ࡱ> \^[5@ Nbjbj22 (VXX$&&Zl%%%%%%%$'R*%Q   %F&q"q"q" v%q" %q"q"""N PTf .""\&0&"* *"*",0"q"4%%$  [" Massachusetts State Frameworks Number Sense and Operations for Grades 8 8.N.1Compare, order, estimate, and translate among  HYPERLINK "http://www.doe.mass.edu/frameworks/math/2000/append3.html" \l "Integer" \t "_blank" integers, fractions and mixed numbers (i.e.,  HYPERLINK "http://www.doe.mass.edu/frameworks/math/2000/append3.html" \l "Rational" \t "_blank" rational numbers), decimals, and percents. 8.N.2Define, compare, order, and apply frequently used  HYPERLINK "http://www.doe.mass.edu/frameworks/math/2000/append3.html" \l "Irrational" \t "_blank" irrational numbers, such as "2 and . 8.N.3Use ratios and  HYPERLINK "http://www.doe.mass.edu/frameworks/math/2000/append3.html" \l "Proportion" \t "_blank" proportions in the solution of problems, in particular, problems involving unit rates, scale factors, and rate of change. 8.N.4Represent numbers in  HYPERLINK "http://www.doe.mass.edu/frameworks/math/2000/append3.html" \l "Scientific" \t "_blank" scientific notation, and use them in calculations and problem situations. 8.N.5Apply number theory concepts, including prime factorization and relatively prime numbers, to the solution of problems. 8.N.6Demonstrate an understanding of absolute value, e.g., |-3| = |3| = 3. 8.N.7Apply the rules of powers and roots to the solution of problems. Extend the  HYPERLINK "http://www.doe.mass.edu/frameworks/math/2000/append3.html" \l "Order" \t "_blank" Order of Operations to include positive integer  HYPERLINK "http://www.doe.mass.edu/frameworks/math/2000/append3.html" \l "Exponent" \t "_blank" exponents and square roots. 8.N.8Demonstrate an understanding of the properties of arithmetic operations on rational numbers. Use the associative, commutative, and distributive properties; properties of the identity and inverse elements (e.g., -7 + 7 = 0; 3/4 x 4/3 = 1); and the notion of  HYPERLINK "http://www.doe.mass.edu/frameworks/math/2000/append3.html" \l "Closure" \t "_blank" closure of a subset of the rational numbers under an operation (e.g., the set of odd integers is closed under multiplication but not under addition). 8.N.9Use the inverse relationships of addition and subtraction, multiplication and division, and squaring and finding square roots to simplify computations and solve problems, e.g. multiplying by 1/2 or 0.5 is the same as dividing by 2. 8.N.10Estimate and compute with fractions (including simplification of fractions), integers, decimals, and percents (including those greater than 100 and less than 1). 8.N.11Determine when an estimate rather than an exact answer is appropriate and apply in problem situations. 8.N.12Select and use appropriate operationsaddition, subtraction, multiplication, division, and positive  HYPERLINK "http://www.doe.mass.edu/frameworks/math/2000/append3.html" \l "Integer" \t "_blank" integer exponentsto solve problems with rational numbers (including negatives). Patterns, Relations, and Algebra for Grades 8 8.P.1Extend, represent, analyze, and generalize a variety of patterns with tables, graphs, words, and, when possible, symbolic expressions. Include arithmetic and geometric  HYPERLINK "http://www.doe.mass.edu/frameworks/math/2000/append3.html" \l "Sequence" \t "_blank" progressions, e.g., compounding.8.P.2Evaluate simple algebraic expressions for given  HYPERLINK "http://www.doe.mass.edu/frameworks/math/2000/append3.html" \l "Variable" \t "_blank" variable values, e.g., 3a2 - b for a = 3 and b = 7.8.P.3Demonstrate an understanding of the identity (-x)(-y) = xy. Use this identity to simplify algebraic expressions, e.g., (-2)(-x+2) = 2x - 4.8.P.4Create and use symbolic expressions and relate them to verbal, tabular, and graphical representations.8.P.5Identify the slope of a line as a measure of its steepness and as a constant