Fourth_Grade

Document Sample
Fourth_Grade Powered By Docstoc
					Lake County Schools
 Fourth Grade Math
  Curriculum Map
                                                                                               Preface
Teams of Lake County teachers created the curriculum maps in order to ensure that all students throughout the district receive a common curriculum. The maps help ensure that all state
requirements are taught and that the content is divided into teachable segments with appropriate pacing. The curriculum maps will guide your instruction but provide flexibility based on the individual
needs of students. The maps are living documents and feedback is requested of teachers to ensure continuous improvement.

All teachers are expected to use the curriculum maps, in conjunction with data, to drive instruction. The maps were designed for the instruction to take place by quarter. There is some flexibility within
the quarters for mastery and re-teaching. The expectation is that teachers will finish the content within each quarter in its entirety. The maps have been structured in such a way as to scaffold student
learning.

Listed below are a few of the new or updated features common to all curriculum maps:

Essential Question(s):
    o Provide application of the skills/concepts
    o Have more than one right answer which promotes student discourse
    o Increase the rigor in the classroom, by changing from teacher-centered to student-centered learning
    o Are referred to at the beginning, middle, and end of the lesson
    o Require you to make a decision
    o Promote critical thinking and problem solving
    o Encourage interdependence
    o Are open-ended

Academic Vocabulary are:
    o Unfamiliar vocabulary that are essential to understanding new content within explicit instruction
    o Not necessarily the bold words in the chapter.
    o Cumulative and continuously used throughout the year.
    o Integrated into word walls, a research-based strategy that will facilitate vocabulary acquisition.

Common Board Configuration Elements (specific layouts may vary by sites, but must include each of these):
Purpose: For the student to know what is being taught and what the student will learn
    o Date
    o Benchmark
    o Measurable, student-friendly objective
    o Essential Question
    o Bell work
    o Agenda (Specific daily schedule)
    o Homework
    o Exit Strategy/Card

Lessons that infuse reading, writing, and discussion are imperative components of every subject area. There should be daily:
    o Teacher to student and student to student discourse utilizing academic vocabulary.
    o Reading and authentic writing

                                                                                                                                                                                                           2
                                                                               June 11, 2010…DRAFT
                                                               **Problem solving to be embedded throughout the year**
                                                                                      Preface
    o    Writing that includes higher-order thinking
    o    Incorporation of effective reading and writing instructional strategies

Maps are organized to include the following:

    o    Pacing
    o    Objective
    o    Essential questions, content and understanding, benchmarks, and assessment
    o    Appendix/ resources




                                                                                                                        3
                                                                               June 11, 2010…DRAFT
                                                               **Problem solving to be embedded throughout the year**
                                                Elementary Mathematics Fourth Grade Pacing Guide
          First Nine Weeks                     Second Nine Weeks                        Third Nine Weeks                     Fourth Nine Weeks
Big Idea #1: Multiplication            Big Idea #2: Decimals and Fractions     Big Idea #3: Area of 2-dimensional   Finding Sums of Decimal Amounts
                                                                               shapes
Use and Represent Whole Numbers (3     Multiply by 2-Digit and 3-Digit Whole                                        Multiplication to Estimate Quotients
weeks)                                 Numbers (3 weeks)                       Decimal Place Value and Number
                                                                               Sense (2 weeks)                      Fractions and Division
Multiplication and Division Concepts   Model Division by 1-Digit and 2-Digit
and Facts (2 weeks)                    Division (3 weeks)                      Understand Area (2 weeks)            Divisibility Rules

Algebra: Expressions, Equations, and   Factors, Multiples, and Fractions (2    Angles and Two-Dimensional Shapes    Factor Whole Numbers
Patterns (2 Weeks)                     weeks)                                  (3 weeks)
                                                                                                                    Fractions and Mixed Numbers
Multiply by 1-Digit Whole Numbers (2   Understand Decimal Place Value (2       Transformations and Symmetry (1
weeks)                                 weeks)                                  week)                                Order of Operations

                                                                               Relate Two-Dimensional Shapes and    Addition Properties
                                                                               Three-Dimensional Shapes
                                                                               (1 Week)                             Compare and Order Numbers

                                                                                                                    Temperature

                                                                                                                    Points on a Grid

                                                                                                                    Points, Lines, and Angles

                                                                                                                    Measuring Angles

                                                                                                                    Line Relationships

                                                                                                                    Fractions and Area

                                                                                                                    Congruent Three-Dimensional Shapes




                                                                                                                                                           4
                                                                June 11, 2010…DRAFT
                                                **Problem solving to be embedded throughout the year**
                                                Elementary Mathematics Fourth Grade Curriculum Map
Use and Represent Whole Numbers (3 weeks)
Objectives:
1. Use appropriate symbols to compare various equivalent forms of numbers through the millions period.
2. Build and represent numbers through the millions period two or more different ways.
3. Estimate sums and differences through the millions period and justify reasonableness of estimate.
4. Place numbers through the millions period on a number line.
Academic Vocabulary: millions period, million, ten million, hundred million.
Essential Questions      Essential Content & Understanding                          Essential Skills and Benchmarks     Assessment
How does place value     1. Use and represent numbers through millions              MA.4.A.6.1                          Chapter Test
affect numbers?                   Recognize differences in numbers, distances, Use and represent numbers               Unit Test (Textbook)
                                      etc.                                          through millions in various
When is an estimate an            Place value charts                               contexts, including estimation of   Sample Resources:
appropriate answer to             Standard form                                    relative sizes of amounts or        Navigating through Numbers &
a mathematical                    Expanded form                                    distances.                          Operations: pgs. 15-21
problem?                          Word form
                                  Number lines                                                                         http://www.linkslearning.org/
                                  “make a list”                                                                        Teachers/1_Math/6_Learning_Resour
                         2. **Present data through the millions period in real-                                         ces/1_Illustrated_Lessons/3_Place_V
                             world situations:                                                                          alue/index.html
                              Tables
                              Graphs                                                                                   http://www.archtech.org/java/b10bl
                                                                                                                        ocks/description.html
                              Lists
                              Charts
                         3. **Identify, compare, and or order numbers through
                             the millions place in real-world contexts
                         4. **Find answers to real-world problems that involve
                             adding and subtracting numbers through millions
                         5. **Estimations of numbers through millions and
                             determine reasonableness of estimate.
                              Practice with standard units
                              Using number lines
                              Using place value
                              Benchmark numbers
                         6. **Use the following Inequality symbols
                                                                                                                                                         5
                                                                 June 11, 2010…DRAFT
                                                 **Problem solving to be embedded throughout the year**
                    Elementary Mathematics Fourth Grade Curriculum Map
   appropriately (>,<, ≤, ≥, ≠)
7. Exact answer versus estimation in real-world
   situations
        Compatible numbers
        Place Value
8. **Finding numbers or ranges of numbers that are
   most appropriate or reasonable




