7th grade math pacing guide by huanghengdong

VIEWS: 9 PAGES: 22

									        7th Grade Math

                                                    Arch Ford/Northwest Arkansas Instructional Alignment
                                                                Seventh Grade Mathematics
                              AR Department of Education
 NCTM Focal    # of                                                                                                                                                 Essential
                                                                                                                                                                                      Materials/
   Point or   Times    CONTENT STANDARD/ Student Learning                          Objective                                  Task Analysis                        Vocabulary
                                                                                                                                                                                      Resources
  Connector   Tested           Expectations (SLE)                                                                                                                *teacher word


                       Enduring Understanding - Successful problem solvers possess a set of core beliefs that support their work:
                       problem solving is important, takes significant time and repeated efforts, and requires reflection.
                       Essential Question - What are the specific strategies that have wide application in attacking problems and
                       can help in problem solving?
C.7.2                  NO.3.7.2                                     Solve with and without appropriate          with and without appropriate technology:      mental computation
                       Solve, with and without appropriate          technology, multi-step problems using a     *represent multi-step problems using          technology
                       technology, multi-step problems using a      variety of methods and tools                manipulatives (including 2 or more steps)     Distributive Property
                       variety of methods and tools                 Ex.                                         *solve problems mentally                      rational numbers
                       Ex.                                          objects, mental computation, paper and      *solve multi-step problems with paper and     like terms
                       objects, mental computation, paper and       pencil                                      pencil                                        problem solving
                       pencil                                                                                                                                 strategy



                                                                             FIRST NINE WEEKS
                       1. Enduring Understanding - Real numbers are either rational or irrational.
                       1a. Essential Question - What kinds of numbers make up the set of real numbers?
F.7.3                  NO.1.7.6                                    Identify subsets of the real number system   *demonstrate that natural numbers are         real number system
                       Recognize subsets of the real number        (natural, whole, integers, rational, and     counting numbers beginning with 1 and         natural numbers
                       system (natural, whole, integers, rational, irrational numbers)                          that they build on one another                whole numbers
                       and irrational numbers)                                                                  *identify whole numbers as numbers            integers
                                                                                                                whose value includes zero and all natural     rational numbers
                                                                                                                numbers                                       irrational numbers
                                                                                                                *integers are all whole numbers and their     perfect square
                                                                                                                opposites                                     square root
                                                                                                                *apply the definition of a rational number    undefined fraction
                                                                                                                (any number that can be written as a/b
                                                                                                                where a is any integer and b is any integer
                                                                                                                except 0. Including any terminating
                                                                                                                decimals, repeating decimals and perfect
                                                                                                                squares)
                                                                                                                *recognize that a fraction whose
                                                                                                                denominator is zero is undefined
                                                                                                                *identify irrational numbers as numbers
                                                                                                                that have infinite but non-repeating
                                                                                                                decimal representations (Ex. π; any
                                                                                                                square root that is not a perfect square)
                                                                                                                *identify subsets of the real number
                                                                                                                system




        rev. 05-2009                                                                                                                                                                               1 of 22
        7th Grade Math

                                                    Arch Ford/Northwest Arkansas Instructional Alignment
                                                                Seventh Grade Mathematics
                              AR Department of Education
 NCTM Focal    # of                                                                                                                                               Essential
                                                                                                                                                                                  Materials/
   Point or   Times    CONTENT STANDARD/ Student Learning                           Objective                               Task Analysis                        Vocabulary
                                                                                                                                                                                  Resources
  Connector   Tested           Expectations (SLE)                                                                                                              *teacher word


                       Enduring Understanding - Successful problem solvers possess a set of core ways ofthat support numbers.
                       2. Enduring Understanding - Exponential and scientific notation are efficient beliefs expressing their work:
                       problem solving is important, takes significant time and repeated efforts, and requires reflection.
                       2a. Essential Question - What is the purpose of exponents?
F.7.3                  NO.1.7.2                                     A. Demonstrate, with and without           with and without appropriate technology:     scientific notation
                       Demonstrate, with and without                appropriate technology, an understanding   *write the number in expanded notation       exponents
                       appropriate technology, an understanding     of place value using powers of 10          Ex. 103 = 10×10×10                           place value
                       of place value using powers of 10 and        B. Write numbers greater than one in       *multiply and divide by multiples of 10      expanded notation
                       write numbers greater than one in            scientific notation                        *demonstrate the value of a decimal when     power
                       scientific notation                                                                     dividing or multiplying by a power           base
                                                                                                               (multiple) of 10
                                                                                                               *demonstrate that exponents are repeated
                                                                                                               multiplication
                                                                                                               *identify the whole number of a scientific
                                                                                                               notation number as a value ≥ 1 and < 10



F.7.3           1      NO.1.7.3                                     Convert between scientific notation and    *multiply and divide by powers of ten to     scientific notation
                       Convert between scientific notation and      standard notation using numbers greater    convert between standard and scientific      standard notation
                       standard notation using numbers greater      than one                                   notation                                     powers of ten
                       than one

                       3. Enduring Understanding - Fractions, decimals, and percents can be used interchangeably.
                       3a. Essential Question - What determines an appropriate representation for a number?
F.7.3                  NO.1.7.5                                     Compare and represent integers,            *locate integers on a number line            integers
                       Compare and represent integers, fractions,   fractions, decimals and mixed numbers      *locate fractions on a number line           number line
                       decimals and mixed numbers and find their    and find their approximate location on a   *locate decimals on a number line
                       approximate location on a number line        number line                                *locate mixed numbers on a number line
                                                                                                               *locate and compare the values of
                                                                                                               integers, fractions, decimals and mixed
                                                                                                               numbers on a number line


F.7.1                  M.13.7.6                                     A. Find the distance between two points    *plot two points on a number line        distance
                       Find the distance between two points on a    on a number line                           *find the distance between two points    midpoint
                       number line and locate the midpoint          B. Locate the midpoint                     *average two numbers on a number line to number line
                                                                                                               locate the midpoint




        rev. 05-2009                                                                                                                                                                           2 of 22
        7th Grade Math

                                                    Arch Ford/Northwest Arkansas Instructional Alignment
                                                                Seventh Grade Mathematics
                              AR Department of Education
 NCTM Focal    # of                                                                                                                                                   Essential
                                                                                                                                                                                       Materials/
   Point or   Times    CONTENT STANDARD/ Student Learning                              Objective                                Task Analysis                        Vocabulary
                                                                                                                                                                                       Resources
  Connector   Tested           Expectations (SLE)                                                                                                                  *teacher word

F.7.1                  NO.1.7.4                                     A. Find decimals for mixed numbers &     *explain how a part relates to a whole   decimal
                       Enduring Understanding
                       Find decimal and percent equivalents for - Successful problem solvers possess a set of core beliefs that support
                                                                    explain why they represent the same      *restate a mixed number as a whole       percent                         their work:
                                                                    value                                    number + fraction
                       mixed numbers and explain why they
                                                                                                               repeated efforts, denominator equivalents
                       problem solving is important, takes significant time and*convert fractions by dividing and requires reflection.
                       represent the same value                     B. Find percent equivalents of mixed                                              convert
                                                                    numbers & explain why they represent the into numerator
                                                                    same value                               *write a decimal as a mixed number
                                                                                                             *express mixed numbers as percents >
                                                                                                             100
                                                                                                             *demonstrate that the percent can be
                                                                                                             found by finding the fraction-to-decimal
                                                                                                             equivalent and then multiply the decimal
                                                                                                             by 100


