (G-S.5)
Area and perimeter in the coordinate plane II (G-S.6)
Area and circumference of circles (G-S.7)
Area of compound figures (G-S.8)
Area and perimeter of similar figures (G-S.10)
Heron's formula (G-S.11)
Area and perimeter mixed review (G-S.12)
9-12.2.1.c State and prove geometric theorems using deductive reasoning (e.g., parallel lines with transversals, congruent triangles, similar triangles)
Perpendicular Bisector Theorem (G-B.6)
Transversals of parallel lines: find angle measures (G-D.4)
Proofs involving parallel lines I (G-D.6)
Proofs involving parallel lines II (G-D.7)
Triangle Angle-Sum Theorem (G-F.2)
Exterior Angle Theorem (G-F.3)
SSS and SAS Theorems (G-K.1)
Proving triangles congruent by SSS and SAS (G-K.2)
ASA and AAS Theorems (G-K.3)
Proving triangles congruent by ASA and AAS (G-K.4)
SSS, SAS, ASA, and AAS Theorems (G-K.5)
Proving triangles congruent by SSS, SAS, ASA, and AAS (G-K.7)
Proofs involving corresponding parts of congruent triangles (G-K.8)
Proofs involving isosceles triangles (G-K.10)
Hypotenuse-Leg Theorem (G-K.11)
Triangle Inequality Theorem (G-M.5)
Proofs involving triangles I (G-M.8)
Proofs involving triangles II (G-M.9)
Proofs involving quadrilaterals I (G-N.9)
Proofs involving quadrilaterals II (G-N.10)
Similarity rules for triangles (G-P.7)
Triangle Proportionality Theorem (G-P.10)
Pythagorean Theorem (G-Q.1)
Converse of the Pythagorean theorem (G-Q.2)
Pythagorean Inequality Theorems (G-Q.3)
9-12.2.1.d Apply geometric properties to solve problems (e.g., parallel lines, line transversals, similar triangles, congruent triangles, proportions)
Similar figures: side lengths and angle measures (A1-F.6)
Similar triangles and indirect measurement (A1-F.7)
Area and perimeter of similar figures (A1-F.9)
Similar solids (A1-F.11)
Volume and surface area of similar solids (A1-F.12)
Slopes of parallel and perpendicular lines (A1-S.23)
Write an equation for a parallel or perpendicular line (A1-S.24)
Perpendicular Bisector Theorem (G-B.6)
Construct the midpoint or perpendicular bisector of a segment (G-B.9)
Construct an angle bisector (G-C.6)
Construct a congruent angle (G-C.7)
Construct a perpendicular line (G-D.2)
Transversals of parallel lines: find angle measures (G-D.4)
Construct parallel lines (G-D.5)
Triangle Angle-Sum Theorem (G-F.2)
Exterior Angle Theorem (G-F.3)
Construct an equilateral triangle or regular hexagon (G-G.5)
Construct a square (G-G.6)
SSS and SAS Theorems (G-K.1)
ASA and AAS Theorems (G-K.3)
SSS, SAS, ASA, and AAS Theorems (G-K.5)
Hypotenuse-Leg Theorem (G-K.11)
Midsegments of triangles (G-M.1)
Triangles and bisectors (G-M.2)
Triangle Inequality Theorem (G-M.5)
Construct the circumcenter or incenter of a triangle (G-M.6)
Similarity rules for triangles (G-P.7)
Triangle Proportionality Theorem (G-P.10)
Areas of similar figures (G-P.11)
Pythagorean Theorem (G-Q.1)
Converse of the Pythagorean theorem (G-Q.2)
Pythagorean Inequality Theorems (G-Q.3)
9-12.2.1.e Identify and apply right triangle relationships (e.g., sine, cosine, tangent, special right triangles, converse of Pythagorean Theorem)
Pythagorean theorem (A1-F.14)
Pythagorean theorem: word problems (A1-F.15)
Converse of the Pythagorean theorem: is it a right triangle? (A1-F.16)
Special right triangles (A1-F.17)
Pythagorean Theorem (G-Q.1)
Converse of the Pythagorean theorem (G-Q.2)
Pythagorean Inequality Theorems (G-Q.3)
Special right triangles (G-Q.4)
Pythagorean Theorem and its converse (A2-Y.1)
Special right triangles (A2-Y.2)
Trigonometric ratios: sin, cos, and tan (A2-Y.3)
Trigonometric ratios: csc, sec, and cot (A2-Y.4)
Trigonometric ratios in similar right triangles (A2-Y.5)
Csc, sec, and cot of special angles (A2-Y.8)
Inverses of csc, sec, and cot (A2-Y.11)
Trigonometric ratios: find a side length (A2-Y.14)
Trigonometric ratios: find an angle measure (A2-Y.15)
Solve a right triangle (A2-Y.16)
Coterminal and reference angles (PC-M.4)
Find trigonometric ratios using right triangles (PC-M.5)
Find trigonometric ratios using the unit circle (PC-M.6)
Find trigonometric ratios using reference angles (PC-M.7)
Trigonometric ratios: find a side length (PC-M.10)
