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9.N
Understand and use numeration
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9.M1.4.1
Read, write, model, order, and define real numbers and subsets.
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9.M1.4.2
Add in a different base system.
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9.M1.4.3
Compare and contrast the relationship between various applications of the same operation.
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9.M1.4.4
Translate between equivalent representations of the same exponential expression.
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9.M1.4.5
Recognize, describe, and use properties of the real number system.
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9.N-1
converting between a rational number in scientific notation and standard form
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9.N-2
equating different equivalent representations of the same exponential expression (e.g., 2 to the 3rd • 2 to the 5th = 28)
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9.N-3
using models, explanations, number lines, real-life situations, describing or illustrating the effects of arithmetic operations on real numbers
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9.N-4
using models, explanations, number lines, real-life situations, describing or illustrating the use of inverse operations (squaring/square root)
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9.N-5
applying the rules for order of operations to real numbers and variables
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9.N-6
[using distributive property with variables]
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9.MEA
Select and use systems, units, and tools of measurement
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9.M2.4.1
Evaluate measurements for accuracy, precision, and error with respect to the measuring tools, methods, and the computational process.
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9.M2.4.2
Estimate and convert measurements between different systems.
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9.M2.4.3
Apply various measurement systems to describe situations and solve problems.
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9.M2.4.4
Use indirect methods, including the Pythagorean Theorem and right triangle trigonometry, to find missing dimensions.
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9.MEA-1
estimating or converting measurements between the English and metric systems in real-world applications, given a conversion factor (e.g., miles/kilometers)
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9.MEA-2
applying indirect methods, such as the Pythagorean theorem to find missing dimensions, in real-world applications
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9.E&C
Perform basic arithmetic functions, make reasoned estimates, and select and use appropriate methods or tools
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9.M3.4.1
Use estimation to solve problems and to check the accuracy of solutions; state whether the estimation is greater or less than the exact answer.
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9.M3.4.2
Add and subtract real numbers using scientific notation, powers, and roots.
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9.M3.4.3
Multiply and divide real numbers in various forms including scientific notation, powers, and roots.
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9.M3.4.4
Select, convert, and apply an equivalent representation of a number for a specified situation.
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9.M3.4.5
Use ratios and proportions to model and solve fraction and percent problems with variables.
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9.E&C-1
judging whether the strategy will result in an answer greater or less than the exact answer
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9.E&C-2
adding or subtracting rational numbers including integers with whole number exponents
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9.E&C-3
multiplying or dividing rational numbers including integers with whole number exponents
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9.E&C-4
determining rate by using ratio and proportion
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9.E&C-5
[multiplying or dividing numbers in scientific notation]
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9.F&R
Represent, analyze, and use patterns, relations, and functions
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9.M4.4.1
Identify, graph, and describe the graphs of basic families of functions including linear, absolute value, quadratic, and exponential using a graphing calculator.
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9.M4.4.2
Create and solve linear and quadratic equations and inequalities.
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9.M4.4.3
Create and solve simple systems of equations, algebraically and graphically, using a graphing calculator.
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9.M4.4.4
Use discrete structures, such as networks, matrices, sequences, and iterations as tools to analyze patterns, expressions, and equations.
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9.M4.4.5
Add, subtract, multiply, divide, and simplify rational expressions; add, subtract, and multiply polynomials.
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9.F&R-1
describing or extending patterns (families of functions: linear quadratic, absolute value,), up to the nth term, represented in tables, sequences, graphs, or in problem situations
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9.F&R-2
generalizing relationships (linear, quadratic, absolute value,) using a table of ordered pairs, a graph, or an equation
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9.F&R-3
describing in words how a change in one variable in a formula affects the remaining variables (e.g., how changing the radius affects the volume of a cylinder)
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9.F&R-4
[using a calculator as a tool when describing, extending, representing, or graphing patterns or linear equations]
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9.F&R-5
modeling (graphically or algebraically) or solving situations (including real-world applications) using systems of linear equations
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9.F&R-6
solving or identifying solutions to multi-step linear equations of the form ax ± b = cx ± d, where a, b, c and d are rational numbers and a is not equal to 0, c is not equal to 0
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9.F&R-7
solving literal equations or formulas for a variable involving one step (e.g. solve for t when d = rt)
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9.G
Construct, transform, and analyze geometric figures.
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9.M5.4.1
Identify and use the properties of polygons, including interior and exterior angles, and circles (including angles, arcs, chord, secants, and tangents) to solve problems.
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9.M5.4.2
Create 2-dimensional representations of 3-dimensional objects.
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9.M5.4.3
Identify congruent and similar figures using Euclidean and coordinate geometries; apply this information to solve problems.
