Docstoc

GRADE 4 curriculum Quarter 2

Document Sample
GRADE 4 curriculum Quarter 2 Powered By Docstoc
					Updated 10/1/10
                                Baltimore City Schools




     Dr. Andrés Alonso                        Dr. Sonja Santelises                         Linda Eberhart
   Chief Executive Officer                  Chief Academic Officer                      Executive Director
                                                                                      Teaching and Learning


                                               Curriculum Writers
Thanks to all City Schools teachers who wrote, revised, and provided feedback for this curriculum. A special thanks to
the following curriculum writers:

           Kim Alexander                           Geneve Garcia                           Elizabeth Renwick
            Margo Berish                           Beth Goldscher                            Estelito Reyes
          Julia Bonkowski                          Andrew Hlavka                            Katherine Schlee
            Megan Bovill                              Gil Laqui                            Weston Schreiber
         Thomas Coleman                         Maggie Lasaga-Flister                         Levi Straight
           Megan Cooper                          Benjamin Lawrence                          Odessa Tamayo
        Matthew Damseaux                              Luis Lima                             Siriporn Vinijkul
          Kimberly David                          Genevieve Mason                         Smitha Viswanathan
         Melanie Davison                           Scott Messinger                         Shanekwa Winfield
           Chritian Fisher                           Kevin Older
              Math Works Homework                                       Other Useful Links

Homework can be an effective part of your math               MSA Daily Reviews
program - giving students the practice they need to
master skills. Below are some Math Works methods for
utilizing homework.
                                                             Mathematics Study Guide
Suggested Homework Procedures:
o Check homework every night
o Give students an opportunity to revise homework            Vocabulary Activities
o Start the homework assignment together at the
  beginning or end of class.
o Dedicate 10 minutes to going over 2-5 problems that        Math Templates
  students are having trouble with (they pick some, you
  pick some). Model how you work through the
  problems on the board.                                     Structuring Your Math Block -
o Reward students for doing homework and revising it.
                                                              Weekly Planning Grid
Homework Tips:
o Homework should consist primarily of skills that
  students have already been exposed to. Skills should       Sample Lesson Plan Template
  cycle in and out depending on what your students
  have been taught AND what they have mastered.
o Require students to show their work on homework
  problems, not just write the answer. Give credit only
  when there is work.
o Circulate throughout the classroom while talking
  about homework problems to be sure students are
  writing down what you are talking about and are
  showing work.
o At the beginning of the year, homework should
  consist of skills taught in the previous grade level.



              Grade 4 Homework
            Grade 4 Math Curriculum Sequence
                                School Year 2010-2011

                      QUARTER 1 (Aug 30 – Nov 5)                             Suggested Time
                                    45 days                                      Frame
BENCHMARK A                                                                  Sept 7 - Sept 17
(same skills as June Benchmark in previous grade)                            testing window
UNIT 1: Whole Number Concepts                                                   (7-12 days)
           Read, Write, Represent Whole Numbers
             Represent numbers with models through the millions
*COMMON




             Represent numbers in numeric and word form through the
  CORE




                                                                                2 – 4 days
               millions
             Create equivalent representations through the millions
             Represent numbers in expanded form through the millions
*COMMON




           Place Value and Expanded Form of Whole Numbers
  CORE




             Identify the value of a digit through the millions using the      3 – 5 days
               base ten model
*COMMON




           Compare and Order Whole Numbers
  CORE




             Compare numbers through the millions                              2 – 3 days
             Order numbers through the millions

UNIT 2: Whole Number Computation 1                                              (7-11 days)
           Add Whole Numbers
*COMMON




             Add up to 4-digit whole numbers with regrouping
  CORE




                                                                                1 – 2 days


           Subtract Whole Numbers
*COMMON




             Subtract up to 4-digit minus 4-digit regrouping once
  CORE




             Subtract up to 4-digit minus 4-digit regrouping twice             3 – 4 days
             Subtract up to 4-digit minus 4-digit regrouping three times
           Estimate Sums and Differences
*COMMON




             Rounding whole numbers
  CORE




             Estimating sums and differences                                   2 – 3 days


 Compare Values of Mixed Currency
   Identify value of mixed currency                                            1 – 2 days
   Compare money sets
Unit 3: Number Theory and Computation 2                                        (10-20 days)
 Multiples
                                                                                1 – 2 days
   Identify multiples
 Factors
   Identify factors                                                1 – 3 days
   Create and interpret factor arrays
     Multiply Whole Numbers
*COMMON




         Multiply up to 3-digits by 1 digit no regrouping
  CORE




         Multiply up to 3-digits by 1 digit with regrouping        2 – 4 days
         Multiply up to 4-digits by 1 digit with regrouping
           Divide Whole Numbers
*COMMON




             Divide 2-digits by 1-digit
  CORE




             Divide 3-digits by 1 digit                            3 – 5 days
             Divide 4-digits by 1 digit
 Estimate Products and Quotients
   Estimate products                                               2 – 3 days
   Estimate quotients
 Divisibility Rules
   Identify numbers divisible by 2
   Identify numbers divisible by 5                                 1 – 3 days
   Identify numbers divisible by 10
   Identify numbers divisible by a combination of 2, 5, or 10
UNIT 4: Algebra 1                                                  (7–14 days)
 Numeric Patterns
                                                                    1 – 2 days
   Identify the rule for and extend a number pattern
 Repeating Patterns
                                                                    1 - 2 days
   Identify the rule for and extend a repeating pattern
 Growing Patterns
                                                                    1 - 3 days
   Identify a rule for and extend a growing pattern
 Solve for Unknown Quantities
    Find the unknown using addition and subtraction                2 – 3 days
    Find the unknown using multiplication
 Function Tables
    Complete function tables using addition and subtraction
                                                                    2 - 4 days
    Complete function tables using multiplication
    Complete function tables using division
                                                                 Suggested Time
                      QUARTER 2 (Nov 8 – Jan 21)
                                                                     Frame
                                   46 days
BENCHMARK B
                                                                 Nov 1 – Nov 12
(all Quarter 1 skills assessed)
                                                                 testing window

