K-6 2008 Math Core in Table Format by kellys3ps

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K-6 2008 Math Core in Table Format

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									K-6 Elementary Mathematics Core Curriculum in Table Format
                    st                nd                 rd                 th                  th                  th
Kindergarten       1 Grade           2 Grade            3 Grade            4 Grade             5 Grade             6 Grade
Standard 1:        Standard 1:       Standard 1:        Standard 1:        Standard 1:         Standard 1:         Standard 1:
Students will      Students will     Students will      Students will      Students will       Students will       Students will
understand         acquire number    acquire number     understand the     acquire number      expand number       expand number
simple number      sense and         sense with         base-ten           sense and           sense to include    sense to include
concepts and       perform simple    whole numbers      numeration         perform             integers and        operations with
relationships.     operations with   and fractions      system, place      operations with     perform             rational
                   whole numbers.    and                value              whole               operations with     numbers.
                                     perform            concepts, simple   numbers, simple     whole numbers,
                                     operations with    fractions and      fractions, and      simple fractions,
                                     whole numbers.     perform            decimals.           and decimals.
                                                        operations with
                                                        whole numbers.
Objective 1:       Objective 1:      Objective 1:       Objective 1:       Objective 1:        Objective 1:        Objective 1:
Identify and use   Represent and     Identify and       Represent whole    Demonstrate         Represent whole     Represent rational
whole numbers      use whole         represent the      numbers up to      multiple ways to    numbers and         numbers in a variety
up to 30.          numbers up to     relationships      10,000,            represent whole     decimals from       of ways.
                   100.              among numbers,     comprehend         numbers and         thousandths to
                                     quantities, and    place value        decimals, from      one billion,
                                     place value        concepts, and      hundredths to one   fractions,
                                     in whole numbers   identify           million, and        percents, and
                                     up to 1000.        relationships      fractions.          integers.
                                                        among whole
                                                        numbers using
                                                        base-ten models
                                                        and symbolic
a. Represent       a. Count, read,   a. Represent       a. Read, write,    a. Read and write   a. Read and write   a. Recognize a
whole numbers      and write whole   whole numbers in   and represent      numbers in          numbers in          rational number as a
using concrete,    numbers.          groups of          whole numbers      standard and        standard and        ratio of two integers,
pictorial, and                       hundreds, tens,    using standard     expanded form.      expanded form.      a to b, where b is not
symbolic                             and ones using     and expanded                                               equal to zero.
representations.                     base ten models    form.
                                            write the numeral
                                            representing the
                                            set in standard
                                            and expanded
b. Order a set of      b. Represent         b. Identify the      b. Demonstrate          b. Demonstrate         b. Demonstrate        b. Change whole
up to ten objects      whole numbers        place and the        multiple ways to        multiple ways to       multiple ways to      numbers with
and use ordinal        using the number     value of a given     represent               represent whole        represent whole       exponents to
numbers from first     line, models, and    digit in a three-    numbers using           numbers and            numbers,              standard form (e.g.,
to tenth to identify   number               digit numeral.       models and              decimals by using      decimals,             24 = 16) and
the                    sentences.                                symbolic                models and             fractions,            recognize that
position of the                                                  representations         symbolic               percents, and         any non-zero whole
object in the                                                    (e.g., fifty is the     representations        integers using        number to the zero
chosen order.                                                    same as two             (e.g., 36 is the       models and            power equals 1 (e.g.,
                                                                 groups of 25, the       same as the            symbolic              9^0 = 1).
                                                                 number of               square of six,         representations
                                                                 pennies in five         three dozen, or 9      (e.g., 108 = 2 x 50
                                                                 dimes, or 75 - 25).     x 4).                  + 8; 108 = 102 +
                                                                                                                  90% = 90 out of
                                                                                                                 100 squares on a
                                                                                                                  hundred chart).
c. Use one-to-one      c. Represent         c. Represent the     c. Identify the         c. Identify the        c. Identify, read,    c. Write a whole
correspondence         whole numbers        composition and      place and the           place and the          and locate            number in expanded
when counting a        greater than 10 in   decomposition of     value of a given        value of a given       fractions, mixed      form using
set of objects and     groups of tens       numbers in a         digit in a four-digit   digit in a six-digit   numbers,              exponents (e.g.,
develop a              and ones using       variety of ways.     numeral and             numeral, including     decimals, and         876,539 = 8 x 10^5
strategy for           objects,                                  round numbers           decimals               integers on the       +7x
keeping track of       pictures, and                             to the nearest ten,     to hundredths,         number                10^4 + 6 x 10^3 + 5
counted and            expanded                                  hundred, and            and round to the       line.                 x 10^2 + 3 x 10^1 +
uncounted              notation.                                 thousand.               nearest tenth.                               9 x 10^0).
                                            d. Compare and       d. Order and            d. Divide regions,     d. Represent          d. Express numbers
                                            order numbers        compare whole           lengths, and sets      repeated factors      in scientific notation
                                            using the terms,     numbers on a            of objects into        using exponents.      using positive
                                            greater than, less   number line and         equal parts using                            powers of ten.
                                          than, or equal to,    use the symbols       a variety of
                                          and the               <, >, ≠, and =        models and
                                          symbols, >, <,        when comparing        illustrations.
                                          and =, using          whole numbers.
                                          various strategies,
                                          including the
                                          number line.
                                          e. Identify and       e. Identify factors   e. Name and write   e. Describe
                                          describe even         and multiples of      a fraction to       situations where
                                          and odd whole         whole numbers.        represent a         integers could be
                                          numbers.                                    portion of a unit   used in the
                                                                                      whole, length, or   students’
                                                                                      set for halves,     environment.
                                                                                      thirds, fourths,
                                                                                      fifths, sixths,
                                                                                      eighths, and
                                                                                      f. Identify and
                                                                                      represent square
                                                                                      numbers using
                                                                                      models and
Objective 2:          Objective 2:        Objective 2: Use      Objective 2: Use      Objective 2:        Objective 2:        Objective 2: Explain
Identify and use      Identify simple     unit fractions to     fractions to          Analyze             Explain             relationships and
simple                relationships       identify parts of     describe and          relationships       relationships and   equivalencies
relationships         among whole         the whole and         compare parts of      among whole         equivalencies       among rational
among whole           numbers up to       parts of a set.       the whole.            numbers,            among integers,     numbers.
numbers up to 30.     100.                                                            commonly used       fractions,
                                                                                      fractions, and      decimals, and
                                                                                      decimals to         percents.
a. Estimate           a. Compare and      a. Divide             a. Identify the       a. Compare the      a. Compare          a. Place rational
quantities in a set   order sets of       geometric shapes      denominator of a      relative size of    fractions by        numbers on the
of objects using      objects and         into two, three, or   fraction as the       numbers (e.g.,      finding a common    number line.
multiples of 10 as    numbers using       four equal parts      number of equal       475 is comparable   denominator.
benchmark             the terms greater   and identify the      parts of the unit     to 500; 475 is
numbers.              than, less than,    parts as              whole and             small
                      and                 halves, thirds, or    the numerator of a    compared to
                      equal to when       fourths.              fraction as the       10,000 but large
                      describing the                            number of equal       compared to 98).
                      comparisons.                              parts being
b. Compose and        b. Make             b. Divide sets of     b. Define regions     b. Order whole      b. Order integers,   b. Compare and
decompose             reasonable          objects into two,     and sets of           numbers up to six   fractions            order rational
quantities to         estimates of the    three, or four        objects as a          digits, simple      (including mixed     numbers, including
establish a           quantitative        parts of equal        whole and divide      fractions, and      numbers), and        positive and
relationship          difference          number of objects     the whole into        decimals using a    decimals using a     negative mixed
between the parts     between two sets    and identify          equal parts using     variety of          variety of           fractions and
and the               of objects.         the parts as          a                     methods (e.g.,      methods,             decimals, using a
whole.                                    halves, thirds, or    variety of objects,   number line,        including the        variety of methods
                                          fourths.              models, and           fraction pieces)    number line.         and symbols,
                                                                illustrations.        and use the                              including the number
                                                                                      symbols <, >, and                        line and finding
                                                                                      = to record the                          common
                                                                                      relationships.                           denominators.
c. Recognize 5 or     c. Identify one     c. Represent the      c. Name and write     c. Identify a       c. Rewrite mixed     c. Find equivalent
10 as a part of the   more, one less,     unit fractions 1/2,   a fraction to         number that is      numbers and          forms for common
part-whole            10 more, and 10     1/3, and 1/4 with     represent a           between two         improper fractions   fractions, decimals,
relationship of       less than a given   objects, pictures,    portion of a unit     given numbers       from one form to     percents, and ratios,
numbers.              number.             words (e.g.,          whole for halves,     (e.g., 3.2 is       the other and        including
                                          ___out of             thirds, fourths,      between 3 and 4;    represent            repeating or
                                          ___ equal parts),     sixths, and           find a              each using           terminating
                                          and symbols.          eighths.              number between      regions, sets of     decimals.