                                                                               6
                                      June 11, 2010…DRAFT
                      **Problem solving to be embedded throughout the year**
                                                Elementary Mathematics Fourth Grade Curriculum Map

Multiplication and Division Concepts and Facts. (2 weeks)
Objectives:
1) Describe various models for multiplication in problem solving situations.
2) Recall basic multiplication and related division facts.
3) Interpret situational story problems to create expressions, equations, and visual representations.
4) Model division as:
    a) The inverse of multiplication
    b) Partitioning
    c) Successive subtraction
Academic Vocabulary: multiply, divide, factor, product, dividend, divisor, quotient, inverse operations, fact family, square number, multiple
Essential Questions        Essential Content & Understanding                            Essential Skills and Benchmarks       Assessment
How is multiplication      1. Develop quick recall of basic multiplication and          MA.4.A.1.1                            Chapter Test
and division relevant in       division facts through 12                                Use and describe various models       Unit Test (Textbook)
daily situations?              Continuous until mastery                                for multiplication in problem-
                               Orally                                                  solving situations, and               Sample Resources:
How are properties             Written                                                 demonstrate recall of basic           http://www.naturalmath.com/mult/
helpful when solving           Mastery achieved when recall is 5 sec. or less          multiplication and related division
mathematical               2. Use real-world problems using models in problem           facts with ease.                      Navigating through Numbers &
problems?                      solving situations                                                                             Operations: pgs. 72-79; 108-113;
                                Arrays                                                                                       128-133; 141-146
                                Equal intervals on a number line                       M.A.4.A.4.2                           *Splitting Arrays* applet on CD
                                Facts from 0x0 through 12x12                           Describe mathematics
                                Patterns                                               relationships using expressions,
                                Square numbers                                         equations, and visual
                           3. Properties of multiplication                              representations
                              Multiplying with zeros
                                                                                    M.A.4.A.6.2
                              Zero Property
                                                                                    Use models to represent division
                              Identity Property
                                                                                    as:
                              Commutative Property
                                                                                         The inverse of
                              Distributive Property
                                                                                           multiplication
                              Associate Property
                                                                                         As partitioning
                          **Use vocabulary terms factors and multiples
                                                                                         As successive subtraction
                          **Number being factored must be less than or equal to
                                                                                                                                                                 7
                                                                 June 11, 2010…DRAFT
                                                 **Problem solving to be embedded throughout the year**
                     Elementary Mathematics Fourth Grade Curriculum Map
100
**Multiple number must be 1-12, 25, 50, 100
                                                     M.A.4.A.6.4
                                                     Determine factors and multiples
                                                     for specific whole numbers




                                                                                       8
                                      June 11, 2010…DRAFT
                      **Problem solving to be embedded throughout the year**
                                               Elementary Mathematics Fourth Grade Curriculum Map


Chapter 3—Algebra: Expressions, Equations and Patterns (2 weeks)
Objectives:
1. Use a pattern (numeric or non-numeric) to determine the expression or equation that can be used to find the value of the variable (or rule).
2. Extend patterns (numeric or non-numeric) to determine the “rule”.
Academic Vocabulary: Distributive Property, numerical expression, algebraic expression, variable, function, equation
Essential Questions      Essential Content & Understanding                           Essential Skills and Benchmarks     Assessment
How can understanding 1. Generate algebraic rules to describe patterns using         M.A.4.A.4.1                         Chapter Test
mathematical                 basic operations (+. -. X, ÷)                           Generate algebraic rules and use    Unit Test (Textbook)
properties help you      **Include any of the four operations but will use only      all four operations to describe
solve mathematical       one operation in each numeric pattern                       patterns, including nonnumeric      Sample Resources:
problems?                2. Numeric:                                                 growing or repeating patterns       Navigating through Numbers &
                           Using numbers (3,6,9,12,15,18,…n)                                                            Operations: pgs. 22-26
                                                    th
How are algebraic rules               What is the n number?
useful in describing       Write an expression to determine input.                                                      Navigating through Numbers &
patterns?                  Review and extend finding input/output                                                       Operations: pgs. 72-79; 108-113;
                           Example: S=12 + r                                                                            128-133; 141-146
                                     S        r                                                                          *Splitting Arrays* applet on CD
                                    17      ____
                                    23      ____                                                                         Navigating through Algebra: pgs. 12-
                                    ___       7                                                                          14; 15-17; 18-22; 27-30; 61-63
                           Mental math/ multiplication-                                                                 *Function Machine* applet on CD
                                    division patterns
                         3. Non-numeric                                                                                  Sample Resources:
                           Shapes                                                                                       http://www.illuminations.nctm.org/le
                         4. Example:  n                                                                             ssonplans/3-5/variablemach/
                         5. Identify and describe the algebraic rule for                                                 index.html
                             determining the number of sides of a geometric                                                 A lesson plan that provides an
                             shape: Shape + 1 = n                                                                        introduction to the use of variables.
                           Balance Equations
                           **Extend a pattern beyond its next step
                           **Repeated pattern should be shown with at least
                              three examples of the repeated pattern

                                                                                                                                                            9
                                                                 June 11, 2010…DRAFT
                                                 **Problem solving to be embedded throughout the year**
                      Elementary Mathematics Fourth Grade Curriculum Map
     **May use graphics, tables, or lists to describe
      patterns
6.   Addition and subtraction
       4 + S = 12.
7.   Multiplication
     Example: draw diagram to show 5ℓ + 2 centimeters
      where ℓ is the length of the pencil and 2cm is
      length of the eraser
8.   Basic Division
      12/ F = 3
9.   Algebraic expressions with two operations
     Solve and Evaluate algebraic expressions using two
      operations.
     Write expressions using variable for missing
      numbers
     Example: 10 + 5 – x = 12 (with and without
      parenthesis).
     **Use rules or relationships that involve only one
      operation or one-step function.
     **May include only one variable
     **A relationship must be defined in words, or at
      least four examples of the relationship must be
      provided




