Nebraska State Standards for Mathematics: Grade 8

NE.MA 8.1. Students will communicate number sense concepts using multiple representations to reason, solve problems, and make connections within mathematics and across disciplines.

MA 8.1.1. Number System: Students will represent and show relationships among real numbers.

MA 8.1.1.a. Compare and order real numbers

MA 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)

MA 8.1.1.c. Represent small numbers using scientific notation

MA 8.1.1.d. Classify numbers as natural, whole, integer, rational, irrational, or real

MA 8.1.2. Operations: Students will demonstrate the meaning of arithmetic operations with integers.

MA 8.1.2.a. Use drawings, words, and symbols to explain the meaning of addition, subtraction, multiplication, and division of integers.

MA 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)

MA 8.1.2.c. Use words and symbols to explain why division by zero is undefined

MA 8.1.3. Computation: Students will compute fluently and accurately using appropriate strategies and tools.

MA 8.1.3.a. Compute accurately with rational numbers

MA 8.1.3.b. Evaluate expressions involving absolute value of integers

MA 8.1.3.c. Calculate squares of integers, the square roots of perfect squares, and the square roots of whole numbers using technology

MA 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)

MA 8.1.3.e. Solve problems involving ratios and proportions (e.g., x/5 = 10/17)

MA 8.1.4. Estimation: Students will estimate and check reasonableness of answers using appropriate strategies and tools.

MA 8.1.4.a. Use estimation methods to check the reasonableness of solutions for problems involving rational numbers

NE.MA 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.

MA 8.2.1. Characteristics: Students will describe, compare, and contrast characteristics, properties, and relationships of geometric shapes and objects.

MA 8.2.1.a. Identify and describe similarity of three-dimensional objects

MA 8.2.1.b. Compare and contrast relationships between similar and congruent objects

MA 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)

MA 8.2.1.d. Identify pairs of angles (e.g., adjacent, complementary, supplementary, vertical)

MA 8.2.1.e. Examine the relationships of the interior angles of a triangle (e.g., the sum of the angles is 180 degrees)

MA 8.2.2. Coordinate Geometry: Students will specify locations and describe relationships using coordinate geometry.

MA 8.2.2.a. Use coordinate geometry to represent and examine the properties of rectangles and squares using horizontal and vertical segments

MA 8.2.3. Transformations: Students will perform transformations and use them to analyze the orientation and size of geometric shapes.

MA 8.2.3.a. Identify the similarity of dilated shapes

MA 8.2.3.b. Perform and describe positions and sizes of shapes under dilations (e.g., scale factor, ratios)

MA 8.2.4. Spatial Modeling: Students will use visualization, spatial reasoning, and geometric modeling to solve problems.

MA 8.2.4.a. Draw geometric objects with specified properties (e.g., parallel sides, number of sides, angle measures, number of faces)

MA 8.2.5. Measurement: Students will select and apply appropriate procedures, tools, and formulas to determine measurements.

MA 8.2.5.a. Use strategies to find the perimeter and area of complex shapes

MA 8.2.5.b. Determine surface area and volume of three-dimensional objects (e.g., rectangular prisms, cylinders)

MA 8.2.5.c. Apply the Pythagorean theorem to find missing lengths in right triangles and to solve problems

MA 8.2.5.d. Use scale factors to find missing lengths in similar shapes

MA 8.2.5.e. Convert between metric and standard units of measurement, given conversion factors (e.g., meters to yards)

NE.MA 8.3. Students will communicate algebraic concepts using multiple representations to reason, solve problems, and make connections within mathematics and across disciplines.

MA 8.3.1. Relationships: Students will represent and analyze relationships using algebraic symbols.

MA 8.3.1.a. Represent and analyze a variety of patterns with tables, graphs, words, and algebraic equations

MA 8.3.1.b. Describe relationships using algebraic expressions, equations, and inequalities (e.g., two-step, one variable)

MA 8.3.1.c. Identify constant slope from tables and graphs

MA 8.3.2. Modeling in Context: Students will create, use, and interpret models of quantitative relationships.

MA 8.3.2.a. Model contextualized problems using various representations (e.g., two-step/one variable equations)

MA 8.3.2.b. Represent a variety of quantitative relationships using algebraic expressions and two-step/one variable equations

MA 8.3.3. Procedures: Students will apply properties to solve equations and inequalities.

MA 8.3.3.a. Explain the multiplicative inverse (e.g., 4 * 1/4= 1)

MA 8.3.3.b. Evaluate numerical expressions containing whole number exponents (e.g., if x = 4, then (x + 3)^2 + 5x = ?)

MA 8.3.3.c. Solve multi-step equations involving rational numbers

MA 8.3.3.d. Solve two-step inequalities involving rational numbers

MA 8.3.3.e. Identify and explain the properties used in solving two-step inequalities and multi-step equations

NE.MA 8.4. Students will communicate data analysis/probability concepts using multiple representations to reason, solve problems, and make connections within mathematics and across disciplines.

MA 8.4.1. Display and Analysis: Students will formulate questions that can be addressed with data, and then organize, display, and analyze the relevant data to answer their questions.

MA 8.4.1.a. Represent data using circle graphs and box plots with and without the use of technology

MA 8.4.1.b. Compare characteristics between sets of data or within a given set of data

MA 8.4.1.c. Find, interpret, and compare measures of central tendency (mean, median, mode) and the quartiles for sets of data

MA 8.4.1.d. Select the most appropriate unit of central tendency for sets of data

MA 8.4.1.e. Identify misrepresentation and misinterpretation of data represented in circle graphs and box plots

MA 8.4.2. Predictions and Inferences: Students will evaluate predictions and make inferences based on data.

MA 8.4.2.a. Evaluate predictions to formulate new questions and plan new studies

MA 8.4.2.b. Compare and contrast two sets of data to make inferences

MA 8.4.3. Probability: Students will apply and interpret basic concepts of probability.

MA 8.4.3.a. Identify complementary events and calculate their probabilities

MA 8.4.3.b. Compute probabilities for independent compound events