                                                                                      0.1 and 0.2).       objects, or line
d. Compare sets       d. Identify                               d. Place fractions    d. Identify         d. Represent         d. Relate percents
of objects and        numbers missing                           on the number         equivalences        commonly used        less than 1% or
determine             from a counting                           line and compare      between fractions   fractions as         greater than 100% to
whether they          sequence.                                 and order             and decimals by     decimals and         equivalent fractions,
have the same,                                                  fractions using       connecting          percents in a        decimals, whole
fewer, or more                                                  models, pictures,     models to           variety of ways      numbers, and mixed
objects.                                                        the number line,      symbols.            (e.g.,               numbers.
                                                                and symbols.                              models, fraction
                                                                                                          strips, pictures,
                      e. Represent part-                         e. Find equivalent    e. Generate          e. Model and             e. Recognize that
                      whole                                      fractions using       equivalent           calculate                the sum of an
                      relationships                              concrete and          fractions and        equivalent forms         integer and its
                      using the number                           pictorial             simplify fractions   of a fraction            additive inverse is
                      line.                                      representations.      using models,        (including               zero.
                                                                                       pictures, and        simplest form).
                                                                                                            f. Rename whole
                                                                                                            numbers as
                                                                                                            fractions with
                                                                                                            (e.g., 5 = 5/1, 3 =
                                                                                                            6/2, 1 =
Objective 3:          Objective 3:          Objective 3:         Objective 3:          Objective 3:         Objective 3: Use         Objective 3: Use
Model, describe,      Model, describe,      Estimate, model,     Model problems        Model and            number theory            number theory
and illustrate        and illustrate the    illustrate,          involving addition,   illustrate           concepts to              concepts to find
meanings of           meanings of           describe, and        subtraction,          meanings of          develop and use          prime factorizations,
addition and          addition and          solve problems       multiplication, and   multiplication and   divisibility tests;      least common
subtraction for       subtraction and       involving two- and   division.             division of whole    classify whole           multiples,
whole                 use                   threedigit                                 numbers and          numbers to 50 as         and greatest
numbers less          these operations      addition and                               the addition and     prime, composite,        common factors.
than ten.             to solve              subtraction.                               subtraction of       or neither; and
                      problems.                                                        fractions.           find common
                                                                                                            multiples and
a. Demonstrate        a. Use a variety of   a. Demonstrate       a. Demonstrate        a. Model             a. Identify              a. Determine
the joining and       models, including     quick recall of      the meaning of        multiplication       patterns with skip       whether whole
separating of sets    objects, length-      addition facts (up   multiplication and    (e.g., equal-sized   counting and             numbers to 100 are
of objects to solve   based models,         to 10 + 10) and      division of whole     groups,              multiples to             prime, composite, or
problems.             the number line       related              numbers through       rectangular          develop and use          neither.
                      and the               subtraction facts.   the use               arrays, area         divisibility tests for
                      ten frame to                               of a variety of       models, equal        determining
                      describe problem                           representations       intervals on the     whether a whole
                     types (i.e., part-                         (e.g., equal-sized     number line),          number is
                     whole, combine,                            groups, arrays,        place value, and       divisible by 2, 3,
                     separate,                                  area models, and       properties of          5, 6, 9, and 10.
                     compare).                                  equal                  operations to
                                                                jumps on a             represent
                                                                number line for        multiplication of a
                                                                multiplication,        one- or two-digit
                                                                partitioning and       factor by a two-
                                                                sharing for            digit factor and
                                                                division).             connect the
                                                                                       representation to
                                                                                       an algorithm.
b. Describe the      b. Use the            b. Model addition    b. Use a variety of    b. Use rectangular     b. Use strategies    b. Find the prime
joining or           properties of         and subtraction of   strategies and         arrays to interpret    for classifying      factorization of
separating of sets   addition (i.e.,       two- and three-      tools, such as         factoring (e.g.,       whole numbers to     composite numbers
with informal        commutativity,        digit whole          repeated addition      find all rectangular   50 as prime,         to 100.
language when        associativity,        numbers (sums        or subtraction,        arrays of 36 tiles     composite, or
using models.        identity element)     and                  equal jumps            and                    neither.
                     and the               minuends to          on the number          relate the
                     mathematical          1000) in a variety   line, and counters     dimensions of the
                     relationship          of ways.             arranged in arrays     arrays to factors
                     between addition                           to model               of 36).
                     and subtraction to                         multiplication and
                     solve problems.                            division
c. Record            c. Compute basic      c. Write a story     c. Demonstrate,        c. Demonstrate         c. Rewrite a         c. Find the greatest
pictorially the      addition facts (up    problem that         using objects, that    the mathematical       composite            common factor and
results from         to 10 + 10) and       relates to a given   multiplication and     relationship           number between       least common
joining or           the related           addition or          division by the        between                2 and 50 as a        multiple for two
separating of        subtraction facts     subtraction          same number are        multiplication and     product of only      numbers using a
sets.                using                 equation, and        inverse operations     division (e.g., 3 x    prime numbers.       variety of methods
                     strategies (e.g., 6   write a              (e.g., 3 x □ = 12 is   □ = 12 is the                               (e.g., list of
                     + 7 = (6 + 4) + 3 =   number sentence      the same as 12 ÷       same as 12 ÷ 3 =                            multiples, prime
                     10 + 3 = 13).         to solve a story     3 = □ and □ = 4).      □ and □ = 4) and                            factorization).
                                           problem that is                             use that
                                           related to the                              relationship to
                                           environment.                                explain that
                                                                  division by zero is
                                                                  not possible.
d. Find the sum of   d. Demonstrate         d. Demonstrate        d. Represent           d. Find common
three one-digit      fluency with two-      the effect of place   division of a three-   multiples and
numbers.             and three-digit        value when            digit dividend by a    factors and apply
                     addition and           multiplying whole     one-digit divisor,     to adding and
                     subtraction            numbers by 10.        including whole        subtracting
                     problems, using                              number                 fractions.
                     efficient, accurate,                         remainders, using
                     and generalizable                            a variety of
                     strategies that                              methods (e.g.,
                     include standard                             rectangular
                     algorithms and                               arrays,
                     mental arithmetic,                           manipulatives,
                     and describe why                             pictures), and
                     the procedures                               connect the
                     work.                                        representation to
                                                                  an algorithm.
                     e. Use the             e. Write a story      e. Use models to
                     mathematical           problem that          add and subtract
                     relationship           relates to a given    simple fractions
                     between addition       addition,             where one single-
                     and subtraction        subtraction, or       digit denominator
                     and properties of      multiplication        is 1,
                     addition to model      equation, and         2, or 3 times the
                     and solve              write a number        other (e.g., 2/4 +
                     problems.              sentence to solve     1/4; 3/4 - 1/8).
