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10.1
Number, Number Sense and Operations
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10.1.A
Use scientific notation to express large numbers and numbers less than one.
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10.1.B
Identify subsets of the real number system.
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10.1.C
Apply properties of operations and the real number system, and justify when they hold for a set of numbers.
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10.1.D
Connect physical, verbal and symbolic representations of integers, rational numbers and irrational numbers.
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10
Number and Number Systems
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10.1.D.1
Connect physical, verbal and symbolic representations of irrational numbers; e.g., construct square root of 2 as a hypotenuse or on a number line.
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10
Meaning of Operations
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10.1.D.2
Explain the meaning of the nth root.
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10.1.E
Compare, order and determine equivalent forms of real numbers.
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10.1.F
Explain the effects of operations on the magnitude of quantities.
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10.1.G
Estimate, compute and solve problems involving real numbers, including ratio, proportion and percent, and explain solutions.
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10.1.H
Find the square root of perfect squares, and approximate the square root of non-perfect squares.
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10.1.I
Estimate, compute and solve problems involving scientific notation, square roots and numbers with integer exponents.
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10
Computation and Estimation
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10.1.I.3
Use factorial notation and computations to represent and solve problem situations involving arrangements.
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10.1.I.4
Approximate the nth root of a given number greater than zero between consecutive integers when n is an integer; e.g., the 4th root of 50 is between 2 and 3.
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10.2
Measurement
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10.2.A
Solve increasingly complex non-routine measurement problems and check for reasonableness of results.
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10
Use Measurement Techniques and Tools
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10.2.A.1
Explain how a small error in measurement may lead to a large error in calculated results.
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10.2.A.2
Calculate relative error.
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10.2.A.3
Explain the difference between absolute error and relative error in measurement.
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10.2.A.4
Give examples of how the same absolute error can be problematic in one situation but not in another; e.g., compare "accurate to the nearest foot" when measuring the height of a person versus when measuring the height of a mountain.
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10.2.B
Use formulas to find surface area and volume for specified three-dimensional objects accurate to a specified level of precision.
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10
Use Measurement Techniques and Tools
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10.2.B.1
Explain how a small error in measurement may lead to a large error in calculated results.
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10.2.C
Apply indirect measurement techniques, tools and formulas, as appropriate, to find perimeter, circumference and area of circles, triangles, quadrilaterals and composite shapes, and to find volume of prisms, cylinders, and pyramids.
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10
Use Measurement Techniques and Tools
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10.2.C.1
Explain how a small error in measurement may lead to a large error in calculated results.
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10.2.D
Use proportional reasoning and apply indirect measurement techniques, including right triangle trigonometry and properties of similar triangles, to solve problems involving measurements and rates.
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10
Use Measurement Techniques and Tools
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10.2.D.1
Explain how a small error in measurement may lead to a large error in calculated results.
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10.2.D.5
Determine the measures of central and inscribed angles and their associated major and minor arcs.
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10.2.E
Estimate and compute various attributes, including length, angle measure, area, surface area and volume, to a specified level of precision.
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10
Use Measurement Techniques and Tools
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10.2.E.1
Explain how a small error in measurement may lead to a large error in calculated results.
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10.2.F
Write and solve real-world, multi-step problems involving money, elapsed time and temperature, and verify reasonableness of solutions.
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10.3
Geometry and Spatial Sense
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10.3.A
Formally define geometric figures.
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10
Characteristics and Properties
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10.3.A.1
Formally define and explain key aspects of geometric figures, including:
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10.3.A.1.a
interior and exterior angles of polygons;
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10.3.A.1.b
segments related to triangles (median, altitude, midsegment);
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10.3.A.1.c
points of concurrency related to triangles (centroid, incenter, orthocenter, and circumcenter);
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10.3.A.1.d
circles (radius, diameter, chord, circumference, major arc, minor arc, sector, segment, inscribed angle).
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10.3.A.2
Recognize and explain the necessity for certain terms to remain undefined, such as point, line and plane.
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10
Transformation and Symmetry
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10.3.A.6
Identify the reflection and rotation symmetries of two- and three-dimensional figures.