rate of change from its table of values, equation, or graph. Apply the concept of slope to the solution of problems.8.P.6Identify the roles of variables within an equation, e.g., y = mx + b, expressing y as a  HYPERLINK "http://www.doe.mass.edu/frameworks/math/2000/append3.html" \l "Function" \t "_blank" function of x with parameters m and b.8.P.7Set up and solve  HYPERLINK "http://www.doe.mass.edu/frameworks/math/2000/append3.html" \l "Linear_e" \t "_blank" linear equations and inequalities with one or two variables, using algebraic methods, models, and/or graphs.8.P.8Explain and analyze-both quantitatively and qualitatively, using pictures, graphs, charts, or equations-how a change in one variable results in a change in another variable in functional relationships, e.g., C = d, A = r2 (A as a function of r), Arectangle = lw (Arectangle as a function of l and w).8.P.9Use linear equations to model and analyze problems involving proportional relationships. Use technology as appropriate.8.P.10Use tables and graphs to represent and compare linear growth patterns. In particular, compare rates of change and x- and y-intercepts of different linear patterns. Measurement for Grades 8 8.M.1Select, convert (within the same system of measurement), and use appropriate units of measurement or scale.8.M.2Given the formulas, convert from one system of measurement to another. Use technology as appropriate.8.M.3Demonstrate an understanding of the concepts and apply formulas and procedures for determining measures, including those of area and perimeter/circumference of parallelograms, trapezoids, and circles. Given the formulas, determine the surface area and volume of rectangular prisms, cylinders, and spheres. Use technology as appropriate.8.M.4Use  HYPERLINK "http://www.doe.mass.edu/frameworks/math/2000/append3.html" \l "Ratio" \t "_blank" ratio and proportion (including scale factors) in the solution of problems, including problems involving similar plane figures and indirect measurement.8.M.5Use models, graphs, and formulas to solve simple problems involving rates, e.g., velocity and density. Data Analysis, Statistics, and Probability for Grades 8 8.D.1Describe the characteristics and limitations of a data sample. Identify different ways of selecting a sample, e.g.,  HYPERLINK "http://www.doe.mass.edu/frameworks/math/2000/append3.html" \l "Convenience" \t "_blank" convenience sampling, responses to a survey,  HYPERLINK "http://www.doe.mass.edu/frameworks/math/2000/append3.html" \l "Random_s" \t "_blank" random sampling.8.D.2Select, create, interpret, and utilize various tabular and graphical representations of data, e.g., circle graphs,  HYPERLINK "http://www.doe.mass.edu/frameworks/math/2000/append3.html" \l "Venn" \t "_blank" Venn diagrams, scatterplots, stem-and-leaf plots,  HYPERLINK "http://www.doe.mass.edu/frameworks/math/2000/append3.html" \l "Box-and-whisker" \t "_blank" box-and-whisker plotIN}~  o p t v Z [ ` v w ' ( - GH:;DEYZ_ab[\ah~CJaJh~0JCJOJQJaJjh~CJOJQJUaJh~CJOJQJaJh~0JCJOJQJaJh~J IO Wkd$$If<0!634<ap$If$a$gd~gd~N Z [ a ' KWkd$$If<0!634<ap$IfWkdz$$If<0!634<ap' ( . 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Use these notions to compare different sets of data.8.D.4Use tree diagrams, tables, organized lists, basic combinatorics (" HYPERLINK "http://www.doe.mass.edu/frameworks/math/2000/append3.html" \l "Fundamental" \t "_blank" fundamental counting principle"), and area models to compute probabilities for simple compound events, e.g., multiple coin tosses or rolls of dice.  !M"MMMMMMPNQNoNpNNNNۻh~h~0JCJOJQJaJh~0JCJOJQJaJh~CJaJh~CJOJQJaJjh~CJOJQJUaJ MMMNNNNNKFAAgd~gd~WkdL$$If<0p!634<ap$IfWkd $$If<0p!634<apNNNgd~&1h:p~/ =!"