                                            a problem related
                                            to the students’
                     Objective 4:           Objective 4:          Objective 4: Solve     Objective 4:         Objective 4: Model
                     Model, illustrate,     Compute and           problems               Model and            and illustrate
                     and pictorially        solve problems        involving              illustrate           meanings of
                     record solutions       involving addition    multiplication and     meanings of          operations and
                     to simple              and subtraction of    division of whole      multiplication and   describe how they
                     multiplication and     3- and 4-digit        numbers and            division.            relate.
                     division problems.     numbers and           addition and
                      basic facts of          subtraction of
                      multiplication and      simple fractions
                      division.               and decimals.
a. Represent          a. Use a variety of     a. Use estimation,   a. Represent         a. Relate fractions to
multiplication with   methods to              mental math,         division-with-       multiplication and
equal groups          facilitate              paper and pencil,    remainder using      division and use this
using concrete        computation (e.g.,      and calculators to   whole numbers,       relationship to
objects and skip      estimation, mental      perform              decimals, or         explain
counting by           math strategies,        mathematical         fractions.           procedures for
twos, fives, and      paper and pencil).      calculations and                          multiplying and
tens.                                         identify when to                          dividing fractions.
                                              use each one
b. Represent          b. Find the sum or      b. Select            b. Describe the      b. Recognize that
division as fair      difference of           appropriate          effect of place      ratios derive from
shares using          numbers,                methods to solve     value when           pairs of rows in the
concrete objects      including               a single operation   multiplying and      multiplication table
or pictures.          monetary                problem and          dividing whole       and connect
                      amounts, using          estimate             numbers and          with equivalent
                      models and              computational        decimals by 10,      fractions.
                      strategies such as      results or           100, and 1,000.
                      expanded form,          calculate them
                      compensation,           directly,
                      partial sums, and       depending on the
                      the standard            context and
                      algorithm.              numbers involved
                                              in a
                      c. Compute basic        c. Write a story     c. Model             c. Give mixed
                      multiplication facts    problem that         multiplication of    number and decimal
                      (0-10) and related      relates to a given   fractions and        solutions to division
                      division facts          multiplication or    decimals (e.g.,      problems with whole
                      using a variety of      division equation,   tenths multiplied    numbers.
                      strategies based        and select           by tenths, a whole
                      on properties of        and write a          number multiplied
                      addition and            number sentence      by tenths, or a
                      multiplication (i.e.,   to solve a problem   whole number
commutative,          related to the         with tenths
associative,          environment.           multiplied by
identity, zero, and                          tenths) in a
the distributive                             variety of ways
properties).                                 (e.g.,
                                             number line and
                                             area models,
                      d. Solve problems
                      involving simple
                      fractions and
                      interpret the
                      meaning of the
                      solution (e.g.,
                      A pie has been
                      divided into six
                      pieces and one
                      piece is already
                      gone. How much
                      of the
                      whole pie is there
                      when Mary comes
                      in? If Mary takes
                      two pieces, how
                      much of the
                      whole pie has she
                      taken? How much
                      of the pie is left?)
                      Objective 5:           Objective 5: Solve   Objective 5: Solve
                      Compute                problems             problems involving
                      problems               involving one or     multiple steps.
                      involving              two operations.
                      multiplication and
                      division of whole
                      numbers and
                      addition and
subtraction of
simple fractions
and decimals.
a. Demonstrate        a. Determine         a. Select appropriate
quick recall of       when it is           methods to solve a
basic                 appropriate to use   multi-step problem
multiplication and    estimation, mental   involving
division facts.       math strategies,     multiplication and
                      paper and            division of fractions
                      pencil, and          and decimals.
b. Multiply up to a   b. Make              b. Use estimation to
three- digit factor   reasonable           determine whether
by a two-digit        estimations of       results obtained
factor with           fraction and         using a calculator
fluency, using        decimal sums,        are reasonable.
efficient             differences, and
procedures.           products,
                      including knowing
                      whether results
                      obtained using a
                      calculator are
c. Divide up to a     c. Write number      c. Use estimation or
three-digit           sentences that       calculation to
dividend by a one-    can be used to       compute results,
digit divisor with    solve a two-step     depending on the
fluency, using        problem.             context and numbers
efficient                                  involved in the
procedures.                                problem.
d. Add and            d. Interpret         d. Solve problems
subtract decimals     division-with-       involving ratios and
and simple            remainder            proportions.
fractions where       problems as they
one single-digit      apply to the
denominator is 1,     environment (e.g.,
2,                    If there
or 3 times the       are 53 people,
other (e.g., 2/4 +   how many vans
1/4 = 3/4; 1/3 –     are needed if
1/6 = 1/6).          each van holds 8
                     Objective 6:          Objective 6:
                     Demonstrate           Demonstrate
                     proficiency with      proficiency with the
                     multiplication and    four operations, with
                     division of whole     positive rational
                     numbers and           numbers,
                     compute               and with addition
                     problems              and subtraction of
                     involving addition,   integers.
                     subtraction, and
                     multiplication of
                     decimals and
                     a. Multiply multi-    a. Multiply and divide
                     digit whole           a multi-digit number
                     numbers by a          by a two-digit
                     two-digit whole       number, including
                     number with           decimals.
                     fluency, using
                     b. Divide multi-      b. Add, subtract,
                     digit dividends by    multiply, and divide
                     a one-digit divisor   fractions and mixed
                     with fluency,         numbers.
                     using efficient
                     c. Add and            c. Add and subtract
                     subtract decimals     integers.
                     with fluency,
                     using efficient
                                                                                                              d. Add and
                                                                                                              subtract fractions
                                                                                                              with fluency.
                                                                                                              e. Multiply
Mathematical            Mathematical         Mathematical          Mathematical         Mathematical          Mathematical          Mathematical
Language and            Language and         Language and          Language and         Language and          Language and          Language and
Symbols                 Symbols              Symbols               Symbols              Symbols               Symbols               Symbols Students
Students Should         Students Should      Students Should       Students Should      Students Should       Students Should       Should Use
Use                     Use                  Use                   Use                  Use                   Use                   prime, composite,
add, subtract,          add, sum,            number line, add,     sum, difference,     sum, difference,      prime, composite,     exponent, least
first, second,          subtract,            sum, subtract,        expanded form,       expanded form,        exponent,             common multiple,
third, fourth, fifth,   difference,          difference, greater   factor, product,     standard form,        fractions,            least common
sixth, seventh,         greater than, less   than, less than,      array, multiple,     square number,        numerator,            denominator,
eighth, ninth,          than, equal to       equal to, >, <, =,    numerator,           dividend, divisor,    denominator,          greatest common
tenth, same,                                 even, odd,            denominator,         quotient, factor,     common                factor, decimals,
fewer, more                                  halves, thirds,       halves,              product, array,       denominator,          percents, divisible,
                                             fourths, 1/2, 1/3,    thirds, fourths,     multiple,             common                divisibility, equivalent
                                             1/4.                  sixths, eighths,     numerator,            factor, common        fractions, integer,
                                                                   divisor, dividend,   denominator,          multiple,             dividend, quotient,
                                                                   quotient, greater    sixths, eighths,      decimals,             divisor, factor,
                                                                   than, less than,     tenths, equivalent,   percents,             simplest terms,
                                                                   equal to, <, >, =    estimate, <, >,       divisible,            mixed numeral,
                                                                                        =, ≠                  divisibility,         improper fraction
                                                                                                              fractions, integer,
                                                                                                              dividend, quotient,
                                                                                                              divisor, factor,
                                                                                                              order of
                                                                                                              simplest terms,
                                                                                                              various symbols
                                                                                                              multiplication and
                                                                                                              division, mixed
                                                                                                              numeral, improper
Exploratory         Exploratory          Exploratory          Exploratory            Exploratory          Exploratory            Exploratory
Concepts and        Concepts and         Concepts and         Concepts and           Concepts and         Concepts and           Concepts and
Skills              Skills               Skills               Skills                 Skills               Skills                 Skills
��Count by ones,     ��Use concrete        ��Investigate         ��Extend                ��Use concrete        ��Extend                ��Explore the
beginning from      materials to         addition of          multiplication and     objects and visual   classification of      addition and
any number in the   investigate          common fractions     division to larger-    models to add        whole numbers          subtraction of
counting            situations that      (e.g., ½ + ½ = 1,    digit numbers.         and subtract         from 0-100 as          positive and
sequence.           lead to              ¼ + ¼ = ½ ).         ��Use concrete          common               prime, composite,      negative fractions.