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10
Visualization and Geometric Models
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10.3.A.10
Solve problems involving chords, radii, and arcs within the same circle.
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10.3.B
Describe and apply the properties of similar and congruent figures; and justify conjectures involving similarity and congruence.
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10.3.C
Recognize and apply angle relationships in situations involving intersecting lines, perpendicular lines and parallel lines.
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10.3.D
Use coordinate geometry to represent and examine the properties of geometric figures.
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10.3.E
Draw and construct representations of two- and three-dimensional geometric objects using a variety of tools, such as straightedge, compass and technology.
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10
Spatial Relationships
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10.3.E.4
Construct right triangles, equilateral triangles, parallelograms, trapezoids, rectangles, rhombuses, squares and kites, using compass and straightedge or dynamic geometry software.
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10.3.E.5
Construct congruent or similar figures using tools, such as compass, straightedge, and protractor or dynamic geometry software.
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10
Transformation and Symmetry
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10.3.E.7
Perform reflections and rotations using compass and straightedge constructions and dynamic geometry software.
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10.3.F
Represent and model transformations in a coordinate plane and describe the results.
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10
Transformation and Symmetry
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10.3.F.8
Derive coordinate rules for translations, reflections and rotations of geometric figures in the coordinate plane.
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10.3.F.9
Show and describe the results of combinations of translations, reflections and rotations (compositions); e.g., perform compositions and specify the result of a composition as the outcome of a single motion, when applicable.
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10.3.G
Prove or disprove conjectures and solve problems involving two- and three-dimensional objects represented within a coordinate system.
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10.3.H
Establish the validity of conjectures about geometric objects, their properties and relationships by counter-example, inductive and deductive reasoning, and critiquing arguments made by others.
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10
Characteristics and Properties
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10.3.H.3
Make, test and establish the validity of conjectures about geometric properties and relationships using counterexample, inductive and deductive reasoning, and paragraph or two-column proof, including:
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10.3.H.3.a
prove the Pythagorean Theorem;
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10.3.H.3.b
prove theorems involving triangle similarity and congruence;
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10.3.H.3.c
prove theorems involving properties of lines, angles, triangles and quadrilaterals;
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10.3.H.3.d
test a conjecture using basic constructions made with a compass and straightedge or technology.
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10
Visualization and Geometric Models
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10.3.H.10
Solve problems involving chords, radii, and arcs within the same circle.
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10.3.I
Use right triangle trigonometric relationships to determine lengths and angle measures.
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10.4
Patterns, Functions and Algebra
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10.4.A
Generalize and explain patterns and sequences in order to find the next term and the nth term.
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10.4.B
Identify and classify functions as linear or nonlinear, and contrast their properties using tables, graphs or equations.
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10
Use Patterns, Relations and Functions
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10.4.B.1
Define function formally and with f(x) notation.
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10.4.B.2
Describe and compare characteristics of the following families of functions: square root, cubic, absolute value and basic trigonometric functions; e.g., general shape, possible number of roots, domain and range.
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10.4.C
Translate information from one representation (words, table, graph or equation) to another representation of a relation or function.