F.7.1           1      NO.1.7.1                                        A. Show with and without models and         *explain how a part relates to a whole and   part-to-part
                       Relate, with and without models and pictures,   pictures the concept of ratio including     vice versa                                   part-to-whole
                       concepts of ratio, proportion, and percent,     ratios <1 and >100                          *match decimals and percents of the          ratio
                       including percents less than 1 and greater      B. Show with and without models and         same value                                   proportion
                       than 100                                        pictures the concept of percent including   *represent percents out of 100               percent
                                                                       percents <1 and >100                        *describe a situation in which a percent
                                                                       C. Show with and without models &           might be between 1 & 100
                                                                       pictures proportion including proportions   *draw a picture or model a number as a
                                                                       <1 and >100                                 decimal and percent
                                                                       D. Relate with and without models and
                                                                       pictures concepts of ratio, percent, and
                                                                       proportions including percents <1 and
                                                                       >100

F.7.3                  NO.3.7.4                                        A. Apply factorization to solve problems    *find multiples and factors of given         prime numbers
                       Apply factorization, LCM, and GCF to solve      using more than two numbers and explain     numbers                                      composite numbers
                       problems using more than two numbers            the solution                                *find the prime factorization of a number    prime factorization
                       and explain the solution                        B. Apply LCM to solve problems using        (Ex. tree diagram)                           LCM
                                                                       more than two numbers and explain the       *identify numbers as prime or composite      GCF
                                                                       solution                                    *find the LCM and GCF of more than two
                                                                       C. Apply GCF to solve problems using        numbers
                                                                       more than two numbers and explain the       *apply and explain solutions
                                                                       solution




        rev. 05-2009                                                                                                                                                                                3 of 22
        7th Grade Math

                                                     Arch Ford/Northwest Arkansas Instructional Alignment
                                                                 Seventh Grade Mathematics
                              AR Department of Education
 NCTM Focal    # of                                                                                                                                                   Essential
                                                                                                                                                                                       Materials/
   Point or   Times    CONTENT STANDARD/ Student Learning                             Objective                                 Task Analysis                        Vocabulary
                                                                                                                                                                                       Resources
  Connector   Tested           Expectations (SLE)                                                                                                                  *teacher word

F.7.1         MC-1     NO.3.7.6                                Solve, with and without appropriate     with and without appropriate technology: technology
              OR-1     Enduring Understanding - Successful problem solvers possess a set of core beliefs that support
                       Solve, with and without appropriate     technology, real-world percent problems *solve percent problems                   percent                              their work:
                       technology, real-world percent problems Ex.                                     Ex.                                       interest
                                                                                                         repeated efforts,
                       problem solving is important, takes significant time andWhat number is 50% of 80? and requires reflection.
                       Ex.                                     I=PRT                                                                             principal
                       I=PRT (whole unknown)                                                           80 is what percent of 50?                 rate
                                                                                                       80 is 50% of what number?                 time
                                                                                                       *use fractions, decimals and percents
                                                                                                       interchangeably
                                                                                                       *apply knowledge of percent to real-world
                                                                                                       situations
                                                                                                       Ex.
                                                                                                       I = PRT



                       4. Enduring Understanding - Integers have magnitude and direction.
                       4a. Essential Question - How do operations with integers compare to operations with whole numbers?
F.7.3                  NO.2.7.4                                       A. Model and develop addition and           *model addition and subtraction of positive   integers
                       Model and develop addition, subtraction,       subtraction of integers                     and negative numbers using                    absolute value
                       multiplication and division of integers        B. Model and develop multiplication and     manipulatives                                 opposites
                                                                      division of integers                        *model multiplication and division of         inverse operations
                                                                                                                  positive and negative numbers using
                                                                                                                  manipulatives
F.7.3           2      NO.2.7.3                                       A. Apply rules (conventions) for order of   *solve problems with integers using order     order of operations
                       Apply rules (conventions) for order of         operations to integers including            of operations                                 integers
                       operations to integers and positive rational   parentheses, brackets or exponents          *solve problems with positive rational        rational numbers
                       numbers including parentheses, brackets or     B. Apply rules (conventions) for order of   numbers using order of operations             exponents
                       exponents                                      operations to positive rational numbers     *use rules for order of operations            grouping symbols
                                                                      including parentheses, brackets or          including:                                    (brackets,
                                                                      exponents                                   •grouping symbols ( ), [ ]                    parentheses)
                                                                                                                  •fraction bar
                                                                                                                  •exponents
                                                                                                                  •multiplication & division left to right
                                                                                                                  •addition & subtraction left to right




        rev. 05-2009                                                                                                                                                                                4 of 22
        7th Grade Math

                                                   Arch Ford/Northwest Arkansas Instructional Alignment
                                                               Seventh Grade Mathematics
                              AR Department of Education
 NCTM Focal    # of                                                                                                                                          Essential
                                                                                                                                                                                  Materials/
   Point or   Times    CONTENT STANDARD/ Student Learning                          Objective                               Task Analysis                    Vocabulary
                                                                                                                                                                                  Resources
  Connector   Tested           Expectations (SLE)                                                                                                         *teacher word

F.7.3                  NO.2.7.1                                       A. Apply the Distributive Property of       *solve using Distributive Property to  Distributive Property
                                                                      multiplication over addition or solvers simplify computations of core or
                       Enduring Understanding - Successful problem subtraction possess a set with addition beliefs that support
                       Apply the Distributive Property of                                                                                                integers                their work:
                       multiplication over addition or subtraction to to simplify computations with integers      subtractions of integers               solve
                       problem solving is important, takes significant time and5(2+3)
                       simplify computations with integers, fractions B. Apply the Distributive Property of
                                                                                                                    repeated efforts, and requires reflection.
                                                                                                                                 5(2+3)                  simplify
                       and decimals                                   multiplication over addition or subtraction 5(5)          5(2)+5(3)                evaluate
                                                                      to simplify computations with fractions       25          10 + 15                  decompose
                                                                      C. Apply the Distributive Property of                        25
                                                                      multiplication over addition or subtraction
                                                                      to simplify computations with decimals        5(3-2)        5(3-2)
                                                                                                                  5(3)-5(2)         5(1)
                                                                                                                   15-10            5
                                                                                                                     5
                                                                                                                  *solve using Distributive Property to
                                                                                                                  simplify computations with addition or
                                                                                                                  subtraction to solve problems with
                                                                                                                  fractions
                                                                                                                  2(5 + 1/2)       2(5 - 1/2)
                                                                                                                    10 + 1           10 - 1
                                                                                                                      11              9

                                                                                                             *solve using Distributive Property to
                                                                                                             simplify computations with addition or
                                                                                                             subtraction to solve problems with
                                                                                                             decimals
                                                                                                               5.03 (3)
                                                                                                             5(3) + .03(3)
                                                                                                              15 + .09
                                                                                                               15.09

                                                                                                             *use subtraction to make multiplication of
                                                                                                             decimals easier (mental math)
                                                                                                             5(10.98)       5(11) - 5(.02)
                                                                                                             50+4.90          55 - .10
                                                                                                               54.9            54.9




        rev. 05-2009                                                                                                                                                                           5 of 22
        7th Grade Math

                                                     Arch Ford/Northwest Arkansas Instructional Alignment
                                                                 Seventh Grade Mathematics
                              AR Department of Education
 NCTM Focal    # of                                                                                                                                               Essential
                                                                                                                                                                                Materials/
   Point or   Times    CONTENT STANDARD/ Student Learning                            Objective                              Task Analysis                        Vocabulary
                                                                                                                                                                                Resources
  Connector   Tested           Expectations (SLE)                                                                                                              *teacher word


                       Enduring Understanding - Successful representations generalize patterns and relationships.
                       5. Enduring Understanding - Algebraicproblem solvers possess a set of core beliefs that support their work:

