ࡱ> TVMNOPQRS bjbjVV s<<mUDx x OOOCCC|CEG+#+#:e#e#e#I(V($(FFFFFFF9IKFO*''**Fe#e#JFV2V2V2*Le#"e#FV2*FV2V2?hr"Ae#KEC$+N@FG0EG^@L+DL "A"ABLOdAp(Z1)@V2q)4)3(((FF81(((EG****L(((((((((x :  Version 2.0 Mathematics Grade- and Course-Level Expectations Note: This April, 2008 revisions and updates to the March 2007 version 2.0 GLEs includes: a.) Minor language revisions b.) Updated coding of local and state assessed GLEs and CLEs c.) Integrated Math II and III Course Level ExpectationsThe Mathematics Grade and Course Level Expectations outline related ideas, concepts, skills and procedures that form the foundation for understanding and learning mathematics. They provide a framework to bring focus to teaching, learning, and assessing mathematics. The Grade Level Expectations (GLEs) in grades K-8 specify mathematical content that students need to understand deeply and thoroughly for future mathematics learning. The Course Level Expectations (CLEs) for Algebra I, Geometry, and Algebra II, as well as Integrated Math II and Integrated Math III, outline mathematics expectations for students enrolled in both traditional and integrated mathematics programs. Since the Outstanding Schools Act of 1993, several documents have been developed prior to the 2004 K-12 Grade Level Expectations to aid Missouri school districts in creating curriculum that will enable all students to achieve their maximum potential. Those include: The Show-Me Standards which identify broad content knowledge and process skills for all students to be successful as they continue their education, enter the workforce, and assume civic responsibilities The Framework for Curriculum Development which provides districts with a frame for building curricula using the Show-Me Standards as a foundation The Assessment Annotations for the Curriculum Frameworks which identify content and processes that should be assessed at the local and state level in grades 4, 8, and 10 mathematics Essential content, aligned to state and national documents included in the Grade and Course Level Expectations should be addressed in contexts that promote problem solving, reasoning, communication, making connections, and designing and analyzing representations. Each Grade and Course Level Expectation is aligned to the Show-Me Content and Process Standards (1996). In addition, a Depth-of-Knowledge level has been assigned to each grade or course level expectation. The Depth of Knowledge identifies the highest level at which the expectation will be assessed, based upon the demand of the GLE. Depth-of-Knowledge levels include: Level 1-recall; Level 2-skill/concept; Level 3-strategic thinking; and Level 4-extended thinking. Expectations coded with an asterisk *, indicate that it should be assessed at the local level. Those with no asterisk, indicate an expectation that will be assessed at the state level on a 3rd 8th grade MAP Assessment or End-of-Course Exam. It is essential to include all expectations in your course or grade level curriculum, as they are important components in the understanding and learning of mathematics. Sources: College Board Standards for College Success: Mathematics and Statistics (College Board, 2006). Curriculum Focal Points for Prekindergarten through Grade 8 Mathematics (National Council of Teachers of Mathematics, 2007); Indicators of College Readiness within Missouris Two-Year Colleges (Missouri Development Education Consortium); Depth-of-Knowledge Levels (Norman Webb); Mathematics Engineering Technology & Science (METS) Alliance Report (2006); Principles and Standards for School Mathematics (National Council of Teachers of Mathematics, 2000); Show-Me Standards (Missouri Department of Elementary and Secondary Education). 