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Relations and functions: Relations: convert between tables, graphs, mappings, and lists of points (Algebra - Q.1)
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Relations and functions: Complete a function table (Algebra - Q.6)
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Relations and functions: Graph a function (Algebra - Q.9)
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Relations and functions: Write a function rule: word problems (Algebra - Q.10)
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Relations and functions: Find points on a function graph (Algebra - Q.11)
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Relations and functions: Write a rule for a function table (Algebra - Q.12)
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Direct and inverse variation: Graph a proportional relationship (Algebra - R.3)
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Direct and inverse variation: Write direct variation equations (Algebra - R.4)
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Direct and inverse variation: Write and solve direct variation equations (Algebra - R.5)
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Direct and inverse variation: Write inverse variation equations (Algebra - R.7)
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Direct and inverse variation: Write and solve inverse variation equations (Algebra - R.8)
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Linear functions: Slope-intercept form: find slope and y-intercept (Algebra - S.4)
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Linear functions: Slope-intercept form: graph an equation (Algebra - S.5)
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Linear functions: Slope-intercept form: write an equation from a graph (Algebra - S.6)
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Linear functions: Slope-intercept form: write an equation (Algebra - S.7)
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Linear functions: Linear function word problems (Algebra - S.8)
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Linear functions: Write equations in standard form (Algebra - S.9)
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Linear functions: Standard form: find x- and y-intercepts (Algebra - S.10)
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Linear functions: Standard form: graph an equation (Algebra - S.11)
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Linear functions: Equations of horizontal and vertical lines (Algebra - S.12)
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Linear functions: Graph a horizontal or vertical line (Algebra - S.13)
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Linear functions: Point-slope form: graph an equation (Algebra - S.14)
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Linear functions: Point-slope form: write an equation from a graph (Algebra - S.15)
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Linear functions: Point-slope form: write an equation (Algebra - S.16)
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Linear functions: Write an equation for a parallel or perpendicular line (Algebra - S.18)
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Functions: linear, quadratic, exponential: Identify linear, quadratic, and exponential functions from graphs (Algebra - CC.1)
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Functions: linear, quadratic, exponential: Identify linear, quadratic, and exponential functions from tables (Algebra - CC.2)
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Functions: linear, quadratic, exponential: Write linear, quadratic, and exponential functions (Algebra - CC.3)
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Rational functions and expressions: Rational functions: asymptotes and excluded values (Algebra - GG.1)
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10.4.D
Use algebraic representations, such as tables, graphs, expressions, functions and inequalities, to model and solve problem situations.
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10
Use Algebraic Representations
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10.4.D.3
Solve equations and formulas for a specified variable; e.g., express the base of a triangle in terms of the area and height.
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10.4.D.4
Use algebraic representations and functions to describe and generalize geometric properties and relationships.
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10.4.D.5
Solve simple linear and nonlinear equations and inequalities having square roots as coefficients and solutions.
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10.4.D.6
Solve equations and inequalities having rational expressions as coefficients and solutions.
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10.4.E
Analyze and compare functions and their graphs using attributes, such as rates of change, intercepts and zeros.
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Linear functions: Slope-intercept form: find slope and y-intercept (Algebra - S.4)
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Linear functions: Standard form: find x- and y-intercepts (Algebra - S.10)
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Linear functions: Slopes of parallel and perpendicular lines (Algebra - S.17)
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Exponential functions: Match exponential functions and graphs (Algebra - X.2)
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Quadratic equations: Characteristics of quadratic functions (Algebra - BB.1)
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Functions: linear, quadratic, exponential: Identify linear, quadratic, and exponential functions from graphs (Algebra - CC.1)
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Functions: linear, quadratic, exponential: Identify linear, quadratic, and exponential functions from tables (Algebra - CC.2)
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Functions: linear, quadratic, exponential: Write linear, quadratic, and exponential functions (Algebra - CC.3)
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Absolute value functions: Domain and range of absolute value functions (Algebra - DD.2)
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Radical functions and equations: Domain and range of radical functions (Algebra - FF.2)
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Rational functions and expressions: Rational functions: asymptotes and excluded values (Algebra - GG.1)
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10.4.F
Solve and graph linear equations and inequalities.
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10
Use Algebraic Representations
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10.4.F.10
Solve real-world problems that can be modeled using linear, quadratic, exponential or square root functions.
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10.4.G
Solve quadratic equations with real roots by graphing, formula and factoring.
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10
Use Algebraic Representations
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10.4.G.8
Graph the quadratic relationship that defines circles.
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10.4.G.10
Solve real-world problems that can be modeled using linear, quadratic, exponential or square root functions.
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10.4.H
Solve systems of linear equations involving two variables graphically and symbolically.
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10
Use Algebraic Representations
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10.4.H.7
Solve systems of linear inequalities.
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10.4.H.11
Solve real-world problems that can be modeled, using systems of linear equations and inequalities.