��Represent          multiplication and   ��Investigate         objects and visual     decimals.            or neither.            ��Investigate the
quantities using    division.            comparing            models to add          ��Explore             ��Apply rules of        concepts of ratio and
concrete objects    ��Develop and         fractions in terms   and subtract           numbers less than    divisibility.          proportion.
and investigate     use strategies for   of greater than,     common                 zero by extending    ��Explore adding        ��Investigate the
partitioning of     addition and         less than, and       decimals.              the number line      and subtracting        distributive property
sets.               subtraction of       equal to.            ��Investigate the       and by using         integers.              of multiplication over
��Create             multi-digit whole    ��Understand          distributive           familiar             ��Divide multi-         addition of double-
problems that can   numbers.             situations that      property of            applications such    digit dividends by     digit
be solved using     ��Investigate the     entail               multiplication over    as temperature.      a two-digit divisor.   multipliers
addition and        meaning of           multiplication and   addition for single-   ��Investigate the
subtraction.        fraction concepts.   division, such as    digit                  concept of ratio
                    ��Understand          equal groupings      multipliers (e.g., 7   (e.g., the number
                    situations that      of                   x 15 is equivalent     of students to the
                    entail               objects and          to 7 x (10 + 5) is     number of
                    multiplication and   sharing equally.     equivalent to (7 x     teachers).
                    division, such as                         10) + (7 x 5).
                    equal groupings
                    objects and
                    sharing equally.

Standard 2:         Standard 2:          Standard 2:          Standard 2:            Standard 2:          Standard 2:            Standard 2:
Students will       Students will        Students will        Students will use      Students will use    Students will          Students will use
sort and classify   identify and use     model,               patterns,              patterns and         use patterns and       patterns, relations,
objects as well     number patterns      represent, and       symbols,               relations to         relations to           and algebraic
as recognize and    and properties       interpret            operations, and        represent            represent and          expressions to
create simple       to describe and      patterns and         properties of          mathematical         analyze                represent
patterns.           represent            number               addition               problems             mathematical           and analyze
                    mathematical         relationships to     and                    and number           problems and           mathematical
                      relationships.         create and solve      multiplication to    relationships.       number                problems and
                                             problems with         represent and                             relationships         number
                                             addition and          describe simple                           using algebraic       relationships.
                                             subtraction.          number                                    symbols.
Objective 1:          Objective 1:           Objective 1:          Objective 1:         Objective 1:         Objective 1:          Objective 1: Analyze
Identify, sort, and   Recognize,             Recognize,            Create, represent,   Identify, analyze,   Identify, analyze     algebraic
classify objects      describe, and          describe, create,     and analyze          and determine        and determine a       expressions, tables,
according to          represent              and extend            growing patterns.    rules for            rule for predicting   and graphs to
common                patterns with          growing patterns.                          describing           and extending         determine patterns,
attributes.           more than one                                                     numerical            numerical             relations,
                      attribute.                                                        patterns involving   patterns involving    and rules.
                                                                                        operations and       operations whole
                                                                                        nonnumerical         numbers,
                                                                                        growing patterns.    decimals, and
a. Sort objects       a. Sort and            a. Determine the      a. Create and        a. Analyze           a. Analyze and        a. Describe simple
into groups by        classify objects       next term in linear   extend growing       growing patterns     make predictions      relationships by
attribute and         using more than        patterns (e.g., 2,    patterns using       using objects,       about numeric         creating and
identify which        one attribute.         4, 6…; the            objects, numbers,    pictures,            patterns, including   analyzing tables,
attribute was                                number of hands       and tables.          numbers, and         decimals and          equations, and
used.                                        on one                                     tables to            fractions.            expressions.
                                             person, two                                determine a rule
                                             people, three                              for the pattern.
b. Describe           b. Identify, create,   b. Construct          b. Describe how      b. Recognize,        b. Determine a        b. Draw a graph and
multiple ways to      and label              models and skip       patterns are         represent, and       rule for the          write an equation
sort and classify a   repeating patterns     count by twos,        extended using       extend simple        pattern using         from a table of
group of objects.     using objects,         threes, fives, and    manipulatives,       patterns involving   organized lists,      values.
                      pictures, and          tens and relate to    pictures, and        multiples and        tables, objects,
                      symbolic notation.     repeated              numerical            other number         and variables.
                                             addition.             representations.     patterns (e.g.,
                                                                                        square numbers)
                                                                                        using objects,
                                                                                        numbers, and
                       c. Identify, create,                                          c. Identify simple                          c. Draw a graph and
                       and label growing                                             relationships in                            create a table of
                       patterns using                                                real-life contexts                          values from an
                       objects, pictures,                                            and use                                     equation.
                       and symbolic                                                  mathematical
                       notation.                                                     operations to
                                                                                     describe the
                                                                                     pattern (e.g., the
                                                                                     number of legs on
                                                                                     a given number of
                                                                                     chairs may be
                                                                                     determined by
                                                                                     counting by fours
                                                                                     or by multiplying
                                                                                     the number of
                                                                                     chairs by 4).
                       d. Use patterns to
                       establish skip
                       counting by twos,
                       fives, and tens.
Objective 2:           Objective 2:           Objective 2:        Objective 2:       Objective 2: Use      Objective 2: Use      Objective 2: Write,
Identify, duplicate,   Recognize and          Model, represent,   Recognize,         algebraic             algebraic             interpret, and use
describe, and          represent              and interpret       represent, and     expressions,          expressions,          mathematical
extend simple          mathematical           number              simplify simple    symbols, and          inequalities, or      expressions,
repeating and          relationships          relationships       number             properties of the     equations to          equations, and
growing patterns.      using symbols          using               relationships      operations to         represent and         formulas to
                       and use number         mathematical        using symbols,     represent,            solve simple          represent and solve
                       sentences with         symbols.            operations, and    simplify, and solve   real-world            problems that
                       operational                                properties.        mathematical          problems.             correspond to given
                       symbols to solve                                              equations and                               situations.
                       problems.                                                     inequalities.
a. Identify and        a. Recognize that      a. Recognize that   a. Represent       a. Use the order      a. Use properties     a. Solve single
describe simple        ―=‖ indicates that     ―≠‖ indicates a     numerical          of operations to      and the order of      variable linear
repeating patterns     the two sides of       relationship in     relationships as   evaluate, simplify,   operations            equations using a
with numbers and       an equation are        which the two       expressions,       and compare           involving addition,   variety of strategies.
shapes.                expressions of         sides of the        equations, and     mathematical          subtraction,
                       the same               inequality are      inequalities.      expressions           multiplication,
                     number.               expressions of                            involving the four     division, and the
                                           different numbers.                        operations,            use of
                                                                                     parentheses, and       parentheses to
                                                                                     the symbols <, >,      compute with
                                                                                     and = (e.g., 2x (4 -   whole numbers,
                                                                                     1) +                   decimals, and
                                                                                     3; of the two          fractions.
