21^st CENTURY

8^th Grade MATH

CONTENT STANDARDS AND OBJECTIVES FOR WEST VIRGINIA SCHOOLS (2520.2)

Janet Benincosa, TI Specialist

The West Virginia Standards for 21st Century Learning include the following components: 21st Century Content Standards and Objectives and 21st Century Learning Skills and Technology Tools. 

All West Virginia teachers are responsible for classroom instruction that integrates learning skills, technology tools and content standards and objectives. 

Eighth Grade

Grade 8		Mathematics
Standard 1		Number and Operations
M.S.8.1		Through communication, representation, reasoning and proof, problem solving, and making connections within and beyond the field of mathematics, students will demonstrate understanding of numbers, ways of representing numbers, and relationships among numbers and number systems, demonstrate meanings of operations and how they relate to one another, and compute fluently and make reasonable estimates.
Performance Descriptors (M.PD.8.1)
Distinguished			Above Mastery	Mastery	Partial Mastery	Novice
Eighth grade students at the distinguished level in mathematics analyze, describe and compare the characteristics of rational and irrational numbers and use rational and irrational numbers to create and solve problems. They create and solve problems involving powers and radicals; they solve problems using numbers in scientific notation. They analyze and solve application problems involving properties of rational and irrational number, radicals, and powers and, in a clear, concise manner, justify solutions and explain the process used in solving.			Eighth grade students at the above mastery level in mathematics analyze, describe and compare the characteristics of rational and irrational numbers ; and use rational and irrational numbers; they add, subtract, multiply and divide with rational and irrational numbers. They solve problems involving powers and radicals; they solve problems using numbers in scientific notation. They analyze and solve application problems involving rational and irrational numbers, verify solutions using estimation techniques, and explain the process used in solving.	Eighth grade students at the mastery level in mathematics analyze, describe and compare the characteristics of rational and irrational numbers They solve problems using powers and square roots; they solve problems using numbers in scientific notation They analyze and solve application problems involving any rational numbers (e.g. rates, tips, discounts, sales tax, and interest) and verify solutions using estimation techniques.	Eighth grade students at the partial mastery level in mathematics describe, order and compare rational and irrational numbers. They evaluate powers of integers; they solve problems using numbers in scientific notation. They analyze and solve application problems involving no more than two operations with whole numbers, integers, decimals, fractions, and percents (e.g. rates, tips, discounts, sales tax, and interest) and verify solutions using estimation techniques.	Eighth grade students at the novice level in mathematics compare and order rational and irrational numbers by converting to and comparing their decimal forms. They evaluate powers of integers; they convert between numbers in scientific notation and standard form. They solve application problems involving one operation with whole numbers, integers, decimals, fractions, and percents (e.g. rates, tips, discounts, sales tax, and interest) and verify solutions using estimation techniques.
	Objectives	Students will
	M.O.8.1.1	analyze, describe and compare the characteristics of rational and irrational numbers.
	M.O.8.1.2	analyze and solve application problems with powers, / squares, / square roots, / scientific notation, and / verify solutions using estimation techniques.
	M.O.8.1.3	analyze and solve grade-appropriate real-world problems with whole numbers, / decimals, / fractions, / percents, percent increase and decrease, / integers, and / including, but not limited to, rates, tips, discounts, sales tax and interest and verify solutions using estimation techniques.

