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8.MA-08-1
Number Properties and Operations
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8.MA-08-1.1
Number Sense
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8.MA-08-1.1.1
Students will provide examples of and identify rational numbers and irrational numbers (square roots and pi only).
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8.MA-08-1.1.2
Students will describe and provide examples of representations of numbers (rational, square roots, and pi) and operations in a variety of equivalent forms using models, diagrams and symbols (e.g., number lines, 10 by 10 grids, rectangular arrays, number sentences) based on real-world and mathematical problems.
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8.MA-08-1.1.3
Students will convert, compare and order multiple numerical representations (e.g., fractions, decimals, percentages) of rational numbers and irrational numbers (square roots and pi only).
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8.MA-08-1.2
Estimation
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8.MA-08-1.2.1
Students will estimate to solve real-world and mathematical problems with rational numbers, checking for reasonable and appropriate computational results.
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8.MA-08-1.3
Number Operations
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8.MA-08-1.3.1
Students will add, subtract, multiply and divide rational numbers to solve real-world problems and apply order of operations (including positive whole number exponents) to simplify numerical expressions.
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8.MA-08-1.3.2
Students will explain how operations (additions and subtraction; multiplication and division; squaring and taking the square root of a number) are inversely related.
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8.MA-08-1.4
Ratios and Proportional Reasoning
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8.MA-08-1.4.1
Students will apply ratios and proportional reasoning to solve real-world problems (e.g., percents, constant rate of change, unit pricing, percent of increase or decrease).
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8.MA-08-1.5
Properties of Numbers and Operations
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8.MA-08-1.5.2
Students will identify the use of properties (commutative properties of addition and multiplication, the associative properties of addition and multiplication, the identity properties for addition and multiplication, inverse properties and the distributive property of multiplication over addition and subtraction) to justify a given step in solving problems.
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8.MA-08-2
Measurement
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8.MA-08-2.1
Measuring Physical Attributes
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8.MA-08-2.1.1
Students will measure lengths (to the nearest sixteenth of an inch or the nearest millimeter) and will determine and use in real-world or mathematical problems:
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8.MA-08-2.1.1.a
area and perimeter of triangles and quadrilaterals;
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8.MA-08-2.1.1.b
area and circumference of circles;
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8.MA-08-2.1.1.c
area and perimeter of compound figures composed of triangles, quadrilaterals and circles;
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8.MA-08-2.1.1.d
area from circumference or perimeter and
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8.MA-08-2.1.1.e
circumference or perimeter from area.
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8.MA-08-2.1.2
Students will estimate measurements in standard units in real-world and mathematical problems.
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8.MA-08-2.1.3
Students will evaluate the measures of angles by estimation, measurement with a protractor or angle ruler and determine angle measures in mathematical and/or real-world situations (e.g., supplementary, external, vertical).
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8.MA-08-2.1.4
Students will apply formulas to determine the volume of right rectangular prisms in real-world problems.
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8.MA-08-2.1.5
Students will use formulas to find surface area of right rectangular prisms in real-world and mathematical problems.
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8.MA-08-2.1.6
Students will apply the Pythagorean theorem to determine the length of a hypotenuse.
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8.MA-08-2.2
Systems of Measurement
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8.MA-08-2.2.1
Students will convert units within the same measurement system and use these units to solve real-world problems.
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8.MA-08-3
Geometry
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8.MA-08-3.1
Shapes and Relationships
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8.MA-08-3.1.1
Students will describe and provide examples of basic geometric elements that include points, segments, rays, lines, angles, and planes and will use these elements in real-world and mathematical problems.
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8.MA-08-3.1.2
Students will identify and compare properties of two-dimensional figures (circles, triangles acute, right, obtuse, scalene, isosceles, equilateral], quadrilaterals [square, rectangle, rhombus, parallelogram, trapezoid], regular/irregular polygons), and will apply these properties and figures to solve real-world and mathematical problems.
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8.MA-08-3.1.3
Students will compare properties of three-dimensional figures (spheres, cones, cylinders, prisms, pyramids), and will apply these properties and figures to solve real-world and mathematical problems.
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8.MA-08-3.1.4
Students will:
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8.MA-08-3.1.4.a
provide examples of congruent and similar figures;
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8.MA-08-3.1.4.b
apply congruent and similar figures to solve real-world and mathematical problems and
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8.MA-08-3.1.4.c
apply proportional reasoning to solve problems involving scale drawings and proportional figures.