Trigonometric ratios: find an angle measure (PC-M.11)
Solve a right triangle (PC-M.12)
Law of Sines (PC-M.13)
Law of Cosines (PC-M.14)
Solve a triangle (PC-M.15)
Area of a triangle: sine formula (PC-M.16)
9-12.2.1.f Recognize that there are geometries, other than Euclidean geometry, in which the parallel postulate is not true
9-12.2.1.g Know the definitions and basic properties of a circle and use them to prove basic theorems and solve problems
Circles, semicircles, and quarter circles (8-T.5)
Circles: word problems (8-T.6)
Similarity of circles (G-P.9)
Parts of a circle (G-U.1)
Central angles (G-U.2)
Arc measure and arc length (G-U.3)
Area of sectors (G-U.4)
Circle measurements: mixed review (G-U.5)
Arcs and chords (G-U.6)
Tangent lines (G-U.7)
Perimeter of polygons with an inscribed circle (G-U.8)
Inscribed angles (G-U.9)
Angles in inscribed right triangles (G-U.10)
Angles in inscribed quadrilaterals (G-U.11)
Construct a tangent line to a circle (G-U.12)
Construct an equilateral triangle inscribed in a circle (G-U.13)
Construct a square inscribed in a circle (G-U.14)
Construct a regular hexagon inscribed in a circle (G-U.15)
Construct the inscribed or circumscribed circle of a triangle (G-U.16)
Find the center of a circle (A2-U.1)
Find the radius or diameter of a circle (A2-U.2)
9-12.2.2 Student will use coordinate geometry to analyze and describe relationships in the coordinate plane.
9-12.2.2.a Use coordinate geometry to analyze geometric situations (e.g., parallel lines, perpendicular lines, circle equations)
Slopes of parallel and perpendicular lines (A1-S.23)
Write an equation for a parallel or perpendicular line (A1-S.24)
Slopes of parallel and perpendicular lines (G-E.5)
Equations of parallel and perpendicular lines (G-E.6)
Identify the direction a parabola opens (A2-T.1)
Find the vertex of a parabola (A2-T.2)
Find the focus or directrix of a parabola (A2-T.3)
Find the axis of symmetry of a parabola (A2-T.4)
Write equations of parabolas in vertex form from graphs (A2-T.5)
Write equations of parabolas in vertex form using properties (A2-T.6)
Write equations of circles in standard form from graphs (A2-U.3)
Write equations of circles in standard form using properties (A2-U.4)
Convert equations of circles from general to standard form (A2-U.5)
Find properties of circles from equations in general form (A2-U.6)
Graph circles (A2-U.7)
Find the center, vertices, or co-vertices of an ellipse (A2-V.1)
Find the length of the major or minor axes of an ellipse (A2-V.2)
Find the foci of an ellipse (A2-V.3)
Write equations of ellipses in standard form from graphs (A2-V.4)
Write equations of ellipses in standard form using properties (A2-V.5)
Find the center of a hyperbola (A2-W.1)
Find the vertices of a hyperbola (A2-W.2)
Find the length of the transverse or conjugate axes of a hyperbola (A2-W.3)
Find the equations for the asymptotes of a hyperbola (A2-W.4)
Find the foci of a hyperbola (A2-W.5)
Write equations of hyperbolas in standard form from graphs (A2-W.6)
Write equations of hyperbolas in standard form using properties (A2-W.7)
Find properties of circles (PC-P.4)
Write equations of circles in standard form (PC-P.5)
Graph circles (PC-P.6)
9-12.2.2.b Apply the midpoint formula
Midpoints (A1-G.2)
Midpoint formula (G-B.7)
9-12.2.2.c Apply the distance formula
Find the distance between two points (A1-G.3)
Find the distance between two points (G-B.8)
9-12.2.2.d Prove special types of triangles and quadrilaterals (e.g., right triangles, isosceles trapezoid, parallelogram, rectangle, square)
Classify triangles (G-F.1)
Proofs involving isosceles triangles (G-K.10)
Proofs involving triangles I (G-M.8)
Proofs involving triangles II (G-M.9)
Classify quadrilaterals (G-N.1)
Properties of parallelograms (G-N.2)
Proving a quadrilateral is a parallelogram (G-N.3)
Properties of rhombuses (G-N.4)
Properties of squares and rectangles (G-N.5)
Properties of trapezoids (G-N.6)
Properties of kites (G-N.7)
Review: properties of quadrilaterals (G-N.8)
Proofs involving quadrilaterals I (G-N.9)
Proofs involving quadrilaterals II (G-N.10)
Pythagorean Theorem (G-Q.1)
9-12.2.3 Students will apply and analyze transformations.