Grade 8		Mathematics
Standard 2		Algebra
M.S.8.2		Through communication, representation, reasoning and proof, problem solving, and making connections within and beyond the field of mathematics, students will demonstrate understanding of patterns, relations and functions, represent and analyze mathematical situations and structures using algebraic symbols, use mathematical models to represent and understand quantitative relationships, and analyze change in various contexts.
Performance Descriptors (M.PD.8.2)
Distinguished			Above Mastery	Mastery	Partial Mastery	Novice
Eighth grade students at the distinguished level in mathematics formulate an algebraic expression from data in a table arithmetic, geometric, or algebraic pattern; they analyze the table and rule to determine and explain whether or not there exists a functional relationship. They solve multi-step linear equations and literal equations and solve and graph multi-step inequalities in one variable with variables on both sides. They graph linear equations and inequalities; they determine the slope of a line given the graph of the line, two points, or the slope/intercept equation; they determine the equation of a line, given the graph or a table of values. They solve problems by creating and simplifying polynomial expressions; they justify their process and solution.			Eighth grade students at the above mastery level in mathematics formulate an algebraic expression from data in a table arithmetic, geometric, or algebraic pattern; they analyze the table and rule to determine if a function relationship exists. They solve multi-step linear equations and solve and graph multi-step inequalities in one variable with variables on both sides. They graph linear equations and inequalities; they determine the slope of a line given the graph of the line, two points, or the slope/intercept equation; they determine the equation of a line, given the graph. They generate and apply expressions and equations, including proportions, to solve problems and justify solutions; they add and subtract polynomials to solve problems.	Eighth grade students at the mastery level in mathematics formulate a rule from data in a table to generate an arithmetic, geometric, or algebraic pattern; they analyze tables and rules to determine if a functional relationship exists. They solve two-step linear equations and solve and graph two-step inequalities with rational solutions. They graph linear equations and inequalities; they determine the slope of a line given the graph of the line, two points, or the slope/intercept equation. They generate and apply expressions and equations, including proportions, to solve real-world problems; they add and subtract polynomials limited to two variables and positive exponents.	Eighth grade students at the partial mastery level in mathematics complete a table to predict values in a problem solving situation involving an arithmetic, geometric, or algebraic pattern; they analyze the table and rule to determine if a function relationship exists. They solve one and two-step linear equations and solve and graph one and two-step inequalities involving integers. They create a table of values for and graph linear equations; they determine the slope of a line from its graph. They write and simplify algebraic expressions with whole numbers, integers, rational numbers, absolute value, and exponents using order of operations; they add and subtract polynomials limited to two variables and no exponents	Eighth grade students at the novice level in mathematics create a table of values for and graph linear equations; they identify the slope of a line from its graph as being positive or negative. They solve one and two-step linear equations and solve and graph one and two-step inequalities involving whole numbers. They complete a table to generate an arithmetic, geometric, or algebraic pattern; they analyze the table and rule to determine if a function relationship exists. They write algebraic expressions for word phrases, solve proportions, and identify like terms in monomials; they add and subtract polynomials limited to two variables and no exponents.
	Objectives	Students will
	M.O.8.2.1	use a variety of strategies to solve one and two-step linear equations and inequalities with rational solutions; defend the selection of the strategy; graph the solutions and justify the reasonableness of the solution.
	M.O.8.2.2	identify proportional relationships in real-world situations, then find and select an appropriate method to determine the solution; justify the reasonableness of the solution.
	M.O.8.2.3	add and subtract polynomials limited to two variables and positive exponents.
	M.O.8.2.4	use systems of linear equations to analyze situations and solve problems.
	M.O.8.2.5	apply inductive and deductive reasoning to write a rule from data in an input/output table, analyze the table and the rule to determine if a functional relationship exists.
	M.O.8.2.6	graph linear equations and inequalities within the Cartesian coordinate plane by generating a table of values (with and without technology).
	M.O.8.2.7	formulate and apply a rule to generate an arithmetic, geometric and algebraic pattern.
	M.O.8.2.8	determine the slope of a line using a variety of methods including graphing change in y over change in x equation
	M.O.8.2.9	represent and solve real-world grade-appropriate problems using multiple strategies and justify solutions.
	M.O.8.2.10	identify a real life problem involving change over time; make a prediction as to the outcome; develop, justify, and implement a method to collect, organize, and analyze data; generalize the results to make a conclusion; compare the prediction and the result of the investigation; present the problem using words, graphs, drawings, models, or tables.

