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6.1
Number and Operations
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6.1.1
Understand and apply numbers, ways of representing numbers, and the relationships among numbers and different number systems.
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6.1.1.PO 1
Convert between expressions for positive rational numbers, including fractions, decimals, percents, and ratios.
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6.1.1.PO 2
Use prime factorization to
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6.1.1.PO 2.a
express a whole number as a product of its prime factors and
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6.1.1.PO 2.b
determine the greatest common factor and least common multiple of two whole numbers.
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6.1.1.PO 3
Demonstrate an understanding of fractions as rates, division of whole numbers, parts of a whole, parts of a set, and locations on a real number line.
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6.1.1.PO 4
Compare and order integers; and positive fractions, decimals, and percents.
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6.1.1.PO 5
Express that a number's distance from zero on the number line is its absolute value.
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6.1.1.PO 6
Express the inverse relationships between exponents and roots for perfect squares and cubes.
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6.1.2
Understand and apply numerical operations and their relationship to one another.
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6.1.2.PO 1
Apply and interpret the concepts of addition and subtraction with integers using models.
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6.1.2.PO 2
Multiply multi-digit decimals through thousandths.
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6.1.2.PO 3
Divide multi-digit whole numbers and decimals by decimal divisors with and without remainders.
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6.1.2.PO 4
Multiply and divide fractions.
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6.1.2.PO 5
Provide a mathematical argument to explain operations with two or more fractions or decimals.
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6.1.2.PO 6
Apply the commutative, associative, distributive, and identity properties to evaluate numerical expressions involving whole numbers.
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6.1.2.PO 7
Simplify numerical expressions (involving fractions, decimals, and exponents) using the order of operations with or without grouping symbols.
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6.1.3
Use estimation strategies reasonably and fluently while integrating content from each of the other strands.
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6.1.3.PO 1
Use benchmarks as meaningful points of comparison for rational numbers.
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6.1.3.PO 2
Make estimates appropriate to a given situation and verify the reasonableness of the results.
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6.2
Data Analysis, Probability, and Discrete Mathematics
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6.2.1
Understand and apply data collection, organization, and representation to analyze and sort data.
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6.2.1.PO 1
Solve problems by selecting, constructing, and interpreting displays of data, including histograms and stem-and-leaf plots.
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6.2.1.PO 2
Formulate and answer questions by interpreting, analyzing, and drawing inferences from displays of data, including histograms and stem-and-leaf plots.
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6.2.1.PO 3
Use extreme values, mean, median, mode, and range to analyze and describe the distribution of a given data set.
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6.PO 4.
Compare two or more sets of data by identifying trends.
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6.2.2
Understand and apply the basic concepts of
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6.2.2.PO 1
Use data collected from multiple trials of a single event to form a conjecture about the theoretical probability.
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6.2.2.PO 2
Use theoretical probability to
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6.2.2.PO 2.a
predict experimental outcomes,
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6.2.2.PO 2.b
compare the outcome of the experiment to the prediction, and
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6.2.2.PO 2.c
replicate the experiment and compare results.
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6.2.2.PO 3
Determine all possible outcomes (sample space) of a given situation using a systematic approach.
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6.2.3
Understand and demonstrate the systematic listing and counting of possible outcomes.
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6.2.3.PO 1
Build and explore tree diagrams where items repeat.
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6.2.3.PO 2
Explore counting problems with Venn diagrams using three attributes.
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6.2.4
Understand and apply vertex-edge graphs.
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6.2.4.PO 1
Investigate properties of vertex-edge graphs
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6.2.4.PO 1.a
Hamilton paths,
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6.2.4.PO 1.b
Hamilton circuits, and
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6.2.4.PO 1.c
shortest route.
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6.2.4.PO 2
Solve problems related to Hamilton paths and circuits.
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6.3
Patterns, Algebra, and Functions
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6.3.1
Identify patterns and apply pattern recognition to reason mathematically while integrating content from each of the other strands.