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10.4.I
Model and solve problem situations involving direct and inverse variation.
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10.4.J
Describe and interpret rates of change from graphical and numerical data.
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10
Use Algebraic Representations
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10.4.J.9
Recognize and explain that the slopes of parallel lines are equal and the slopes of perpendicular lines are negative reciprocals.
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10
Analyze Change
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10.4.J.12
Describe the relationship between slope of a line through the origin and the tangent function of the angle created by the line and the positive x-axis.
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10.5
Data Analysis and Probability
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10.5.A
Create, interpret and use graphical displays and statistical measures to describe data; e.g., box-and-whisker plots, histograms, scatterplots, measures of center and variability.
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10
Data Collection
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10.5.A.2
Represent and analyze bivariate data using appropriate graphical displays (scatterplots, parallel box-and-whisker plots, histograms with more than one set of data, tables, charts, spreadsheets) with and without technology.
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10.5.A.3
Display bivariate data where at least one variable is categorical.
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10.5.A.4
Identify outliers on a data display; e.g., use the interquartile range to identify outliers on a box-and-whisker plot.
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10
Statistical Methods
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10.5.A.6
Interpret the relationship between two variables using multiple graphical displays and statistical measures; e.g., scatterplots, parallel box-and-whisker plots, and measures of center and spread.
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10.5.B
Evaluate different graphical representations of the same data to determine which is the most appropriate representation for an identified purpose.
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10.5.C
Compare the characteristics of the mean, median and mode for a given set of data, and explain which measure of center best represents the data.
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10
Data Collection
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10.5.C.1
Describe measures of center and the range verbally, graphically and algebraically.
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10.5.D
Find, use and interpret measures of center and spread, such as mean and quartiles, and use those measures to compare and draw conclusions about sets of data.
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10
Statistical Methods
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10.5.D.6
Interpret the relationship between two variables using multiple graphical displays and statistical measures; e.g., scatterplots, parallel box-and-whisker plots, and measures of center and spread.
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10.5.E
Evaluate the validity of claims and predictions that are based on data by examining the appropriateness of the data collection and analysis.
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10.5.F
Construct convincing arguments based on analysis of data and interpretation of graphs.
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10.5.G
Describe sampling methods and analyze the effects of method chosen on how well the resulting sample represents the population.
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10
Statistical Methods
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10.5.G.5
Provide examples and explain how a statistic may or may not be an attribute of the entire population; e.g., intentional or unintentional bias may be present.
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10.5.H
Use counting techniques, such as permutations and combinations, to determine the total number of options and possible outcomes.
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10.5.I
Design an experiment to test a theoretical probability, and record and explain results.
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10.5.J
Compute probabilities of compound events, independent events, and simple dependent events.
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10
Probability
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10.5.J.7
Model problems dealing with uncertainty with area models (geometric probability).
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10.5.K
Make predictions based on theoretical probabilities and experimental results.
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10
Probability
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10.5.K.8
Differentiate and explain the relationship between the probability of an event and the odds of an event, and compute one given the other.
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10.6
Mathematical Processes
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10.6.A
Formulate a problem or mathematical model in response to a specific need or situation, determine information required to solve the problem, choose method for obtaining this information, and set limits for acceptable solution.
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10.6.B
Apply mathematical knowledge and skills routinely in other content areas and practical situations.
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10.6.C
Recognize and use connections between equivalent representations and related procedures for a mathematical concept; e.g., zero of a function and the x-intercept of the graph of the function, apply proportional thinking when measuring, describing functions, and comparing probabilities.
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10.6.D
Apply reasoning processes and skills to construct logical verifications or counter-examples to test conjectures and to justify and defend algorithms and solutions.
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10.6.E
Use a variety of mathematical representations flexibly and appropriately to organize, record and communicate mathematical ideas.
