MATHEMATICS Grade 8 Standards Met by Nature Net Sites

• A.          MATHEMATICAL PROCESSES

• B.          NUMBER OPERATIONS AND RELATIONSHIPS

• C.          GEOMETRY

• D.          MEASUREMENT

• E.          STATISTICS AND PROBABILITY

• F.         ALGEBRAIC RELATIONSHIPS

 A.8.1    Use reasoning abilities to

            •      evaluate information

            •      perceive patterns

            •      identify relationships

            •      formulate questions for further exploration

            •      evaluate strategies

            •      justify statements

            •     test reasonableness of results

            •      defend work

            [ALNC; BHNC+; CM*+; ICF+; JSF; MKE*; OBG+; OWP; UWA+]

 A.8.2      Communicate logical arguments clearly to show why a result makes sense

            [ALNC*+; BHNC*; CM*+; ICF+; JSF*; MKE*; OBG+; OWP*]

 A.8.3    Analyze nonroutine* problems by modeling*, illustrating, guessing, simplifying, generalizing, shifting to another point of view, etc.

            [ALNC*+; BHNC*; CM*+; ICF+; MKE*; OBG+]

 A.8.4      Develop effective oral and written presentations that include

            •      appropriate use of technology

            •     the conventions of mathematical discourse (e.g., symbols, definitions, labeled drawings)

            •      mathematical language

            •      clear organization of ideas and procedures

            •      understanding of purpose and audience

            [ALNC+; BHNC*; CM*+; ICF+; MKE+]

 A.8.5    Explain mathematical concepts, procedures, and ideas to others who may not be familiar with them

            [ALNC+; BHNC*; CM*; ICF+; MKE]

 A.8.6    Read and understand mathematical texts and other instructional materials and recognize mathematical ideas as they appear in other contexts

            [BHNC*; ICF+; MKE]

 B.8.1    Read, represent, and interpret various rational numbers* (whole numbers*, integers*, decimals, fractions, and percents) with verbal descriptions, geometric models*, and mathematical notation (e.g., expanded*, scientific*, exponential*)

            [ALNC*; CM*; ICF+; MKE*]

 B.8.2      Perform and explain operations on rational* numbers (add, subtract, multiply, divide, raise to a power, extract a root, take opposites and reciprocals, determine absolute value)

            [BHNC*; ICF+]

B.8.3      Generate and explain equivalencies among fractions, decimals, and percents

            [ALNC*; ICF+]

B.8.4    Express order relationships among rational numbers using appropriate symbols

            (>, <, ³, £, ¹)

            [ALNC*; MKE*]

 B.8.5    Apply proportional thinking in a variety of problem situations that include, but are not limited to

            •      ratios and proportions (e.g., rates, scale drawings*, similarity*)

            •      percents, including those greater than 100 and less than one (e.g., discounts, rate of increase or decrease, sales tax)

            [ALNC*+; BHNC*; ICF+; MKE*; UWA*]

 B.8.6    Model* and solve problems involving number-theory concepts such as

            •      prime* and composite numbers

            •      divisibility and remainders

            •      greatest common factors

            •      least common multiples

 B.8.7    In problem-solving situations, select and use appropriate computational procedures with rational numbers such as

            •      calculating mentally

            •      estimating

            •      creating, using, and explaining algorithms* using technology (e.g., scientific calculators, spreadsheets)

            [ALNC*; BHNC*; CM*; ICF+; MKE*]

 C.8.1         Describe special and complex two- and three-dimensional figures (e.g., rhombus,                   polyhedron, cylinder) and their component parts (e.g., base, altitude, and slant                   height) by

            •    naming, defining, and giving examples

            •      comparing, sorting, and classifying them

            •      identifying and contrasting their properties (e.g., symmetrical*, isosceles, regular)

·         explaining how these figures are related to objects in the environment

            [ALNC*+; BHNC*; CM+; OBG+]

C.8.2    Identify and use relationships among the component parts of special and complex two- and three-dimensional figures (e.g., parallel sides, congruent* faces)

            [ALNC*; OBG+]

C.8.3    Identify three-dimensional shapes from two-dimensional perspectives and draw two-dimensional sketches of three-dimensional objects preserving their significant features

            [ALNC*; OBG+]

C.8.4     Perform transformations* on two-dimensional figures and describe and analyze the             effects of the transformations on the figures

            [ALNC*; OBG+]

C.8.5    Locate objects using the rectangular coordinate system*

            [ALNC*; BHNC*; CM*]

D.8.1    Identify and describe attributes* in situations where they are not directly* or easily measurable (e.g., distance, area of an irregular figure, likelihood of occurrence)

            [ALNC*+; BHNC*; CM*; OBG+; UWA*]

D.8.2      Demonstrate understanding of basic measurement facts, principles, and techniques including the following