Unit 5: Fraction Concepts
                                                                   (7-12 days)
 Proper Fractions and Mixed Numbers
   Read, write, represent fractions as part of a whole
                                                                    2 - 3 days
   Read, write, represent fractions as part of a set
   Read, write, represent mixed numbers
 Compare and Order Fractions and Mixed Numbers
   Compare proper fractions and mixed numbers               1 – 2 days
   Order proper fractions and mixed numbers
 Fractional Number Lines
   Create fractional number lines
   Write fractions on number lines                          2 – 4 days
   Identify locations on number lines
   Write and identify mixed numbers on number lines
      Add and Subtract Proper Fractions and Mixed Numbers
*COMMON




         Add proper fractions
  CORE




         Subtract proper fractions                          2 – 3 days
         Add mixed numbers
         Subtract mixed numbers
Unit 6: Statistics and Probability                           (11-18 days)
 Probability
   Express object probability as a fraction
                                                              3 - 5 days
   Express spinner probability as a fraction
   Express conditional probability as a fraction
 Median, Mode and Range
    Determine the range of a set of data
                                                             2 – 3 days
    Determine the mode of a set of data
    Determine the median of a set of data
 Line Plots
     Create line plots                                      3 – 5 days
     Interpret line plots
 Coordinate Grids
   Identify locations on a coordinate grid given object     1 – 2 days
   Identify objects on a coordinate grid given location
 Line Graphs
                                                             2 – 3 days
   Interpret line graphs
UNIT 7: Algebra 2                                            (5-9 days)
 Write Expressions
   Write expressions using addition or subtraction          2 – 3 days
   Write expressions using multiplication or division
 Equivalent Expressions
                                                             1 – 2 days
   Write equivalent expressions
 Write Relationships
   Evaluate relationships with missing relational symbols   2 – 4 days
   Represent relationships in word problems
Unit 8: Geometry 1                                            (4-8 days)
 Angles
   Identify right angles
                                                             2 – 4 days
   Identify acute and obtuse angles
   Identify angles in shapes and objects
 Transformations
   Identify and create translations
                                                                          2 – 4 days
   Identify and create reflections
   Identify and create rotations
                                                                       Suggested Time
                  QUARTER 3 (Jan 25 – Apr 7)
                                                                           Frame
                                45 days
BENCHMARK C – Mock MSA                                                 Jan 31 – Feb 11
(all VSC assessed skills)                                              testing window
Unit 9: Geometry 2
                                                                          (6-9 days)
 Geometric Solids
   Identify cones and cylinders
   Identify and describe pyramids by the number of edges, faces, or
                                                                          4 – 6 days
      vertices
   Identify and describe prisms by the number of edges, faces, or
      vertices
 Nets for Cubes and Pyramids
   Identify the number and arrangement of squares needed to
     create cubes                                                         2 – 3 days
   Identify the number and arrangement of rectangles/triangles
     needed to create pyramids
Unit 10: Decimals                                                         (8-16 days)
 Read, Write, Represent Decimals
   Read, write, represent decimals in the tenths                         2 – 4 days
   Read, write, represent decimals in the hundredths
 Place Value and Expanded Form of Decimals
                                                                          1 – 3 days
   Represent decimals in expanded form through the hundredths
 Compare and Order Decimals
   Compare decimals through the hundredths                               1 – 2 days
   Order decimals through the hundredths
 Add Decimals
   Add decimals through the tenths                                       1 – 2 days
   Add decimals through the hundredths
 Subtract Decimals
   Subtract decimals through the tenths                                  1 – 2 days
   Subtract decimals through the hundredths
 Estimate Decimal Sums and Differences
   Round decimals
   Estimate sums to the tenths
                                                                          2 – 3 days
   Estimate sums to the ones place
   Estimate differences to the tenths
   Estimate differences to the ones place
Unit 11: Measurement 1                                                    (5-9 days)
 Measure Length
   Draw length to nearest ¼ inch
                                                                           2 – 4 days
   Measure length to nearest ¼ inch
   Measure length to nearest mm
 Determine Equivalent Units of Length
   Convert yards to inches                                                3 – 5 days
   Convert inches to yards, feet
Unit 12: Measurement 2                                                    (7-11 days)
 Perimeter
   Find perimeter given all sides                                         2 – 3 days
   Find perimeter with missing sides
 Area
   Find area on grid                                                      2 – 3 days
   Find area using formula
 Start time, Elapsed Time, and End Time
   Find end time
                                                                           3 – 5 days
   Find start time
   Find elapsed time

                                                                        March 7 to
Maryland State Assessment
                                                                        March 16


                                                                       Suggested Time
                    POST-MSA CURRICULUM
                                                                           Frame
Unit 13: Fraction Concepts 2                                             (10 - 15 days)
 Least Common Multiple
   Identify the least common multiple of 2 numbers                       2 - 3 days
   Identify the least common multiple of 3 numbers
     Equivalent Forms of Fractions
        Concrete representations of equivalent fractions using
*COMMON




          visual models with attention to how the number and size of
  CORE




                                                                          3 - 5 days
          the parts differ even though the two fractions themselves
          are the same size
        Process of finding equivalent fractions
     Add and Subtract Proper Fractions with Unlike Denominators
*COMMON




        Add proper fractions with unlike denominators
  CORE




        Subtract proper fractions with unlike denominators               5 - 7 days


Unit 14: Simplify & Compare Fractions                                    (10 - 14 days)
 Identify GCF and Simplify Fractions
   Identify the Greatest Common Factor                                   5 - 7 days
   Use the Greatest Common Factor to simplify fractions
           Compare and Order Fractions with Unlike Denominators
             Compare fractions with unlike denominators
*COMMON