1. Understand numbers, ways of representing numbers, relationships among numbers and number systemsKindergartenGrade 1Grade 2Grade 3Grade 4Grade 5Grade 6Grade 7Grade 8 A*rote count to 100 and recognize numbers up to 31 *read, write, and compare whole numbers less than 100 *read, write, and compare whole numbers less than 1000 read, write and compare whole numbers up to 10,000 read, write and compare and whole numbers less than 100,000 *read, write and compare whole numbers less than 1,000,000, unit fractions and decimals to hundredths (including location on the number line) apply and understand whole numbers to millions, fractions and decimals to the thousandths (including location on the number line)compare and order all positive rational numbers and find their approximate location on a number line *compare and order all rational numbers including percents, and find their approximate location on a number line Read, write and compare numbersDOK111111111STMA 5 1.10MA 5 1.10MA 5 1.10MA 5 1.10MA 5 1.10MA 5 1.10MA 5 1.10MA 5 1.10MA 5 1.10B*recognize of a shape *recognize and of a shape *recognize unit fractions of a shape *represents halves, thirds and fourths *use models, benchmarks (0, 1/2 and 1) and equivalent forms to judge the size of fractions recognize and generate equivalent forms of commonly used fractions and decimalsrecognize and generate equivalent forms of fractions, decimals and benchmark percents recognize and generate equivalent forms of fractions, decimals and percentsuse fractions, decimals and percents to solve problemsRepresent and use rational numbersDOK111122222STMA 5 1.10MA 5MA 5 1.10MA 5 1.10MA 5 1.10MA 5 1.10MA 5 1.10MA 5 1.10MA 5 3.3C*use concrete objects to compose and decompose values up to 10*compose or decompose whole numbers up to 20 using multiple strategies such as known facts, doubles and close to doubles, tens, and one place value *compose or decompose numbers by using a variety of strategies, such as using known facts, tens place value or landmark numbers to solve problems recognize equivalent representations for the same number and generate them by decomposing and composing numbers including expanded notation recognize equivalent representations for the same number and generate them by decomposing and composing numbers *recognize equivalent representations for the same number and generate them by decomposing and composing numbers, *recognize equivalent representations for the same number and generate them by decomposing and composing numbers*recognize equivalent representations for the same number and generate them by decomposing and composing numbers, including exponential notation *recognize equivalent representations for the same number and generate them by decomposing and composing numbers, including scientific notation Compose and decompose numbersDOK222222222STMA 1 1.6MA 1 1.6MA 1 1.6MA 1 1.6MA 1 1.6MA 5 1.6MA 5 1.6MA 5 1.6MA 5 1.6 1. Understand numbers, ways of representing numbers, relationships among numbers and number systems -- continuedKindergartenGrade 1Grade 2Grade 3Grade 4Grade 5Grade 6Grade 7Grade 8D*skip count by 2s, 5s and 10s*skip count by multiples of numbers less than 10classify numbers by their characteristics, including odd and even classify and describe numbers by their characteristics, including odd, even, multiples and factors *describe numbers according to their characteristics, including whole number common factors and multiples, prime or composite, and square numbers Classify and describe numeric relationshipsDOK11122STMA 5 1.6MA 5 1.6MA 5 1.6MA 5 1.10MA 5 1.10 2. Understand meanings of operations and how they relate to one anotherKindergartenGrade 1Grade 2Grade 3Grade 4Grade 5Grade 6Grade 7Grade 8A*represent/ model a given situation involving addition and subtraction of whole numbers using pictures, objects, or symbols *represent/ model a given situation involving two-digit whole number addition or subtraction *represent/ model a given situation in- Volving multi- plication and related division using various models includ- ing sets, arrays, areas, repeated addition/sub-traction, sharing and partitioning *represent and recognize multiplication and related division using various models, including equal intervals on the number line, equal size groups, distributive property, etc. represent and recognize division using various models, including quotative and partitiveRepresent operationsDOK22222STMA 1 1.10MA 1 1.10MA 1 1.0MA 1 1.10MA 1 1.10B*describe the effects of adding and subtracting whole numbers as well as the relationship between the two operationsdescribe the effects of multiplying and dividing whole numbers as well as the relationship between the two operations*describe the effects of addition and subtraction on fractions and decimalsdescribe the effects of