                                                                                     quantities 7 - (3 -
                                                                                     2) or (7 - 3) - 2,
                                                                                     which is greater?).
b. Duplicate and     b. Recognize that     b. Recognize that    b. Solve             b. Express single-     b. Use patterns,      b. Recognize that
extend simple        ―+‖ indicates the     symbols such as      equations            operation problem      models, and           expressions in
repeating patterns   joining of sets and   x, �� or ��in an
                                               ,                involving            situations as          relationships as      different forms can
with numbers and     that ―-‖ indicates    addition or          equivalent           equations and          contexts for          be equivalent and
shapes.              the separation of     subtraction          expressions (e.g.,   solve the              writing and           rewrite an
                     sets.                 equation             6 + 4 = Δ + 7).      equation.              solving simple        expression
                                           represent                                                        equations and         to represent a
                                           a number that will                                               inequalities with     quantity in a different
                                           make the                                                         whole number          way.
                                           statement true.                                                  solutions (e.g., 6x
                                                                                                            = 54; x + 3 = 7).
c. Describe          c. Write and solve    c. Use the           c. Use the >, <,     c. Recognize that                            c. Evaluate and
simple growing       number                commutative and      and = symbols to     a symbol                                     simplify expressions
patterns with        sentences from        associative          compare two          represents the                               and formulas,
shapes.              problem               properties of        expressions          same number                                  substituting given
                     situations            addition to          involving addition   throughout an                                values for the
                     involving addition    simplify             and                  equation or                                  variables
                     and                   calculations.        subtraction (e.g.,   expression                                   (e.g., 2x + 4; x = 2;
                     subtraction, using                         4 + 6 □ 3 + 2; 3 +   (e.g., Δ + Δ = 8;                            therefore, 2 (2) + 4 =
                     symbolic notation                          5 □ 16 - 9).         thus, Δ = 4).                                8).
                     for the missing
                     value (e.g., △+ 4
                     = 7).
d. Identify simple   d. Create problem                          d. Recognize and     d. Describe and
patterns in the      situations from                            use the              use the
environment.         given number                               commutative,         commutative,
                     sentences                                  associative,         associative,
                    involving addition                          distributive, and     distributive, and
                    and                                         identity properties   identity properties
                    subtraction.                                of                    of
                                                                addition and          addition and
                                                                multiplication, and   multiplication, and
                                                                the zero property     the zero property
                                                                of multiplication.    of multiplication.
Mathematical        Mathematical         Mathematical           Mathematical          Mathematical          Mathematical         Mathematical
Language and        Language and         Language and           Language and          Language and          Language and         Language and
Symbols             Symbols              Symbols                Symbols               Symbols               Symbols              Symbols Students
Students Should     Students Should      Students Should        Students Should       Students Should       Students Should      Should Use
Use                 Use                  Use                    Use                   Use                   Use                  order of operations,
sort, repeating     sort, attribute,     patterns, +, -, =, ≠   growing patterns,     growing pattern,      variety of symbols   sequence, function,
patterns, growing   repeating                                   expressions,          order of              for multiplication   pattern, algebraic
patterns            patterns, growing                           equations, <, >, =    operations,           and division such    expression,
                    patterns, skip                                                    parentheses,                               approximately equal,
                    count, number                                                     inequality,           symbols for          ≈,
                    sentence, symbol,                                                 expression,           multiplication       notation for
                    +, -, =                                                           equation,             and ÷                exponents: 43 or
                                                                                      associative           fraction bar (/ or   4^3, a number in
                                                                                      property,             —) as division       front of a variable
                                                                                      commutative           symbols; variable,   indicates
                                                                                      property,             order of             multiplication (e.g.,
                                                                                      distributive          operations,          3y
                                                                                      property, zero        parentheses,         means 3 times the
                                                                                      property of           inequality,          quantity y), formula,
                                                                                      multiplication, >,    expression,          generalization
                                                                                      <, =                  equation,
Exploratory         Exploratory          Exploratory            Exploratory           Exploratory           Exploratory          Exploratory
Concepts and        Concepts and         Concepts and           Concepts and          Concepts and          Concepts and         Concepts and
Skills              Skills               Skills                 Skills                Skills                Skills               Skills
��Explore skip        ��Investigate          ��Investigate          ��Use concrete        ��Use concrete         ��Solve multi-        ��Use physical
counting by fives,   situations with       situations with       materials to build   materials to build    step equations.      models to
tens, and twos.      variables as          variables as          an understanding     an understanding      ��Construct and       investigate and
                     unknowns and as       unknowns and as       of equality and      of equality and       analyze tables       describe how a
                     quantities that       quantities that       inequality.          inequality.           involving            change in one
                     vary.                 vary.                 ��Explore             ��Explore              equivalent ratios.   variable affects a
                                                                 properties of        properties of                              second variable.
                                                                 equality in number   equality in number                         ��Use models to
                                                                 sentences (e.g.,     sentences (e.g.,                           develop
                                                                 when equals are      when equals are                            understanding of
                                                                 added to equals,     added to equals,                           slope as constant
                                                                 then the sums are    then the sums are                          rate of change.
                                                                 equal; when          equal; when                                ��Model situations
                                                                 equals are           equals are                                 with proportional
                                                                 multiplied by        multiplied by                              relationships and
                                                                 equals, then the     equals, then the                           solve problems.
                                                                 products are         products are
                                                                 equal.               equal).

Standard 3:          Standard 3:           Standard 3:           Standard 3:          Standard 3:           Standard 3:          Standard 3:
Students will        Students will         Students will         Students will        Students will         Students will        Students will use
understand           understand            understand            describe and         understand            use spatial          spatial and logical
basic geometry       simple geometry       simple geometry       analyze              attributes and        reasoning to         reasoning to
and                  and                   and                   attributes of two-   properties of         recognize,           recognize,
measurement          measurement           measurement           dimensional          plane geometric       describe, and        describe, and
concepts as well     concepts as well      concepts as well      shapes.              objects               analyze              analyze geometric
as                   as collect,           as collect,                                and spatial           geometric            shapes and
collect and          represent, and        represent, and                             relationships.        shapes and           principles.
organize data.       draw                  draw                                                             principles.
                     conclusions           conclusions
                     from data.            from data.
Objective 1:         Objective 1:          Objective 1:          Objective 1:         Objective 1:          Objective 1:         Objective 1: Identify
Identify and         Identify, describe,   Describe, classify,   Describe and         Identify and          Describe             and analyze
create simple        and create simple     and create            compare              describe attributes   relationships        attributes and
geometric shapes     geometric figures.    geometric figures.    attributes of two-   of two-               between two- and     properties of
and describe                                                     dimensional          dimensional           three-dimensional    geometric shapes to
simple spatial                                                   shapes.              geometric shapes.     shapes and           solve
relationships.                                                                                                   analyze             problems.
                                                                                                                 attributes and
                                                                                                                 properties of
a. Identify, name,    a. Name, create,     a. Describe and          a. Identify,           a. Name and           a. Draw, label,     a. Identify the
describe, and         and sort             classify plane and       describe, and          describe lines that   and describe line   midpoint of a line
draw circles,         geometric plane      solid geometric          classify polygons      are parallel,         segments, rays,     segment and the
triangles,            figures (i.e.,       figures (i.e., circle,   (e.g., pentagons,      perpendicular,        lines, parallel     center and
rectangles, and       circle, triangle,    triangle,                hexagons,              and intersecting.     lines, and          circumference of a
squares in various    rectangle, square,   rectangle,               octagons).                                   perpendicular       circle.
sizes and             trapezoid,           square, trapezoid,                                                    lines.