             Order fractions with unlike denominators Compare mixed
  CORE




                                                                                  5 - 7 days
              numbers with unlike denominators
             Order mixed numbers with unlike denominators
            
Unit 15: Decimal Notation for Fractions                                           7-13 days
*COMMON




           Express a fraction with denominator 10 as an equivalent
  CORE




                                                                                  2-4 days
            fraction with denominator 100
*COMMON




           Use decimal notation for fractions with denominators 10 or
  CORE




                                                                                  3-5 days
            100
*COMMON




           Compare two decimals to hundredths by reasoning about their
  CORE




                                                                                  2-4 days
            size


Unit 16: Whole Number Computation 2                                              (9 – 15 days)
           Multiply Whole Numbers
*COMMON




             Multiply 2-digit by 2-digit as multiple of ten
  CORE




             Multiply 2-digit by 2-digit                                         3 – 5 days


                Divide Whole Numbers
*COMMON




                Divide with 2-digit divisor as multiple of ten with reminders
  CORE




                Divide with 2-digit divisor with remainders                      3 – 5 days
                Division word problems
BENCHMARK D – End of Year Benchmark                         May 16 – May 27
(all skills from Quarters 1-4 assessed)                     testing window
*Common Core - This skill will infuse the Maryland State Standards and the
                  Common Core.
                                   QUARTER 2 PLANNING CALENDAR* (46 DAYS)                                       Nov 8-Jan 21
                                                                                                                SY 2010-2011

                 MONDAY                  TUESDAY             WEDNESDAY               THURSDAY                      FRIDAY

           8    Quarter 2 Begins    9                   10                    11                          12

                                                                                                           BENCHMARK B
           15                       16                  17                    18                           (Nov 1-12)
                                                                                                          19
NOVEMBER




           22                       23                  24                    25   Thanksgiving Holiday   26   Thanksgiving Holiday


           29                       30



                                                        1                     2                           3


           6                        7                   8                     9                           10
DECEMBER




           13                       14                  15                    16                          17 Early Release Day


           20                       21                  22                    23                          24      Winter Break


           27     Winter Break      28   Winter Break   29     Winter Break   30       Winter Break       31      Winter Break

           3                        4                   5                     6                           7
JANUARY




           10                       11                  12                    13                          14


           17    MLK Holiday        18                  19                    20                          21      Quarter 2 Ends
      Grade 4: Unit 5

Fraction Concepts

                   Unit Resources

 Unit Vocabulary                    Unit Assessment
        Unit 5: Concept 1
        Proper Fractions and Mixed Numbers
                       TIME FRAME: 2-3 days                                        PREREQUISITE SKILLS
                       Proper Fractions and Mixed Numbers                             Fractions of a region (halves, thirds, fourths)
                          Fractions as part of a set                                 Identify fractional sets (halves, thirds, fourths)
                          Fractions as part of a whole                               Represent fractional sets (halves, thirds, fourths)
                          Mixed numbers                                              Writing fractions
                       VSC OBJECTIVE          (calculators allowed)
Knowledge and Skills




                       4.6.A.2.b Read, write, or represent proper fractions of a set which has the same number of items as the denominator using
                       symbols, words, and models
                       ASSESSMENT LIMIT: Use denominators of 6, 8, and 10 with sets of 6, 8, and 10, respectively
                       4.6.A.2.a Read, write, and represent proper fractions of a single region using symbols, words, and models
                       ASSESSMENT LIMIT: Use denominators 6, 8, and 10

                       VOCABULARY                     ENDURING UNDERSTANDINGS
                       fraction                          Fractions represent parts of a whole or group.
                       Numerator                         Fractions can be compared using a variety of models.
                       Denominator                       Fractions express a relationship between two numbers.
                       fraction bar                   ESSENTIAL QUESTIONS
                       set                               How are the numerator and denominator related?
                       region                            How can the fractional parts of a set be modeled?
                       mixed number                      How can fractions be modeled using numerals, regions, sets, and number lines?
                                                         When is it appropriate to use fractions?
                                                      CONCEPT KNOWLEDGE AND PROCESS
                                                         A fraction is an EQUAL part of a whole or EQUAL part of a group.
                                                         The numerator is the number of equal parts you have or want; the denominator is the
                                                          TOTAL number of equal parts in the whole.
                                                         A mixed number is a whole number and a fraction.
                                                      ERROR INTERVENTION
                                                      IF students confuse the THEN consider using the mnemonic that the denominator
                                                          numerator and                   means down. Have students label and count the total
                                                          denominator                     number of equal pieces and write that in the denominator
                                                                                          first before they write the numerator.




        Baltimore City Schools – Office of Mathematics                Grade 4 Math Curriculum DRAFT                          Page 14
        officeofmath@bcps.k12.md.us
Unit 5: Concept 1
Proper Fractions and Mixed Numbers
                                          IF students misread what        THEN consider requiring that students circle key words that
                                                 the question is asking       identify what the question is asking for (e.g. highlight the
                                                 for in the numerator         difference between “How many pieces are shaded?” and
                                                                              “How many pieces are not shaded?”).
                                          IF students do not recall       THEN consider showing numerous examples of equal and non-
                                                 that fractions must          equal pieces.
                                                 have equal pieces




Baltimore City Schools – Office of Mathematics               Grade 4 Math Curriculum DRAFT                       Page 15
officeofmath@bcps.k12.md.us
          Unit 5: Concept 1
          Proper Fractions and Mixed Numbers
                                                                LEARNING ACTIVITIES AND STRATEGIES
                                        Activity                                     Description                                  Materials
                          Visual        Flagging Conversation     The students learn about fractions as a part of a     Picture of signal flags with
                          Spatial       SF Grade 4 TE Lesson      region by looking at boating signal flags.              an explanation of their
                                        9-1 (p. 500b)             *You can extend this activity by giving the             meanings.
                                                                  students a fraction to represent and having them
Suggested Learning Plan