multiplication and division on fractions and decimals *describe the effects of all operations on rational numbers including integersDescribe effects of operationsDOK222222STMA 1 1.10MA 1 1.10MA 1 1.10MA 1 1.10MA 1 1.10MA 1 1.10C*apply properties of operations (including order of operations) to positive rational numbersapply properties of operations (including order of operations) to positive rational numbers and integersapply properties of operations to all rational numbers including order of operations and inverse operationsApply properties of operationsDOK222STMA 1 1.10MA 1 1.10MA 1 1.10 2. Understand meanings of operations and how they relate to one another -- continuedKindergartenGrade 1Grade 2Grade 3Grade 4Grade 5Grade 6Grade 7Grade 8Didentify square and cubic numbers and determine whole number roots and cubes*approximate the value of square roots to the nearest whole numberApply operations on real and complex numbersDOK11STM 5 1.6MA 5 1.6 3. Compute fluently and make reasonable estimates KindergartenGrade 1Grade 2Grade 3Grade 4Grade 5Grade 6Grade 7Grade 8A*describe or represent the mental strategy used to compute addition and subtraction problems*describe or notate the mental strategy used to compute addition or subtraction of whole numbers, including 2-digit numbers *represent a mental strategy used to compute a given multiplication problem up to 9 x 9*represent a mental strategy used to compute a given multiplication problem (up to 2-digit by 2-digit multiple of) *describe a mental strategy used to compute a given division problem, where the quotient is a multiple of 10 and the divisor is a 1-digit number (e.g., 350 /7) Describe or represent mental strategiesDOK22222STMA 1 3.2MA 1 3.2MA 1 3.2MA 1 3.2MA 1 3.2B*connect number words (orally) and quantities they represent*use strategies to develop fluency with basic number relationships of addition and subtraction for sums up to 20*demonstrate fluency including quick recall with basic number relationships of addition and subtraction for sums up to 20use strategies to develop fluency with basic number relationships (9 X 9) of multiplication and divisiondemonstrate fluency with basic number relationships (12 X 12) of multiplication and related division factsdemonstrate fluency with efficient procedures for adding and subtracting decimals and fractions (with unlike denominators) and division of whole numbersDevelop and demonstrate fluencyDOK111111STMA 1 1.10MA.1 1.6MA.1 1.6MA.1 1.6MA.1 1.6MA 1 1.6C*apply and describe the strategy used to solve addition or subtraction problems*apply and describe the strategy used to compute 2-digit addition or subtraction problems with regroupingapply and describe the strategy used to compute up to 3-digit addition or subtraction problemsapply and describe the strategy used to compute a given multiplication of 2-digit by 2-digit numbers and related division factsapply and describe the strategy used to compute a division problem up to a 3- digit by 2-digit and addition and subtraction of fractions and decimalsmultiply and divide positive rational numbersapply all operations on rational numbers including integersCompute problemsDOK2222212STMA 1 3.2MA 1 3.2MA 1 3.2MA 1 3.2MA 1 3.2MA 1 3.1MA 1 3.1 3. Compute fluently and make reasonable estimates -- continuedKindergartenGrade 1Grade 2Grade 3Grade 4Grade 5Grade 6Grade 7Grade 8D*estimate sums and differences of whole numbersestimate and justify sums and differences of whole numbers estimate and justify products of whole numbersestimate and justify products, and quotients of whole numbers and sums differences of decimals and fractions*estimate and justify the results of multiplication and division of positive rational numbers *estimate and justify the results of all operations on rational numbersEstimate and justify solutionsDOK333333STMA 1 3.2MA 1 3.2MA 1 3.2MA 1 3.2MA 1 3.2MA 1 3.2Esolve problems using ratios and ratessolve problems involving proportions, such as scaling and finding equivalent ratiosUse proportional reasoningDOK22STMA 1 3.2MA 1 3.2 1. Understand patterns, relations and functionsKindergartenGrade 1Grade 2Grade 3Grade 4Grade 5Grade 6Grade 7Grade 8A*recognize or repeat sequences of sounds or shapes *extend patterns of sound, shape, motion or a simple numeric