9-12.2.3.a Explain and justify the effects of simple transformations on the ordered pairs of two-dimensional shapes
Classify congruence transformations (G-L.1)
Translations: graph the image (G-L.2)
Translations: find the coordinates (G-L.3)
Translations: write the rule (G-L.4)
Reflections: graph the image (G-L.5)
Reflections: find the coordinates (G-L.6)
Rotate polygons about a point (G-L.7)
Rotations: graph the image (G-L.8)
Rotations: find the coordinates (G-L.9)
Congruence transformations: mixed review (G-L.12)
Dilations: graph the image (G-L.13)
Dilations: find the coordinates (G-L.14)
Dilations: scale factor and classification (G-L.15)
Dilations and parallel lines (G-L.16)
Identify transformation matrices (A2-G.15)
Transformation matrices: write the vertex matrix (A2-G.16)
Transformation matrices: graph the image (A2-G.17)
9-12.2.3.b Perform and describe multiple transformations
Translations: graph the image (G-L.2)
Translations: find the coordinates (G-L.3)
Reflections: graph the image (G-L.5)
Reflections: find the coordinates (G-L.6)
Rotations: graph the image (G-L.8)
Rotations: find the coordinates (G-L.9)
Compositions of congruence transformations: graph the image (G-L.10)
Dilations: graph the image (G-L.13)
Dilations: find the coordinates (G-L.14)
Dilations: scale factor and classification (G-L.15)
9-12.2.4 Students will use visualization, spatial reasoning, and geometric modeling to solve problems.
9-12.2.4.a Sketch and draw appropriate representations of geometric objects using ruler, protractor, or technology
Construct the midpoint or perpendicular bisector of a segment (G-B.9)
Construct an angle bisector (G-C.6)
Construct a congruent angle (G-C.7)
Construct a perpendicular line (G-D.2)
Construct parallel lines (G-D.5)
Construct an equilateral triangle or regular hexagon (G-G.5)
Construct a square (G-G.6)
Construct the circumcenter or incenter of a triangle (G-M.6)
Construct a tangent line to a circle (G-U.12)
Construct an equilateral triangle inscribed in a circle (G-U.13)
Construct a square inscribed in a circle (G-U.14)
Construct a regular hexagon inscribed in a circle (G-U.15)
Construct the inscribed or circumscribed circle of a triangle (G-U.16)
9-12.2.4.b Use geometric models to visualize, describe, and solve problems (e.g., find the height of a tree; find the amount of paint needed for a room; scale model)
Pythagorean theorem: word problems (8-R.4)
Area and perimeter: word problems (8-T.3)
Circles: word problems (8-T.6)
Scale drawings: word problems (G-A.2)
9-12.2.5 Students will apply the units, systems, and formulas to solve problems.
9-12.2.5.a Use strategies to find surface area and volume of complex objects
Volume (A1-F.4)
Surface area (A1-F.5)
Introduction to surface area and volume (G-T.1)
Surface area of prisms and cylinders (G-T.2)
Surface area of pyramids and cones (G-T.3)
Volume of prisms and cylinders (G-T.4)
Volume of pyramids and cones (G-T.5)
Surface area and volume of spheres (G-T.6)
Surface area and volume review (G-T.9)
9-12.2.5.b Apply appropriate units and scales to solve problems involving measurement
Convert rates and measurements: customary units (A1-E.1)
Convert rates and measurements: metric units (A1-E.2)
Unit prices with unit conversions (A1-E.3)
Precision (A1-E.4)
Greatest possible error (A1-E.5)
Minimum and maximum area and volume (A1-E.6)
Percent error (A1-E.7)
Percent error: area and volume (A1-E.8)
Convert rates and measurements: customary units (G-W.1)
Convert rates and measurements: metric units (G-W.2)
Convert square and cubic units of length (G-W.3)
Convert between radians and degrees (PC-M.1)
9-12.2.5.c Convert between various units of area and volume, such as square feet to square yards
Convert rates and measurements: customary units (A1-E.1)
Convert rates and measurements: metric units (A1-E.2)
Convert square and cubic units of length (G-W.3)
9-12.2.5.d Convert equivalent rates (e.g., feet/second to miles/hour)
Unit rates (A1-C.3)
Unit prices (A1-C.4)
Convert rates and measurements: customary units (A1-E.1)
Convert rates and measurements: metric units (A1-E.2)
Convert rates and measurements: customary units (G-W.1)
Convert rates and measurements: metric units (G-W.2)
9-12.2.5.e Find arc length and area of sectors of a circle
Parts of a circle (8-O.11)
Arc measure and arc length (G-U.3)
Area of sectors (G-U.4)
Radians and arc length (A2-X.2)
Radians and arc length (PC-M.2)
9-12.2.5.f Determine surface area and volume of three-dimensional objects (e.g., spheres, cones, pyramids)