                                                                  create their own signal flag with a meaning.
                          Literature    Spelling Fractions        The students shade parts of a region and              Spelling Fractions worksheet
                          Connection                              determine the fraction of consonants or vowels in     List of spelling words from
                          Visual                                  their spelling words.                                   Reading, Science or Social
                                                                                                                          Studies
                                                                                                                        Crayons or colored pencils
                          Visual        What’s Your Favorite?     The students survey their classmates to find out      Crayons
                          Social                                  their favorite pizza and create a pie chart to        What’s Your Favorite?
                                                                  determine different fractional parts.                   worksheet #1
                                                                                                                        What’s Your Favorite?
                                                                                                                          worksheet #2
                          Visual        Fractions in Paintings    The students identify fractional parts in a group     Books or magazines with
                          Spatial       SF Grade 4 TE Lesson      in pictures and in artwork.                             paintings or pictures
                                        9-2 (p.502b)
                          Social        How Many in the Group     The students write the fractions for different
                          Cooperative   SF Grade 4 TE Lesson      characteristics of the students in their tables or
                                        9-2 (p.502b)              groups.
                          Visual        Food and Fractions        The students use food to replicate fractions as a     M&M’s, Skittles or Trail Mix
                          Kinesthetic                             part of a set.
                          Visual        Mixed Number Bamboo       The students use the integration of art to gain an      Water Color Paints
                          Kinesthetic   Painting                  understanding of mixed numbers. The students            White Paper
                                                                  create a bamboo painting to represent a mixed           Bamboo Paint Brushes
                                                                  number.                                                 Bamboo Plant
                          Kinesthetic   Different Names, Same     The students investigate the concept of mixed           10 x 10 grid paper
                                        Number                    numbers using grid paper and by cutting wholes          Teaching Tool 5
                                        SF Grade 4 TE Lesson      into parts.                                             Scissors
                                        9-10 (p. 530a)
                                            DIFFERENTIATION                                        CROSS-CURRICULAR CONNECTIONS
                             Accommodations*                 G.A.T.E./Enrichment                Artful Teaching              Literacy Integration
          Baltimore City Schools – Office of Mathematics                Grade 4 Math Curriculum DRAFT                         Page 16
          officeofmath@bcps.k12.md.us
        Unit 5: Concept 1
        Proper Fractions and Mixed Numbers
                                                                                 RESOURCES
Suggested Learning Plan



                             Sub-Skills       Teacher Created Materials             Adopted Textbooks                         Technology
                          Fractions as part    MW Exploring Fractions          SF Grade 4 TE Lesson 9-1 (pp.       WEB: NLVM - Fraction Naming
                          of a whole           MW Exploring Fractions           500A-501)
                                                 with tiles                     SF Grade 4 TE Lesson 9-2 (pp.
                                               MW Fractional Regions            502A-503)
                                                                                SF Grade 4 TE Lesson 9-10
                          Fractions as part    MW Fractional Sets               (pp. 530-533)
                          of a set



                          Mixed numbers          MW Exploring Mixed
                                                  Numbers
                                                 MW Mixed Numbers




                                                  Writing in Math                                                Other Resources
  Assessments




                                                                     CONCEPT                  MULTIPLE CHOICE                 OTHER WAYS TO
                              TRACKING SHEET
                                                                    ASSESSMENT                QUESTION BANK                      ASSESS




        Baltimore City Schools – Office of Mathematics                   Grade 4 Math Curriculum DRAFT                        Page 17
        officeofmath@bcps.k12.md.us
        Unit 5: Concept 2
        Compare and Order Fractions and Mixed Numbers
                       TIME FRAME: 1 – 2 days                                                       PREREQUISITE SKILLS
                       Compare and Order Fractions and Mixed Numbers                                   Comparing numbers
                          Compare proper fractions and mixed numbers                                  Ordering numbers
                          Order proper fractions and mixed numbers                                    Fractional number lines
                       VSC OBJECTIVE (calculators allowed)
                       4.6.A.2.g Compare and order fractions and mixed numbers with or without using the symbols (<, >, or =)
                       Assessment Limit: Use like denominators and no more than 3 numbers (0 to 20)
Knowledge and Skills




                       VOCABULARY              ENDURING UNDERSTANDINGS
                       fraction                   Fractions represent parts of a whole or group.
                       numerator                  Fractions can be compared using a variety of models.
                       denominator                Fractions express a relationship between two numbers.
                       fraction bar            ESSENTIAL QUESTIONS
                       mixed number               How is the ordering of fractions the same as ordering whole numbers and how is it different?
                       whole number               How are the numerator and denominator related?
                       compare                    How can the fractional parts of a set be modeled?
                       order                      How can fractions be modeled using numerals, regions, sets, and number lines?
                       greater than               When is it appropriate to use fractions?
                       less than               CONCEPT KNOWLEDGE AND PROCESS
                       equal to                   A fraction is an EQUAL part of a whole or EQUAL part of a group.
                                                  The numerator is the number of equal parts you have or want; the denominator is the TOTAL
                                                   number of equal parts in the whole.
                                                  A mixed number is a whole number and a fraction.
                                               ERROR INTERVENTION
                                               IF students are having trouble     THEN consider using fraction tiles and have students compare
                                                  visualizing the size of                and order fractions by laying out the tiles on their desks.
                                                  fractions
                                               IF students overlook the value     THEN consider requiring that students circle the whole
                                                  of the whole number when            numbers first and then compare/order the fractions.
                                                  comparing/ordering fractions        They should learn to compare the whole numbers first
                                                  and mixed numbers                   and then the numerators when the denominators are the
                                                                                      same.
                                               IF students read the relational    THEN consider having them draw teeth inside the > or <
                                                   symbol incorrectly                 symbol because the sign wants to “eat” the greater
                                                                                      fraction or mixed number.
        Baltimore City Schools – Office of Mathematics              Grade 4 Math Curriculum DRAFT                            Page 18
        officeofmath@bcps.k12.md.us
        Unit 5: Concept 2
        Compare and Order Fractions and Mixed Numbers