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6.3.1.PO 1
Recognize, describe, create, and analyze a numerical sequence involving fractions and decimals using all four basic operations.
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6.3.2
Describe and model functions and their relationships.
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6.3.2.PO 1
Recognize and describe a relationship between two quantities, given by a chart, table, or graph, using words and expressions.
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6.3.3
Represent and analyze mathematical situations and structures using algebraic representations.
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6.3.3.PO 1
Use an algebraic expression to represent a quantity in a given context.
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6.3.3.PO 2
Create and solve two-step equations that can be solved using inverse properties with fractions and decimals.
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6.3.3.PO 3
Translate both ways between a verbal description and an algebraic expression or equation.
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6.3.3.PO 4
Evaluate an expression involving the four basic operations by substituting given fractions and decimals for the variable.
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6.3.4
Analyze how changing the values of one quantity corresponds to change in the values of another quantity.
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6.3.4.PO 1
Determine a pattern to predict missing values on a line graph or scatterplot.
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6.4
Geometry and Measurement
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6.4.1
Analyze the attributes and properties of 2- and 3- dimensional figures and develop mathematical arguments about their relationships.
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6.4.1.PO 1
Define pi as the ratio between the circumference and diameter of a circle and explain the relationship among the diameter, radius, and circumference.
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6.4.1.PO 2
Solve problems using properties of supplementary, complementary, and vertical angles.
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6.4.2
Apply spatial reasoning to create transformations and use symmetry to analyze mathematical situations.
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6.4.2.PO 1
Identify a simple translation or reflection and model its effect on a 2-dimensional figure on a coordinate plane using all four quadrants.
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6.4.2.PO 2
Draw a reflection of a polygon in the coordinate plane using a horizontal or vertical line of reflection.
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6.4.3
Specify and describe spatial relationships using rectangular and other coordinate systems while integrating content from each of the other strands.
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6.4.3.PO 1
Graph ordered pairs in any quadrant of the coordinate plane.
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6.4.3.PO 2
State the missing coordinate of a given figure on the coordinate plane using geometric properties to justify the solution.
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6.4.4
Understand and apply appropriate units of measure, measurement techniques, and formulas to determine measurements.
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6.4.4.PO 1
Determine the appropriate unit of measure for a given context and the appropriate tool to measure to the needed precision (including length, capacity, angles, time, and mass).
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6.4.4.PO 2
Solve problems involving conversion within the U.S. Customary and within the metric system.
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6.4.4.PO 3
Estimate the measure of objects using a scale drawing or map.
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6.4.4.PO 4
Solve problems involving the area of simple polygons using formulas for rectangles and triangles.
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6.4.4.PO 5
Solve problems involving area and perimeter of regular and irregular polygons.
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6.4.4.PO 6
Describe the relationship between the volume of a figure and the area of its base.
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6.5
Structure and Logic
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6.5.1
Use reasoning to solve mathematical problems.
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6.5.1.PO 1
Analyze algorithms for multiplying and dividing fractions and decimals using the associative, commutative, and distributive properties.
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6.5.1.PO 2
Create and justify an algorithm to determine the area of a given compound figure using parallelograms and triangles.
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6.5.2
Evaluate situations, select problem-solving strategies, draw logical conclusions, develop and describe solutions, and recognize their applications.
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6.5.2.PO 1
Analyze a problem situation to determine the question(s) to be answered.
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6.5.2.PO 2
Identify relevant, missing, and extraneous information related to the solution to a problem.
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6.5.2.PO 3
Analyze and compare mathematical strategies for efficient problem solving; select and use one or more strategies to solve a problem.
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6.5.2.PO 4
Apply a previously used problem-solving strategy in a new context.
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6.5.2.PO 5
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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6.5.2.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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6.5.2.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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6.5.2.PO 8
Make and test conjectures based on information collected from explorations and experiments.
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6.5.2.PO 9
Solve simple logic problems, including conditional statements, and justify solution methods and reasoning.
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