pattern *describe and extend simple numeric patterns and change from one representation to another extend geometric (shapes) and numeric patterns to find the next term describe geometric and numeric patterns make and describe generalizations about geometric and numeric patternsRecognize and extend patternsDOK222222STMA 4 1.6MA 4 1.6MA 4 1.6MA 4 1.6MA 4 1.6MA 4 1.6B*create and continue patterns*describe how simple repeating patterns are generated *describe how simple growing patterns are generated represent patterns using words, tables or graphs analyze patterns using words, tables and graphs represent and analyze patterns using words, tables and graphs represent and describe patterns with tables, graphs, pictures, symbolic rules or words analyze patterns represented graphically or numerically with words or symbolic rules, including recursive notationgeneralize patterns represented graphically or numerically with words or symbolic rules, using explicit notationCreate and analyze patternsDOK222233232STMA 4 1.6MA 4 1.6MA 4 1.6MA 4 1.6MA 4 1.6MA 4 1.6MA 4 1.6MA 4 1.6MA 4 1.6C*compare various forms of representations to identify patternscompare and contrast various forms of representations of patterns compare and contrast various forms of representations of patterns Classify objects and representationsDOK233STMA 4 1.6MA 4 1.6MA 4 1.6 1. Understand patterns, relations and functions -- continuedKindergartenGrade 1Grade 2Grade 3Grade 4Grade 5Grade 6Grade 7Grade 8D  *identify functions as linear or nonlinear from tables or graphsidentify functions as linear or nonlinear from tables, graphs or equationsidentify functions as linear or nonlinear from tables, graphs or equations Identify and compare functionsDOK111STMA 4 1.6MA 4 1.6MA 4 1.6EDescribe the effects of parameter changesDOKST 2. Represent and analyze mathematical situations and structures using algebraic symbolsKindergartenGrade 1Grade 2Grade 3Grade 4Grade 5Grade 6Grade 7Grade 8A*using addition or subtraction, represent a mathematical situation as an expression or number sentence *using addition or subtraction, represent a mathematical situation as an expression or number sentence using all operations, represent a mathematical situation as an expression or number sentence using all operations, represent a mathematical situation as an expression or number sentenceusing all operations, represent a mathematical situation as an expression or number sentence using a letter or symbol use symbolic algebra to represent unknown quantities in expressions or equations and solve one-step equationsuse symbolic algebra to represent unknown quantities in expressions or equations and solve linear equations with one variableuse symbolic algebra to represent and solve problems that involve linear relationshipsRepresent mathematical situationsDOK22222223STMA 4 1.10MA 4 1.10MA 4 1.10MA 4 1.10MA 4 1.10MA 4 3.3MA 4 3.3MA 4 3.3B*apply the commutative and associative properties of addition to whole numbers *solve problems with whole numbers using the commutative and associative properties of additionuse the commutative, distributive and associative properties for basic facts of whole numbersuse the commutative, distributive and associative properties of addition and multiplication for multidigit numbers*use the commutative, distributive and associative properties for fractions and decimalsuse the commutative, distributive and associative properties to generate equivalent forms for simple algebraic expressionsuse properties to generate equivalent forms for simple algebraic expressions that include positive rationals and integers use properties to generate equivalent forms for simple algebraic expressions that include all rationals Describe and use mathematical manipulationDOK22222222STMA 4 1.10MA 4 3.2MA 4 3.2MA 4 3.2MA 4 3.2MA 4 3.2MA 4 3.2MA 4 3.2 2. Represent and analyze mathematical situations and structures using algebraic symbols -- continuedKindergartenGrade 1Grade 2Grade 3Grade 4Grade 5Grade 6Grade 7Grade 8CUtilize equivalent formsDOKSTDUtilize systemsST 3. Use mathematical models to represent and understand quantitative relationshipsKindergartenGrade 1Grade 2Grade 3Grade 4Grade 5Grade 6Grade 7Grade 8A*model situations that involve whole numbers, using pictures, objects