                                                            LEARNING ACTIVITIES AND STRATEGIES
                                         Activity                                 Description                                   Materials
                          Kinesthetic   Comparing Fraction Tiles   The students use fraction tiles to compare          Fraction tiles *
                          Visual                                   fractions and are able to visualize which           Blank paper
Suggested Learning Plan




                          Spatial                                  fraction is greater or smaller.                     Pencil

                          Cooperative   Place Your Order           The students work with their groups to              Index cards with fractions
                          Visual                                   represent and order fractions with like              written on them
                          Kinesthetic                              denominators.                                       Pencil or crayons

                          Visual        I Spy                      The students spy on their classmates to             I Spy! worksheet
                                                                   determine fractions as a part of a group.           Pencil




                                           DIFFERENTIATION                                     CROSS-CURRICULAR CONNECTIONS

                              Accommodations*              G.A.T.E./Enrichment              Artful Teaching                 Literacy Integration


        Baltimore City Schools – Office of Mathematics              Grade 4 Math Curriculum DRAFT                            Page 19
        officeofmath@bcps.k12.md.us
        Unit 5: Concept 2
        Compare and Order Fractions and Mixed Numbers
                                                                              RESOURCES
Suggested Learning Plan


                            Sub-Skills     Teacher Created Materials             Adopted Textbooks                         Technology
                          Compare proper      MW Exploring Compare &        SF Grade 4 TE Lesson 9-9 (pp.       WEB: Greater Than, Less Than,
                          fractions and        Order Fractions                524A-527)                            or the Same
                          mixed numbers       MW Compare Fractions
                                              MW Exploring Compare
                                               Mixed Numbers
                                              MW Compare Mixed
                                               Numbers

                          Order proper        MW Order Fractions
                          fractions and       MW Order Mixed
                          mixed numbers        Numbers




                                               Writing in Math                                                Other Resources
  Assessments




                                                                  CONCEPT                  MULTIPLE CHOICE                 OTHER WAYS TO
                             TRACKING SHEET
                                                                 ASSESSMENT                QUESTION BANK                      ASSESS




        Baltimore City Schools – Office of Mathematics                Grade 4 Math Curriculum DRAFT                        Page 20
        officeofmath@bcps.k12.md.us
        Unit 5: Concept 3
        Proper Fractions and Mixed Numbers on a Number Line

                       TIME FRAME: 2-4 days                                                     PREREQUISITE SKILLS
                       Proper Fractions and Mixed Numbers on a                                      Finding a fraction on a number line (up to
                                                                                                     fourths)
                       Number Line                                                                  Finding a location on a number line (up to
                          Create fractional number lines
                                                                                                     fourths)
                          Write numbers on number line
                          Identify locations on number line
Knowledge and Skills




                          Write and Identify mixed numbers on number line
                       VSC OBJECTIVE       (calculators allowed)
                       4.1.C.1.a Represent mixed numbers and proper fractions on a number line
                       Assessment Line: Use proper fractions with a denominators of 6, 8, or 10

                       VOCABULARY                   ENDURING UNDERSTANDINGS
                       fraction                         Fractions represent parts of a whole or group.
                       numerator                        Fractions can be compared using a variety of models.
                       denominator                  ESSENTIAL QUESTIONS
                       fraction bar                     How are the numerator and denominator related?
                       mixed number                     How can the fractional parts of a set be modeled?
                       whole number                     How can fractions be modeled using numerals, regions, set, and number lines?
                                                    CONCEPT KNOWLEDGE AND PROCESS
                                                        A fraction is an equal part of a whole or part of a group (set).
                                                        The numerator is the number of equal parts you have or want; the denominator is the
                                                         TOTAL number of equal parts in the whole.
                                                    ERROR INTERVENTION
                                                    IF students count the number of lines       THEN consider having students highlight each
                                                         instead of the number of spaces                space with a different color to find the
                                                                                                        denominator of the fraction.
                                                    IF students forget to label the whole       THEN consider having students trace each whole
                                                         number past 1 on a number line                 number on a number line in a different color
                                                         (mixed numbers on a number line)               and write in the whole number before they
                                                                                                        actually write the mixed number/fraction.



        Baltimore City Schools – Office of Mathematics               Grade 4 Math Curriculum DRAFT                           Page 21
        officeofmath@bcps.k12.md.us
Unit 5: Concept 3
Proper Fractions and Mixed Numbers on a Number Line
                                          IF students find the denominator by        THEN consider modeling this common mistake and
                                             counting all of the equal spaces on           emphasizing that the denominator is only the
                                             a number line and not just the                number of equal spaces between two whole
                                             number of spaces between whole                numbers.
                                             numbers
                                          IF students have trouble identifying a     THEN consider requiring that students fill in all
                                             fraction/mixed number located                 missing fractions on the number line before
                                             between two other fractions                   choosing the correct answer.