F.7.3           1
                       5a. Essential Question - Why are mathematical rulesand repeated efforts, and requires reflection.
                       problem solving is important, takes significant time necessary?
                       NO.3.7.1                                       Compute, with and without appropriate    with and without appropriate technology:     technology
                       Compute, with and without appropriate          technology, with integers and positive   *solve word problems using addition of       integers
                       technology, with integers and positive         rational numbers using real-world        positive integers, decimals, and fractions   positive rational
                       rational numbers using real-world situations   situations to solve problems             (including mixed numbers)                    numbers
                       to solve problems                                                                       *solve word problems using subtraction of    absolute value
                                                                                                               positive integers, decimals, and fractions
                                                                                                               (including mixed numbers)
                                                                                                               *solve word problems using multiplication
                                                                                                               of positive integers, decimals, and
                                                                                                               fractions (including mixed numbers)
                                                                                                               *solve word problems using division of
                                                                                                               positive integers, decimals, and fractions
                                                                                                               (including mixed numbers)
                                                                                                               *explain solution




                       6. Enduring Understanding - Computational estimations produce approximate results.
                       6a. Essential Question - What determines a reasonable estimation for a given situation?
F.7.3           1      NO.3.7.3                                       A. Determine when an estimate is         *determine when an estimate is sufficient    estimate
                       Determine when an estimate is sufficient and   sufficient                               *use estimation strategies to check for      estimation
                       use estimation to decide whether answers       B. Use estimation to decide whether      reasonableness of solutions                  reasonable
                       are reasonable in problems including           answers are reasonable in problems
                       fractions and decimals                         including fractions and decimals




        rev. 05-2009                                                                                                                                                                         6 of 22
        7th Grade Math

                                                    Arch Ford/Northwest Arkansas Instructional Alignment
                                                                Seventh Grade Mathematics
                              AR Department of Education
 NCTM Focal    # of                                                                                                                                               Essential
                                                                                                                                                                               Materials/
   Point or   Times    CONTENT STANDARD/ Student Learning                           Objective                                 Task Analysis                      Vocabulary
                                                                                                                                                                               Resources
  Connector   Tested           Expectations (SLE)                                                                                                              *teacher word


                       Enduring Understanding - Successful problem are related.
                       7. Enduring Understanding - Powers and roots solvers possess a set of core beliefs that support their work:
                       7a. Essential question - How are powers and roots related?
                       problem solving is important, takes significant time and repeated efforts, and requires reflection.
F.7.3                  NO.3.7.5                                      A. Represent and solve problem situations   with and without appropriate technology:   absolute value
                       Represent and solve problem situations that   that can be modeled by and solved using     *write and solve problems using the        exponents
                       can be modeled by and solved using            concepts of absolute value with and         concept of absolute value                  square roots
                       concepts of absolute value, exponents and     without appropriate technology              *write and solve problems using            perfect squares
                       square roots (for perfect squares) with and   B. Represent and solve problem situations   exponents                                  technology
                       without appropriate technology                that can be modeled by and solved using     *write and solve problems using square
                                                                     concepts of exponents with and without      roots
                                                                     appropriate technology
                                                                     C. Represent and solve problem situations
                                                                     that can be modeled by and solved using
                                                                     concepts of square roots (for perfect
                                                                     squares) with and without appropriate
                                                                     technology




        rev. 05-2009                                                                                                                                                                        7 of 22
        7th Grade Math

                                                      Arch Ford/Northwest Arkansas Instructional Alignment
                                                                  Seventh Grade Mathematics
                              AR Department of Education
 NCTM Focal    # of                                                                                                                                                       Essential
                                                                                                                                                                                          Materials/
   Point or   Times    CONTENT STANDARD/ Student Learning                                Objective                                 Task Analysis                         Vocabulary
                                                                                                                                                                                          Resources
  Connector   Tested           Expectations (SLE)                                                                                                                      *teacher word


                                                        SECOND NINE WEEKS
                       Enduring Understanding - Successful problem solvers possess a set of core beliefs that support their work:
                       1. Enduring Understanding - Patterns and relationships can be expressedand requires numerically,
                       problem solving is important, takes significant time and repeated efforts, graphically, reflection.
                       symbolically, and verbally.
                       1a. Essential Question - What can be learned from an identified pattern/function?
F.7.3         MC-2     A.4.7.2                                          Identify and extend patterns in real-world   *use skills in A.4.7.1                         patterns
              OR-1     Identify and extend patterns in real-world       situations                                   *find missing terms and numbers in a           term
                       situations                                                                                    pattern or a function table                    arithmetic sequence
                                                                                                                     *predict patterns in real-world situations     geometric sequence
                                                                                                                     *write a rule to extend a pattern to the nth
                                                                                                                     term


F.7.3                  A.4.7.3                                          Interpret and write a rule for a two-        *A.4.6.2                                       function table
                       Interpret and write a rule for a two-operation   operation function table                     *interpret and write the algebraic rule for
                       function table                                   Ex.                                          one- and two-operation function tables
                       Ex.                                              multiply by 2, add 1
                       multiply by 2, add 1
F.7.3                  A.4.7.1                                          Create and complete a function table         *identify (x-value) as input and (y-value)     function table
                       Create and complete a function table             (input/output) using a given rule with two   as output                                      input/output
                       (input/output) using a given rule with two       operations                                   *apply a given rule with two operations to
                       operations                                                                                    create and complete a function table


F.7.3                  A.6.7.3                                          Create and complete a function table         *create and complete a function table          function table
                       Create and complete a function table             (input/output) using a given rule with two   using a given rule with two operations in      input/output
                       (input/output) using a given rule with two       operations in real-world situations          real-world situations
                       operations in real-world situations
F.7.1                  A.7.7.1                                          Use, with and without appropriate            *use tables to identify situations with        technology
                       Use, with and without appropriate technology,    technology, tables and graphs to compare     constant or varying rates of change (Ex..      rates
                       tables and graphs to compare and identify        and identify situations with constant or     d=rt)                                          constant rate of
                       situations with constant or varying rates of     varying rates of change                      *use graphs to identify situations with        change
                       change                                                                                        constant or varying rates of change            varying rates of
                                                                                                                                                                    change




        rev. 05-2009                                                                                                                                                                                   8 of 22
        7th Grade Math

                                                    Arch Ford/Northwest Arkansas Instructional Alignment
                                                                Seventh Grade Mathematics
                              AR Department of Education
 NCTM Focal    # of                                                                                                                                                       Essential
                                                                                                                                                                                       Materials/
   Point or   Times    CONTENT STANDARD/ Student Learning                              Objective                                   Task Analysis                         Vocabulary
                                                                                                                                                                                       Resources
  Connector   Tested           Expectations (SLE)                                                                                                                      *teacher word


                       Enduring Understanding - Successful problem solvers possess a set of verbally, graphically, numerically,
                       2. Enduring Understanding - Functional relationships can be expressed core beliefs that support their work:
                       and symbolicallyis important, takes significant time and repeated efforts, and requires reflection.
                       problem solving and are used to solve real-world problems.
                       2a. Essential Question - How can a function be identified?
F.7.3                  A.6.7.1                                         A. Use tables to represent linear equations   *use tables to represent the relationship in   linear equations
                       Use tables and graphs to represent linear       by plotting, with and without appropriate     a linear equation, with and without            technology
                       equations by plotting, with and without         technology, points in a coordinate plane      appropriate technology                         coordinate plane
                       appropriate technology, points in a             B. Graph linear equations by plotting, with   *use graphs to represent the relationship      x-axis
                       coordinate plane                                and without appropriate technology, points    in a linear equation on a coordinate plane,    y-axis
                                                                       in a coordinate plane                         with and without appropriate technology        ordered pairs
                                                                                                                                                                    origin


