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6.NO
Numbers and Operations
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6.1
Understand numbers, ways of representing numbers, relationships among numbers, and number systems
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6
Numbers and Number Systems
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6.1.1
Compare and order fractions, decimals, and percents
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6.1.2
Explain and give examples of number theory concepts (e.g., prime factorization, common factors, greatest common factor, common multiples, least common multiple, divisibility)
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6.2
Understand the meaning of operations and how they relate to each other
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6
Operation
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6.2.1
Apply the order of operations when calculating with whole numbers
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6
Operation Properties
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6.2.2
Use the operation properties to simplify computations with fractions, decimals, and percents
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6.3
Use computational tools and strategies fluently and, when appropriate, use estimation
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6
Estimation
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6.3.1
Use estimation prior to computing with fractions and decimals and compare the estimation to the actual result
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6.3.2
Recognize situations in which it is more appropriate to estimate than to compute an exact answer
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6.MEA
Measurement
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6.4
Understand attributes, units, and systems of units in measurement; and develop and use techniques, tools, and formulas for measuring
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6
Measurement Attributes and Units
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6.4.1
Estimate the circumference and area of a circle (with no reference to a formula)
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6.4.2
Construct angles with a given degree measure
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6
Measurement Formulas
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6.4.3
Apply strategies and formulas to solve area and perimeter problems involving polygons (e.g., regular hexagons) and complex shapes (i.e., shapes composed of two or more common shapes)
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6.GEO
Geometry and Spatial Sense
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6.5
Analyze properties of objects and relationships among the properties
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6
Geometric Shapes and Their Properties and Relationships
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6.5.1
Analyze and describe the relationships among the angles, side lengths, perimeters, and areas of similar geometric figures
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6.5.2
Create arguments for proving that two shapes are congruent
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6.6
Use transformations and symmetry to analyze mathematical situations
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6
Symmetry
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6.6.1
Use line symmetry and rotational symmetry to describe classifications of shapes (e.g., squares have 4 lines of symmetry and 90° rotational symmetry)
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6.7
Use visualization and spatial reasoning to solve problems both within and outside of mathematics
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6
Visualization and Spatial Reasoning
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6.7.1
Construct a two-dimensional representation from different angles of a three-dimensional object
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6.7.2
Draw two-dimensional shapes with specified properties
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6.8
Select and use different representational systems, including coordinate geometry
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6
Coordinate Geometry
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6.8.1
Predict the shape that is formed by connecting the points represented by given coordinates
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6.8.2
Use coordinate geometry to represent and analyze properties of geometric shapes
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6.PFA
Patterns, Functions, and Algebra
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6.9
Understand various types of patterns and functional relationships
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6
Patterns
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6.9.1
Represent visual and numerical patterns with tables and graphs and generalize the "rule" using words and symbols
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6
Functions
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6.9.2
Describe simple one-step functions using words and symbols when given a table of "input" and "output" values
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6.1
Use symbolic forms to represent, model, and analyze mathematical situations
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6
Numeric and Algebraic Representations
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6.10.1
Interpret and solve problem situations involving two different variables
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6.10.2
Use fact families to solve for an unknown in an open sentence
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6.10.3
Evaluate algebraic expressions
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6.DASP
Data Analysis, Statistics, and Probability
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6.11
Pose questions and collect, organize, and represent data to answer those questions
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6
Data Collection and Representation
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6.11.1
Analyze how data collection methods and sample size can affect the results of data sets
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6.12
Interpret data using methods of exploratory data analysis
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6
Data Interpretation
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6.12.1
Determine and interpret the measures of center (mean, median, mode) of a data set and explain what each measure indicates about the data set
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6.12.2
Use a stem-and-leaf plot to analyze a set of data
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6.13
Develop and evaluate inferences, predictions, and arguments that are based on data
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6
Predictions and Inferences
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6.13.1
Make inferences about a population based on the interpretation of a sample data set
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6.14
Understand and apply basic notions of chance and probability
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6
Probability
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6.14.1
Compute probabilities of simple compound events (e.g., rolling two dice, using two different spinners at the same time)
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