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8.1
Number and Operations
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8.1.1
Understand and apply numbers, ways of representing numbers, and the relationships among numbers and different number systems.
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8.1.1.PO 1
Compare and order real numbers including very large and small integers, and decimals and fractions close to zero.
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8.1.1.PO 2
Classify real numbers as rational or irrational.
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8.1.1.PO 3
Model the relationship between the subsets of the real number system.
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8.1.1.PO 4
Model and solve problems involving absolute value.
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8.1.2
Understand and apply numerical operations and their relationship to one another.
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8.1.2.PO 1
Solve problems with factors, multiples, divisibility or remainders, prime numbers, and composite numbers.
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8.1.2.PO 2
Describe the effect of multiplying and dividing a rational number by
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8.1.2.PO 2.a
a number less than zero,
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8.1.2.PO 2.b
a number between zero and one,
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8.1.2.PO 2.c
one, and
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8.1.2.PO 2.d
a number greater than one.
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8.1.2.PO 3
Solve problems involving percent increase, percent decrease, and simple interest rates.
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8.1.2.PO 4
Convert standard notation to scientific notation and vice versa (include positive and negative exponents).
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8.1.2.PO 5
Simplify numerical expressions using the order of operations that include grouping symbols, square roots, cube roots, absolute values, and positive exponents.
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8.1.3
Use estimation strategies reasonably and fluently while integrating content from each of the other strands.
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8.1.3.PO 1
Make estimates appropriate to a given situation.
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8.1.3.PO 2
Estimate the location of rational and common irrational numbers on a number line.
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8.2
Data Analysis, Probability, and Discrete Mathematics
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8.2.1
Understand and apply data collection, organization, and representation to analyze and sort data.
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8.2.1.PO 1
Solve problems by selecting, constructing, interpreting, and calculating with displays of data, including box and whisker plots and scatterplots.
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8.2.1.PO 2
Make inferences by comparing the same summary statistic for two or more data sets.
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8.2.1.PO 3
Describe how summary statistics relate to the shape of the distribution.
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8.2.1.PO 4
Determine whether information is represented effectively and appropriately given a graph or a set of data by identifying sources of bias and compare and contrast the effectiveness of different representations of data.
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8.2.1.PO 5
Evaluate the design of an experiment.
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8.2.2
Understand and apply the basic concepts of probability.
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8.2.2.PO 1
Determine theoretical and experimental conditional probabilities in compound probability experiments.
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8.2.2.PO 2
Interpret probabilities within a given context and compare the outcome of an experiment to predictions made prior to performing the experiment.
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8.2.2.PO 3
Use all possible outcomes (sample space) to determine the probability of dependent and independent events.
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8.2.3
Understand and demonstrate the systematic listing and counting of possible outcomes.
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8.2.3.PO 1
Represent, analyze, and solve counting problems with or without ordering and repetitions.
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8.2.3.PO 2
Solve counting problems and represent counting principles algebraically including factorial notation.
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8.2.4
Understand and apply vertex-edge graphs.
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8.2.4.PO 1
Use directed graphs to solve problems.
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8.3
Patterns, Algebra, and Functions
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8.3.1
Identify patterns and apply pattern recognition to reason mathematically while integrating content from each of the other strands.
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8.3.1.PO 1
Recognize, describe, create, and analyze numerical and geometric sequences using tables, graphs, words, or symbols; make conjectures about these sequences.
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8.3.2
Describe and model functions and their relationships.
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8.3.2.PO 1
Sketch and interpret a graph that models a given context; describe a context that is modeled by a given graph.
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8.3.2.PO 2
Determine if a relationship represented by a graph or table is a function.
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8.3.2.PO 3
Write the rule for a simple function using algebraic notation.
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8.3.2.PO 4
Identify functions as linear or nonlinear and contrast distinguishing properties of functions using equations, graphs, or tables.
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8.3.2.PO 5
Demonstrate that proportional relationships are linear using equations, graphs, or tables.
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8.3.3
Represent and analyze mathematical situations and structures using algebraic representations.
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8.3.3.PO 1
Write or identify algebraic expressions, equations, or inequalities that represent a situation.