                                                                                 10
                                        June 11, 2010…DRAFT
                        **Problem solving to be embedded throughout the year**
                                                Elementary Mathematics Fourth Grade Curriculum Map
Multiply by 1-digit Whole Numbers and Multiply by 2-digit and 3-digit Whole Numbers (5 Weeks)
Objectives:
1. Determine factors and multiples of numbers through 100.
2. Demonstrate fluency of basic facts when solving multi-digit multiplication problems.
3. Derive partial products from invented and standard algorithm for multi-digit multiplication problems.
4. Use the distributive property to solve multi-digit multiplication problems fluently.
Academic Vocabulary: Partial product, compatible numbers
Essential Questions           Essential Content & Understanding                    Essential Skills and Benchmarks             Assessment
What strategies can be        1. Multiply multi-digit whole numbers through MA.4.A.1.2—Multiply multi-digit whole              Chapter Test
used to multiply multiples        4 digits fluently                                numbers through four digits fluently,       Unit Test (Textbook)
of 10, 100, 1000 by a one-         **Factors may not exceed three digits          demonstrating understanding of the
digit number?                         by three digits or four digits by two        standard algorithm, and checking for        Sample Resources:
                                      digits                                       reasonableness of results, including        Navigating through Numbers &
How can the distributive           **One digit must be zero in a three digit solving real-world problems.                     Operations: pgs. 72-79; 108-113;
property help solve multi-            by three digit multiplication problem        M.A.4.A.1.1                                 128-133; 141-146
digit multiplication          2. Use the Distributive Property (Example: 13 x Use and describe various models for              *Splitting Arrays* applet on CD
problems?                         14 can be thought of as (10 + 3)x (10 +          multiplication in problem-solving
                                  4)…10 x 10 and 10 x 4 then (3 x 10 ) and (3 x situations, and demonstrate recall of
Justify your procedure for        4) a.k.a. partial products                       basic multiplication and related division
finding products of multi-    3. Provide several classroom experiences with        facts with ease.
digit multiplication              base ten blocks demonstrating standard           MA.4.A.4.2
problems.                         algorithm’s derivation                           Describe mathematics relationships using
                              4. Develop understanding of standard                 expressions, equations, and visual
                                  algorithm.                                       representations.
                              5. Check for reasonableness                          M.A.4.A.6.4
                              6. Find errors in multiplication problems to         Determine factors and multiples for
                                  check understanding of partial products and specific whole numbers
                                  standard algorithm.                              M.A.4.A.6.6.
                                 Use inverse operation to check for correct Estimate and describe reasonableness of
                                    answer                                         estimates; determine the
                                 solve read-world word problems                   appropriateness of an estimate versus an
                              7. **Solve multi-digit whole-number                  exact answer
                                  multiplication problems or supply partial
                                  products in real-world situations.

                                                                                                                                                              11
                                                                  June 11, 2010…DRAFT
                                                  **Problem solving to be embedded throughout the year**
                                                                      End of First Quarter
                                                Elementary Mathematics Fourth Grade Curriculum Map
 Model Division by 1-digit and 2-digit Divisors ( 3 weeks)
Objectives:
1. Use models to represent division as:
        a. The inverse of multiplication
        b. Partitioning
        c. Successive subtraction
2. Translate situational story problems into division expressions or equations from models (such as array, equal-sized groups, area)
Academic Vocabulary: Remainder, successive subtraction
Essential Questions        Essential Content & Understanding                    Essential Skills and Benchmarks            Assessment
                           1. Use models to represent division                  MA.4.A.6.2                                 Chapter Test
How can models be             Inverse of multiplication                        Use models to represent division as:       Unit Test (Textbook)
used to                       Fact families for multiplication and division         The inverse of multiplication
Represent division’s               a. (e.g. 13 x 14 = 182 and 182 ÷ 13 = 14)         As partitioning                      Sample Resources:
different modalities?         As successive subtraction                             As successive subtraction            http://www.beaconlearningcenter.co
                                   b. (Example: Find quotient 184 ÷ 13 by       M.A.4.A.1.2                                m/lessons/
                                        repeatedly subtracting 13 and           Multiply multi-digit whole numbers            Lesson plans submitted by Florida
                                        counting number of groups of 13         through four digits fluently,              Teachers that are linked to the
                                        subtracted before reaching zero)        demonstrating understanding of the         Sunshine State Standards.
                              As partitioning (separating) using base-ten      standard algorithm, and checking for
What problem solving             blocks or counters                             reasonableness of results, including
strategies can be used     2. Divisibility rules                                solving real-world problems.
to solve division          3. **Include only whole numbers and whole-           M.A.4.A.4.2
problems?                      number remainders                                Describe mathematics relationships
                           4. **Translate a word problem to a                   using expressions, equations, and visual
                               multiplication or division expression or         representations.
                               equation (from arrays, equal-sized groups,       M.A.4.A.6.4
                               area, or visual representations)                 Estimate and describe reasonableness of
                                                                                estimates; determine the
                                                                                appropriateness of an estimate versus
                                                                                an exact answer




                                                                                                                                                            12
                                                                 June 11, 2010…DRAFT
                                                 **Problem solving to be embedded throughout the year**
                                             Elementary Mathematics Fourth Grade Curriculum Map
 Factors, Multiples, and Fractions (2 weeks)
Objectives:
1. Determine factors and multiples for specific whole numbers.
2. Apply knowledge of factors and multiples to generate equivalent fractions.
3. Apply knowledge of factors and multiples to simplify fractions.
4. Explain why fractions, including fractions greater than one, are equivalent.
Academic Vocabulary: common factor, common multiple, equivalent fractions, simplest form, common denominator, benchmark
Essential Questions        Essential Content & Understanding                    Essential Skills and Benchmarks     Assessment
How can arrays be use      1. Determine factors and multiples                   M.A.4.A.6.4                         Chapter Test
to find the factors of a      Determine divisibility rules for 2, 3, 5, 9,10   Determine factors and multiples for Unit Test (Textbook)
number?                       Find missing factors in patterns of multiples specific whole numbers
                              Use array and number lines to find factors       M.A.4.A.6.3                         Sample Resources:
                                 and multiples                                  Generate equivalent fractions and   http://www.pen.k12.va.us/VDOE/Inst
How can common                Use arrays to find prime and composite           simplify fractions                  ruction/Math/FractionsDecimalsPerc
factors be found?             Skip counting                                                                        ent.pdf
                           2. Find square numbers/square
                              Arrays creating squares                                                              Navigating through Numbers and
How can you find              multiplication tables                                                                Operations: *Fraction Models*
common multiples?          3. Find common denominators for fractions                                                applet on CD
                                     Two-color counters
                                     Circle fractions                                                              Navigating through Geometry: pgs.
                                                                                                                    88-89
                                     Cuisenaire Rods
                                     Virtual Manipulatives
                           3. Generate equivalent fractions
                              Generate rules for finding equivalent
                                 fractions and simplifying fractions using:
                             Previous knowledge of factors/primes
                             Models (student made)
                             Fraction bars
                             Number line
                             Fraction Tiles
                             Linear Models
                             Area models
                             Set models
                                                                                                                                                   13
                                                              June 11, 2010…DRAFT
                                              **Problem solving to be embedded throughout the year**
                    Elementary Mathematics Fourth Grade Curriculum Map
4. **Rename fractions as mixed numbers or vice
   versa
5. **Common factors of the numerator and
   denominator must be less that or equal to 10
6. **Responses may or may not be in lowest
   terms.