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Solve equations: Model and solve equations using algebra tiles (Algebra - J.1)
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Solve equations: Write and solve equations that represent diagrams (Algebra - J.2)
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Single-variable inequalities: Graph inequalities (Algebra - K.1)
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Single-variable inequalities: Write inequalities from graphs (Algebra - K.2)
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Single-variable inequalities: Graph solutions to one-step linear inequalities (Algebra - K.7)
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Single-variable inequalities: Graph solutions to two-step linear inequalities (Algebra - K.9)
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Single-variable inequalities: Graph solutions to advanced linear inequalities (Algebra - K.11)
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Single-variable inequalities: Graph compound inequalities (Algebra - K.12)
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Single-variable inequalities: Write compound inequalities from graphs (Algebra - K.13)
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Single-variable inequalities: Graph solutions to compound inequalities (Algebra - K.15)
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Absolute value equations and inequalities: Graph solutions to absolute value equations (Algebra - L.2)
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Absolute value equations and inequalities: Graph solutions to absolute value inequalities (Algebra - L.4)
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Relations and functions: Complete a function table (Algebra - Q.6)
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Relations and functions: Graph a function (Algebra - Q.9)
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Relations and functions: Write a function rule: word problems (Algebra - Q.10)
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Relations and functions: Find points on a function graph (Algebra - Q.11)
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Relations and functions: Write a rule for a function table (Algebra - Q.12)
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Direct and inverse variation: Write direct variation equations (Algebra - R.4)
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Direct and inverse variation: Write and solve direct variation equations (Algebra - R.5)
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Direct and inverse variation: Write inverse variation equations (Algebra - R.7)
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Direct and inverse variation: Write and solve inverse variation equations (Algebra - R.8)
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Linear functions: Slope-intercept form: graph an equation (Algebra - S.5)
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Linear functions: Slope-intercept form: write an equation from a graph (Algebra - S.6)
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Linear functions: Linear function word problems (Algebra - S.8)
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Linear functions: Standard form: graph an equation (Algebra - S.11)
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Linear functions: Graph a horizontal or vertical line (Algebra - S.13)
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Linear functions: Point-slope form: graph an equation (Algebra - S.14)
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Linear functions: Point-slope form: write an equation from a graph (Algebra - S.15)
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Systems of linear equations: Solve a system of equations by graphing (Algebra - U.2)
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Systems of linear equations: Solve a system of equations by graphing: word problems (Algebra - U.3)
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Systems of linear equations: Find the number of solutions to a system of equations by graphing (Algebra - U.4)
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Systems of linear equations: Solve a system of equations using substitution (Algebra - U.8)
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Systems of linear equations: Solve a system of equations using substitution: word problems (Algebra - U.9)
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Systems of linear equations: Solve a system of equations using elimination (Algebra - U.10)
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Systems of linear equations: Solve a system of equations using elimination: word problems (Algebra - U.11)
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Systems of linear equations: Solve a system of equations using augmented matrices (Algebra - U.12)
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Systems of linear equations: Solve a system of equations using augmented matrices: word problems (Algebra - U.13)
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Systems of linear equations: Solve a system of equations using any method (Algebra - U.14)
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Systems of linear equations: Solve a system of equations using any method: word problems (Algebra - U.15)
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Scientific notation: Convert between standard and scientific notation (Algebra - W.1)
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Scientific notation: Compare numbers written in scientific notation (Algebra - W.2)
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Polynomials: Model polynomials with algebra tiles (Algebra - Z.2)
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Polynomials: Add and subtract polynomials using algebra tiles (Algebra - Z.3)
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Functions: linear, quadratic, exponential: Identify linear, quadratic, and exponential functions from graphs (Algebra - CC.1)
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Functions: linear, quadratic, exponential: Identify linear, quadratic, and exponential functions from tables (Algebra - CC.2)
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Functions: linear, quadratic, exponential: Write linear, quadratic, and exponential functions (Algebra - CC.3)
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Rational functions and expressions: Rational functions: asymptotes and excluded values (Algebra - GG.1)
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10.6.F
Use precise mathematical language and notations to represent problem situations and mathematical ideas.
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10.6.G
Write clearly and coherently about mathematical thinking and ideas.
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10.6.H
Locate and interpret mathematical information accurately, and communicate ideas, processes and solutions in a complete and easily understood manner.
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