Grade 8		Mathematics
Standard 3		Geometry
M.S.8.3		Through communication, representation, reasoning and proof, problem solving, and making connections within and beyond the field of mathematics, students will: · analyze characteristics and properties of two- and three- dimensional geometric shapes and develop mathematical arguments about geometric relationships, · specify locations and describe spatial relationships using coordinate geometry and other representational systems, · apply transformation and use symmetry to analyze mathematical situations, and · solve problems using visualization, spatial reasoning, and geometric modeling.
Performance Descriptors (M.PD.8.3)
Distinguished			Above Mastery	Mastery	Partial Mastery	Novice
Eighth grade students at the distinguished level in mathematics apply relationships among angles formed by parallel lines cut by a transversal to determine missing measures and justify their solution; they construct perpendicular and angle bisectors. They use transformations to create Escher-like tessellations. They create scale models of three-dimensional prisms; they use ratio, proportion to determine scale factor in similar figures. They solve problems involving intersections and unions of plane and solid figures. They make and test conjectures concerning relationships between the dimensions of geometric figures; state and justify the results and refine the conjecture. They classify polyhedrons according to the number and shape of faces; and use inductive reasoning to determine and algebraically state the relationship between vertices, faces and edges.			Eighth grade students at the above mastery level in mathematics apply relationships among angles formed by parallel lines cut by a transversal to determine missing measures; they construct perpendicular and angle bisectors. They use transformations to create tessellations. They create scale models of three-dimensional rectangular prisms; they use ratio, proportion to determine scale factor in similar figures. They prove conjectures involving regular polygons and uses coordinate geometry to solve problems involving similar figures and transformations. They make and test conjectures concerning regular polygons, cross section of a solid such as a cylinder, cone and pyramid, or the intersection of two or more geometric figures in the plan; refine the conjecture. They classify polyhedrons according to the number and shape of faces; use inductive reasoning to determine and state the relationship between vertices, faces and edges.	Eighth grade students at the mastery level in mathematics recognize relationships among angles formed by parallel lines cut by a transversal; they construct perpendicular and angle bisectors. They create geometric patterns and transformations to predict results of combining, subdividing and changing shapes of plane figures and solids. They create scale models; they use ratio, proportion to determine scale factor in similar figures. They make and test conjectures concerning regular polygons, cross section of a solid such as a cylinder, cone and pyramid, or the intersection of two or more geometric figures in the plan; justify the results. They classify polyhedrons according to the number and shape of faces and use inductive reasoning to determine the relationship between vertices, faces and edges.	Eighth grade students at the partial mastery level in mathematics identify the classifications of angles formed by parallel lines cut by a transversal (alternate interior angles, alternate exterior angles, corresponding angles) and recognize congruent angles pairs formed by parallel lines cut by a transversal; they recognize perpendicular and angle bisectors. They identify geometric patterns and transformations to predict results of combining, subdividing and changing shapes of plane figures and solids. They create scale models of rectangles and right triangles; they use ratio, proportion to determine scale factor in similar figures. They make and test conjectures concerning regular polygons, cross section of a solid such as a cylinder, cone and pyramid, or the intersection of two or more geometric figures in the plan; state the results. They classify polyhedrons according to the number and shape of faces and determine the number of vertices, faces and edges.	Eighth grade students at the novice level in mathematics identify the classifications of angles formed by parallel lines cut by a transversal (alternate interior angles, alternate exterior angles, and corresponding angles); they recognize perpendicular and angle bisectors. They recognize geometric patterns, transformations and results of combining, subdividing and changing shapes of plane figures and solids. They create scale models of rectangles; they use ratio, proportion to determine scale factor in similar figures. They test conjectures concerning regular polygons, cross section of a solid such as a cylinder, cone and pyramid, or the intersection of two or more geometric figures in the plan; state the results. They determine the number of vertices, faces and edges and distinguish between prisms and pyramids
	Objectives	Students will
	M.O.8.3.1	justify the relationships among corresponding, alternate interior, alternate exterior and vertical angles when parallel lines are cut by a transversal using models, pencil/paper, graphing calculator, and technology.
	M.O.8.3.2	classify polyhedrons according to the number and shape of faces; use inductive reasoning to determine the relationship between vertices, faces and edges (edges + 2 = faces + vertices).
	M.O.8.3.3	identify, apply, and construct perpendicular and angle bisectors with and without technology ) given a real-world situation,.
	M.O.8.3.4	create geometric patterns including tiling, art design, tessellations and scaling using transformations (rotations, reflections, translations) and predict results of combining, subdividing, and changing shapes of plane figures and solids.
	M.O.8.3.5	create scale models of similar figures using ratio, proportion with pencil/paper and technology and determine scale factor
	M.O.8.3.6	make and test a conjecture concerning regular polygons, the cross section of a solid such as a cylinder, cone, and pyramid, the intersection of two or more geometric figures in the plane (e.g., intersection of a circle and a line), and justify the results.