or symbols*model situations that involve the addition of whole numbers, using pictures, objects or symbols *model situations that involve addition and subtraction of whole numbers, using pictures, objects or symbols *model problem situations, including multiplication with objects or drawings *model problem situations, using representations such as graphs, tables or number sentences model problem situations and draw conclusions, using representations such as graphs, tables or number sentence model and solve problems, using multiple representations such as tables, expressions and one-step equations model and solve problems, using multiple representations such as graphs, tables, expressions, and linear equationsmodel and solve problems, using multiple representations such as graphs, tables, and linear equationsUse mathematical modelsDOK222223222STMA 1 1.6MA 1 1..6MA 1 1.6MA 4 1.6MA 4 1.6MA 4 1.6MA 4 3.6MA 4 1.6,3.6MA 4 3.6 4. Analyze change in various contextsKindergartenGrade 1Grade 2Grade 3Grade 4Grade 5Grade 6Grade 7Grade 8A*describe qualitative change, such as students growing taller *describe quantitative change, such as students growing two inches in a year *describe mathematical relationships in terms of constant rates of change*identify, model and describe situations with constant or varying rates of change *construct and analyze representations to compare situations with constant or varying rates of change compare situations with constant or varying rates of change analyze the nature of changes (including slope and intercepts) in quantities in linear relationships Analyze changeDOK2223333STMA 4 1.6MA 4 1.6MA 4 1.6MA 4 1.6MA 4 1.6MA 4 1.6MA 4 1.6 1. Analyze characteristics and properties of two- and three-dimensional geometric shapes and develop mathematical arguments about geometric relationshipsKindergartenGrade 1Grade 2Grade 3Grade 4Grade 5Grade 6Grade 7Grade 8A*identify and describe 2- and 3-dimensional shapes using physical models (circle, rhombus, rectangle, triangle, sphere, rectangular prism, cylinder, pyramid) that represent shapes in their environment *identify, name and describe 2- and 3-dimensional shapes using physical models (circle, triangle, trapezoid, rectangle, rhombus, sphere, rectangular prism, cylinder, pyramid)*describe attributes and parts of 2- and 3-dimensional shapes (circle, triangle, trapezoid, rectangle, rhombus, sphere, rectangular prism, cylinder, pyramid)compare and analyze 2- dimensional shapes by describing their attributes (circle, rectangle, rhombus, trapezoid, triangle)name and identify properties of 1-, 2- and 3-dimensional shapes and describe the attributes of 2- and 3-dimensional shapes using appropriate geometric vocabulary (rectangular prism, cylinder, pyramid, sphere, cone, parallelism, perpendic-ularity)*analyze and classify 2- and 3-dimensional shapes by describing the attributes identify similar and congruent shapes *identify the 2-diimensional cross-section of a 3-dimensional shape*describe, classify and generalize relationships between and among types of a) 2-dimensional objects and b) 3- dimensional objects using their defining properties including Pythagorean Theorem Describe and use geometric relationshipsDOK222222123STMA 2 1.10MA 2 1.10MA 2 1.10MA 2 1.10MA 2 1.10MA 2 1.10MA 2 1.10MA 2 1.10MA 2 1.6Bdescribe relationships between corresponding sides, corresponding angles and corresponding perimeters of similar polygonsApply geometric relationshipsDOK2STMA 2 1.6 1. Analyze characteristics and properties of two- and three-dimensional geometric shapes and develop mathematical arguments about geometric relationships continuedKindergartenGrade 1Grade 2Grade 3Grade 4Grade 5Grade 6Grade 7Grade 8C*use models to compose and decompose 2-dimensional shapes *predict the results of putting together or taking apart 2- and 3- dimensional shapes*describe the results of subdividing, combining and transforming shapespredict and justify the results of subdividing, combining and transforming shapesCompose and decompose shapesDOK2323STMA 2 1.6MA 2 1.6MA 2 1.6MA 2 1.6 2. Specify locations and describe spatial relationships using coordinate geometry and other representational systemsKindergartenGrade 1Grade 2Grade 3Grade 4Grade 5Grade 6Grade 7Grade 8A*describe, name