Volume (A1-F.4)
Surface area (A1-F.5)
Introduction to surface area and volume (G-T.1)
Surface area of prisms and cylinders (G-T.2)
Surface area of pyramids and cones (G-T.3)
Volume of prisms and cylinders (G-T.4)
Volume of pyramids and cones (G-T.5)
Surface area and volume of spheres (G-T.6)
Surface area and volume review (G-T.9)
9-12.2.5.g Know that the effect of a scale factor k on length, area and volume is to multiply each by k, k^{2} and k^{3}, respectively
Dilations and scale factors (A1-F.8)
Perimeter, area, and volume: changes in scale (A1-F.13)
Perimeters of similar figures (G-P.6)
Area and perimeter of similar figures (G-S.10)
Introduction to similar solids (G-T.7)
Surface area and volume of similar solids (G-T.8)
9-12.3 Students will communicate algebraic concepts using multiple representations to reason, solve problems, and make connections within mathematics and across disciplines.
9-12.3.1 Students will generalize, represent, and analyze relationships using algebraic symbols.
9-12.3.1.a Represent, interpret, and analyze functions with graphs, tables, and algebraic notation and convert among these representations (e.g., linear, non-linear)
Interpret the graph of a function: word problems (A1-Q.11)
Slope-intercept form: graph an equation (A1-S.6)
Slope-intercept form: write an equation from a graph (A1-S.7)
Slope-intercept form: write an equation from a table (A1-S.9)
Complete a table and graph a linear function (A1-S.13)
Standard form: graph an equation (A1-S.17)
Point-slope form: graph an equation (A1-S.20)
Point-slope form: write an equation from a graph (A1-S.22)
Identify linear, quadratic, and exponential functions from graphs (A1-CC.1)
Identify linear, quadratic, and exponential functions from tables (A1-CC.2)
Write linear, quadratic, and exponential functions (A1-CC.3)
Write variable expressions (G-A.5)
Graph a linear equation (G-E.3)
Equations of lines (G-E.4)
Evaluate functions (A2-D.3)
Graph a linear function (A2-D.7)
Write the equation of a linear function (A2-D.8)
Complete a function table: quadratic functions (A2-J.2)
Graph a quadratic function (A2-J.3)
Match quadratic functions and graphs (A2-J.11)
Match polynomials and graphs (A2-K.14)
Evaluate exponential functions (A2-S.2)
Match exponential functions and graphs (A2-S.3)
Write equations of sine functions from graphs (A2-Z.2)
Write equations of sine functions using properties (A2-Z.3)
Graph sine functions (A2-Z.4)
Write equations of cosine functions from graphs (A2-Z.6)
Write equations of cosine functions using properties (A2-Z.7)
Graph cosine functions (A2-Z.8)
Graph sine and cosine functions (A2-Z.9)
Symmetry and periodicity of trigonometric functions (A2-AA.2)
Evaluate functions (PC-A.3)
Linear functions (PC-A.6)
Graph a quadratic function (PC-C.3)
Match quadratic functions and graphs (PC-C.4)
Match polynomials and graphs (PC-D.11)
Find properties of sine functions (PC-N.1)
Write equations of sine functions from graphs (PC-N.2)
Write equations of sine functions using properties (PC-N.3)
Graph sine functions (PC-N.4)
Find properties of cosine functions (PC-N.5)
Write equations of cosine functions from graphs (PC-N.6)
Write equations of cosine functions using properties (PC-N.7)
Graph cosine functions (PC-N.8)
Graph sine and cosine functions (PC-N.9)
Symmetry and periodicity of trigonometric functions (PC-O.2)
9-12.3.1.b Identify domain and range of functions represented in either symbolic or graphical form (e.g., linear, non-linear)
Domain and range of relations (A1-Q.2)
Domain and range of absolute value functions (A1-DD.2)
Domain and range of radical functions (A1-FF.2)
Domain and range (A2-D.1)
Domain and range of radical functions (A2-L.12)
Domain and range of exponential and logarithmic functions (A2-S.1)
Domain and range (PC-A.1)
Domain and range of exponential and logarithmic functions (PC-F.1)
Domain and range of radical functions (PC-G.1)
9-12.3.1.c Identify the slope and intercepts of a linear relationship from an equation or graph
Find the constant of variation (A1-R.2)
Find the slope of a graph (A1-S.2)
Find the slope from two points (A1-S.3)
Slope-intercept form: find the slope and y-intercept (A1-S.5)
Linear equations: solve for y (A1-S.11)
Standard form: find x- and y-intercepts (A1-S.16)
Slopes of lines (G-E.2)
Equations of lines (G-E.4)
Find the slope of a linear function (A2-D.6)
Write the equation of a linear function (A2-D.8)
Find the constant of variation (A2-Q.5)