Grade 8		Mathematics
Standard 4		Measurement
M.S.8.4		Through communication, representation, reasoning and proof, problem solving, and making connections within and beyond the field of mathematics, students will demonstrate understanding of measurable attributes of objects and the units, systems, and processes of measurements, and apply appropriate techniques, tools, and formulas to determine measurements.
Performance Descriptors (M.PD.8.4)
Distinguished			Above Mastery	Mastery	Partial Mastery	Novice
Eighth grade students at the distinguished level in mathematics determine the volume of prisms, pyramids, cylinders, cones, and spheres in real-world problem situations; they explain and justify the reasonableness of their method and solution in a clear, concise manner. They solve problems involving missing measurements in plane and solid geometric figures; they justify the results in a clear, concise manner. They create and solve problems involving the Pythagorean Theorem and indirect measurement in right triangles; they justify the results in a clear, concise manner.			Eighth grade students at the above mastery level in mathematics determine the volume of prisms, pyramids, cylinders, cones, and spheres in real-world problem situations; they explain and justify the reasonableness of their method and solution. They solve problems involving missing measurements in plane and solid geometric figures; they justify the results. They create and solve problems involving the Pythagorean Theorem and indirect measurement in right triangles.	Eighth grade students at the mastery level in mathematics determine the volume of prisms, pyramids, cylinders, cones, and spheres in real-world problem situations and justify the reasonableness of the solution. They solve problems involving missing measurements in plane and solid geometric figures. They use the Pythagorean Theorem, indirect measure, and definitions to solve right-triangle application problems.	Eighth grade students at the partial mastery level in mathematics determine the volume of prisms, cylinders, cones, and pyramids in real-world problem situations and justify the reasonableness of the solution. They solve problems involving missing measurements in rectangular prisms and plane geometric figures. They use the Pythagorean Theorem to find unknown sides of right triangles.	Eighth grade students at the novice level in mathematics determine the volume of prisms, cylinders, and pyramids in real-world problem situations and justify the reasonableness of the solution. They solve problems involving missing measurements in plane geometric figures. They use the Pythagorean Theorem to find the hypotenuse of right triangles.
	Objectives	Students will
	M.O.8.4.1	select and apply an appropriate method to solve; justify the method and the reasonableness of the solution of problems involving volume of · prisms · cylinders · cones · pyramids · spheres given real-world problem solving situations.
	M.O.8.4.2	solve problems involving missing measurements in plane and solid geometric figures using formulas and drawings including irregular figures, models or definitions.
	M.O.8.4.3	solve right triangle problems where the existence of triangles is not obvious using the Pythagorean Theorem and indirect measurement in real-world problem solving situations.

Grade 8		Mathematics
Standard 5		Data Analysis and Probability
M.S.8.5		Through communication, representation, reasoning and proof, problem solving, and making connections within and beyond the field of mathematics, students will: · formulate questions that can be addressed with data and collect, organize, and display relevant data to answer them, · select and use appropriate statistical methods to analyze data, · develop and evaluate inferences and predictions that are based on models, and · apply and demonstrate an understanding of basic concepts of probability.
Performance Descriptors (M.PD.8.5)
Distinguished			Above Mastery	Mastery	Partial Mastery	Novice
Eighth grade students at the distinguished level in mathematics make hypotheses, collect data, create and extrapolate information from multiple data displays and construct convincing arguments based on data analysis. They use appropriate technology to solve application problems involving combinations and permutations and investigation compound probability of dependent and independent events; they compare and contrast simple probability with compound probability and dependent events with independent events; they design and conduct experiments involving compound probability, dependent events, or independent events.			Eighth grade students at the above mastery level in mathematics collect data, create and extrapolate information from multiple data displays and construct convincing arguments based on data analysis. They use appropriate technology to solve application problems involving combinations and permutations and investigation compound probability of dependent and independent events; they compare and contrast simple probability with compound probability and dependent events with independent events.	Eighth grade students at the mastery level in mathematics create and extrapolate information from multiple data displays and construct convincing arguments based on data analysis. They use appropriate technology to solve application problems involving combinations and permutations and investigation compound probability of dependent and independent events.	Eighth grade students at the partial mastery level in mathematics create and extrapolate data from multiple displays and draw conclusions based on data analysis. They determine combinations and permutations by constructing sample spaces and determine experimental and theoretical probability of compound independent events.	Eighth grade students at the novice level in mathematics extrapolate information from data displays. They determine combinations and permutations by constructing sample spaces and determine experimental and theoretical probability of simple events.
	Objectives	Students will
	M.O.8.5.1	determine and explain whether a real-world situation involves permutations or combinations, then use appropriate technology to solve the problem.
	M.O.8.5.2	compare the experimental and theoretical probability of a given situation (including compound probability of a dependent and independent event).
	M.O.8.5.3	create and extrapolate information from multiple-bar graphs, box and whisker plots, and other data displays using appropriate technology.
	M.O.8.5.4	analyze problem situations, games of chance, and consumer applications using random and non-random samplings to determine probability, make predictions, and identify sources of bias.
	M.O.8.5.5	draw inferences, make conjectures and construct convincing arguments involving different effects that changes in data values have on measures of central tendency · misuses of statistical or numeric information, based on data analysis of same and different sets of data.