Baltimore City Schools – Office of Mathematics            Grade 4 Math Curriculum DRAFT                         Page 22
officeofmath@bcps.k12.md.us
        Unit 5: Concept 3
        Proper Fractions and Mixed Numbers on a Number Line

                                                             LEARNING ACTIVITIES AND STRATEGIES
                                         Activity                                  Description                               Materials
                          Visual        Make a Number Line         The students use fraction tiles to create a      Fraction tiles *
                          Spatial                                  number line.
Suggested Learning Plan




                          Concrete

                          Kinesthetic   In the Fold                The students create fractional number            Strips of paper that are at
                                        SF Grade 4 TE Lesson 9-3   lines by folding strips of paper into equal       least 11 inches long
                                        (p. 504b)                  sections and by labeling the fractions.          Pencils

                          Kinesthetic   Pin the Fraction on the    The students place Post-it notes on              Post-it notes with various
                          Visual        Number Line                number lines to begin to the connection           fractions written on them
                                                                   between the denominator and the equal            Blank number lines to
                                                                   number of spaces on a number line.                accommodate fractions with
                                                                                                                     different denominators
                          Kinesthetic   Number Line on a Floor     The students use the floor and create a          Fraction cards
                          Visual                                   class-size number line to plot specific          Students
                                                                   points                                           Sentence strip




                                           DIFFERENTIATION                                      CROSS-CURRICULAR CONNECTIONS

                                Accommodations*           G.A.T.E./Enrichment                Artful Teaching             Literacy Integration


        Baltimore City Schools – Office of Mathematics               Grade 4 Math Curriculum DRAFT                        Page 23
        officeofmath@bcps.k12.md.us
   Unit 5: Concept 3
   Proper Fractions and Mixed Numbers on a Number Line
                                                                      RESOURCES
Suggested Learning


                     Sub-Skills    Teacher Created Materials             Adopted Textbooks                         Technology
               Create fractional      MW Create Fractional          SF Grade 4 TE Lesson 9-3 (pp.       WEB: Identify Fractions
               number lines            Number Line                    504A-507)                           WEB: Fractions on a Number Line
                                                                     SF Grade 4 TE Lesson 9-11            – Drag and Drop
                                                                      (pp. 534-535)                       WEB: Find Grammy
               Write numbers          MW Write Fractions on a
                                                                                                          WEB: Identify Mixed Fractions
               on number line          Number Line
       Plan




               Find locations on      MW Identify Locations on
               number line             a Number Line



               Mixed numbers          MW Mixed Numbers on a
               on number line          Number Line




                                       Writing in Math                                                Other Resources
Assessments




                                                          CONCEPT                  MULTIPLE CHOICE                 OTHER WAYS TO
                     TRACKING SHEET
                                                         ASSESSMENT                QUESTION BANK                      ASSESS




   Baltimore City Schools – Office of Mathematics             Grade 4 Math Curriculum DRAFT                        Page 24
   officeofmath@bcps.k12.md.us
        Unit 5: Concept 4
        Add and Subtract Proper Fractions and Mixed Numbers

                       TIME FRAME: 2-3 days                                              PREREQUISITE SKILLS
                       Add and Subtract Proper Fractions and                                Basic addition and subtraction facts
                       Mixed Numbers
                          Add proper fractions
                          Subtract proper fractions
                          Add mixed numbers
                          Subtract mixed numbers
Knowledge and Skills




                       VSC OBJECTIVE         (calculators not allowed)
                       4.6.C.1.e Add and subtract proper fractions and mixed
                       numbers
                       Assessment Limits: Use 2 proper fractions with a single digit
                       like denominators, 2 mixed numbers with a single digit,
                       like denominators a whole number and a proper fraction
                       with a single digit denominator and numbers (0 to 20)

                       VOCABULARY                ENDURING UNDERSTANDINGS
                       fraction                       Operation strategies with fractions are similar to those used with whole numbers.
                       numerator                      Fractions represent parts of a whole or group.
                       denominator                    Fractions can be compared using a variety of models.
                       fraction bar              ESSENTIAL QUESTIONS
                       mixed number                   What strategies can be developed to show computation with fractions?
                       whole number                   How are models used to show how fractional parts are combined or separated?
                       proper fraction                How can fractions be modeled using numerals, regions, sets, and number lines?
                                                 CONCEPT KNOWLEDGE AND PROCESS
                                                      A fraction is an equal part of a whole or part of a group (set).
                                                      The numerator is the number of equal parts you have or want; the denominator is the TOTAL
                                                       number of equal parts in the whole.
                                                 ERROR INTERVENTION
                                                 IF students add both the                THEN consider emphasizing repeatedly that the
                                                       numerator and denominator             denominator stays the same when you are adding and
                                                                                             subtracting like denominators.
                                                 IF students add both the                THEN consider having the students show the work with
                                                       numerator and denominator             fraction tiles.

        Baltimore City Schools – Office of Mathematics                  Grade 4 Math Curriculum DRAFT                         Page 25
        officeofmath@bcps.k12.md.us
Unit 5: Concept 4
Add and Subtract Proper Fractions and Mixed Numbers
                                    IF students have trouble adding      THEN consider requiring that students draw a picture before
                                       and subtracting a whole                  adding or subtracting. If subtracting, they should
                                       number with a fraction (e.g. 3           cross out the part that needs to be taken away.
                                       – ½)
                                    IF students have trouble knowing     THEN consider having students line up the problem
                                       what parts of a mixed number             vertically with one column for the fraction and one
                                       and fraction to add together or          column for the whole number. This should help them
                                       subtract                                 stay organized.




Baltimore City Schools – Office of Mathematics          Grade 4 Math Curriculum DRAFT                        Page 26
officeofmath@bcps.k12.md.us
        Unit 5: Concept 4
        Add and Subtract Proper Fractions and Mixed Numbers

                                                               LEARNING ACTIVITIES AND STRATEGIES
                                            Activity                                  Description                               Materials
                          Visual       Adding Fraction Tiles          The students use fraction tiles to visualize    Fraction tiles *
                          Concrete                                    the concept of adding fractions with like
Suggested Learning Plan




                                                                      denominators.