                       2b. Essential Question - What can be learned from studying functions?
F.7.3           1      A.5.7.2                                         A. Solve simple linear equations using        *solve linear equations                        linear equations
                       Solve simple linear equations using             integers                                      *graph solution points on a coordinate         integers
                       integers and graph on a coordinate plane        B. Graph simple linear equations in a         plane using a T-chart                          coordinate plane
                       Ex.                                             coordinate plane                                                                             quadrant
                       use a T-chart                                                                                                                                x-axis
                                                                                                                                                                    y-axis
                                                                                                                                                                    origin
F.7.1                  G.10.7.1                                        Plot points in the coordinate plane           *identify four quadrants on coordinate         coordinate plane
                       Plot points in the coordinate plane                                                           plane                                          x-axis
                                                                                                                     *identify x and y axis                         y-axis
                                                                                                                     *use ordered pairs to plot points on           ordered pairs
                                                                                                                     coordinate plane                               quadrants
                                                                                                                                                                    origin
F.7.3           1      A.6.7.2                                         Represent, with and without appropriate       *same as A.6.7.1 with real-world               technology
                       Represent, with and without appropriate         technology, linear equations by plotting      applications                                   linear equations
                       technology, linear equations by plotting and    and graphing points in the coordinate                                                        coordinate plane
                       graphing points in the coordinate plane using   plane using all four quadrants given data                                                    quadrants
                       all four quadrants given data in a table from   in a table from a real-world situation                                                       origin
                       a real-world situation                                                                                                                       x-axis
                                                                                                                                                                    y-axis

                       3. Enduring Understanding - Algebraic representations generalize patterns and relationships.
                       3a. Essential Question - Why are equations and inequalities useful?
F.7.3                  A.5.7.4                                         A. Write algebraic expressions using          *write and solve algebraic expressions         algebraic
                       Write and evaluate algebraic expressions        positive rational numbers                     with one or more variables using positive      expressions
                       using positive rational numbers                 B. Evaluate algebraic expressions using       rational numbers                               rational numbers
                                                                       positive rational numbers                                                                    variables




        rev. 05-2009                                                                                                                                                                                9 of 22
        7th Grade Math

                                                      Arch Ford/Northwest Arkansas Instructional Alignment
                                                                  Seventh Grade Mathematics
                              AR Department of Education
 NCTM Focal    # of                                                                                                                                                        Essential
                                                                                                                                                                                               Materials/
   Point or   Times    CONTENT STANDARD/ Student Learning                                 Objective                                 Task Analysis                         Vocabulary
                                                                                                                                                                                               Resources
  Connector   Tested           Expectations (SLE)                                                                                                                       *teacher word

F.7.3           4      A.5.7.3                                 A. Translate phrases into algebraic     *express word phrases using variables, algebraic
                                                                                                       positive numbers, rational core and expressions
                       Enduring Understanding - Successful problem solvers possess a set of numbers,beliefs that support
                       Translate phrases and sentences into    expressions                                                                                                                    their work:
                       algebraic expressions and equations     B. Translate sentences into equations
                       problem solving is important, takes significant time andoperations use of the Distributive requires reflection.
                       including parentheses and positive and
                                                                                                         repeated efforts, and
                                                               including parentheses, positive numbers *explain the
                                                                                                                                              equations
                                                                                                                                              rational numbers
                       rational numbers and simplify algebraic and rational numbers                    Property to simplify like terms        coefficient
                       expressions by combining like terms     C. Simplify algebraic expressions by    *simplify algebraic expressions by     constant
                                                               combining like terms                    combining like terms                   variable
F.7.3                  A.5.7.1                                           A. Solve and graph one-step linear           *identify phrases that indicate inequalities   linear equations
                       Solve and graph one-step linear equations         equations using a variety of methods (Ex.    in real-world situations                       inequalities
                       and inequalities using a variety of methods       hands-on, inverse operations, symbolic)      *solve one-step linear equations and           inverse operations
                       (Ex. hands-on, inverse operations, symbolic)      with real-world application with and         inequalities, with and without appropriate     technology
                       with real-world application, with and without     without appropriate technology               technology, using a variety of methods         variables
                       appropriate technology                            B. Solve and graph one-step linear           *graph one-step equations and
                                                                         inequalities using a variety of methods      inequalities on a number line
                                                                         (Ex. hands-on, inverse operations,
                                                                         symbolic) with real-world application with
                                                                         and without appropriate technology



F.7.3           1      NO.2.7.2                                          A. Apply the addition, subtraction,          *know the properties of equality for           equations
                       Apply the addition, subtraction, multiplication   multiplication and division properties of    addition, subtraction, multiplication, and     integers
                       and division properties of equality to one-step   equality to one-step equations with          division and apply to one-step equations       properties of equality
                       equations with integers, fractions, and           integers                                     using integers                                 inverse operations
                       decimals                                          B. Apply the addition, subtraction,          *know the properties of equality for           one-step equations
                                                                         multiplication and division properties of    addition, subtraction, multiplication, and
                                                                         equality to one-step equations with          division and apply to one-step equations
                                                                         fractions                                    using fractions
                                                                         C. Apply the addition, subtraction,          *know the properties of equality for
                                                                         multiplication and division properties of    addition, subtraction, multiplication, and
                                                                         equality to one-step equations with          division and apply to one-step equations
                                                                         decimals                                     using decimals




        rev. 05-2009                                                                                                                                                                                   10 of 22
        7th Grade Math

                                                     Arch Ford/Northwest Arkansas Instructional Alignment
                                                                 Seventh Grade Mathematics
                              AR Department of Education
 NCTM Focal    # of                                                                                                                                                        Essential
                                                                                                                                                                                          Materials/
   Point or   Times    CONTENT STANDARD/ Student Learning                               Objective                                   Task Analysis                         Vocabulary
                                                                                                                                                                                          Resources
  Connector   Tested           Expectations (SLE)                                                                                                                       *teacher word


                                                         THIRD NINE WEEKS
                       Enduring Understanding - Successful problem solvers possess a set of core beliefs that support their work:
                       1. Enduring Understanding - Graphical representations and statistical measures influence interpretations
                       problem solving is important, takes significant time and repeated efforts, and requires reflection.
                       and predictions about data.
                       1a. Essential Question - How can the results of a statistical investigation be used to support an argument?

F.7.1           2      DAP.14.7.1                                       Identify different ways of selecting          *develop appropriate questions for             sample vs.
                       Identify different ways of selecting samples     samples and compose appropriate               surveys                                        population
                       and compose appropriate questions                questions                                     *identify survey response, random sample,      random sample
                       Ex.                                              Ex.                                           representative sample & convenience            survey response
                       survey response, random sample,                  survey response, random sample,               sample                                         representative
                       representative sample and convenience            representative sample and convenience                                                        sample
                       sample                                           sample                                                                                       convenience sample


F.7.1                  DAP.14.7.2                                       A. Explain that line graphs are appropriate   *identify that line graphs are used to graph   line graph
                       Explain which types of display are appropriate   for graphing change over time                 change over time                               circle graph
                       for various data sets (line graph for change     B. Explain that circle graphs are             *identify that circle graphs are used to       part-to-whole
                       over time, circle graph for part-to-whole        appropriate for graphing part-to-whole        graph part-to-whole comparisons                comparison
                       comparison, scatter plot for trends)             comparisons                                   *identify that scatter plots are used to       scatter plot
                                                                        C. Explain that scatter plots are             graph trends                                   trends
                                                                        appropriate graphing trends


F.7.3           1      DAP.15.7.2                                       A. Analyze, with and without appropriate      with and without appropriate technology: technology
                       Analyze, with and without appropriate            technology, a set of data by using and        *find the mean, median and mode for a      central tendencies
                       technology, a set of data by using and           comparing measures of central tendencies      set of data                                mean
                       comparing measures of central tendencies         (mean, median, mode)                          *compare the mean, median, mode for a average
                       (mean, median, mode) and measures of             B. Analyze, with and without appropriate      set of data                                median
                       spread (range, quartile, interquartile range)    technology, a set of data by using and        *find measures of spread (range, quartile, mode
                                                                        comparing measures of spread (range,          interquartile range) for a set of data     measure of spread
                                                                        quartile, interquartile range)                *compare measures of spread using a box- range
                                                                                                                      and-whiskers plot                          quartile
                                                                                                                      *analyze measures of central tendency      interquartile range
                                                                                                                      and measures of spread (including          outliers
                                                                                                                      outliers) for a set of data