                                                                               14
                                      June 11, 2010…DRAFT
                      **Problem solving to be embedded throughout the year**
                                                 Elementary Mathematics Fourth Grade Curriculum Map
 Understanding Decimal Place Value (2 weeks)Objectives:
Objectives:
 1. Name decimal (to the thousandths place) and fraction numbers between whole numbers.
 2. Describe decimals as an extension of the base ten system.
 3. Identify place value of digits to the right of the decimal to the thousandths place.
 4. Relate commonly used fractions and decimals with models and on a number line.
Academic Vocabulary: decimal, decimal point, tenths, hundredths, thousandths
Essential Questions       Essential Content & Understanding                       Essential Skills and Benchmarks            Assessment
How does placement of 1. Decimals through Thousandths                             MA.4.A.2.1                                 Chapter Test
decimals affect place       Use area model (graph paper) to represent            Use decimals through the thousandths       Unit Test (Textbook)
value?                          decimals                                          place to name numbers between whole
                            Use base 10 blocks to represent tenths and           numbers.                                   Sample Resources:
                                hundredths                                                                                   http://www.linkslearning.org/
What does a decimal                                                               MA.4.A.2.2
represent?                  Name and locate values between whole                                                            Teachers/1_Math/6_Learning_Resour
                                                                                  Describe decimals as an extension of the   ces/1_Illustrated_Lessons/3_Place_V
                                numbers using a number line
                                                                                  base-ten number system
                            **Identify decimals and/or fractions from a                                                     alue/index.html
How can decimals and            graphical representation or a number line         MA.4.A.2.3                                    Students work with place value
fractions be related on 2. Decimals as extension of base-ten number               Relate equivalent fractions and            using whole numbers as well as
a number line?                 system                                             decimals with and without models,          decimals. This interactive, computer-
                                                                                   including locations on a number           based lesson includes activities and
                            Know that the relationship between adjacent
                                                                                  line                                       assessments
                                places in whole numbers is or can be
                                described by a ten-to-one rule
                                                                                                                             Sample Resources:
                               **Identify the place value of a digit to the                                                 http://www.archtech.org/java/b10bl
                                right of the decimal point                                                                   ocks/description.html
                          3.   Relate equivalent fractions and decimals                                                         Visual representations of base-10
                               Models fractions and decimals with number                                                    place value and multi-digit
                                line                                                                                         operations, a valuable tool for
                               Fraction bars                                                                                teachers to use in class or for
                               Fraction kits (students made)                                                                students to use on their own.
                               Fraction tiles
                               **Identify decimals that are equivalent to
                                commonly used fractions or mixed numbers
                               **May include mixed numbers and/or

                                                                                                                                                               15
                                                                   June 11, 2010…DRAFT
                                                   **Problem solving to be embedded throughout the year**
                                                                     End of Second Quarter
                      Elementary Mathematics Fourth Grade Curriculum Map
    fractions
   **May assess translating the following
    commonly used fractions or mixed numbers
    to decimals (or their decimal equivalents):
    1/10, ¼, ½, ¾, all fifths, tenths, hundredths,
    and thousandths. (eg. 0.2, 0.20, 0.200, and
    2/10 are all equivalent. Also, 0.5 = ½, 3/5, =
    0.6, 3/2 = 1.5, or 7 ½ = 7.5.
4. Use coins as basis for understanding place
   value of tenths and hundredths




                                                                                 16
                                        June 11, 2010…DRAFT
                        **Problem solving to be embedded throughout the year**
                                          End of Second Quarter
                                                  Elementary Mathematics Fourth Grade Curriculum Map
Decimal Place Value and Number Sense (3 weeks)
Objectives:
1. Compare and order decimals on a number line.
2. Relate halves, fourths, tenths, and hundredths to decimals.
3. Relate halves, fourths, tenths, and hundredths to percents.
4. Estimate fraction and decimal amounts in real-world problems.
5. Justify reasonableness of estimates.
Academic Vocabulary: decimals, not equal to ( ≠ ), greater than ( > ), less than ( < ), greater than or equal to ( ≥ ), less than or equal to ( ≤ ) percent
Essential Questions       Essential Content & Understanding                        Essential Skills and Benchmarks                 Assessment
How are comparing and 1. Compare and order decimals                                MA.4.A.2.4                                      Chapter Test
estimating decimals                 Relate decimals to fractions                  Compare and order decimals, and                 Unit Test (Textbook)
and fractions used in               Number lines                                  estimate fractions and decimal amounts
everyday life?                      Representative drawings                       in real-world problems.                         Sample Resources:
                                                                                                                                   http://askeric.org/cgi-
                                    Making charts
How can models be                                                                  MA.4.A.6.5                                      bin/printlessons.cgi/Virtual/Lessons/
                                    Benchmark decimals:
used to compare                                                                    Relate halves, fourths, tenths, and             Mathematics/Number_Sense/NUS02
                                          1. 5ths as decimals (e.g., 3/5 =
decimals?                                                                          hundredths to decimals and                      00.html
                                               0.6)
                                                                                   Percents.                                          An activity in which students
                                          2. halves as decimals (e.g. 7 ½ =
                                                                                                                                   arrange themselves into decimal
                                               7.5)
                                                                                                                                   numbers.
                                    **Compare and order mixed numbers
                                      and decimals through the thousandths
                                                                                                                                   http://funbrain.com/football/index.h
                                      place with no more than five digits
                                                                                                                                   tml
                                    **Compare and order decimals,                                                                    Power Football provides
                                      fractions, and/or mixed numbers                                                              interactive practice with the decimal
                                      between two numbers                                                                          concepts.
                          2. Estimate fraction and decimal
                                  amounts                                                                                          http://www.pen.k12.va.us/VDOE/Inst
                                    Using number lines                                                                            ruction/Math/FractionsDecimalsPerc
                                    Dollar amounts, money and cents, to                                                           ent.pdf
                                      hundredths
                                    Real-world setting                                                                            Navigating through Numbers &
                                    **Identify a fraction or decimal that is                                                      Operations: pgs. 41-48
                                      closest to another number or a                                                               *Fraction Models* applet on CD
                                      benchmark fraction, eg., 7/16 of a
                                                                                                                                                                     17
                                                                    June 11, 2010…DRAFT
                                                    **Problem solving to be embedded throughout the year**
                     Elementary Mathematics Fourth Grade Curriculum Map
            circle is closer to ½ than 1/3
3. May include fractions with denominators of 1
   through 12, 16, 20, 25, 50, 100, and 1000
4. Relate common fractions to decimals and
   percents using:
  Models
  Symbols
  (Such as ¼ = 0.25 = 25%)
  **Convert a percent to a fractions or a
    decimal
  **Convert a fraction or a decimal to a
    percent
  **Fractions: ¼. ½. ¾. all tenths, and all
    hundredths may be converted to percents
    (e.g., ¼ = 25%, or ¾ = 75%) or vice versa.
5. Real world problem solving using percent off,
   etc.
 **May include graphic models of fractions,
   decimals, or percents