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8.MA-08-3.2
Transformations of Shapes
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8.MA-08-3.2.1
Students will describe, provide examples of, and apply to real-world and mathematical problems rotational symmetry (90?, 180?, 360?).
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8.MA-08-3.2.2
Students will transform (translations, reflections, and dilations with the center of dilation at the origin) figures in a coordinate plane and determine the new coordinates of the image after the transformation.
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8.MA-08-3.2.3
Students will identify rotations (clockwise or counterclockwise) of figures about the origin in a coordinate plane.
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8.MA-08-3.3
Coordinate Geometry
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8.MA-08-3.3.1
Students will identify and graph ordered pairs on a coordinate system, correctly identifying the origin, axes and ordered pairs; and will apply graphing in the coordinate system to solve real-world and mathematical problems.
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8.MA-08-4
Data Analysis and Probability
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8.MA-08-4.1
Representations of Data Sets
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8.MA-08-4.1.1
Students will analyze and make inferences from data displays (drawings, tables/charts, pictographs, bar graphs, circle graphs, line plots, Venn diagrams, line graphs, stem-and-leaf plots, scatter plots, histograms, box-and-whiskers plots).
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8.MA-08-4.1.2
Students will explain how different representations of data (e.g., tables, graphs, diagrams, plots) are related.
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8.MA-08-4.1.4
Students will:
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8.MA-08-4.1.4.a
construct data displays (Venn diagrams, tables, line graphs, stem-and-leaf plots, circle graphs, scatter plots);
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8.MA-08-4.1.4.b
explain why the type of display is appropriate for the data and
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8.MA-08-4.1.4.c
explain how misleading representations affect interpretations and conclusions about data (e.g., changing the scale on a graph).
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8.MA-08-4.1.5
Students will construct box-and-whiskers plots.
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8.MA-08-4.2
Characteristics of Data Sets
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8.MA-08-4.2.1
Students will:
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8.MA-08-4.2.1.a
determine the mean, median, mode, and range of a set of data;
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8.MA-08-4.2.1.b
identify clusters, gaps, and outliers and
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8.MA-08-4.2.1.c
apply these concepts to compare sets of data.
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8.MA-08-4.3
Experiments and Samples
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8.MA-08-4.3.1
Students will explain how data gathering, bias issues, and faulty data analysis can affect the results of data collection.
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8.MA-08-4.4
Probability
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8.MA-08-4.4.1
Students will apply counting techniques to determine the size of a sample space for a real-world or mathematical situation.
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8.MA-08-4.4.2
Students will:
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8.MA-08-4.4.2.a
determine theoretical probabilities of simple events;
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8.MA-08-4.4.2.b
determine probabilities based on the results of an experiment and
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8.MA-08-4.4.2.c
make inferences from probability data.
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8.MA-08-4.4.3
Students will tabulate experimental results from simulations and explain how theoretical and experimental probabilities are related.
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8.MA-08-4.4.4
Students will determine theoretical probabilities and represent them using area models.
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8.MA-08-5
Algebraic Thinking
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8.MA-08-5.1
Patterns, Relations and Functions
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8.MA-08-5.1.1
Students will use variables to describe numerical patterns based on arithmetic sequences in real-world and mathematical problems (e.g., f(N) = 2N + 3).
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8.MA-08-5.1.2
Students will represent, analyze and generalize simple first and second degree relationships using tables, graphs, words and algebraic notations, and will apply the relationships to solve real-world and mathematical problems.
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8.MA-08-5.1.5
Students will explain how the change in one variable affects the change in another variable (e.g., if rate remains constant, an increase in time results in an increase in distance).
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8.MA-08-5.2
Variables, Expressions and Operations
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8.MA-08-5.2.1
Students will evaluate and simplify algebraic expressions applying the order of operations.
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8.MA-08-5.2.2
Students will describe, define and provide examples of variables and expressions with a missing value based on real-world and mathematical problems.
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8.MA-08-5.3
Equations and Inequalities
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8.MA-08-5.3.1
Students will model and solve single variable, first-degree real-world and mathematical problems (e.g., 5x + 2 = x + 22, x-4 < -60).
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