orientations.         rhombus,             rhombus,
                      parallelogram,       parallelogram,
                      hexagon).            pentagon,
                                           hexagon, cube,
                                           sphere, cone)
                                           according to the
                                           number of sides
                                           and angles or
                                           faces, edges, and
b. Combine            b. Identify          b. Compose and           b. Identify            b. Identify and       b. Draw, label,     b. Identify angles as
shapes to create      geometric plane      decompose                attributes for         describe right,       and define an       vertical, adjacent,
two-dimensional       and solid figures    shapes and               classifying            acute, obtuse,        angle as two rays   complementary, or
objects (e.g.,        (i.e., circle,       figures by               triangles (e.g., two   and straight          sharing a           supplementary and
using a triangle      triangle,            substituting             equal sides for the    angles.               common endpoint     provide
and square to         rectangle, square,   arrangements of          isosceles triangle,                          (vertex).           descriptions of these
create a picture of   trapezoid,           smaller                  three equal sides                                                terms.
a house).             hexagon,             shapes for larger        for the equilateral
                      rhombus,             shapes or                triangle, right
                      parallelogram,       substituting larger      angle for the right
                      cube, sphere,        shapes for               triangle).
                      cone) in the         arrangements of
                      students’            smaller shapes.
c. Use words to       c. Compose and       c. Compose and           c. Identify            c. Identify and       c. Classify         c. Develop and use
describe position     decompose plane      decompose            attributes for        describe the        triangles and          the properties of
and distance.         and solid figures    shapes and           classifying           radius and          quadrilaterals and     complementary and
                      (e.g., make two      figures and          quadrilaterals        diameter of a       analyze the            supplementary
                      triangles from a     describe the part-   (e.g., parallel       circle.             relationships          angles and the sum
                      square)              whole                sides for the                             among the              of the angles of a
                      and describe the     relationships,       parallelogram,                            shapes in              triangle to solve
                      part-whole           similarities, and    right angles for                          each classification    problems involving
                      relationships, the   differences.         the rectangle,                            (e.g., a square is     an unknown angle in
                      attributes of the                         equal sides and                           a rectangle).          a triangle or
                      figures, and how                          right angles for                                                 quadrilateral.
                      they are                                  the square).
                      different and
d. Investigate two-                                             d. Identify right     d. Identify and     d. Relate
and three-                                                      angles in             describe figures    pyramids and
dimensional                                                     geometric figures,    that have line      right prisms to the
shapes including                                                or in appropriate     symmetry and        two-dimensional
hexagons,                                                       objects, and          rotational          shapes (nets)
trapezoids,                                                     determine             symmetry.           from which they
spheres,                                                        whether                                   were created.
cubes, and cones.                                               other angles are
                                                                greater or less
                                                                than a right angle.
                                                                                                          e. Identify
                                                                                                          properties and
                                                                                                          attributes of solids
                                                                                                          (i.e., right prisms,
                                                                                                          cylinders, cones)
                                                                                                          and describe
                                                                                                          them by the
                                                                                                          number of edges,
                                                                                                          faces, and
                                                                                                          vertices as well as
                                                                                                          the types of faces.
Objective 2:          Objective 2:         Objective 2:         Objective 2:          Objective 2:        Objective 2:           Objective 2:
Identify and use      Identify             Identify and use     Demonstrate the       Specify locations   Specify locations      Visualize and
measurable           measurable           units of measure,     meaning of          using grids and       in a coordinate      identify geometric
attributes of        attributes of        iterate (repeat)      congruence          maps.                 plane.               shapes after
objects and units    objects and units    that unit, and        through applying                                               applying
of measurement.      of measurement,      compare the           transformations.                                               transformations on a
                     and use              number of                                                                            coordinate plane.
                     appropriate          iterations to the
                     techniques and       item being
                     tools to determine   measured.
a. Identify clocks   a. Identify the      a. Identify and       a. Demonstrate      a. Locate             a. Locate points     a. Rotate a polygon
and calendars as     appropriate tools    use measurement       the effect of       coordinates in the    defined by           about the origin by a
tools that           for measuring        units to measure,     reflection,         first quadrant of a   ordered pairs of     multiple of 90° and
measure time.        length, weight,      to the nearest        translation, or     coordinate grid.      integers.            identify the location
                     capacity,            unit, length (i.e.,   rotation using                                                 of the new
                     temperature, and     inch,                 objects.                                                       vertices.
                     time.                centimeter),
                                          weight in pounds,
                                          and capacity in
b. Identify a day,   b. Measure the       b. Estimate and       b. Determine        b. Give the           b. Write an          b. Translate a
week, and month      length of an         measure length        whether two         coordinates in the    ordered pair for a   polygon either
on a calendar and    object using         by iterating a        polygons are        first quadrant of a   point in a           horizontally or
name the days of     nonstandard units    nonstandard or        congruent by        coordinate grid.      coordinate plane     vertically on a
the week in order.   and count the        standard unit of      reflecting,                               with integer         coordinate grid and
                     units using          measure.              translating, or                           coordinates.         identify the
                     groups                                     rotating one                                                   location of the new
                     of tens and ones.                          polygon to                                                     vertices.
                                                                physically fit on
                                                                top of the other.
c. Identify          c. Identify the      c. Use different                          c. Locate regions     c. Specify           c. Reflect a polygon
pennies, nickels,    value of a penny,    units to measure                          on a map of Utah.     possible paths       across either the x-
dimes, and           nickel, dime,        the length of the                                               between locations    or y-axis and identify
quarters as units    quarter, and         same object and                                                 on a coordinate      the location of the
of money.            dollar, and          recognize that the                                              plane and            new
                     determine the        smaller                                                         compare              vertices.
                     value of             the unit, the more                                              distances of
                     a set of the same    iterations needed                                               the various paths.
                    coins that total      to cover a given
                    25¢ or less (e.g.,    length.
                    a set of 5 nickels
                    equals 25¢).
d. Compare two      d. Tell time to the   d. Determine the      d. Give the
objects by          hour and half-        value of a set of     regions of a
measurable          hour.                 up to five coins      position on a map
attributes (i.e.,                         that total $1.00 or   of Utah.
length, weight)                           less (e.g., three
and order several                         dimes,
objects by                                one nickel, and
measurable                                one penny equals
attributes (i.e.,                         36¢).
length, weight).
                    e. Name the           e. Tell time to the
                    months of the         quarter-hour and
                    year and seasons      sequence a series
                    in order, and use     of daily events by
                    a calendar to         time (e.g.,
                    determine the day     breakfast
                    of the week and       at 7:00 a.m.,
                    date.                 school begins at
                                          9:00 a.m, school
                                          ends at 3:00
Objective 3:        Objective 3:          Objective 3:          Objective 3:
Collect and         Collect, organize,    Collect, record,      Visualize and
organize simple     and represent         organize, display,    identify geometric
data.               simple data.          and interpret         shapes after
                                          numerical data.       applying
a. Pose questions   a. Collect and        a. Collect and        a. Identify a
and gather data     represent data        record data           translation,
about self and      using tables, tally   systematically,       rotation, or a
surroundings.       marks,                using a strategy      reflection of a
                    pictographs, and      for keeping track     geometric shape.
                    bar graphs.           of what has been
b. Organize data     b. Describe and      b. Organize and                             b. Recognize that
obtained from        interpret data.      represent the                               90°, 180°, 270°,
sorting and                               same data in                                and 360° are
classifying                               more than one                               associated,
objects.                                  way.                                        respectively, with
                                                                                      1/4, 1/2, 3/4,
                                                                                      and full turns.
                                          c. Organize,
                                          display, and label
                                          including keys,
                                          using pictographs,
                                          tallies, bar
                                          graphs, and
                                          organized tables.