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9.M5.4.4
Use transformations to demonstrate geometric properties.
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9.M5.4.5
Use coordinate geometry to graph linear equations, determine slopes of lines, identify parallel and perpendicular lines, and to find possible solutions to sets of equations.
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9.M5.4.6
Construct geometric models, transformations, and scale drawings using a variety of methods including paper folding, compass, straight edge, protractor, and technology.
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9.G-1
identifying, analyzing, comparing, or using properties of angles (including supplementary or complementary) or circles (degrees in a circle)
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9.G-2
using a coordinate plane to solve problems involving congruent or similar shapes
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9.G-3
[drawing or describing the results of applying transformations (translations, rotations, reflections, or dilations) to figures on a coordinate plane]
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9.G-4
determining the volume or surface area of prisms, cylinders, cones or pyramids
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9.G-5
graphing or identifying (using equations or formulas to determine the slope of line segments on a coordinate plane)
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9.G-6
[drawing, measuring, or constructing geometric models of plane figures (containing parallel and/or perpendicular lines)]
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9.S&P
Formulate questions, gather and interpret data, and make predictions
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9.M6.4.1
Analyze and draw inferences from a wide variety of data sources that summarize data; constructing graphical displays with and without technology.
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9.M6.4.2
Determine the line of best fit and use it to predict unknown data values.
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9.M6.4.3
Describe data, selecting measures of central tendencies and distribution, to convey information in the data.
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9.M6.4.4
Analyze the validity of statistical conclusions and the use, misuse, and abuse of data caused by a wide variety of factors including choices of scale, inappropriate choices of measures of center, incorrect curve fitting, and inappropriate uses of controls or sample groups.
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9.M6.4.5
Analyze data from multiple events and predict theoretical probability; find and compare experimental and theoretical probability for a simple situation, discussing possible differences between two results.
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9.M6.4.6
Design, conduct, analyze, and communicate the results of multi-stage probability experiments.
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9.S&P-1
[designing, collecting], organizing, displaying, or explaining the classification of data in real-world problems (e.g., science or humanities, peers, community, or careers) using information from tables or graphs that display two sets of data [or with technology]
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9.S&P-2
using information from a variety of displays or analyzing the validity of statistical conclusions found in the media
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9.S&P-3
using range and measures of central tendency to determine the best representation of the data for a practical situation
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9.S&P-4
identifying and/or showing the meaning of a best fit line
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9.S&P-5
determining or comparing the experimental and/or theoretical probability of independent or dependent events
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9.S&P-6
making predictions about the probability of independent or dependent events and using the information to solve problems
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9.S&P-7
[designing, conducting, analyzing, and communicating the results of a probability experiment]
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9
Understand and be able to select and use a variety of problem-solving strategies
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9.M7.4.1
Recognize and formulate mathematical problems from within and outside the field of mathematics.
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9.M7.4.2
Apply multi-step, integrated, mathematical problem-solving strategies, persisting until a solution is found or it is clear no solution exits.
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9.M7.4.3
Verify the answer by using an alternative strategy.
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9.PS-1
selecting, modifying, and applying a variety of problem-solving strategies (e.g., charts, graphing, inductive and deductive reasoning, Venn diagrams) and verifying the results
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9.PS-2
evaluating, interpreting, and justifying solutions to problems by using an alternative strategy
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9
Form and use appropriate methods to define and explain mathematical relationships
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9.M8.4.1
Use appropriate technology to represent the information and ideas in a problem.
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9.M8.4.2
Use numerical, graphic, and symbolic representations to support oral and written communication about math 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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9.M8.4.3
Explain, justify, and defend mathematical ideas, solutions, and methods to various audiences.
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9.PS-3
representing mathematical problems numerically, graphically, and/or symbolically, translating among these alternative representations; or using appropriate vocabulary, symbols, or technology to explain, justify, and defend strategies and solutions
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9
Use logic and reason to solve mathematical problems
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9.M9.4.1
Follow and evaluate an argument, judging its validity using inductive or deductive reasoning and logic.
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9.M9.4.2
Make and test conjectures.
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9.M9.4.3
Use methods of proofs including direct, indirect, and counterexamples, to validate conjectures.
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9.PS-4
following and evaluating an argument, judging its validity using inductive, or deductive reasoning and logic; or making and testing conjectures
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9
Apply mathematical concepts and processes to situations within and outside of school.
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9.M10.4.1
Apply mathematical skills and processes to global issues.
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9.M10.4.2
Describe how mathematics can be used in knowing how to prepare for careers.
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9.PS-5
using real-world contexts such as science, humanities, peers, community, careers, and national issues
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