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8.1
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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8.1.1
Students will represent and show relationships among real numbers.
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8.1.1.a
Compare and order real numbers
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8.1.1.b
Demonstrate relative position of real numbers on the number line (e.g., square root of 2 is left of 1.5)
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8.1.1.c
Represent small numbers using scientific notation
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8.1.1.d
Classify numbers as natural, whole, integer, rational, irrational, or real
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8.1.2
Students will demonstrate the meaning of arithmetic operations with integers.
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8.1.2.a
Use drawings, words, and symbols to explain the meaning of addition, subtraction, multiplication, and division of integers.
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8.1.2.b
Use words and symbols to explain the zero property of multiplication (e.g., if ab = 0 then a or b or both must be zero)
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8.1.2.c
Use words and symbols to explain why division by zero is undefined
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8.1.3
Students will compute fluently and accurately using appropriate strategies and tools.
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8.1.3.a
Compute accurately with rational numbers
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8.1.3.b
Evaluate expressions involving absolute value of integers
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8.1.3.c
Calculate squares of integers, the square roots of perfect squares, and the square roots of whole numbers using technology
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8.1.3.d
Select, apply, and explain the method of computation when problem solving using rational numbers (e.g., models, mental computation, paper-pencil, technology, divisibility rules)
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8.1.3.e
Solve problems involving ratios and proportions (e.g., x/5 = 10/17)
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8.1.4
Students will estimate and check reasonableness of answers using appropriate strategies and tools.
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8.1.4.a
Use estimation methods to check the reasonableness of solutions for problems involving rational numbers
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8.2
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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8.2.1
Students will describe, compare, and contrast characteristics, properties, and relationships of geometric shapes and objects.
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8.2.1.a
Identify and describe similarity of three-dimensional objects
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8.2.1.b
Compare and contrast relationships between similar and congruent objects
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8.2.1.c
Identify geometric properties of parallel lines cut by a transversal and related angles (e.g., perpendicular and parallel lines with transversals) and angles (e.g., corresponding, alternate interior, alternate exterior)
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8.2.1.d
Identify pairs of angles (e.g., adjacent, complementary, supplementary, vertical)
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8.2.1.e
Examine the relationships of the interior angles of a triangle (e.g., the sum of the angles is 180 degrees)
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8.2.2
Students will specify locations and describe relationships using coordinate geometry.
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8.2.2.a
Use coordinate geometry to represent and examine the properties of rectangles and squares using horizontal and vertical segments
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8.2.3
Students will perform transformations and use them to analyze the orientation and size of geometric shapes.
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8.2.3.a
Identify the similarity of dilated shapes
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8.2.3.b
Perform and describe positions and sizes of shapes under dilations (e.g., scale factor, ratios)
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8.2.4
Students will use visualization, spatial reasoning, and geometric modeling to solve problems.
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8.2.4.a
Draw geometric objects with specified properties (e.g., parallel sides, number of sides, angle measures, number of faces)
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8.2.5
Students will select and apply appropriate procedures, tools, and formulas to determine measurements.
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8.2.5.a
Use strategies to find the perimeter and area of complex shapes
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8.2.5.b
Determine surface area and volume of three-dimensional objects (e.g., rectangular prisms, cylinders)
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8.2.5.c
Apply the Pythagorean theorem to find missing lengths in right triangles and to solve problems
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8.2.5.d
Use scale factors to find missing lengths in similar shapes
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8.2.5.e
Convert between metric and standard units of measurement, given conversion factors (e.g., meters to yards)
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8.3
Students will communicate algebraic concepts using multiple representations to reason, solve problems, and make connections within mathematics and across disciplines.
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8.3.1
Students will represent and analyze relationships using algebraic symbols.
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8.3.1.a
Represent and analyze a variety of patterns with tables, graphs, words, and algebraic equations
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8.3.1.b
Describe relationships using algebraic expressions, equations, and inequalities (e.g., two-step, one variable)
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8.3.1.c
Identify constant slope from tables and graphs
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8.3.2
Students will create, use, and interpret models of quantitative relationships.
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8.3.2.a
Model contextualized problems using various representations (e.g., two-step/one variable equations)
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8.3.2.b
Represent a variety of quantitative relationships using algebraic expressions and two-step/one variable equations
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8.3.3
Students will apply properties to solve equations and inequalities.
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8.3.3.a
Explain the multiplicative inverse (e.g., 4 * ¼ = 1)
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8.3.3.b
Evaluate numerical expressions containing whole number exponents (e.g., if x = 4, then (x + 3)² + 5x = ?)
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8.3.3.c
Solve multi-step equations involving rational numbers
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8.3.3.d
Solve two-step inequalities involving rational numbers
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8.3.3.e
Identify and explain the properties used in solving two-step inequalities and multi-step equations
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8.4
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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8.4.1
Students will formulate questions that can be addressed with data, and then organize, display, and analyze the relevant data to answer their questions.
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8.4.1.a
Represent data using circle graphs and box plots with and without the use of technology
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8.4.1.b
Compare characteristics between sets of data or within a given set of data
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8.4.1.c
Find, interpret, and compare measures of central tendency (mean, median, mode) and the quartiles for sets of data
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Statistics: Calculate mean, median, mode, and range (Eighth grade - BB.1)
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Statistics: Interpret charts to find mean, median, mode, and range (Eighth grade - BB.2)
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Statistics: Mean, median, mode, and range: find the missing number (Eighth grade - BB.3)
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Statistics: Changes in mean, median, mode, and range (Eighth grade - BB.4)
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Statistics: Quartiles (Eighth grade - BB.5)
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8.4.1.d
Select the most appropriate unit of central tendency for sets of data
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8.4.1.e
Identify misrepresentation and misinterpretation of data represented in circle graphs and box plots
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8.4.2
Students will evaluate predictions and make inferences based on data.
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8.4.2.a
Evaluate predictions to formulate new questions and plan new studies
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8.4.2.b
Compare and contrast two sets of data to make inferences
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8.4.3
Students will apply and interpret basic concepts of probability.
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8.4.3.a
Identify complementary events and calculate their probabilities
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8.4.3.b
Compute probabilities for independent compound events
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