F.7.1           1      DAP.15.7.1                                       Analyze data displays, including ways that *identify data display composition:               misleading
                       Analyze data displays, including ways that       they can be misleading                     •scale                                            scale
                       they can be misleading                                                                      •data sample population techniques                intervals
                                                                                                                   •misuse of central tendencies                     central tendencies




        rev. 05-2009                                                                                                                                                                              11 of 22
        7th Grade Math

                                                   Arch Ford/Northwest Arkansas Instructional Alignment
                                                               Seventh Grade Mathematics
                              AR Department of Education
 NCTM Focal    # of                                                                                                                                          Essential
                                                                                                                                                                                 Materials/
   Point or   Times    CONTENT STANDARD/ Student Learning                          Objective                               Task Analysis                    Vocabulary
                                                                                                                                                                                 Resources
  Connector   Tested           Expectations (SLE)                                                                                                         *teacher word

F.7.1         MC-3     DAP.14.7.3                                     A. Construct and interpret circle graphs   with and without appropriate technology: double bar graphs
              OR-1     Enduring Understanding - with and without appropriate solvers *circle
                       Construct and interpret circle graphs, box- Successful problemtechnology possess a set of core beliefs that support                circle graphs         their work:
                       and-whisker plots, histograms, scatter         B. Construct and interpret box-and-
                       problem solving is important, takes significant time and repeated efforts, and            •explain part-to-whole correlation requires reflection.
                                                                                                                                                          box-and-whisker
                       plots and double-line graphs, with and without whisker plots with and without appropriate •demonstrate taking numbers from         plots
                       appropriate technology                         technology                                 fractions to decimals to percents to     histograms
                                                                      C. Construct and interpret histograms with degrees                                  scatter plots
                                                                      and without appropriate technology         •use a protractor to create angles       double line graphs
                                                                      D. Construct and interpret scatter plots   •construct circle graph                  technology
                                                                      with and without appropriate technology    •interpret data                          correlation
                                                                      E. Construct and interpret double-line     *box-and-whisker plots                   trend line
                                                                      graphs with and without appropriate        •represent each quartile as 25%          line of best fit
                                                                      technology                                 •analyze and record the spread           stem-and-leaf plots
                                                                                                                 •interpret central tendencies            Venn diagrams
                                                                                                             •find medians and extremes
                                                                                                             •construct box-and-whisker plot & identify
                                                                                                             outliers, if any
                                                                                                             *histogram
                                                                                                             •create a frequency table, place the
                                                                                                             frequency of occurency on y-axis &
                                                                                                             intervals of continuous data on x-axis
                                                                                                             •construct histogram (similar to a bar
                                                                                                             graph except bars touch)
                                                                                                             •compare independent variables to
                                                                                                             dependent variables
                                                                                                             •interpret data
                                                                                                             *scatter plot
                                                                                                             •determine dependent (y) variable &
                                                                                                             independent (x) variable
                                                                                                             •plot points (x,y)
                                                                                                             •decide the overall correlation
                                                                                                             •interpret data
                                                                                                             *double line graphs
                                                                                                             •determine dependent (y) & independent
                                                                                                             (x) variable
                                                                                                             •identify the data sets (2 or more)




        rev. 05-2009                                                                                                                                                                     12 of 22
        7th Grade Math

                                                      Arch Ford/Northwest Arkansas Instructional Alignment
                                                                  Seventh Grade Mathematics
                              AR Department of Education
 NCTM Focal    # of                                                                                                                                                      Essential
                                                                                                                                                                                             Materials/
   Point or   Times    CONTENT STANDARD/ Student Learning                               Objective                                  Task Analysis                        Vocabulary
                                                                                                                                                                                             Resources
  Connector   Tested           Expectations (SLE)                                                                                                                     *teacher word

                                                                                                                     •plot points & connect data set
                       Enduring Understanding - Successful problem solvers possess a set of core beliefs that support their work:
                                                                               independently
                                                                                               compare changes over time
                       problem solving is important, takes significant time and•evaluate andkey efforts, and requires reflection.
                                                                                 repeated all graphs appropriately
                                                                               *title, label &



                       2. Enduring Understanding - Sampling affects the relationship between experimental and theoretical
                       probability.
                       2a. Essential Question - How are experimental and theoretical probability related?
F.7.1           1      DAP.17.7.1                                      Demonstrate that probability can take any     *describe events that will not occur as       probability
                       Understand that probability can take any        value between 0 and 1 (events that are        probability 0                                 certainty
                       value between 0 and 1 (events that are not      not going to occur have probability 0,        *describe events that will certainly occur    outcome
                       going to occur have probability 0, events       events certain to occur have probability 1)   as probability of 1                           most likely
                       certain to occur have probability 1)                                                          *create situations in which the probability   least likely
                                                                                                                     falls between 0 & 1                           equally likely
F.7.1                  DAP.17.7.2                                    Design, with and without appropriate            with and without appropriate technology:      technology
                       Design, with and without appropriate          technology, an experiment to test a             *create theoretical probabilities and test    theoretical probability
                       technology, an experiment to test a           theoretical probability and explain how the     them (experiment)                             experimental
                       theoretical probability and explain how the   results may vary                                *explain how results vary                     probability
                       results may vary                              Ex.                                             *formulate reasons why theoretical and
                       Ex.                                           suggested materials for simulations are         experimental results vary
                       suggested materials for simulations are: two- two-color counters, a number cube, and
                       color counters, a number cube, and spinners spinners


                       3. Enduring Understanding - Linear relationships are characterized by a constant rate of change.
                       3a. Essential Question - Why are linear functions useful?
F.7.1           1      DAP.16.7.1                                      A. Make, with and without appropriate         *given a scatter plot determine a             technology
                       Make, with and without appropriate              technology, conjectures of possible           relationship between the dependent and        conjectures
                       technology, conjectures of possible             relationships in a scatter plot               independent variables                         scatter plot
                       relationships in a scatter plot and             B. Approximate the line of best fit (trend    *make a conjecture about possible             line of best fit
                       approximate the line of best fit (trend line)   line)                                         relationships between variables               trend line
                                                                                                                     *construct a line of best fit to most         dependent variable
                                                                                                                     appropriately represent the "average"         independent variable
                                                                                                                     relationship between dependent and            relationship
                                                                                                                     independent variables




        rev. 05-2009                                                                                                                                                                                 13 of 22
        7th Grade Math

                                                     Arch Ford/Northwest Arkansas Instructional Alignment
                                                                 Seventh Grade Mathematics
                              AR Department of Education
 NCTM Focal    # of                                                                                                                                                    Essential
                                                                                                                                                                                         Materials/
   Point or   Times    CONTENT STANDARD/ Student Learning                               Objective                                 Task Analysis                       Vocabulary
                                                                                                                                                                                         Resources
  Connector   Tested           Expectations (SLE)                                                                                                                   *teacher word