                                          d. Describe data
                                          represented on
                                          charts and graphs
                                          and answer
                                          simple questions
                                          related to data
Mathematical         Mathematical         Mathematical          Mathematical          Mathematical          Mathematical        Mathematical
Language and         Language and         Language and          Language and          Language and          Language and        Language and
Symbols              Symbols              Symbols               Symbols               Symbols               Symbols             Symbols Students
Students Should      Students Should      Students Should       Students Should       Students Should       Students Should     Should Use
Use                  Use                  Use                   Use                   Use                   Use                 midpoint,
circle, triangle,    circle, triangle,    inch, centimeter,     polygon, attribute,   parallel,             perpendicular and   circumference,
rectangle, square,   rectangle, square,   pound, cup, circle,   quadrilateral,        perpendicular,        parallel lines,     complementary and
Sunday, Monday,      trapezoid,           triangle,             equilateral           intersecting lines,   rays, angles        supplementary
Tuesday,             hexagon,             rectangle, square,    triangle, isosceles   right angle, acute    (acute, obtuse,     angles, rotate,
Wednesday,           rhombus,             trapezoid,            triangle, right       angle, obtuse         right, straight),   translate, reflect,
Thursday, Friday,    parallelogram,       rhombus,              triangle,             angle, straight       triangles           transformation
Saturday, penny,     cube, sphere,        parallelogram,        pentagon,             angle,                (equilateral,
nickel, dime,        cone,                pentagon,             hexagon,              circle, radius,       isosceles,
quarter, shorter,    penny, nickel,       hexagon, cube,        octagon, parallel,    diameter, line        scalene, right,
longer, above,       dime, quarter,       sphere, cone,      right angle,           symmetry,              acute, obtuse),
below, near, far,    dollar, January,     vertices, angle,   reflect, translate,    rotational             vertex, vertices,
between              February, March,     face, edge,        rotate, slide, flip,   symmetry,              edge, face,
                     April, May , June,   weight, length,    turn, congruent        coordinate, first      corresponding
                     July, August,        capacity                                  quadrant, degree,      angles, similar,
                     September,                                                     translate, rotate,     polygon, pyramid,
                     October,                                                       reflect,               right prism
                     November,                                                      transformation
                     winter, spring,
                     summer, fall,
                     data, value,
                     graph, tally
Exploratory          Exploratory          Exploratory        Exploratory            Exploratory            Exploratory           Exploratory
Concepts and         Concepts and         Concepts and       Concepts and           Concepts and           Concepts and          Concepts and
Skills               Skills               Skills             Skills                 Skills                 Skills                Skills
��Measure             ��Compare             ��Use verbal        ��Explore line          ��Analyze results       ��Compare              ��Use manipulatives
objects using non-   objects using        instructions to    symmetry and           of transformations     corresponding         and technology to
standard units.      non-standard         move within the    rotational             (e.g., translations,   angles of two         model geometric
��Identify the        units.               environment.       symmetry.              rotations,             triangles and         shapes.
value of a penny,    ��Interpret data      ��Determine         ��Investigate two-      reflections) on        determine             ��Investigate
nickel, dime, and    from charts and      simple             dimensional            twodimensional         whether the           tessellations.
quarter.             graphs.              equivalencies of   representations of     shapes.                triangles are         ��Explore the angles
��Organize data                            measurements.      three-dimensional      ��Investigate two-      similar.              formed by
in lists, tables,                         ��Conduct simple    objects.               dimensional            ��Rotate a shape       intersecting lines.
and simple                                probability                               representations of     around a fixed        ��Identify and draw
graphs.                                   experiments.                              three-dimensional      point and identify    shapes and figures
                                                                                    objects.               the location of the   from different
                                                                                                           new vertices.         views/perspectives.
                                                                                                           ��Translate a
                                                                                                           polygon either
                                                                                                           horizontally or
                                                                                                           vertically on a
                                                                                                           coordinate grid
                                                                                                           and identify the
                                                                                                           location of the
                                            new vertices.
                                            ��Reflect a shape
                                            across either the
                                            x- or y-axis and
                                            identify the
                                            location of the
                                            new vertices.

Standard 4:            Standard 4:          Standard 4:          Standard 4:
Students will          Students will        Students will        Students will
select and use         describe             determine area       understand and
appropriate units      relationships        of polygons and      apply
and                    among units of       surface area and     measurement tools
measurement            measure, use         volume of            and techniques
tools to solve         appropriate          three-               and
problems.              measurement          dimensional          find the
                       tools, and use       shapes.              circumference and
                       formulas to find                          area of a circle.
Objective 1:           Objective 1:         Objective 1:         Objective 1:
Select and use         Describe             Determine the        Describe and find
appropriate tools      relationships        area of polygons     the circumference
and units to           among units of       and apply to real-   and area of a circle.
estimate and           measure for          world problems.
measure length,        length, capacity,
weight,                and weight,
capacity, time,        and determine
and perimeter of       measurements of
two-dimensional        angles using
figures.               appropriate tools.
a. Describe the        a. Describe the      a. Determine the     a. Explore the
part-whole             relative size        area of a            relationship between
relationships (e.g.,   among metric         trapezoid by the     the radius and
3 feet in a yard, a    units of length      composition and      diameter of a circle
foot is 1/3 of a       (i.e., millimeter,   decomposition of     to the circle’s
yard) between          centimeter,          rectangles,          circumference to
metric units of        meter),                triangles, and       develop the formula
length (i.e.,          between metric         parallelograms.      for circumference.
centimeter,            units of capacity
meter), and            (i.e., milliliter,
among customary        liter), and
units of length        between metric
(i.e.,                 units of weight
inch, foot, yard),     (i.e., gram,
capacity (i.e., cup,   kilogram).
quart), and weight
(i.e., pound,
b. Measure the         b. Describe the        b. Determine the     b. Find the
length of objects      relative size          area of irregular    circumference of a
to the nearest         among customary        and regular          circle using a
centimeter, meter,     units of capacity      polygons by the      formula.
half- and quarter-     (i.e., cup, pint,      composition and
inch, foot,            quart, gallon).        decomposition of
and yard.                                     rectangles,
                                              triangles, and
c. Measure             c. Estimate and        c. Compare areas     c. Describe pi as the
capacity using         measure capacity       of polygons using    ratio of the
cups and quarts,       using milliliters,     different units of   circumference to the
and measure            liters, cups, pints,   measure within       diameter of a circle.
weight using           quarts, and            the same
pounds and             gallons, and           measurement
ounces.                measure weight         system (e.g.,
                       using grams and        square feet,
                       kilograms.             square yards).
d. Identify the        d. Recognize that                           d. Decompose a
number of              angles are                                  circle into a number
minutes in an          measured in                                 of wedges and
hour, the number       degrees and                                 rearrange the
of hours in a day,     develop                                     wedges into a shape
the number of          benchmark angles                            that
days in a year,        (e.g., 45°,                                 approximates a
and the number of    60°, 120°) using                           parallelogram to
weeks in a year.     90° angles to                              develop the formula
                     estimate angle                             for the area of a
                     measurement.                               circle.
e. Describe          e. Measure                                 e. Find the area of a
perimeter as a       angles using a                             circle using a
measurable           protractor or angle                        formula.
attribute of two-    ruler.
figures, and
estimate and
perimeter with
metric and
customary units.
Objective 2: Solve   Objective 2:           Objective 2:        Objective 2: Identify
problems             Recognize and          Recognize,          and describe
involving            describe area as       describe, and       measurable
measurements.        a measurable           determine surface   attributes of objects
                     attribute of two-      area and volume     and units of
                     dimensional            of three-           measurement,
                     shapes                 dimensional         and solve problems
                     and calculate area     shapes.             involving
                     measurements.                              measurement.
a. Determine         a. Quantify area       a. Quantify         a. Recognize that
simple               by finding the total   volume by finding   measurements are
equivalences of      number of same-        the total number    approximations and
measurements         sized units of area    of same-sized       describe how the
(e.g., 30 inches =   needed to fill the     units of volume     size of the unit
2 feet and 6         region without         needed to fill      used in measuring
inches; 6            gaps or overlaps.      the space without   affects the precision.
cups = 1½ quarts;                           gaps or overlaps.