#h$%x$$If!vh55#v#v:V <6534<px$$If!vh55#v#v:V <6534<px$$If!vh55#v#v:V <6534<px$$If!vh55#v#v:V <6534<px$$If!vh55#v#v:V <6534<px$$If!vh55#v#v:V <6534<px$$If!vh55#v#v:V <6534<px$$If!vh55#v#v:V <6534<px$$If!vh55#v#v:V <6534<px$$If!vh55#v#v:V <6534<px$$If!vh55#v#v:V <6534<px$$If!vh55#v#v:V <6534<px$$If!vh55;#v#v;:V <6534<px$$If!vh55;#v#v;:V <6534<px$$If!vh55;#v#v;:V <6534<px$$If!vh55;#v#v;:V <6534<px$$If!vh55;#v#v;:V <6534<px$$If!vh55;#v#v;:V <6534<px$$If!vh55;#v#v;:V <6534<px$$If!vh55;#v#v;:V <6534<px$$If!vh55;#v#v;:V <6534<px$$If!vh55;#v#v;:V <6534<px$$If!vh55f#v#vf:V <6534<px$$If!vh55f#v#vf:V <6534<px$$If!vh55f#v#vf:V <6534<px$$If!vh55f#v#vf:V <6534<px$$If!vh55f#v#vf:V <6534<px$$If!vh55#v#v:V <6534<px$$If!vh55#v#v:V <6534<px$$If!vh55#v#v:V <6534<px$$If!vh55#v#v:V <6534<p@@@ NormalCJ_HaJmH sH tH ``2` ~ Heading 3dd@&[$\$5B*CJOJQJ\aJphDA@D Default Paragraph FontRi@R  Table Normal4 l4a (k@(No List4U`4 ~ Hyperlink >*ph*W`* ~Strong5\8o8 ~small1CJOJQJaJo(R^`"R ~ Normal (Web)dd[$\$CJOJQJaJV IOcdjZ[a'(.YZ`[\bK L S f g n KLRlmsUV\  DEK  }~9:@67=fgm(00(0p(0p0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 (00 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 (0(00 0 0 0 0 0 0 0 0 0 0 0 0 0 0 (00 0 0 0 0 0 0 0 0 0 0 0 0(0(0(00IOcdjZ[a'(.YZ`[\bK L S f g n KLRlmsUV\  DEK  }~9:@67=fgmO90Oy0Oy0Oy0 Oy0Oy0Oy0 Oy0Oy0Oy0 Oy0Oy0Oy0 Oy0Oy0Oy0 Oy0  Oy0  Oy0 Oy0  Oy0  Oy0 Oy0 Oy0 Oy0 Oy0 Oy0 Oy0 Oy0 Oy0 Oy0 Oy0 Oy0 Oy0 Oy0 Oy0 Oy0 O90'Oy0 Oy0 Oy0 Oy0 Oy0 Oy0 Oy0 Oy0 My0 My0 My0 My0 My0 My0 My0 My0  My0  My0 My0  My0  My0 My0 My0 My0 My0 My0 My0 My0 My0 My0 O90GM90GMy0 My0 My0 My0 My0 My0 My0 My0 My0 My0 My0 My0 My0 My0 My0 M90XMy0 My0 My0 My0 My0 My0 My0 My0 My0 My0 My0 My0 M90`M90XO90GO90%a!MN ( ' [lE!"MNN!"#$%)*N} o:MyvG:Da 3 ; d CLsy0&6Eg3XXXXXXXXXXXXXXXXXXXX d   =*urn:schemas-microsoft-com:office:smarttags PlaceType=*urn:schemas-microsoft-com:office:smarttags PlaceName9*urn:schemas-microsoft-com:office:smarttagsplace  02T^aceo". 9;33IOdj[a(.Z`\bL S g n C LRmsV\EK:@7=1m Pat Butler\'=~BHIOcdjZ[a'(.YZ`[\bK L S f g n KLRlmsUV\  DEK  }~9:@67=fgm@݌L`@` `@``<@`@UnknownGz Times New Roman5Symbol3& z Arial7Georgia7&  Verdana"qhȹ¹nD5nD5!h243H)?BMassachusetts State Frameworks Pat Butler Pat ButlerOh+'0 $0 L X d p|Massachusetts State Frameworksass Pat Butlertat at Normall Pat Butlert1t Microsoft Word 10.0@`4<@!e@^Pc@"enD՜.+,D՜.+,` hp  Norwell Public Schools5A Massachusetts State Frameworks Title 8@ _PID_HLINKSA\x-49:http://www.doe.mass.edu/frameworks/math/2000/append3.html Fundamental,#6:http://www.doe.mass.edu/frameworks/math/2000/append3.htmlMeasure?83:http://www.doe.mass.edu/frameworks/math/2000/append3.htmlBox-and-whiskerML0:http://www.doe.mass.edu/frameworks/math/2000/append3.htmlVenny\-:http://www.doe.mass.edu/frameworks/math/2000/append3.html Random_s:6*:http://www.doe.mass.edu/frameworks/math/2000/append3.html ConvenienceSO':http://www.doe.mass.edu/frameworks/math/2000/append3.htmlRatioi\$:http://www.doe.mass.edu/frameworks/math/2000/append3.html Linear_eFV!:http://www.doe.mass.edu/frameworks/math/2000/append3.html Function\H:http://www.doe.mass.edu/frameworks/math/2000/append3.html VariableQ\:http://www.doe.mass.edu/frameworks/math/2000/append3.html Sequence/):http://www.doe.mass.edu/frameworks/math/2000/append3.htmlInteger,*:http://www.doe.mass.edu/frameworks/math/2000/append3.htmlClosure@A:http://www.doe.mass.edu/frameworks/math/2000/append3.html Exponent^P:http://www.doe.mass.edu/frameworks/math/2000/append3.htmlOrder!0 :http://www.doe.mass.edu/frameworks/math/2000/append3.html Scientific>0 :http://www.doe.mass.edu/frameworks/math/2000/append3.html Proportion4?:http://www.doe.mass.edu/frameworks/math/2000/append3.html Irrational]M:http://www.doe.mass.edu/frameworks/math/2000/append3.html Rational/):http://www.doe.mass.edu/frameworks/math/2000/append3.htmlInteger  !"#$%&'()*+-./012356789:;<=>?@ABCDEFGHIKLMNOPQSTUVWXYZ]Root Entry Fbf_Data ,1Table4*WordDocument(VSummaryInformation(JDocumentSummaryInformation8RCompObjj  FMicrosoft Word Document MSWordDocWord.Document.89q