                       4. Enduring Understanding - Selectionproblem solvers possess atools and units depends on real-world
                       Enduring Understanding - Successful of standard measurement set of core beliefs that support their work:
                       situations.
                       problem solving is important, takes significant time and repeated efforts, and requires reflection.
                       4a. Essential Question - Why are scientific units and tools used to measure different attributes?
F.7.2           1      M.12.7.1                                         For real-world problems to the required     *state the common standard units             customary
                       Understand, select and use the appropriate       degree of accuracy:                         *apply the prefixes of the metric system     measurement
                       units and tools (metric and customary) to        A. Select and use the appropriate units     *select the appropriate tool to measure in   hours to minutes
                       measure length, weight, mass and volume to       and tools (metric and customary) to         applicable units (Ex. ruler, meter stick,    feet to inches
                       the required degree of accuracy for real-world   measure length                              gallon, liter, grams, pound, tons,           quarts to gallons
                       problems                                         B. Select and use the appropriate units     protractor, degrees, etc.)                   benchmark prefixes:
                                                                        and tools (metric and customary) to         *apply the appropriate tool to measure       milli-, centi-, kilo-
                       Note: Use the appropriate tool to measure        measure weight                              length, weight, mass, and volume of a        length
                       degrees of angles. Students are given a          C. Select and use the appropriate units     variety of real-world objects                weight
                       protractor to use on the Benchmark test.         and tools (metric and customary) to         *use a variety of measurement tools          mass
                       There have been test questions concerning        measure mass                                (graduated cylinder, triple beam balance,    volume
                       the use of the protractor.                       D. Select and use the appropriate units     meter stick, protractor and others)          degree
                                                                        and tools (metric and customary) to                                                      metric units
                                                                        measure volume                                                                           gram/liter/meter
                                                                        E. Select and use the appropriate tool to                                                pounds
                                                                        measure angle degrees (protractor)                                                       gallons
                                                                                                                                                                 yards
                                                                                                                                                                 capacity
                                                                                                                                                                 protractor



C.7.1                  M.13.7.2                                         A. Draw and measure distance to the         *know measuring begins with the first tic accurately
                       Draw and measure distance to the nearest         nearest 1/16 inch accurately                mark                                        precision
                       millimeter and 1/16 inch accurately.             B. Draw and measure distance to the         *be able to record distance to the nearest tic mark/origin
                                                                        nearest millimeter accurately               1/16 inch
                                                                                                                    *be able to draw a line to the nearest 1/16
                                                                                                                    inch
                                                                                                                    *be able to record distance to the nearest
                                                                                                                    millimeter
                                                                                                                    *be able to draw a line to the nearest
                                                                                                                    millimeter




        rev. 05-2009                                                                                                                                                                             14 of 22
        7th Grade Math

                                                    Arch Ford/Northwest Arkansas Instructional Alignment
                                                                Seventh Grade Mathematics
                              AR Department of Education
 NCTM Focal    # of                                                                                                                                                   Essential
                                                                                                                                                                                     Materials/
   Point or   Times    CONTENT STANDARD/ Student Learning                           Objective                                  Task Analysis                         Vocabulary
                                                                                                                                                                                     Resources
  Connector   Tested           Expectations (SLE)                                                                                                                  *teacher word

F.7.1           2      M.12.7.2                                    Compare units within the same system *compare standard units
                       Enduring Understanding - Successful problem solvers possess a set of
                       Understand relationships among units within                              core beliefs that support their work:
                                                                                                        *compare metric units
                       the same system                                                                    seconds↔minutes↔
                       problem solving is important, takes significant time and repeated efforts, and requires reflection.
                                                                                                                                                                hours↔days
                                                                                                                                                                inches↔feet↔
                                                                                                                                                                yards↔miles
                                                                                                                                                                ounces↔cups↔
                                                                                                                                                                pints↔
                                                                                                                                                                quarts↔gallons
                                                                                                                                                                benchmark prefixes
                                                                                                                                                                kilo-↔deci-↔centi-
                                                                                                                                                                ↔milli-
                                                                                                                                                                grams
                                                                                                                                                                liters
                                                                                                                                                                meters
C.7.1                  M.13.7.1                                     A. Solve real-world problems involving two   *explain time concepts (clock and              elapsed time
                       Solve real-world problems involving two or   or more elapsed times, counting forward      calendar; Ex. number of days in each
                       more elapsed times, counting forward and     and backward on a calendar                   month) in the context of counting forward
                       backward (calendar and clock)                B. Solve real-world problems involving two   and backward
                                                                    or more elapsed times, counting forward      *solve real-world situations involving two
                                                                    and backward on a clock                      or more elapsed times




                       5. Enduring Understanding - Relationships exist among the angles, sides, lengths, perimeters, areas, and
                       volumes of geometric figures.
                       5a. Essential Question - How are interior angles and the number of sides of the polygon related?
C.7.1         OR-1     G.8.7.4                                      A. Use paper or physical models to           *fold/cut paper to make physical models of     interior angles
                       Use paper or physical models to              determine the sum of the measures of         quadrilaterals & triangles                     quadrilaterals
                       determine the sum of the measures of         interior angles of triangles                 *demonstrate that the measures of the          triangles
                       interior angles of triangles and             B. Use paper or physical models to           sum of the interior angles of quadrilaterals   non-overlapping
                       quadrilaterals                               determine the sum of the measures of         is 360º                                        overlapping
                                                                    interior angles of quadrilaterals            *demonstrate that the measures of the          diagonals
                                                                                                                 sum of the interior angles of triangles is
                                                                                                                 180º
                                                                                                                 *find a missing angle given two angles in a
                                                                                                                 triangle
                                                                                                                 *find a missing angle given three angles in
                                                                                                                 a quadrilateral




        rev. 05-2009                                                                                                                                                                         15 of 22
        7th Grade Math

                                                     Arch Ford/Northwest Arkansas Instructional Alignment
                                                                 Seventh Grade Mathematics
                              AR Department of Education
 NCTM Focal    # of                                                                                                                                                        Essential
                                                                                                                                                                                        Materials/
   Point or   Times    CONTENT STANDARD/ Student Learning                               Objective                                  Task Analysis                          Vocabulary
                                                                                                                                                                                        Resources
  Connector   Tested           Expectations (SLE)                                                                                                                       *teacher word


                       Enduring Understanding - Successful problem can change position and maintain the same attributes work:
                       6. Enduring Understanding - Geometric figures solvers possess a set of core beliefs that support their on a
                       coordinate plane. important, takes significant time and repeated efforts, and requires reflection.
                       problem solving is
                       6a. Essential Question - How does the movement of a geometric figure affect its attributes?
F.7.1                  G.10.7.2                                        Plot points that form the vertices of a       *identify vertices of polygons             vertices
                       Plot points that form the vertices of a         geometric figure and draw, identify and       *replicate (draw) polygons on a coordinate faces
                       geometric figure and draw, identify and         classify the figure                           plane using ordered pairs                  edges
                       classify the figure                                                                           *classify figures according to number of
                                                                                                                     vertices
C.7.1           1      G.9.7.2                                         A. Perform translations of two-dimensional    *fold/cut paper to perform translations of 2-   rotation
                       Perform translations and reflections of two-    figures using a variety of methods (paper     dimensional figures                             translation
                       dimensional figures using a variety of          folding, tracing, graph paper)                *trace to perform translations of 2-            reflection
                       methods (paper folding, tracing, graph paper)   B. Perform reflections of two-dimensional     dimensional figures                             two-dimensional
                                                                       figures using a variety of methods (paper     *use graph paper to perform translations        figure
                                                                       folding, tracing, graph paper)                of 2-dimensional figures
                                                                                                                     *fold/cut paper to perform reflections of 2-
                                                                                                                     dimensional figures
                                                                                                                     *trace to perform reflections of 2-
                                                                                                                     dimensional figures
                                                                                                                     *use graph paper to perform reflections of
                                                                                                                     2-dimensional figures

                       7. Enduring Understanding - Relationships exist among angles, sides and triangles.
                       7a. Essential question - How can properties of triangles be applied to solve problems?
F.7.1                  G.8.7.6                                         Develop the properties of similar figures     *categorize shapes                              similar figures
                       Develop the properties of similar figures       (ratio of sides and congruent angles)         *explain the concept of similarity and scale    congruent angles
                       (ratio of sides and congruent angles)                                                         *identify similar figures according to          ratio
                                                                                                                     properties of sides and angles                  scale