                          Linguistic   Quilt Story                    The students create stories and illustrate      Centimeter grid paper
                                       SF Grade 4 TE Lesson 10-2      them to demonstrate adding fractions.
                                       (p. 564b)




                                             DIFFERENTIATION                                       CROSS-CURRICULAR CONNECTIONS

                              Accommodations*                  G.A.T.E./Enrichment              Artful Teaching             Literacy Integration


        Baltimore City Schools – Office of Mathematics                  Grade 4 Math Curriculum DRAFT                         Page 27
        officeofmath@bcps.k12.md.us
   Unit 5: Concept 4
   Add and Subtract Proper Fractions and Mixed Numbers
                                                                      RESOURCES
                     Sub-Skills   Teacher Created Materials              Adopted Textbooks                   Technology
Suggested Learning




               Add proper            MW Exploring Fraction          SF Grade 4 TE Lesson 10-2
               fractions              Computation                     (pp. 564-567)
                                     MW Add Proper Fractions        SF Grade 4 TE Lesson 10-4
                                                                      (pp. 574A-577)

               Subtract proper       MW Subtraction Proper
               fractions              Fractions
       Plan




               Add mixed             MW Exploring Mixed
               numbers                Number Computation
                                     MW Add Mixed Numbers
               Subtract mixed        MW Subtract Mixed
               numbers                Numbers



                                         Writing in Math                                             Other Resources
Assessments




                                                     CONCEPT                       MULTIPLE CHOICE           OTHER WAYS TO
                     TRACKING SHEET
                                                    ASSESSMENT                     QUESTION BANK                ASSESS




   Baltimore City Schools – Office of Mathematics             Grade 4 Math Curriculum DRAFT                   Page 28
   officeofmath@bcps.k12.md.us
                                 Grade 4: Unit 6

                                           Statistics

                                                      Unit Resources

                              Unit Vocabulary                                    Unit Assessment




Baltimore City Schools – Office of Mathematics   Grade 4 Math Curriculum DRAFT                     Page 29
officeofmath@bcps.k12.md.us
        Unit 6: Concept 1
        Probability
                       TIME FRAME: 3-5 days                                                           PREREQUISITE SKILLS
                       Probability                                                                        Object probability (describing using words)
                          Express object probability as a fraction                                       Spinner probability (describing using words)
                          Express spinner probability as a fraction                                      Fractions
                          Express conditional probability as a fraction
                       VSC OBJECTIVE         (calculators allowed)
                       4.5.B.1.a Express the probability as a fraction
                       Assessment Limit: Use a sample space of no more than 6 outcomes
Knowledge and Skills




                       VOCABULARY                      ENDURING UNDERSTANDINGS
                       probability                        The likelihood of an event depends on the possible outcomes.
                       favorable outcomes                 Probability can be represented numerically and graphically.
                       total outcomes                  ESSENTIAL QUESTIONS
                       possible outcomes                  How can the possible outcomes for an event be determined?
                       numerator                          How is probability represented numerically?
                       denominator                        How is the likelihood of an event determined and communicated?
                       fraction bar                    CONCEPT KNOWLEDGE AND PROCESS
                       event                              Probability is the chance or likelihood of something happening.
                       likely                             Probability can be written in terms of certain [WILL ALWAYS HAPPEN], impossible [WILL
                       unlikely                            NEVER HAPPEN], less likely, more likely, or equally likely.
                       equally likely
                                                       ERROR INTERVENTION
                       impossible
                       certain                         IF students forget to write probability        THEN consider modeling this error for them and
                       fair                                as a fraction (e.g., they simply               create a process chart for finding the
                       unfair                              write the number of favorable                  probability with probability itself written as a
                                                           outcomes)                                      fraction.     Example: proba
                                                                                                                                  Bility
                                                       IF students forget that adding or              THEN consider requiring that students draw
                                                          taking away objects changes the                 pictures to show items that are added or
                                                          denominator and may change the                  taken away.
                                                          numerator
                                                       IF students write the fraction as the          THEN consider requiring that students label and
                                                          number of favorable outcomes over                   count the total number of objects and write
                                                          the number of remaining objects                     that in the denominator first. Students
                                                          instead of the number of total                      should then circle the objects that make up
                                                          outcomes                                            the favorable outcomes.
        Baltimore City Schools – Office of Mathematics                     Grade 4 Math Curriculum DRAFT                          Page 30
        officeofmath@bcps.k12.md.us
        Unit 6: Concept 1
        Probability
                                                               LEARNING ACTIVITIES AND STRATEGIES
                                         Activity                                     Description                               Materials
                          Kinesthetic   Food and Probability          The students use food to explore the            Skittles, M&Ms, Trail Mix or
                          Visual                                      probability of a certain outcome. The             Fruit Loops
Suggested Learning Plan




                          Concrete                                    students also discover how conditions can       Pencil and paper
                                                                      change the probability of an event.
                          Visual        Raffle Jar                    The students win raffle tickets in class and    Raffle jar *
                          Concrete                                    participate in a weekly drawing in order to     Raffle tickets or strips of paper
                                                                      learn the concept of events and outcomes.

                          Linguistic    Hundred Penny Box         The students find the probability of picking        Book Hundred Penny Box by
                          Literature    SF Grade 4 TE Lesson 12-7 a penny with certain years printed on                 Sharon Bell Mathis
                          Connection    (p. 706b)                 them after reading the story Hundred
                                                                  Penny Box.
                          Kinesthetic   Coin Toss                 The students flip coins to determine the            Play money or
                                        SF Grade 4 TE Lesson 12-7 possible outcomes and the probability of            Teaching Tool 7
                                        (p. 706b)                 flipping heads or tails.                            Coins

                          Social        Probability Design        The students develop a set of index cards           Index Cards
                          Cooperative   SF Grade 4 TE Lesson 12-7 and determine the probability of picking
                                        (p. 706b)                 certain favorable outcomes.