9-12.3.1.d Identify characteristics of linear and non-linear functions
Identify linear functions (A1-S.1)
Characteristics of quadratic functions (A1-BB.1)
Rational functions: asymptotes and excluded values (A1-GG.1)
Characteristics of quadratic functions (A2-J.1)
Rational functions: asymptotes and excluded values (A2-N.1)
Find properties of sine functions (A2-Z.1)
Find properties of cosine functions (A2-Z.5)
Identify functions (PC-A.2)
Characteristics of quadratic functions (PC-C.1)
Find the maximum or minimum value of a quadratic function (PC-C.2)
Rational functions: asymptotes and excluded values (PC-E.1)
Symmetry and periodicity of trigonometric functions (PC-O.2)
9-12.3.1.e Graph linear and non-linear functions
Graph a proportional relationship (A1-R.3)
Slope-intercept form: graph an equation (A1-S.6)
Complete a table and graph a linear function (A1-S.13)
Standard form: graph an equation (A1-S.17)
Point-slope form: graph an equation (A1-S.20)
Match exponential functions and graphs (A1-X.2)
Graph a linear equation (G-E.3)
Graph a linear function (A2-D.7)
Graph a quadratic function (A2-J.3)
Match quadratic functions and graphs (A2-J.11)
Match polynomials and graphs (A2-K.14)
Match exponential functions and graphs (A2-S.3)
Graph parabolas (A2-T.9)
Graph sine functions (A2-Z.4)
Graph cosine functions (A2-Z.8)
Graph sine and cosine functions (A2-Z.9)
Graph a quadratic function (PC-C.3)
Match quadratic functions and graphs (PC-C.4)
Match polynomials and graphs (PC-D.11)
Graph sine functions (PC-N.4)
Graph cosine functions (PC-N.8)
Graph sine and cosine functions (PC-N.9)
9-12.3.1.f Compare and analyze the rate of change by using ordered pairs, tables, graphs, and equations
Percent of change (A1-D.4)
Percent of change: word problems (A1-D.5)
Rate of travel: word problems (A1-O.4)
Find the constant of variation (A1-R.2)
Find the slope of a graph (A1-S.2)
Find the slope from two points (A1-S.3)
Slope-intercept form: write an equation from a word problem (A1-S.10)
Write linear functions to solve word problems (A1-S.12)
Solve linear equations: word problems (A2-B.2)
Find the slope of a linear function (A2-D.6)
9-12.3.1.g Graph and interpret linear inequalities
Graph inequalities (A1-K.1)
Identify solutions to inequalities (A1-K.3)
Graph solutions to one-step linear inequalities (A1-K.7)
Graph solutions to two-step linear inequalities (A1-K.9)
Graph solutions to advanced linear inequalities (A1-K.11)
Graph compound inequalities (A1-K.12)
Graph solutions to compound inequalities (A1-K.15)
Graph solutions to absolute value equations (A1-L.2)
Graph solutions to absolute value inequalities (A1-L.4)
Does (x, y) satisfy the inequality? (A1-T.1)
Graph a two-variable linear inequality (A1-T.3)
Is (x, y) a solution to the system of inequalities? (A1-T.5)
Solve linear inequalities (G-A.7)
Graph a linear inequality in one variable (A2-C.1)
Solve linear inequalities (A2-C.4)
Graph solutions to linear inequalities (A2-C.5)
Graph solutions to absolute value inequalities (A2-C.7)
Graph a two-variable linear inequality (A2-C.8)
Is (x, y) a solution to the system of inequalities? (A2-F.1)
Solve systems of linear inequalities by graphing (A2-F.2)
Solve systems of linear and absolute value inequalities by graphing (A2-F.3)
Solve systems of linear inequalities by graphing (PC-J.1)
Solve systems of linear and absolute value inequalities by graphing (PC-J.2)
9-12.3.1.h Represent, interpret, and analyze functions and their inverses
Identify inverse functions (A2-O.6)
Find inverse functions and relations (A2-O.9)
Function transformation rules (A2-P.1)
Translations of functions (A2-P.2)
Reflections of functions (A2-P.3)
Dilations of functions (A2-P.4)
Transformations of functions (A2-P.5)
Describe function transformations (A2-P.6)
Inverses of csc, sec, and cot (A2-Y.11)
Identify inverse functions (PC-A.10)
Find inverse functions and relations (PC-A.13)
Function transformation rules (PC-B.1)
Translations of functions (PC-B.2)
Reflections of functions (PC-B.3)
Dilations of functions (PC-B.4)
Transformations of functions (PC-B.5)
Describe function transformations (PC-B.6)
Check whether two rational functions are inverses (PC-E.3)
Inverses of trigonometric functions (PC-M.8)
9-12.3.1.i Determine if a relation is a function
Identify functions (A1-Q.4)
Identify functions: vertical line test (A1-Q.5)
Identify functions (A2-D.2)
Identify functions (PC-A.2)
9-12.3.2 Students will model and analyze quantitative relationships.