F.7.1         MC-1     M.13.7.5                                        Apply properties (scale factors, ratio, and   *identify corresponding parts of triangles      scale factors
              OR-1     Apply properties (scale factors, ratio, and     proportion) of congruent or similar           *set up proportion formulas (scale factors,     ratio
                       proportion) of congruent or similar             triangles to solve problems involving         ratios) using variables to find a missing       proportion
                       triangles to solve problems involving           missing lengths and angle measures            length of a triangle                            congruent
                       missing lengths and angle measures                                                            *apply correlation properties to find a         similar
                                                                                                                     missing angle of a triangle                     correlation




        rev. 05-2009                                                                                                                                                                            16 of 22
        7th Grade Math

                                                    Arch Ford/Northwest Arkansas Instructional Alignment
                                                                Seventh Grade Mathematics
                              AR Department of Education
 NCTM Focal    # of                                                                                                                                                Essential
                                                                                                                                                                                       Materials/
   Point or   Times    CONTENT STANDARD/ Student Learning                           Objective                                 Task Analysis                       Vocabulary
                                                                                                                                                                                       Resources
  Connector   Tested           Expectations (SLE)                                                                                                               *teacher word


                                                        FOURTH NINE WEEKS
                       Enduring Understanding - Successful problem solvers possess a set of core beliefs that support their work:
                       1. Enduring Understanding - Constructions are time and repeated efforts, and requires reflection.
                       problem solving is important, takes significant based on properties of geometric figures.
                       1a. Essential Question - How are geometric properties used in constructions?
F.7.2           2      G.8.7.1                                      A. Identify, draw, classify and compare 2- *identify and model 2-dimensional             regular polygon
                       Identify, draw, classify and compare         D geometric figures using models and real- geometric figures including regular and       irregular polygon
                       geometric figures using models and real-     world examples                             irregular polygons                            two-dimensional
                       world examples                               B. Identify, draw, classify and compare 3- *classify 2-dimensional geometric figures     figures
                                                                    D geometric figures using models and real- *compare 2-dimensional geometric figures      three-dimensional
                                                                    world examples                             using real-world examples                     figures (pyramid,
                                                                                                               *draw 2-dimensional geometric figures         cone, sphere,
                                                                                                               *identify and model 3-dimensional figures     cylinder, cube, prism)
                                                                                                               *classify geometric 3-dimensional figures     quadrilaterals
                                                                                                               *compare geometric 3-dimensional figures      (rectangle, square,
                                                                                                               using real-world examples                     parallelogram,
                                                                                                               *draw 3-dimensional geometric figures         trapezoid, rhombus)
                                                                                                                                                             circle
                                                                                                                                                             ellipse
                                                                                                                                                             triangles (scalene,
                                                                                                                                                             isosceles, equilateral,
                                                                                                                                                             right, acute, obtuse)
                                                                                                                                                             pentagons,
                                                                                                                                                             hexagons, octagon,
                                                                                                                                                             decagon, n-gon




F.7.2           3      G.8.7.2                                      Investigate geometric properties and their   *draw convex and concave polygons           one-dimensional
                       Investigate geometric properties and their   relationships in one-, two-, and three-      *compare and contrast the characteristics   model
                       relationships in one-, two-, and three-      dimensional models, including convex and     of one-, two-, and three-dimensional        two-dimensional
                       dimensional models, including convex and     concave polygons                             models to see relationships among them      model
                       concave polygons                                                                                                                      three-dimensional
                                                                                                                                                             model
                                                                                                                                                             angles
                                                                                                                                                             convex polygon
                                                                                                                                                             concave polygon
                                                                                                                                                             classification of
                                                                                                                                                             polygons by sides
                                                                                                                                                             classification of
                                                                                                                                                             polygons by angles




        rev. 05-2009                                                                                                                                                                           17 of 22
        7th Grade Math

                                                     Arch Ford/Northwest Arkansas Instructional Alignment
                                                                 Seventh Grade Mathematics
                              AR Department of Education
 NCTM Focal    # of                                                                                                                                                Essential
                                                                                                                                                                                         Materials/
   Point or   Times    CONTENT STANDARD/ Student Learning                             Objective                                Task Analysis                      Vocabulary
                                                                                                                                                                                         Resources
  Connector   Tested           Expectations (SLE)                                                                                                               *teacher word

F.7.2                  G.8.7.3                                        A. Identify the pairs of angles formed and *identify vertical angles and know that they angles
                       Enduring Understanding - Successful between the solvers are congruent
                       Recognize the pairs of angles formed and the relationship problemangles of two possess a set of core beliefs that support                   right angle          their work:
                       the relationship between the angles            intersecting lines (vertical, adjacent, linear *identify supplementary angles and know acute angle
                       problem solving is important, takes significant time andthat they are congruent to 180º
                                                                      pair, supplementary, perpendicular)
                                                                                                                       repeated efforts, and requires reflection.  obtuse angle
                       including two intersecting lines and
                       parallel lines cut by a transversal (vertical, B. Identify the pairs of angles formed and *identify complementary angles and know intersecting lines
                       supplementary, complementary,                  the relationship between parallel lines cut that they are congruent to 90º                   transversal
                       corresponding, alternate interior, alternate by a transversal (vertical, supplementary, *identify corresponding angles and know vertical angles
                       exterior angles and linear pair)               corresponding, alternate interior, alternate that they are congruent                         supplementary
                                                                      exterior angles and linear pair)               *identify alternate interior angles/alternate angles
                                                                      C. Identify the pairs of angles and the        exterior angles and know that they are        complementary
                                                                      relationship that exists to form               congruent                                     angles
                                                                      complementary angles                           *identify linear pairs and adjacent angles corresponding
                                                                                                                     *identify the relationship of the angles      angles
                                                                                                                     formed by a transversal and parallel lines alternate interior
                                                                                                                                                                   angles
                                                                                                                                                                   alternate exterior
                                                                                                                                                                   angles
                                                                                                                                                                   linear pair
                                                                                                                                                                   alternate pair
                                                                                                                                                                   parallel lines
                                                                                                                                                                   interior
                                                                                                                                                                   exterior
                                                                                                                                                                   adjacent
                                                                                                                                                                   congruent




        rev. 05-2009                                                                                                                                                                             18 of 22
        7th Grade Math

                                                   Arch Ford/Northwest Arkansas Instructional Alignment
                                                               Seventh Grade Mathematics
                              AR Department of Education
 NCTM Focal    # of                                                                                                                                                 Essential
                                                                                                                                                                                 Materials/
   Point or   Times    CONTENT STANDARD/ Student Learning                              Objective                                Task Analysis                      Vocabulary
                                                                                                                                                                                 Resources
  Connector   Tested           Expectations (SLE)                                                                                                                *teacher word

                       2. Enduring Understanding - Relationships exist among the angles, sides, lengths, perimeters, and two-
                       Enduring Understanding - Successful problem solvers possess a set of core beliefs that support their work:
                       dimensional areas. important, takes significant time and repeated efforts, and requires reflection.
                       problem solving is
                       2a. Essential Question - How are the areas of rectangles, parallelograms, triangles, trapezoids, and circles
                       related?
F.7.2                  M.13.7.3                                       A. Develop and use strategies to solve      *use a variety of strategies to solve for   trapezoid
                       Develop and use strategies to solve problems   problems involving area of a trapezoid      area of a trapezoid                         altitude/height
                       involving area of a trapezoid and              B. Develop and use strategies to solve      *apply formula for area of trapezoid        base 1, base 2
                       circumference and area of a circle             problems involving circumference of a       *use a variety of strategies to solve for   circumference
                                                                      circle                                      finding the circumference of a circle       area of a circle
                                                                      C. Develop and use strategies to solve      *apply the formula for circumference of a   radius
                                                                      problems involving area of a circle         circle                                      pi (π)
                                                                                                                  *use a variety of strategies to solve for
                                                                                                                  finding the area of a circle
                                                                                                                  *apply the formula for area of a circle


