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6.1
Students will communicate number sense concepts using multiple representations to reason, solve problems, and make connections within mathematics and across disciplines.
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6.1.1
Students will represent and show relationships among positive rational numbers and integers.
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6.1.1.a
Show equivalence among common fractions and non-repeating decimals and percents
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6.1.1.b
Compare and order positive and negative integers
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6.1.1.c
Identify integers less than 0 on a number line
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6.1.1.d
Represent large numbers using exponential notation (e.g., 1,000 = 10³)
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6.1.1.e
Identify the prime factorization of numbers (e.g., 12 = 2 x 2 x 3 or 2² x 3)
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6.1.1.f
Classify numbers as natural, whole, or integer
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6.1.2
Students will demonstrate the meaning of arithmetic operations with positive fractions and decimals.
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6.1.2.a
Use drawings, words, and symbols to explain the meaning of addition and subtraction of fractions
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6.1.2.b
Use drawings, words, and symbols to explain the meaning of addition and subtraction of decimals
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6.1.3
Students will compute fluently and accurately using appropriate strategies and tools.
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6.1.3.a
Multiply and divide positive rational numbers
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6.1.3.b
Select and apply the appropriate method of computation when problem solving (e.g., models, mental computation, paper-pencil, technology, divisibility rules)
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6.1.4
Students will estimate and check reasonableness of answers using appropriate strategies and tools.
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6.1.4.a
Use appropriate estimation methods to check the reasonableness of solutions for problems involving positive rational numbers
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6.2
Students will communicate geometric concepts and measurement concepts using multiple representations to reason, solve problems, and make connections within mathematics and across disciplines.
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6.2.1
Students will compare and contrast properties among two-dimensional shapes and among three-dimensional objects.
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6.2.1.a
Justify the classification of three dimensional objects
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6.2.2
Students will label points using coordinate geometry.
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6.2.2.a
Identify the ordered pair of a plotted point in the coordinate plane
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6.2.3
Students will use and describe results of transformations on geometric shapes.
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6.2.3.a
Perform and describe positions and orientation of shapes under single transformations (translation, rotation, reflection) not on a coordinate plane
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6.2.4
Students will use visualization of geometric models to solve problems.
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6.2.4.a
Identify two-dimensional drawings of three-dimensional objects
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6.2.5
Students will apply appropriate procedures, tools, and formulas to determine measurements.
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6.2.5.a
Estimate and measure length with customary and metric units to the nearest 1/16 inch and mm
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6.2.5.b
Measure volume/capacity using the metric system
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6.2.5.c
Convert length, weight (mass), and liquid capacity from one unit to another within the same system
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6.2.5.d
Determine the perimeter of polygons
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6.2.5.e
Determine the area of parallelograms and triangles
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6.2.5.f
Determine the volume of rectangular prisms
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6.3
Students will communicate algebraic concepts using multiple representations to reason, solve problems, and make connections within mathematics and across disciplines.
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6.3.1
Students will represent, analyze, and use relationships to make generalizations.
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6.3.1.a
Describe and create simple algebraic expressions (e.g., one operation, one variable) from words and tables
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6.3.1.b
Use a variable to describe a situation with an equation (e.g., one-step, one variable)
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6.3.1.c
Identify relationships as increasing, decreasing, or constant
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6.3.2
Students will create, use, and interpret models of quantitative relationships.
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6.3.2.a
Model contextualized problems using various representations (e.g., graphs, tables)
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6.3.2.b
Represent a variety of quantitative relationships using symbols and words
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6.3.3
Students will apply properties to solve equations.
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6.3.3.a
Explain the multiplication property of equality (e.g., if a = b, then ac = bc)
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6.3.3.b
Evaluate numerical expressions containing multiple operations with respect to order of operations (e.g., 2 + 4 x 5)
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6.3.3.c
Evaluate simple algebraic expressions involving multiplication and division
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6.3.3.d
Solve one-step equations involving positive rational numbers
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6.3.3.e
Identify and explain the properties of equality used in solving one-step equations (e.g., addition, subtraction, division)
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6.4
Students will communicate data analysis/probability concepts using multiple representations to reason, solve problems, and make connections within mathematics and across disciplines.
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6.4.1
Students will organize, display, compare, and interpret data.
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6.4.1.a
Represent data using stem and leaf plots, histograms, and frequency charts
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6.4.1.b
Compare and interpret data sets and their graphical representations
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6.4.1.c
Find the mean, median, mode, and range for a set of data
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6.4.1.d
Compare the mean, median, mode, and range from two sets of data
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6.4.2
Students will construct predictions based on data.
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6.4.2.a
Make predictions based on data and create questions to further investigate the quality of the predictions
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6.4.3
Students will apply basic concepts of probability.
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6.4.3.a
Describe the theoretical probability of an event using a fraction, percentage, decimal, or ratio
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6.4.3.b
Compute theoretical probabilities for independent events
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6.4.3.c
Find experimental probability for independent events
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