9-12.3.2.a Model contextualized problems using various representations (e.g., graphs, tables, one variable equalities, one variable inequalities, linear equations in slope intercept form, inequalities in slope intercept form, system of linear equations with two variables)
Solve proportions: word problems (A1-C.6)
Solve linear equations: word problems (A1-J.9)
Rate of travel: word problems (A1-O.4)
Weighted averages: word problems (A1-O.5)
Slope-intercept form: write an equation from a word problem (A1-S.10)
Write linear functions to solve word problems (A1-S.12)
Linear inequalities: word problems (A1-T.4)
Solve a system of equations by graphing: word problems (A1-U.3)
Solve a system of equations using substitution: word problems (A1-U.9)
Solve a system of equations using elimination: word problems (A1-U.11)
Solve a system of equations using augmented matrices: word problems (A1-U.13)
Solve a system of equations using any method: word problems (A1-U.15)
Solve linear equations: word problems (A2-B.2)
Write a linear inequality: word problems (A2-C.3)
Solve a system of equations by graphing: word problems (A2-E.3)
Solve a system of equations using substitution: word problems (A2-E.7)
Solve a system of equations using elimination: word problems (A2-E.9)
Solve a system of equations using any method: word problems (A2-E.11)
Solve a system of equations by graphing: word problems (PC-I.2)
Solve a system of equations using substitution: word problems (PC-I.5)
Solve a system of equations using elimination: word problems (PC-I.7)
9-12.3.2.b Represent a variety of quantitative relationships using linear equations and one variable inequalities
Write variable equations (A1-I.4)
Write and solve equations that represent diagrams (A1-J.2)
Write inequalities from graphs (A1-K.2)
Write compound inequalities from graphs (A1-K.13)
Write direct variation equations (A1-R.4)
Write and solve direct variation equations (A1-R.5)
Write inverse variation equations (A1-R.7)
Write and solve inverse variation equations (A1-R.8)
Slope-intercept form: write an equation from a graph (A1-S.7)
Slope-intercept form: write an equation from a table (A1-S.9)
Slope-intercept form: write an equation from a word problem (A1-S.10)
Point-slope form: write an equation from a graph (A1-S.22)
Write variable expressions (G-A.5)
Write inequalities from graphs (A2-C.2)
Write the equation of a linear function (A2-D.8)
Write and solve direct variation equations (A2-Q.1)
9-12.3.2.c Analyze situations to determine the type of algebraic relationship (e.g., linear, nonlinear)
Identify linear functions (A1-S.1)
Identify linear, quadratic, and exponential functions from graphs (A1-CC.1)
Identify linear, quadratic, and exponential functions from tables (A1-CC.2)
Write linear, quadratic, and exponential functions (A1-CC.3)
Classify variation (A2-Q.3)
9-12.3.2.d Model contextualized problems using various representations for non-linear functions (e.g., quadratic, exponential, square root, and absolute value)
Exponential growth and decay: word problems (A1-X.4)
Write and solve inverse variation equations (A2-Q.2)
Exponential growth and decay: word problems (A2-S.12)
Compound interest: word problems (A2-S.13)
Continuously compounded interest: word problems (A2-S.14)
Exponential growth and decay: word problems (PC-F.16)
Compound interest: word problems (PC-F.17)
9-12.3.3 Students will represent and solve equations and inequalities.