F.7.3                  M.12.7.3                                       A. Find different areas for a given         *given a perimeter, solve for area of       linear units
                       Find different areas for a given perimeter     perimeter                                   various shapes                              volume
                       and find a different perimeter for a given     B. Find a different perimeter for a given   *label using appropriate units              perimeter
                       area                                           area                                        *given an area, identify all perimeter      area
                                                                                                                  combinations using whole numbers            square units
                                                                                                                  *label using appropriate units




        rev. 05-2009                                                                                                                                                                     19 of 22
        7th Grade Math

                                                    Arch Ford/Northwest Arkansas Instructional Alignment
                                                                Seventh Grade Mathematics
                              AR Department of Education
 NCTM Focal    # of                                                                                                                                                     Essential
                                                                                                                                                                                     Materials/
   Point or   Times    CONTENT STANDARD/ Student Learning                             Objective                                  Task Analysis                         Vocabulary
                                                                                                                                                                                     Resources
  Connector   Tested           Expectations (SLE)                                                                                                                    *teacher word

                       3. Enduring Understanding - Generalizations can be made to represent the relationship between area and
                       Enduring Understanding - Successful problem solvers possess a set of core beliefs that support their work:
                       volume. solving is important, takes significant time and repeated efforts, and requires reflection.
                       problem
                       3a. Essential Question - How do the dimensions of a geometric figure affect area, surface area, and
                       volume?
F.7.2           2      M.13.7.4                                       A. Derive and use formulas for surface       *use the formulas for finding the areas of     surface area
                       Derive and use formulas for surface area and   area of prisms and justify them using        common shapes: circles, squares,               volume
                       volume of prisms and cylinders and justify     geometric models and common materials        triangles and rectangles                       prisms
                       them using geometric models and common         B. Derive and use formulas for surface       *draw nets and use them to find the            cylinders
                       materials                                      area of cylinders and justify them using     formula for the surface area of a prism        nets
                                                                      geometric models and common materials        *use the formula to find the surface area      derived formula
                                                                      C. Derive and use formulas for volume of     of a prism
                                                                      prisms and justify them using geometric      *use real world items to compare to nets
                                                                      models and common materials                  *apply appropriate units to surface area
                                                                      D. Derive and use formulas for volume of     *draw nets and use them to find the
                                                                      cylinders and justify them using geometric   formula for the surface area of a cylinder
                                                                      models and common materials                  *use the formula to find the surface area
                                                                                                                   of a cylinder
                                                                                                                   *use manipulatives to find a formula for
                                                                                                                   the volume of rectangular prisms
                                                                                                                   *apply the derived formula of volume to a
                                                                                                                   variety of rectangular prisms (including
                                                                                                                   common item i.e., matchbox, tissue box,
                                                                                                                   shoebox, etc.)
                                                                                                                   *identify the surface area parts of a
                                                                                                                   cylinder as a rectangle attached to two
                                                                                                                   circles at each end
                                                                                                                   *use manipulatives to find a formula for
                                                                                                                   the volume of cylinders
                                                                                                                   *apply the derived formula of volume to a
                                                                                                                   variety of cylinders (paper towel roll, soup
                                                                                                                   can, etc.)




        rev. 05-2009                                                                                                                                                                         20 of 22
        7th Grade Math

                                                     Arch Ford/Northwest Arkansas Instructional Alignment
                                                                 Seventh Grade Mathematics
                              AR Department of Education
 NCTM Focal    # of                                                                                                                                                   Essential
                                                                                                                                                                                       Materials/
   Point or   Times    CONTENT STANDARD/ Student Learning                            Objective                                  Task Analysis                        Vocabulary
                                                                                                                                                                                       Resources
  Connector   Tested           Expectations (SLE)                                                                                                                  *teacher word

                       3b. Essential Question - How can formulas be developed using models?core beliefs that support their work:
                       Enduring Understanding - Successful problem solvers possess a set of
F.7.2                  M.13.7.7                                Estimate and compute the area of more   *apply the formulas for finding the areas of regular two-
                       problem solving is of more              complex or significant time
                       Estimate and compute the areaimportant, takes irregular two-dimensional and repeated efforts, and requires reflection.
                                                                                                       basic shapes: circles, quadrilateral,        dimensional shapes
                       complex or irregular two-dimensional    shapes by dividing them into more basic triangles                                    irregular two-
                       shapes by dividing them into more basic shapes                                  *divide irregular/complex figures into basic dimensional shapes
                       shapes                                                                          2-dimensional shapes                         area
                                                                                                       *find the area of basic shapes and           complex
                                                                                                       combine these areas to find the area of
                                                                                                       the irregular figure

F.7.2                  G.8.7.5                                        Model and develop the concept that pi (π)   *measure the radius and diameter              pi (π)
                       Model and develop the concept that pi (π) is is the ratio of the circumference to the      *measure the circumference of circle          ratio
                       the ratio of the circumference to the diameter diameter of any circle                      *discover a relationship between the          circumference
                       of any circle                                                                              diameter and circumference (known as pi)      diameter
                                                                                                                  *apply the formula for finding the            radius
                                                                                                                  circumference of a circle                     chord


                       4. Enduring Understanding - Geometric relationships exist between two-dimensional and three-dimensional
                       figures.
                       4a. Essential Question - How are two-dimensional and three-dimensional figures related?
F.7.2           1      G.11.7.1                                      Build three-dimensional solids from two-     *match 2-dimensional patterns to 3-           rectangular prism
                       Build three-dimensional solids from two-      dimensional patterns (nets)                  dimensional solids                            pyramids
                       dimensional patterns (nets)                                                                *build 3-dimensional solids from a given 2-   cylinders
                                                                                                                  dimensional pattern (net)                     cones
                                                                                                                                                                3-dimensional solids
                                                                                                                                                                2-dimensional
                                                                                                                                                                patterns
                                                                                                                                                                nets


F.7.2           1      G.11.7.2                                      Construct a building out of cubes from a     *practice visualization skills using sets of cubes
                       Construct a building out of cubes from a      set of views (front, top, side)              cubes (front, back, right side, left side and
                       set of views (front, top, side)                                                            top)
                                                                                                                  *construct buildings using cubes




        rev. 05-2009                                                                                                                                                                           21 of 22
        7th Grade Math

                                                  Arch Ford/Northwest Arkansas Instructional Alignment
                                                              Seventh Grade Mathematics
                             AR Department of Education
 NCTM Focal    # of                                                                                                                                    Essential
                                                                                                                                                                           Materials/
   Point or   Times    CONTENT STANDARD/ Student Learning                       Objective                             Task Analysis                   Vocabulary
                                                                                                                                                                           Resources
  Connector   Tested           Expectations (SLE)                                                                                                   *teacher word

F.7.1           1      G.9.7.1                                      Examine the congruence, similarity, and *describe transformations-translations, congruence
                       Enduring Understanding - Successful symmetry of solvers possess arotations core beliefs that support
                       Examine the congruence, similarity, and line line or rotationalproblem objects       reflections, and set of                 similarity            their work:
                       or rotational symmetry of objects using      using transformations                   *identify symmetrical objects using     line symmetry
                                                                                                              repeated
                       problem solving is important, takes significant time andtransformations efforts, and requires reflection.
                       transformations                                                                                                              rotational symmetry
                                                                                                            *identify congruence/similarity in      transformations
                                                                                                            relationship to transformations         translations
                                                                                                                                                    reflections
                                                                                                                                                    rotations

                       




        rev. 05-2009                                                                                                                                                               22 of 22
                    problem solving is important, takes significant time andtransformations efforts, and requires reflection.
                       transformations                                                                                                              rotational symmetry
                                                                                                            *identify congruence/similarity in      transformations
                                                                                                            relationship to transformations         translations
                                                                                                                                                    reflections
                                                                                                                                                    rotations

                       




        rev. 05-2009                                                                                                                                                               22 of 22

								
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