                                                                                18
                                       June 11, 2010…DRAFT
                       **Problem solving to be embedded throughout the year**
                                               Elementary Mathematics Fourth Grade Curriculum Map
 Understanding Area (2 Weeks)
Objectives:
1. Describe and model area as the number of same-sized units that cover a region in the plane.
2. Use appropriate units of measure when solving area problems.
3. Justify the formula for the area of the rectangle “area = base x height”.
4. Select appropriate tools (customary and metric) to measure area in real-world situations.
5. Estimate area and justify reasonableness of estimate.
6. Identify real-world uses of the area formula.
Academic Vocabulary: area, square unit (sq un), base, height, formula
Essential Questions       Essential Content & Understanding                   Essential Skills and Benchmarks           Assessment
How can real world        1. Determine area and focus on countable            MA.4.G.3.1                                Chapter Test
problems be solved             square units:                                  Describe and determine area as the        Unit Test (Textbook)
using area?                         Geo boards                               number of same-sized units that cover a
                                    Tiles                                    region in the plane, recognizing that a   Sample Resources:
How can the area of a               Grid paper                               unit square is the standard unit for      Navigating through Measurement:
non-standard shape be               Snap cubes                               measuring area                            pgs. 53-57; 62-65
found?                              Tables                                   MA.4.G.3.2
                          2. **Determine the area of a figure or a region     Justify the formula for the area of the   www.shodor.org/intgeractivate/lesso
How can the area of a          on a plane by using countable units rather     rectangle “area = base X height”          ns/lpa.html
complex shape be               than multiplying dimensions.                   MA.4.G.3.3                                   This lesson is designed to examine
found?                    3. **Estimate areas of irregular geometric          Select and use appropriate units, both    the mathematical concepts of length,
                               shapes                                         customary and metric, strategies, and     perimeter, and area.
                          4. **Include countable units that estimate to a     measuring tools to estimate and solve
                               whole unit or half unit                        real-world area problems                  www.funbrain.com/poly/
                          5. **Use one-to-one scale                                                                       Activities involving area and
                          6. ** show shapes on a grid, with grid lines                                                  perimeter
                               extended through the shape, and without.
                          7. Area formula                                                                               Navigating through Measurement:
                              Derive relationship between counting units                                               pgs. 58-61
                                 to find area and finding area by multiplying                                           *Stuck on Stickers* applet on CD
                          8. **Identify situations that require the use of
                               the area formula in real-world contexts
                          9. **Identify the number of square units of a
                               rectangle as the base times the height

                                                                                                                                                           19
                                                                 June 11, 2010…DRAFT
                                                 **Problem solving to be embedded throughout the year**
                      Elementary Mathematics Fourth Grade Curriculum Map
10. **Derive or explain the area of a rectangle in
    order to solve real-world problems
11. **Responses should include units.
12. Select and use appropriate measuring tools
    and strategies
   decompose area of composite shape into
      two rectangles and determine area of both
      shapes and then combine together
   Use customary and metric measuring tools
      to measure base and height to determine
      area.
13. Solving real world problems involving above
    units
   Recognize difference in measurement units
   Use appropriate metric units
   Identify appropriate measurement tools
14. **Solve problems involving the area of a
    rectangle or a composite shape
15. **Include figures with whole-number
    dimensions of 100 or fewer units.
16. Find errors in measuring and area situations,
    including incorrect units of measurement




                                                                                 20
                                        June 11, 2010…DRAFT
                        **Problem solving to be embedded throughout the year**
                                                Elementary Mathematics Fourth Grade Curriculum Map


 Angles and Two-Dimensional Shapes (3 Weeks)
Objectives:
1. Identify acute, obtuse, and right angles.
2. Identify benchmark angle measurements of 45°, 90°, 180°, and 360°.
3. Classify angles of 2-D shapes using benchmark angles.
4. Use appropriate geometric notation for angles and degrees.
Academic Vocabulary: angle, right angle, degree (° ), vertex, clockwise, counterclockwise, acute angle, obtuse angle, reflex angle
Essential Questions        Essential Content & Understanding                     Essential Skills and Benchmarks             Assessment
How can angles be          1. Classify angles using plane figures                MA.4.G.5.1                                  Chapter Test
classified, measured,               identify angles in environment              Classify angles of two-dimensional          Unit Test (Textbook)
and drawn using                     Review lines, rays, and line                shapes using benchmark angles (i.e.
                                                                                                                             Sample Resources:
benchmark angles?                      relationships                              45°, 90°, 180°, and 360°).
                                                                                                                             Navigating through Geometry: pgs.
                                    Set right angles as identifiers                                                         15-21
                                    Use protractor to draw angles of
                                       various degrees making sure to
                                       emphasize the benchmark angles.
                                    Use geo boards or square dot paper to
                                       draw shapes with angles
                                    **Classify angles by the following
                                       terms: acute, obtuse, right, or straight
                                    **Identify the benchmark angle
                                       measurements of 45°, 90°, 180°,
                                       and/or 360°.
                                    **Use the geometric notation for
                                       angle and degrees ( <, ° )