9-12.3.3.a Explain/apply the reflexive, symmetric, and transitive properties of equality
Properties of equality (A1-H.4)
9-12.3.3.b Simplify algebraic expressions involving exponents (e.g., (3x to the 4th power)^{2})
Powers of monomials (A1-Y.5)
Power rule (A2-M.4)
Simplify expressions involving rational exponents I (A2-M.5)
Simplify expressions involving rational exponents II (A2-M.6)
Complete a function table: quadratic functions (A2-J.2)
Evaluate polynomials using synthetic division (A2-K.6)
Evaluate rational expressions I (A2-N.2)
Evaluate rational expressions II (A2-N.3)
Evaluate functions (PC-A.3)
Evaluate polynomials using synthetic division (PC-D.3)
9-12.3.3.m Derive and use the formulas for the general term and summation of finite arithmetic and geometric series
Write variable expressions for arithmetic sequences (A1-P.5)
Write variable expressions for geometric sequences (A1-P.6)
Evaluate explicit formulas for sequences (A2-BB.3)
Write a formula for an arithmetic sequence (A2-BB.6)
Write a formula for a geometric sequence (A2-BB.7)
Find terms of a sequence (PC-W.1)
Find terms of a recursive sequence (PC-W.2)
Find a recursive formula (PC-W.4)
Identify arithmetic and geometric series (PC-W.9)
Introduction to sigma notation (PC-W.10)
Find the sum of a finite arithmetic or geometric series (PC-W.11)
Introduction to partial sums (PC-W.12)
Partial sums of arithmetic series (PC-W.13)
Partial sums of geometric series (PC-W.14)
Partial sums: mixed review (PC-W.15)
9-12.3.3.n Combine functions by composition, as well as by addition, subtraction, multiplication, and division
Add and subtract functions (A2-O.1)
Multiply functions (A2-O.2)
Divide functions (A2-O.3)
Composition of linear functions (A2-O.4)
Composition of linear and quadratic functions (A2-O.5)
Add, subtract, multiply, and divide functions (PC-A.8)
Composition of functions (PC-A.9)
9-12.3.3.o Solve an equation involving several variables for one variable in terms of the others
Solve multi-variable equations (A2-B.5)
Write joint and combined variation equations II (A2-Q.6)
Solve a system of equations in three variables using substitution (PC-I.8)
9-12.3.3.p Analyze and solve systems of two linear equations in two variables algebraically and graphically
Is (x, y) a solution to the system of equations? (A1-U.1)
Solve a system of equations by graphing (A1-U.2)
Solve a system of equations by graphing: word problems (A1-U.3)
Find the number of solutions to a system of equations by graphing (A1-U.4)
Find the number of solutions to a system of equations (A1-U.5)
Classify a system of equations by graphing (A1-U.6)
Classify a system of equations (A1-U.7)
Solve a system of equations using substitution (A1-U.8)
Solve a system of equations using substitution: word problems (A1-U.9)
Solve a system of equations using elimination (A1-U.10)
Solve a system of equations using elimination: word problems (A1-U.11)
Solve a system of equations using augmented matrices (A1-U.12)
Solve a system of equations using augmented matrices: word problems (A1-U.13)
Solve a system of equations using any method (A1-U.14)
Solve a system of equations using any method: word problems (A1-U.15)
Solve systems of linear equations (G-A.8)
Is (x, y) a solution to the system of equations? (A2-E.1)
Solve a system of equations by graphing (A2-E.2)
Solve a system of equations by graphing: word problems (A2-E.3)
Find the number of solutions to a system of equations (A2-E.4)
Classify a system of equations (A2-E.5)
Solve a system of equations using substitution (A2-E.6)
Solve a system of equations using substitution: word problems (A2-E.7)
Solve a system of equations using elimination (A2-E.8)
Solve a system of equations using elimination: word problems (A2-E.9)
Solve a system of equations using any method (A2-E.10)
Solve a system of equations using any method: word problems (A2-E.11)
Solve a system of equations using augmented matrices (A2-G.18)
Solve a system of equations using augmented matrices: word problems (A2-G.19)
Solve a system of equations by graphing (PC-I.1)
Solve a system of equations by graphing: word problems (PC-I.2)
Classify a system of equations (PC-I.3)
Solve a system of equations using substitution (PC-I.4)
Solve a system of equations using substitution: word problems (PC-I.5)
Solve a system of equations using elimination (PC-I.6)
Solve a system of equations using elimination: word problems (PC-I.7)
9-12.4 Students will communicate data analysis/probability concepts using multiple representations to reason, solve problems, and make connections within mathematics and across disciplines.
9-12.4.1 Students will formulate a question and design a survey or an experiment in which data is collected and displayed in a variety of formats, then select and use appropriate statistical methods to analyze the data.