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8.3.3.PO 2
Evaluate an expression containing variables by substituting rational numbers for the variables.
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8.3.3.PO 3
Analyze situations, simplify, and solve problems involving linear equations and inequalities using the properties of the real number system.
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8.3.3.PO 4
Translate between different representations of linear equations using symbols, graphs, tables, or written descriptions.
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8.3.3.PO 5
Graph an inequality on a number line.
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8.3.4
Analyze how changing the values of one quantity corresponds to change in the values of another quantity.
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8.3.4.PO 1
Interpret the relationship between a linear equation and its graph, identifying and computing slope and intercepts.
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8.3.4.PO 2
Solve problems involving simple rates.
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8.4
Geometry and Measurement
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8.4.1
Analyze the attributes and properties of 2- and 3- dimensional figures and develop mathematical arguments about their relationships.
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8.4.1.PO 1
Identify the attributes of circles: radius, diameter, chords, tangents, secants, inscribed angles, central angles, intercepted arcs, circumference, and area.
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8.4.1.PO 2
Predict results of combining, subdividing, and changing shapes of plane figures and solids.
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8.4.1.PO 3
Use proportional reasoning to determine congruence and similarity of triangles.
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8.4.1.PO 4
Use the Pythagorean Theorem to solve problems.
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8.4.2
Apply spatial reasoning to create transformations and use symmetry to analyze mathematical situations.
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8.4.2.PO 1
Model the result of rotations in multiples of 45 degrees of a 2-dimensional figure about the origin.
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8.4.2.PO 2
Describe the transformations that create a given tessellation.
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8.4.2.PO 3
Identify lines of symmetry in plane figures or classify types of symmetries of 2-dimensional figures.
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8.4.3
Specify and describe spatial relationships using rectangular and other coordinate systems while integrating content from each of the other strands.
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8.4.3.PO 1
Make and test a conjecture about how to find the midpoint between any two points in the coordinate plane.
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8.4.3.PO 2
Use the Pythagorean Theorem to find the distance between two points in the coordinate plane.
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8.4.4
Understand and apply appropriate units of measure, measurement techniques, and formulas to determine measurements.
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8.4.4.PO 1
Solve problems involving conversions within the same measurement system.
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8.4.4.PO 2
Solve geometric problems using ratios and proportions.
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8.4.4.PO 3
Calculate the surface area and volume of rectangular prisms, right triangular prisms, and cylinders.
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8.5
Structure and Logic
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8.5.1
Use reasoning to solve mathematical problems.
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8.5.1.PO 1
Create an algorithm to solve problems involving indirect measurements, using proportional reasoning, dimensional analysis, and the concepts of density and rate.
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8.5.2
Evaluate situations, select problem-solving strategies, draw logical conclusions, develop and describe solutions, and recognize their applications.
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8.5.2.PO 1
Analyze a problem situation to determine the question(s) to be answered.
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8.5.2.PO 2
Analyze and compare mathematical strategies for efficient problem solving; select and use one or more strategies to solve a problem.
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8.5.2.PO 3
Identify relevant, missing, and extraneous information related to the solution to a problem.
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8.5.2.PO 4
Represent a problem situation using multiple representations, describe the process used to solve the problem, and verify the reasonableness of the solution.
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8.5.2.PO 5
Apply a previously used problem-solving strategy in a new context.
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8.5.2.PO 6
Communicate the answer(s) to the question(s) in a problem using appropriate representations, including symbols and informal and formal mathematical language.
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8.5.2.PO 7
Isolate and organize mathematical information taken from symbols, diagrams, and graphs to make inferences, draw conclusions, and justify reasoning.
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8.5.2.PO 8
Describe when to use proportional reasoning to solve a problem.
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8.5.2.PO 9
Make and test conjectures based on information collected from explorations and experiments.
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8.5.2.PO 10
Solve logic problems involving multiple variables, conditional statements, conjectures, and negation using words, charts, and pictures.
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8.5.2.PO 11
Identify simple valid arguments using if...then statements.
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8.5.2.PO 12
Make, validate, and justify conclusions and generalizations about linear relationships.
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8.5.2.PO 13
Verify the Pythagorean Theorem using a valid argument.
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