                                                                                                                                                             21
                                                                  June 11, 2010…DRAFT
                                                  **Problem solving to be embedded throughout the year**
                                                  Elementary Mathematics Fourth Grade Curriculum Map
 Transformations and Symmetry (1 Week)
Objectives:
1. Identify different types of transformations (i.e. reflection, rotation, translation).
2. Describe the results of a transformation on an object.
3. Use transformations to create new shapes.
4. Rotate figures with rotational symmetry from point of rotation according to descriptors of rotation.
Academic Vocabulary: transformation, translation, reflection, rotation, line symmetry, line of symmetry, tessellation
Essential Questions       Essential Content & Understanding                         Essential Skills and Benchmarks          Assessment
How can shapes be         1. Identify and describe the results of                   MA.4.G.5.2                               Chapter Test
transformed?                   translations, reflections, and rotations             Identify and describe the results of     Unit Test (Textbook)
                                Transformations                                    translations, reflections, and
How does a reflection           Rotational symmetry                                rotations of 45, 90, 180, 270, and 360   Sample Resources:
transform a shape?              Line symmetry                                       degrees, including figures with line    Navigating through Geometry: pgs.
                                Identify degree of change of transformed           and rotational symmetry                  55-58; 77-79
How can a line of                   figures                                                                                  *Tangram Challenges* applet on CD
symmetry be found?              **Include no more than two
                                    transformations
                          2. Identify shapes that can produce tessellations
                          3. Creates tessellations
                          4. Explain how to manipulate shapes to create
                               different shapes using transformations to a
                               partner while they try to recreate the shape
                               being described.




                                                                                                                                                             22
                                                                    June 11, 2010…DRAFT
                                                    **Problem solving to be embedded throughout the year**
                                              Elementary Mathematics Fourth Grade Curriculum Map
 Relate Two-Dimensional Shapes and Three-Dimensional Shapes (2 Weeks)
Objectives:
1. Identify 2-D shapes that compose a 3-D Shape from different orientations (top, bottom, side).
2. Compose 3-D shapes from 2-D view of that shape.
3. Recreate and describe 2-D and 3-D objects viewed from different orientations using appropriate academic vocabulary.
Academic Vocabulary: dimension, face, base, two-dimensional, three-dimensional
Essential Questions      Essential Content & Understanding                    Essential Skills and Benchmarks            Assessment
What are different       1. Build three-dimensional objects from objects      MA.4.G.5.3                                 Chapter Test
ways geometry is used         with two-dimensional representations using:     Identify and build a three-                Unit Test (Textbook)
in our world?                  blocks                                        dimensional object from a two-
                               tiles                                         dimensional representation of that         Sample Resources:
How are two-                   unifix cubes                                  object and vice versa.                     Navigating through Geometry: pgs.
dimensional shapes       2. Identify                                                                                     11-14; 22-25; 26-30; 31-34; 80-82; 83-
and three-dimensional          Geometric shapes                                                                         85; 90-94
shapes related?                faces
                               edges                                                                                    *Exploring Geometric Solids*
                               vertices                                                                                 *Shape Sorter* & *Pattern Patch*
                               **Identify a three-dimensional object                                                    applet on CD
                                  from two-dimensional object                                                            Navigating through Measurement:
                               **Identify one or more of the two-                                                       pgs. 77-82
                                  dimensional views of a three-dimensional
                                  object
                               **Include drawings of views from the top,
                                  sides, front, or base of an object
                         3. Create nets to identify 2-dimensional shapes
                              composing 3-dimensional solids
                         4. **Three-dimensional objects represented in
                              items must be made from cubes
                         5. **Two-dimensional views should show lines
                              indicating square units




                                                                                                                                                            23
                                                                June 11, 2010…DRAFT
                                                **Problem solving to be embedded throughout the year**
                                                                  End of Third Quarter
                                               Elementary Mathematics Fourth Grade Curriculum Map
Remediate                                                               Extend
    Use Big Idea Projects                                              “Getting Ready for First Grade”
    Create small groups based on needs assessment and re-visit         Finding Sums of Decimal Amounts
      skills not yet mastered
                                                                        Multiplication to Estimate Quotients

                                                                        Fractions and Division

                                                                        Divisibility Rules

                                                                        Factor Whole Numbers

                                                                        Fractions and Mixed Numbers

                                                                        Order of Operations

                                                                        Addition Properties

                                                                        Compare and Order Numbers

                                                                        Temperature

                                                                        Points on a Grid

                                                                        Points, Lines, and Angles

                                                                        Measuring Angles

                                                                        Line Relationships

                                                                        Fractions and Area

                                                                              Congruent Three-Dimensional Shapes
**Resources for Big Idea Projects & Getting Ready for First Grade can be found in the “Planning Guide – End of Year Resources”**

                                                                                                                                   24
                                                                 June 11, 2010…DRAFT
                                                 **Problem solving to be embedded throughout the year**
                                                                  End of Fourth Quarter
        Fourth Grade
     Math Curriculum Map
          Appendix




Scope and Sequence Correlated to Textbook Pages
 State Approved Benchmarks with Access Points
                  Resources




                                                  25
                                            Fourth Grade Scope & Sequence
First Nine Weeks

Chapter 1: Use and Represent Whole Numbers (3 weeks)

Chapter 2: Multiplication and Division Concepts and Facts (2 weeks)

Chapter 3: Algebra: Expressions, Equations, and Patterns (2 Weeks)

Chapter 4: Multiply by 1-Digit Whole Numbers (2 weeks)

Second Nine Weeks

Chapter 5: Multiply by 2-Digit and 3-Digit Whole Numbers (3 weeks)

Chapter 6: Model Division by 1-Digit and 2-Digit Division (3 weeks)

Chapter 7: Factors, Multiples, and Fractions (2 weeks)

Chapter 8: Understand Decimal Place Value (2 weeks)

Third Nine Weeks

Chapter 9: Decimal Place Value and Number Sense (2 weeks)

Chapter 10: Understand Area (2 weeks)

Chapter 11: Angles and Two-Dimensional Shapes (3 weeks)

Chapter 12: Transformations and Symmetry (1 week)

Chapter 13: Relate Two-Dimensional Shapes and Three-Dimensional Shapes
(1 Week)

                                                            June 11, 2010… DRAFT   26
            State Approved Fourth Grade Math Standards


                   Benchmark Coding Scheme
MA.           4.                A.                          1.                1
Subject   Grade Level    Body of Knowledge         Big Idea / Supporting   Benchmark
                                                           Idea


                         Body of Knowledge Key:
                              A ~ Algebra
                              C ~ Calculus
                        D ~ Discrete Mathematics
                          F ~ Financial Literacy
                             G ~ Geometry
                             P ~ Probability
                              S ~ Statistics
                            T ~ Trigonometry