and interpret relative positions in space (above, below, front, behind) *describe, name and interpret relative positions in space (left, right) *identify locations with simple relationships on a map (coordinate system) *describe location using common language and geometric vocabulary (forward, back, left, right, north, south, east, west) *describe movement using common language and geometric vocabulary (forward, back, left, right, north, south, east, west) *use coordinate systems to specify locations, describe paths and find the distance between points along horizontal and vertical lines use coordinate systems to construct geometric shapes use coordinate geometry to construct and identify geometric shapes in the coordinate plane using their properties use coordinate geometry to analyze properties of right triangles and quadrilaterals (including the use of the Pythagorean Theorem)Use coordinate systemsDOK221222222STMA 2 1.10MA 2 1.10MA 2 3.1MA 2 1.10MA 2 3.3MA 2 1.10MA 2 1.10MA 2 3.2MA 2 3.2 3. Apply transformations and use symmetry to analyze mathematical situationsKindergartenGrade 1Grade 2Grade 3Grade 4Grade 5Grade 6Grade 7Grade 8A*use manipulatives to recognize from different perspectives and orientations models of slides and turns*use manipulatives to model flips*use manipulatives to model slides and turns determine if two objects are congruent through a slide, flip or turn predict the results of sliding/ translating, flipping/ reflecting or turning/ rotating around the center point of a polygon *predict, draw and describe the results of sliding/ translating, flipping/ reflecting and turning/ rotating around a center point of a polygon *describe the transformation from a given pre-image using the terms reflection/flip, rotation/turn, and translation/ slidereposition shapes under formal transformations such as reflection, rotation and translation Use transformations on objectsDOK22223332STMA 2 1.6MA 2 1.6MA 2 1.6MA 2 3.2MA 2 3.6MA 2 3.6MA 2 3.3MA 2 3.3Bdescribe the relationship between the scale factor and the perimeter of the image using a dilation (contractions- magnifications; stretching/ shrinking) describe the relationship between the scale factor and the area of the image using a dilation (stretching/ shrinking) Use transformations on functionsDOK22STMA 2 3.6MA 2 3.6C*recognize shapes that have symmetry*create shapes that have symmetryidentify lines of symmetry in polygonscreate a figure with multiple lines of symmetry and identify the lines of symmetry identify polygons and designs with rotational symmetry*create polygons and designs with rotational symmetry*determine all lines of symmetry of a polygons*identify the number of rotational symmetries of regular polygons Use symmetryDOK12121211STMA 2 1.10MA 2 1.10MA 2 1.10MA 2 1.10MA 2 1.6MA 2 1.6MA 2 1.6MA 2 1.6 4. Use visualization, spatial reasoning and geometric modeling to solve problemsKindergartenGrade 1Grade 2Grade 3Grade 4Grade 5Grade 6Grade 7Grade 8A*given the picture of a prism, identify the shapes of the faces given a net of a prism or cylinder, identify the 3-dimensional shape *use spatial visualization to identify isometric representations of mat plans *use spatial visualizations to identify various 2-dimensional views of isometric drawings create isometric drawings from a given mat plan Recognize and draw three-dimensional representationsDOK12223STMA 2 3.3MA 2 3.3MA 2 3.3MA 2 3.3MA 2 3.3Bdraw or use visual models to represent and solve problems draw or use visual models to represent and solve problems draw or use visual models to represent and solve problems Draw and use visual modelsDOK333STMA 2 3.3MA 2 3.3MA 2 3.3 1. Understand measurable attributes of objects and the units, systems and processes of measurementKindergartenGrade 1Grade 2Grade 3Grade 4Grade 5Grade 6Grade 7Grade 8A*compare and order objects according to their size or weight*select the appropriate tool for the attribute being measured (size, temperature, time, weight) *select an appropriate unit and tool for the attribute being measured (size, temperature, time, weight) and to the nearest inch, centimeter, degree, hour and pound*identify, justify and use the appropriate unit of measure (linear, time, weight)*identify and justify the unit of linear measure