            •      approximate comparisons between metric and US Customary units (e.g., a liter and a quart are about the same; a kilometer is about six-tenths of a mile)

            •      knowledge that direct measurement* produces approximate, not exact, measures

            •     the use of smaller units to produce more precise measures

            [ALNC*+; BHNC*; MKE*]

D.8.3      Determine measurement directly* using standard units (metric and US Customary) with these suggested degrees of accuracy

            •      lengths to the nearest mm or 1/16 of an inch

            •      weight (mass) to the nearest 0.1 g or 0.5 ounce

            •      liquid capacity to the nearest millileter

            •      angles to the nearest degree

            •      temperature to the nearest C° or F°

            •      elapsed time to the nearest second

            [ALNC*+; BHNC*; CM*; MKE*]

D.8.4    Determine measurements indirectly* using

            •      estimation

            •      conversion of units within a system (e.g., quarts to cups, millimeters to centimeters)

•      geometric formulas to derive lengths, areas, volumes of common figures (e.g., perimeter, circumference, surface area)

            •     the Pythagorean* relationship

            •      geometric relationships and properties for angle size (e.g., parallel lines and transversals; sum of angles of a triangle; vertical angles*)    

            [ALNC*+; BHNC*; CM*; MKE*; UWA*]

 E.8.1    Work with data in the context of real-world situations by

            •      formulating questions that lead to data collection and analysis

            •      designing and conducting a statistical investigation

            •      using technology to generate displays, summary statistics*, and presentations

            [ALNC*+; BHNC*; CM*+; ICF+; JSF* OBG+; OWP*; UWA+]

 E.8.2    Organize and display data from statistical investigations using

•      appropriate tables, graphs, and/or charts (e.g., circle, bar, or line for multiple sets of data)

            •      appropriate plots (e.g., line*, stem-and-leaf*, box*, scatter*)

            [ALNC*+; BHNC*; CM+; ICF+; OBG+; UWA+]

E.8.3    Extract, interpret, and analyze information from organized and displayed data by using

            •      frequency and distribution, including mode* and range*

            •      central tendencies* of data (mean* and median*)

            •      indicators of dispersion (e.g., outliers*)

            [ALNC*; CM+; OBG+; UWA+]

E.8.4    Use the results of data analysis to

            •      make predictions

            •      develop convincing arguments

            •      draw conclusions

            [ALNC*+; BHNC*; CM+; ICF+; MKE*; OBG+; UWA+]

E.8.5      Compare several sets of data to generate, test, and, as the data dictate, confirm or deny hypotheses

            [ALNC*+; CM+; MKE*; OBG+; UWA+]

E.8.6      Evaluate presentations and statistical analyses from a variety of sources for

            •      credibility of the source

            •      techniques of collection, organization, and presentation of data

            •      missing or incorrect data

            •      inferences

            •      possible sources of bias

            [ALNC*; BHNC*; CM+; OBG+; UWA+] 

E.8.7      Determine the likelihood of occurrence of simple events by

            •      using a variety of strategies to identify possible outcomes (e.g., lists, tables, tree diagrams*)

            •      conducting an experiment

•designing and conducting simulations*

            •      applying theoretical notions of probability (e.g., that four equally likely events have a 25 percent chance of happening)

            [ALNC*+; BHNC*; CM+; OBG+; UWA+]

F.8.1     Work with algebraic expressions in a variety of ways, including

            •      using appropriate symbolism, including exponents* and variables*

            •      evaluating expressions through numerical substitution

            •      generating equivalent expressions

            •      adding and subtracting expressions  

F.8.2     Work with linear and nonlinear patterns* and relationships in a variety of ways, including

            •      representing them with tables, with graphs, and with algebraic expressions, equations, and inequalities

            •      describing and interpreting their graphical representations (e.g., slope*, rate of change, intercepts*)

            •      using them as models of real-world phenomena

            •      describing a real-world phenomenon that a given graph might represent

            [ALNC*+; BHNC*; CM*+; ICF+]

F.8.3      Recognize, describe, and analyze functional relationships* by generalizing a rule that characterizes the pattern of change among variables. These functional relationships include exponential growth and decay (e.g., cell division, depreciation)

            [ALNC*+; BHNC*; CM*+; ICF+]

F.8.4     Use linear equations and inequalities in a variety of ways, including

            •      writing them to represent problem situations and to express generalizations

            •      solving them by different methods (e.g., informally, graphically, with formal properties, with technology)

            •      writing and evaluating formulas (including solving for a specified variable)

            •      using them to record and describe solution strategies

            [ALNC*+; ICF+]

F.8.5      Recognize and use generalized properties and relations, including

            •      additive and multiplicative property of equations and inequalities

            •      commutativity* and associativity* of addition and multiplication

            •      distributive* property

            •      inverses* and identities* for addition and multiplication

            •      transitive* property