                        June 11, 2010… DRAFT                                           27
                                           State Approved Fourth Grade Mathematics Standards
Benchmark                            Body Of                                                                                         Cognitive
                   Descriptor                      Idea                               Remarks/Examples
 Number                             Knowledge                                                                                       Complexity
           Use and describe various                         Given real-world problems and accompanying models that include
           models for                                       equal-sized groups, arrays, area, and equal intervals on the number
           multiplication in                                line, students should be able to give the multiplication or division
           problem-solving                                  basic fact associated with the situation.
MA.4.A.1.1 situations, and          Algebra    BIG IDEA 1 The goal is to develop quick recall of multiplication facts and related Moderate
           demonstrate recall of                            division facts.
           basic multiplication and                         Basic multiplication facts include the factors 0 through 9.
           related division facts
           with ease.                                       Related division facts include divisors 1 through 9 and dividends 0-81.
           Multiply multi-digit
           whole numbers through
                                                            Place value and properties of operations and numbers should play
           four digits fluently,
                                                            major roles in developing strategies for multiplying multi-digit whole
           demonstrating
                                                            numbers. For example, 13 x 14 can be thought of as (10 + 3) x (10 +
           understanding of the
                                                            4). The Distributive Property can then be applied along with focus on
MA.4.A.1.2 standard algorithm, and Algebra     BIG IDEA 1                                                                           High
                                                            decomposition of numbers to multiply 10 x 10 and 10 x 4 then 3 x 10
           checking for
                                                            and 3 x 4. These partial products are added to find the product of 13 x
           reasonableness of
                                                            14. This process should be connected to the standard algorithm.
           results, including
           solving real-world
           problems.




                                                         June 11, 2010… DRAFT                                                              28
                                          State Approved Fourth Grade Mathematics Standards
Benchmark                            Body Of                                                                                       Cognitive
                  Descriptor                      Idea                          Remarks/Examples
 Number                             Knowledge                                                                                     Complexity




                                                            13 x 14 = (10 + 3) x (10 + 4) = 10 x 10 + 10 x 4 + 3 x 10 + 3 x 4




                                                            Students may use a place value mat to represent decimal numbers
                                                            through the thousandths with objects, write the symbolic
           Use decimals through                             representation with numerals, and name the decimal represented with
           the thousandths place to                         words.
MA.4.A.2.1                          Algebra    BIG IDEA 2                                                                         Low
           name numbers between
           whole numbers.                                 Students can identify decimal numbers on a number line, write the
                                                          symbolic representation with numerals, and name the decimal value
                                                          with words.
           Describe decimals as an                        By fourth grade, students should know that the relationship between
MA.4.A.2.2 extension of the base-ten Algebra   BIG IDEA 2 adjacent places in whole numbers is described by a ten-to-one rule (…, High
           number system.                                 1000, 100, 10, 1, 0.1, 0.01,...). This relationship should be developed

                                                        June 11, 2010… DRAFT                                                              29
                                          State Approved Fourth Grade Mathematics Standards
Benchmark                            Body Of                                                                                       Cognitive
                  Descriptor                      Idea                             Remarks/Examples
 Number                             Knowledge                                                                                     Complexity
                                                           for decimals.
                                                           Students can explore equivalency of fractions and decimals by using
           Relate equivalent
                                                           rulers.
           fractions and decimals
           with and without
MA.4.A.2.3                          Algebra    BIG IDEA 2                                                                         Moderate
           models, including
           locations on a number
                                                          Models may include rulers, fraction circles, sets of similar objects, and
           line.
                                                          drawings.
                                                          Measurements (e.g., lengths) and dollar amounts provide useful
                                                          contexts for estimating in the real world.
           Compare and order
                                                          Students should understand the relationships and equivalencies
           decimals, and estimate
                                                          between decimals and fractions. . A decimal number may have an
MA.4.A.2.4 fraction and decimal     Algebra    BIG IDEA 2                                                                           Moderate
                                                          equivalent fraction- one where the denominator is (or can be) a power
           amounts in real-world
                                                          of 10, at this grade level 10, 100, or 1000. They should also be able to
           problems.
                                                          represent 5ths as decimals (for example, 3/5= 0.6) and halves as
                                                          decimals (for example, 7 ½ = 7.5).
                                                          Example 1: A number pattern is: 3, 6, 9, 12, 15, 18... What is an
                                                          algebraic rule to describe the nth number in the pattern?
           Generate algebraic rules
           and use all four                                  Example 2: The triangle below is shape 1 and the square is shape 2.
           operations to describe                            This same pattern continues, in which each shape has one more side High
MA.4.A.4.1                          Algebra    Algebra
           patterns, including                               than the previous shape. How many sides would shape n have, where n
           nonnumeric growing or                             can be any natural number? How do you know?
           repeating patterns.


                                                             Example: Mr. Sims has 168 oranges. He wants to pack them into
                                                             boxes with 28 in each box. How many boxes does he need? Use
           Describe mathematics
                                                             pictures or diagrams to show what is happening in the problem.
           relationships using
                                                             Record your solution with equations.
MA.4.A.4.2 expressions, equations, Algebra     Algebra                                                                            High
           and visual
           representations.
                                                             Example Alex is 4 years older than twice as old as Sam What
                                                         June 11, 2010… DRAFT                                                                  30
                                            State Approved Fourth Grade Mathematics Standards
Benchmark                              Body Of                                                                                        Cognitive
                    Descriptor                      Idea                               Remarks/Examples
 Number                               Knowledge                                                                                      Complexity
                                                             expression gives Alex's age if you use the variable "S " to represent
                                                             Sam's age?
                                                             Regina received $50 from her grandmother as her birthday gift. Her
                                                             grandfather told her that his Birthday gift will be to give her $5 each
                                                             month, starting the month after her birthday. Regina decided to save
                                                             her birthday gifts to buy her favorite music player. The table below
                                                             illustrates the total amount of gift money that Regina will have
                                                             received each month. Write an algebraic expression that can be used to
                                                             show the total amount of money that Regina will have each month.
           Recognize and write
           algebraic expressions for
MA.4.A.4.3                           Algebra     Algebra                                                                              High
           functions with two
           operations.                                          Month     0         1         2         …         n


                                                                Amount 50           50 + 5    50+5 +    …         ?
                                                                of                            5
                                                                Money