9-12.4.1.a Interpret data represented by the normal distribution and formulate conclusions
Find probabilities using the normal distribution (A2-CC.21)
Find probabilities using the normal distribution (PC-Y.11)
Use normal distributions to approximate binomial distributions (PC-Y.16)
9-12.4.1.b Compute, identify, and interpret measures of central tendency (mean, median, mode) when provided a graph or data set
Mean, median, mode, and range (A1-KK.2)
Quartiles (A1-KK.3)
Variance and standard deviation of random variables (PC-Y.5)
Mean, variance, and standard deviation of binomial distributions (PC-Y.10)
Variance and standard deviation (PC-Z.2)
9-12.4.1.c Explain how sample size and transformations of data affect measures of central tendency
9-12.4.1.d Describe the shape and determine spread (variance, standard deviation) and outliers of a data set
Quartiles (A1-KK.3)
Mean absolute deviation (A1-KK.6)
Variance and standard deviation (A1-KK.7)
Variance and standard deviation (A2-DD.2)
Variance and standard deviation of random variables (PC-Y.5)
Mean, variance, and standard deviation of binomial distributions (PC-Y.10)
Variance and standard deviation (PC-Z.2)
9-12.4.1.e Explain how statistics are used or misused in the world
9-12.4.1.f Create scatter plots, analyze patterns, and describe relationships in paired data
Create bar graphs, line graphs, and histograms (A1-N.2)
9-12.4.1.g Explain the impact of sampling methods, bias, and the phrasing of questions asked during data collection and the conclusions that can rightfully be made
Identify biased samples (A1-KK.1)
Identify biased samples (A2-DD.1)
Identify biased samples (PC-Z.1)
9-12.4.1.h Explain the differences between randomized experiment and observational studies
9-12.4.2 Students will develop and evaluate inferences to make predictions.
9-12.4.2.a Compare data sets and evaluate conclusions using graphs and summary statistics
Interpret bar graphs, line graphs, and histograms (A1-N.1)
Circle graphs (A1-N.3)
Interpret stem-and-leaf plots (A1-N.4)
Interpret box-and-whisker plots (A1-N.5)
Interpret a scatter plot (A1-KK.8)
9-12.4.2.b Support inferences with valid arguments
9-12.4.2.c Develop linear equations for linear models to predict unobserved outcomes using regression line and correlation coefficient
Scatter plots: line of best fit (A1-KK.12)
Find the equation of a regression line (PC-Z.8)
9-12.4.2.d Recognize when arguments based on data confuse correlation with causation
9-12.4.3 Students will apply and analyze concepts of probability.
9-12.4.3.a Construct a sample space and a probability distribution
Introduction to probability (PC-X.1)
Write a discrete probability distribution (PC-Y.2)
Graph a discrete probability distribution (PC-Y.3)
Write the probability distribution for a game of chance (PC-Y.6)
9-12.4.3.b Identify dependent and independent events and calculate their probabilities
Identify independent and dependent events (A1-JJ.4)
Probability of independent and dependent events (A1-JJ.5)
Theoretical and experimental probability (G-X.1)
Independent and dependent events (G-X.3)
Probability of independent and dependent events (A2-CC.8)
Identify independent events (PC-X.6)
Find conditional probabilities (PC-X.7)
Independence and conditional probability (PC-X.8)
Find conditional probabilities using two-way frequency tables (PC-X.9)
Find probabilities using the addition rule (PC-X.10)
9-12.4.3.c Use the appropriate counting techniques to determine the probability of an event (e.g., combinations, permutations)
Theoretical probability (A1-JJ.1)
Compound events: find the number of outcomes (A1-JJ.3)
Identify independent and dependent events (A1-JJ.4)
Probability of independent and dependent events (A1-JJ.5)
Permutations (A1-JJ.6)
Counting principle (A1-JJ.7)
Permutation and combination notation (A1-JJ.8)
Compound events: find the number of outcomes (G-X.2)
Counting principle (G-X.4)
Permutations (G-X.5)
Permutation and combination notation (G-X.6)
Calculate probabilities of events (A2-CC.2)
Counting principle (A2-CC.3)
Combinations and permutations (A2-CC.4)
Calculate probabilities of events (PC-X.2)
Combinations and permutations (PC-X.3)
Find probabilities using combinations and permutations (PC-X.4)
Find probabilities using two-way frequency tables (PC-X.5)
9-12.4.3.d Analyze events to determine if they are mutually exclusive
Probability of opposite, mutually exclusive, and overlapping events (8-EE.2)
Identify independent events (PC-X.6)
9-12.4.3.e Determine the relative frequency of a specified outcome of an event to estimate the probability of the outcome