including perimeter and (customary metric)*identify and justify the unit of measure for area (customary and metric)identify and justify the unit of measure for area and volume (customary and metric)*identify and justify the unit of measure for volume (customary and metric)Determine unit of measurementDOK22233333STMA 2 1.8MA 2 3.1MA 2 3.1MA 2 3.1MA 2 3.1MA 2 3.1MA 2 3.1MA 2 3.1Bidentify equivalent linear measures within a system of measurement identify the equivalent weights and equivalent capacities within a system of measurement identify the equivalent area and volume measures within a system of measurement (e.g., sq ft. to sq in, m3 to c m3)Identify equivalent measuresDOK111STMA 2 1.6MA 2 1.6MA 2 1.6C*describe passage of time using terms such as today, yesterday, tomorrow *tell time to the nearest half hour *tell time to the nearest one fourth (quarter) hour tell time to the nearest five minutestell time to the nearest minute*solve problems involving elapsed time (hours and minutes)*solve problems involving addition and subtraction of time (hours, minutes and seconds) Tell and use units of timeDOK2111122STMA 2 3.1MA 2 1.10MA 2 1.10MA 2 1.10MA 2 1.10MA 5 3.1MA 5 3.1 1. Understand measurable attributes of objects and the units, systems and processes of measurement -- continuedKindergartenGrade 1Grade 2Grade 3Grade 4Grade 5Grade 6Grade 7Grade 8D*identify and know the value of a penny, nickel, dime, and quarter*count money to a dolllar, including half dollars *make change from a dollardetermine change from $5.00 and add and subtract money values to $5.00determine change from $10.00 and add and subtract money values to $10.00Count and compute moneyDOK22222STMA 1 1.10MA 1 1.10MA 1 1.10MA 1 1.10MA 1 1.10 2. Apply appropriate techniques, tools and formulas to determine measurementsKindergartenGrade 1Grade 2Grade 3Grade 4Grade 5Grade 6Grade 7Grade 8A*measure objects by comparison of lengths (shorter, same, longer) *use repetition of a single unit to measure something larger than the unit, (e.g. length of book with paper clips) *use standard units of measure (cm, inch) and the inverse relationships between the size and number of units *use a referent for measures to make comparisons and estimates *select and use benchmarks to estimate measurements (linear, capacity, weight) Use standard or non-standard measurementDOK11222STMA 2 1.6MA 2 1.10MA 2 1.6MA 2 1.6MA 2 1.6B*select and use benchmarks to estimate measurements of 0-, 45- (acute), 90- (right) greater than 90 (obtuse) degree angles*identify and justify an angle as acute, obtuse, straight, or right*use tools to measure angles to the nearest degree and classify the angle as acute, obtuse, right, straight, or reflexsolve problems of angle measure, including those involving triangles and parallel lines cut by a transversalUse angle measurementDOK2211STMA 2 1.6MA 2 3.2MA 2 3.2MA 2 3.2Cdetermine the perimeter of polygons determine and justify areas of polygons and non-polygonal regions imposed on a rectangular grid determine volume by finding the total number of the same size units needed to fill a space without gaps or overlapssolve problems involving the area or perimeter of polygons solve problems involving circumference and/or area of a circle and surface area/volume of a rectangular or triangular prism, or cylinderApply geometric measurementsDOK23222STMA 2 1.10MA 2 1.10MA 2 1.10MA 2 1.10MA 2 1.10 2. Apply appropriate techniques, tools and formulas to determine measurements -- continuedKindergartenGrade 1Grade 2Grade 3Grade 4Grade 5Grade 6Grade 7Grade 8D analyze precision and accuracy in measurement situations and determine number of significant digits Analyze precisionDOK2STMA 2 1.7Econvert from one unit to another within a system of linear measurement (customary and metric) convert from one unit to another within a system of measurement (mass and weight) convert from one unit to another within a system of measurement (capacity) and convert square or cubic units within the same system of measurementUse relationships within a measurement systemDOK111STMA 2 1.6MA 2 1.6MA 2 1.6 1. Formulate questions that can be addressed with data and collect, organize and display relevant data to answer themKindergartenGrade 1Grade 2Grade 3Grade 4Grade 5Grade 6Grade 7Grade 