           Use and represent
           numbers through
           millions in various
                                                 Number and Students should recognize the difference between distances such as
MA.4.A.6.1 contexts, including     Algebra                                                                                            Moderate
                                                 Operations 100 feet and 1,000 feet or 10 km and 200 cm.
           estimation of relative
           sizes of amounts or
           distances.
           Use models to represent                             The inverse of multiplication: 4 x 45 = 180, 180 ÷ 4 = 45, and 180 ÷
           division as:                                        45 = 4.
                                                 Number and
MA.4.A.6.2         the inverse of    Algebra                                                                                         Moderate
                                                 Operations
                    multiplication
                   as partitioning                            Partitioning: We can share 180 things (possibly represented by base-
                   as successive                              ten blocks) evenly among 4 groups and determine the number of items
                                                           June 11, 2010… DRAFT                                                                  31
                                           State Approved Fourth Grade Mathematics Standards
Benchmark                             Body Of                                                                                          Cognitive
                   Descriptor                      Idea                          Remarks/Examples
 Number                              Knowledge                                                                                        Complexity
                   subtraction                              in each group.



                                                            Successive subtraction: We can find the quotient of 180 ÷45 by
                                                            repeatedly subtracting 45 and counting the number of groups of 45
                                                            subtracted before reaching zero.




                                                          The area model is a useful model for exploring the inverse relationship
                                                          between multiplication and division.
           Generate equivalent                            Earlier work with models of equivalent fractions in grade 3 should
                                               Number and
MA.4.A.6.3 fractions and simplify    Algebra              help students to develop conceptual understanding for the rules for     Moderate
                                               Operations
           fractions.                                     generating equivalent fractions and simplifying fractions.
                                                          Multiples and factors should be explored as students determine
                                                          common denominators for fractions.



           Determine factors and
                                               Number and Use models to identify square numbers to 100.
MA.4.A.6.4 multiples for specified   Algebra                                                                                          Moderate
                                               Operations
           whole numbers.

                                                            Example: You have 28 chairs. Show all of the ways you can arrange
                                                            these chairs into arrays. Draw the arrays. Record the dimensions of the
                                                            arrays.
           Relate halves, fourths,
                                                          Relate common fractions to equivalent decimals and percents such as:
           tenths, and hundredths              Number and
MA.4.A.6.5                           Algebra              1/4 = 0.25 = 25%. These representations should be related through    Moderate
           to decimals and                     Operations
                                                          both models and symbols.
           percents.
MA.4.A.6.6 Estimate and describe     Algebra   Number and An example in which an estimate is more appropriate than an exact           High
                                                       June 11, 2010… DRAFT                                                                      32
                                           State Approved Fourth Grade Mathematics Standards
Benchmark                             Body Of                                                                                       Cognitive
                  Descriptor                       Idea                                Remarks/Examples
 Number                              Knowledge                                                                                     Complexity
           reasonableness of                   Operations answer is in estimating the amount of food needed for a party. You
           estimates; determine the                         know the number of people you invited, but still you need to estimate
           appropriateness of an                            the amount of food and drink to buy.
           estimate versus an exact
           answer.
           Describe and determine
           area as the number of
           same-sized units that
                                                            Geoboards, tiles, and grid paper provide helpful contexts for this
           cover a region in the
MA.4.G.3.1                           Geometry BIG IDEA 3 exploration. The focus is on countable units rather than multiplying      Moderate
           plane, recognizing that a
                                                            dimensions.
           unit square is the
           standard unit for
           measuring area.
                                                            The students should be able to justify the formula for the area of the
                                                            rectangle by explaining how counting units to find area of a rectangle
                                                            is related to finding the area by multiplying.
           Justify the formula for
MA.4.G.3.2 the area of the rectangle Geometry   BIG IDEA 3                                                                             Moderate
           "area = base x height".
                                                             The idea of the area of a rectangle as "base x height" rather than
                                                             "length x width" is useful in connecting to other area formulas.


                                                             Students should recognize that the area of a piece of paper might be
                                                             measured in square inches, the area of a room might be measured in
           Select and use
                                                             square feet, and the area of a large piece of land might be measured in
           appropriate units, both
                                                             square miles. Alternately, these measurements might be in square
           customary and metric,
                                                             centimeters, square meters, and square kilometers, respectively.
MA.4.G.3.3 strategies, and          Geometry    BIG IDEA 3                                                                             Moderate
           measuring tools to
           estimate and solve real-
           world area problems.
                                                             Example: Students find the area of a composite shape. An L-shaped
                                                             region may be decomposed into rectangular regions.

                                                         June 11, 2010… DRAFT                                                                     33
                                         State Approved Fourth Grade Mathematics Standards
Benchmark                           Body Of                                                                                           Cognitive
                  Descriptor                     Idea                          Remarks/Examples
 Number                            Knowledge                                                                                         Complexity



                                                             Example: Find the area of the polygon in the picture. Explain or show
                                                             how you found the area.




                                                             Use pictures of real world objects or diagrams of shapes with angles
                                                             and ask students to classify the given angles by using benchmark
           Classify angles of two-                           angles.
           dimensional shapes                  Geometry
MA.4.G.5.1 using benchmark angles Geometry     and                                                                                   Low
           (45°, 90°, 180°, and                Measurement
           360°)                                             Use protractor to draw the angles of 45, 90, 180, and 360 degrees.


           Identify and describe the
           results of translations,
           reflections, and rotations          Geometry    Paper folding, mirrors, and computer technology may be helpful in
MA.4.G.5.2 of 45, 90, 180, 270, and Geometry   and         developing student understanding of these concepts. Simple             Moderate
           360 degrees, including              Measurement tessellation of plane may provide engaging opportunities for practice.
           figures with line and
           rotational symmetry.

                                                        June 11, 2010… DRAFT                                                                 34
                                       State Approved Fourth Grade Mathematics Standards
Benchmark                         Body Of                                                                                      Cognitive
                 Descriptor                    Idea                              Remarks/Examples
 Number                          Knowledge                                                                                    Complexity
                                                        Example: A cylinder is composed of 2 bases (circles) & a rectangle. A
                                                        cube is composed of six squares. A sphere is not easily decomposed
                                                        into basic two dimensional shapes.
           Identify and build a
           three-dimensional object          Geometry
MA.4.G.5.3 from a two-dimensional Geometry   and                                                                                     Moderate
           representation of that            Measurement
                                                           Provide nets for students to construct 3-dimensional objects. Challenge
           object and vice versa.
                                                           students to create their own nets using grid paper.




                                                     June 11, 2010… DRAFT                                                                       35

				
DOCUMENT INFO