90 min. = 1 hr. 30
b. Compare given     b. Recognize that      b. Recognize that   b. Convert units of
objects according    a square that is 1     a cube having a 1   measurement within
to measurable        unit on a side is      unit edge is the    the metric system
attributes (i.e.,     the standard unit     standard unit for     and convert units of
length, weight,       for measuring         measuring             measurement
capacity).            area.                 volume                within the customary
                                            expressed as a        system.
                                            cubic unit.
c. Solve problems     c. Develop the        c. Derive and use     c. Compare a meter
involving             area formula for a    the formula to        to a yard, a liter to a
perimeter.            rectangle and         determine the         quart, and a
                      connect it with the   volume of a right     kilometer to a mile.
                      area model for        prism with a
                      multiplication.       triangular or
                                            rectangular base.
d. Determine          d. Develop and        d. Relate the         d. Determine when it
elapsed time in       use the area          formulas for the      is appropriate to
hours (e.g., 7:00     formula for a right   areas of triangles,   estimate or use
a.m. to 2:00 p.m.).   triangle by           rectangles, or        precise
                      comparing with        parallelograms to     measurement when
                      the formula for a     the surface           solving
                      rectangle (e.g.,      area of a right       problems.
                      two of the same       prism.
                      right triangles
                      makes a
                      e. Develop, use,      e. Derive and use     e. Derive and use
                      and justify the       the formula to        the formula to
                      relationships         determine the         determine the
                      among area            surface area of a     surface area and
                      formulas of           right prism and       volume of a cylinder.
                      triangles and         express
                      parallelograms by     surface area in
                      decomposing and       square units.
                      comparing with
                      areas of right
                      triangles and
                      f. Determine
                     perimeters, in
                     whole units, for a
                     rectangle with a
                     fixed area, and
                     possible areas
                     when given a
                     rectangle with a
                     fixed perimeter.
Mathematical         Mathematical         Mathematical          Mathematical
Language and         Language and         Language and          Language and
Symbols              Symbols              Symbols               Symbols Students
Students Should      Students Should      Students Should       Should Use
Use                  Use                  Use                   cylinder, radius,
measure, unit,       millimeter,          area, volume,         diameter,
metric system,       centimeter, meter,   surface area,         circumference, area,
customary            milliliter, liter,   volume, right         surface area,
system, length,      gram, kilogram,      prism                 volume, π
pound, ounce,        cup, pint, quart,
centimeter, meter,   gallon, area,
inch,                perimeter
foot, yard,
capacity, weight,
Exploratory          Exploratory          Exploratory           Exploratory
Concepts and         Concepts and         Concepts and          Concepts and
Skills               Skills               Skills                Skills
��Determine the       ��Investigate         ��Investigate pi       ��Investigate
value of a           perimeter of         as the ratio of the   volumes and surface
combination of       rectangles and       circumference to      areas of a variety of
coins and bills.     squares.             the diameter of a     three-dimensional
��Count back          ��Investigate area    circle.               objects.
change from a        of trapezoids.       ��Determine the
single purchase.                          volume of a right
                                          prism with various
Standard 5:           Standard 5:          Standard 5:          Standard 5:
Students will         Students will        Students will        Students will
collect and           interpret and        construct,           analyze, draw
organize data to      organize             analyze, and         conclusions, and
make                  collected data to    construct            make predictions
predictions and       make                 reasonable           based upon
identify basic        predictions,         conclusions          data and apply
concepts of           answer               from                 basic concepts of
probability.          questions, and       data and apply       probability.
                      describe basic       basic concepts
                      concepts of          of probability.
Objective 1:          Objective 1:         Objective 1:         Objective 1: Design
Collect, organize,    Collect, organize,   Formulate and        investigations to
and display data      and display data     answer questions     reach conclusions
to make               to answer            using statistical    using statistical
predictions.          questions.           methods to           methods to make
                                           compare data,        inferences based on
                                           and                  data.
                                           propose and
                                           justify inferences
                                           based on data.
a. Collect, read,     a. Identify a        a. Construct,        a. Design
represent, and        question that can    analyze, and         investigations to
interpret data        be answered by       display data using   answer questions.
using tables,         collecting data.     an appropriate
graphs, and                                format (e.g., line
charts, including                          plots, bar
keys                                       graphs, line
(e.g., pictographs,                        graphs).
bar graphs,
frequency tables,
line plots).
b. Make               b. Collect, read,    b. Recognize the     b. Extend data
predictions based     and interpret data   differences in       display and
on a data display.    from tables,         representing         comparisons to
                      graphs, charts,      categorical and      include scatter plots
                       surveys, and           numerical data.      and circle graphs.
                       c. Represent data      c. Identify          c. Compare two
                       using frequency        minimum and          similar sets of data
                       tables, bar            maximum values       on the same graph
                       graphs, line plots,    for a set of data.   and compare two
                       and stem and leaf                           graphs representing
                       plots.                                      the same set of data.
                       d. Identify and        d. Identify and      d. Recognize that
                       distinguish            calculate the        changing the scale
                       between clusters       mean, median,        influences the
                       and outliers of a      mode, and range.     appearance of a
                       data set.                                   display of data.
                                                                   e. Propose and
                                                                   justify inferences
                                                                   and predictions
                                                                   based on data.
Objective 2:           Objective 2:           Objective 2: Apply   Objective 2: Apply
Identify basic         Describe and           basic concepts of    basic concepts of
concepts of            predict simple         probability.         probability and justify
probability.           random                                      outcomes.
a. Describe the        a. Describe the        a. Describe the      a. Write the results
results of events      results of             results of           of a probability
using the terms        experiments            experiments          experiment as a
―certain,‖ ―likely,‖   involving random       involving random     fraction between
―unlikely,‖ and        outcomes as            outcomes using a     zero and one, or an
―impossible.‖          simple ratios (e.g.,   variety of           equivalent percent.
                       4                      notations (e.g., 4
                       out of 9, 4/9).        out of 9, 4/9).
b. Conduct simple      b. Conduct simple      a. Describe the      b. Compare
probability            probability            results of           experimental results
experiments,           experiments, with      experiments          with theoretical
record possible        and without            involving random     results (e.g.,
outcomes               replacement,           outcomes using a     experimental: 7 out
systematically,        record possible        variety of           of 10 tails;
and                    outcomes               notations (e.g., 4   whereas, theoretical
display results in    systematically,         out of 9, 4/9).     5 out of 10 tails).
an organized way      and display
(e.g., chart,         results in an
graph).               organized way.
c. Use results of     c. Use the results      c. Express the      c. Compare
simple probability    of simple               likelihood of an    individual, small
experiments to        probability             outcome in a        group, and large
describe the          experiments, with       simple experiment   group results of a
likelihood of a       and without             as a value          probability
specific              replacement, to         between 0 and 1     experiment in
outcome in the        describe the            (inclusively).      order to more
future.               likelihood of a                             accurately estimate
                      specific outcome                            the actual
                      in the future.                              probabilities.
Mathematical          Mathematical            Mathematical        Mathematical
Language and          Language and            Language and        Language and
Symbols               Symbols                 Symbols             Symbols Students
Students Should       Students Should         Students Should     Should Use
Use                   Use                     Use                 data display, scatter
data, table, chart,   data, line plot, line   data, minimum       plot, circle graph,
graph, frequency      graph, bar graph,       values, maximum     scale, predict, justify,
table, line plot,     stem and leaf plot,     values, mean,       probability,
pictograph, bar       cluster, outlier,       median, mode,       experimental results,
graph, likely,        frequency table,        average, range      theoretical results
certain, outcome,     probability
Exploratory           Exploratory             Exploratory         Exploratory
Concepts and          Concepts and            Concepts and        Concepts and
Skills                Skills                  Skills              Skills
��Predict              ��Explore                ��Explore the        ��Investigate the
outcomes of           minimum and             differences in      notion of fairness in
simple                maximum values          representing        games.
experiments.          for a set of data.      categorical and
                      ��Explore mean,          numerical data.
                      median, mode,
                      and range.

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