8A*pose questions and gather data about themselves and their surroundings *pose questions and gather data about themselves and their surroundings *design investigations to address a given question collect data using observations, surveys and experiments evaluate data-collection methods formulate questions, design studies and collect data about a characteristic Formulate questionsDOK333233STMA 3 1.2MA 3 1.2MA 3 1.2MA 3 1.2MA 3 1.2MA 3 1.2B*sort items according to their attributes *sort and classify items according to their attributes *sort and classify items according to their attributes and organize data about the items Classify and organize dataDOK233STMA 2 1.8MA 2 1.8MA 3 1.8C*create graphs using physical objects*represent one-to-one correspondence data using pictures and bar graphs*represent one- to-many correspondence data using pictures and bar graphsread and interpret information from line plots and graphs (bar, line, pictorial) create tables or graphs to represent categorical and numerical data (including line plots)*describe methods to collect, organize and represent categorical and numerical data interpret circle graphs; create and interpret stem-and-leaf plots select, create and use appropriate graphical representation of data, including circle graphs, histogramsselect, create and use appropriate graphical representation of data (including scatter plots) and box plots (box and whiskers)Represent and interpret dataDOK222222222STMA 3 1.8MA 3 1.8MA 3 1.8MA 3 1.10MA 3 1.8MA 3 1.2MA 3 1.8MA 3 1.8MA 3 1.8 2. Select and use appropriate statistical methods to analyze dataKindergartenGrade 1Grade 2Grade 3Grade 4Grade 5Grade 6Grade 7Grade 8A*describe the shape of data and analyze it for patterns *describe important features of the data set compare related data sets find the range and measures of center, including median, mode and mean find, use and interpret measures of center and spread, including ranges find, use and interpret measures of center, outliers and spread, including range and interquartile range Describe and analyze dataDOK222222STMA 3 1.6MA 3 1.6MA 3 1.6MA 3 1.10MA 3 1.10MA 3 1.10Bcompare different representations of the same data and evaluate how well each representation shows important aspects of the dataCompare data representationsDOK3STMA 3 1.10CRepresent data algebraicallyDOKST 3. Develop and evaluate inferences and predictions that are based on dataKindergartenGrade 1Grade 2Grade 3Grade 4Grade 5Grade 6Grade 7Grade 8A*discuss events related to students' experiences as likely or unlikely *given a set of data, propose and justify conclusions that are based on the datagiven a set of data make and justify predictionsuse observations about differences between 2 samples to make conjectures about the populations from which the samples were taken use observations about differences between samples to make conjectures about the populations from which the samples were taken make conjectures about possible relationships between 2 characteristics of a sample on the basis of scatter plots of the data and approximate lines of fit Develop and evaluate inferencesDOK233333STMA 3 3.5MA 3 3.5MA 3 3.5MA 3 3.5MA 3 3.5MA 3 3.5BAnalyze basic statistical techniquesDOKST 4. Understand and apply basic concepts of probabilityKindergartenGrade 1Grade 2Grade 3Grade 4Grade 5Grade 6Grade 7Grade 8A*describe the degree of likelihood of events using such words as certain, equally likely and impossible use a model (diagrams, list, sample space, or area model) to illustrate the possible outcomes of an event use models to compute the probability of an event and make conjectures (based on theoretical probability) about the results of experimentsApply basic concepts of probabilityDOK223STMA 3 1.10MA 3 1.10, 3.2MA 3 3.8BUse and describe compound eventsDOKST     April, 2008  PAGE \* MERGEFORMAT 2 Number and Operations Algebraic Relationships PAGE  Geometric and Spatial Relationships PAGE  Measurement PAGE   Data and Probability >?JKWu1 2 6 f Z [  i ~ D \ %6Jt²Бvvi_iivvvvvhA_OJQJ^JhV@hA_OJQJ^JhV@h6OJQJ^JhV@hOJQJ^J hHUh pCJ(OJQJ^JaJ(hHUh p5>*OJQJ^JhHUhA_5>*OJQJ^JhHUhA_5OJQJ^JhHUh p5OJQJ^J h ph pCJ$OJQJ^JaJ$ h phCJ$OJQJ^JaJ$%?1 2 Gsnnnff & Fgdgdnkd$$IfTl_4/5 t0644 laytHUT 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