                          Visual        Fractions = Probability   The students create a spinner and express           Spinner *
                          Concrete      SF Grade 4 TE Lesson 12-7 the probability of landing on different             Teaching Tool 20 with six
                                        (p. 706b)                 colors as a fraction.                                 sections
                                                                                                                      Crayons
                                           DIFFERENTIATION                                         CROSS-CURRICULAR CONNECTIONS

                             Accommodations*                   G.A.T.E./Enrichment              Artful Teaching             Literacy Integration




        Baltimore City Schools – Office of Mathematics                  Grade 4 Math Curriculum DRAFT                         Page 31
        officeofmath@bcps.k12.md.us
                   Unit 6: Concept 1
                   Probability
                                                                                                             RESOURCES
Assessments S u g g e s t e d L e a r n i n g P l a n



                                                           Sub-Skills   Teacher Created Materials               Adopted Textbooks                      Technology
                                                        Object             MW Exploring Probability        SF Grade 4 TE Lesson 12-5       US: “Understanding: Probability
                                                        probability        MW Object Probability            (pp. 700A-703)                   and Odds”
                                                                                                            SF Grade 4 TE Lesson 12-6       WEB: NLVM - Spinners
                                                                                                             (pp. 704A-705)                  US: “Discovering Math:
                                                                                                            SF Grade 4 TE Lesson 12-7        Probability”
                                                        Spinner            MW Spinner Probability           (pp. 706-709)
                                                        probability



                                                        Conditional        MW Conditional
                                                        probability         Probability




                                                                            Writing in Math                                              Other Resources




                                                                                               CONCEPT                    MULTIPLE CHOICE              OTHER WAYS TO
                                                            TRACKING SHEET
                                                                                              ASSESSMENT                  QUESTION BANK                   ASSESS




                   Baltimore City Schools – Office of Mathematics                                    Grade 4 Math Curriculum DRAFT                     Page 32
                   officeofmath@bcps.k12.md.us
        Unit 6: Concept 2
        Median, Mode, and Range
                       TIME FRAME: 2 -3 days                                            PREREQUISITE SKILLS
                       Median, Mode, and Range                                             Interpreting tables
                          Determine the range of a set of data                            Ordering numbers
                          Determine mode of a set of data
                          Determine median of a set of data
                       VSC OBJECTIVE (calculators allowed)
                       4.4.B.2.a Determine median, mode, and range
                       ASSESSMENT LIMIT: Use no more than 8 pieces of data and whole numbers (0 to 100)
Knowledge and Skills




                       VOCABULARY                 ENDURING UNDERSTANDINGS
                       statistics                    The type of data determines how data sets can be organized, displayed, and analyzed.
                       data                          Statistical measures provide a numeric picture of the shape of the data.
                       median                     ESSENTIAL QUESTIONS
                       mode                          In what ways can sets of data be represented by statistical measures?
                       range                         How can the mean, median, mode, and range be used to describe the shape of the data?
                                                     How can range, median, and mode be computed and compared?
                                                  CONCEPT KNOWLEDGE AND PROCESS
                                                     Median is the middle number in a set of ordered data.
                                                     Mode is the number that occurs the most often in a set of data.
                                                     Range is the difference between the greatest number and the least number in a set of data.
                                                  ERROR INTERVENTION
                                                  IF students attempt to find the       THEN consider requiring that they order the numbers from
                                                     median, mode, and range                   least to greatest before they solve the problem.
                                                     without ordering the numbers
                                                     from least to greatest
                                                  IF students do not remember the       THEN consider thinking of creative ways to teach the
                                                     definitions of median, mode,            meanings of the words:
                                                     and range                          Median: the median is the middle barrier on a street; draw
                                                                                             three shirts (small, medium, and large) and label the
                                                                                             middle one with an M for median and middle.
                                                                                        Mode: most often in data; relate the mode to what’s in
                                                                                             style. Median, mode, and range rap
                                                  IF students have trouble finding      THEN consider having them “spread out” the missing
                                                      the median when there is an            numbers between the two middle numbers and then
                                                      event amount of data                   find the median.
        Baltimore City Schools – Office of Mathematics                Grade 4 Math Curriculum DRAFT                         Page 33
        officeofmath@bcps.k12.md.us
        Unit 6: Concept 2
        Median, Mode, and Range
                                                            LEARNING ACTIVITIES AND STRATEGIES
                                          Activity                                 Description                              Materials
                          Social        Pet Summary                 The students are introduced to mode,         Index cards
                          Kinesthetic   SF Grade 4 TE Lesson 4-12   median, and range by taking a survey of
Suggested Learning Plan




                                        (p. 226A)                   how many pets that they have.

                          Kinesthetic   Comparing Cubits            The students work in groups to visualize     Adding machine tape or other
                          Visual        SF Grade 4 TE Lesson 4-12   what mode, median, and range look like.        strips of paper
                                        (p. 226B)                                                                Scissors

                          Kinesthetic   Hands-on Activity           The students use data that is relevant to      Scissors
                          Visual                                    them and complete a hands-on activity in       Construction paper
                          Concrete                                  order to find the mode, median, and            Crayons
                                                                    range of the data.                             1-inch graph paper
                                                                                                                   Data on a transparency
                          Auditory      Mode, Median, Range Rap     The students learn the meaning of mode,        Song on overhead
                                                                    median, and range by learning a rap.           Teacher copy of the rap
                                                                                                                   Student copy of the rap




                                            DIFFERENTIATION                                     CROSS-CURRICULAR CONNECTIONS

                             Accommodations*                G.A.T.E./Enrichment              Artful Teaching             Literacy Integration




        Baltimore City Schools – Office of Mathematics               Grade 4 Math Curriculum DRAFT                        Page 34
        officeofmath@bcps.k12.md.us
        Unit 6: Concept 2
        Median, Mode, and Range
                                                                                RESOURCES
Suggested Learning Plan



                             Sub-Skills      Teacher Created Materials             Adopted Textbooks                      Technology
                          Determine the         MW Exploring Median,          SF Grade 4 TE Lesson 4-12       US: “Estimating a Range"
                          range of a group       Mode, and Range                (pp. 226A-229)                  WEB: "Rags to Riches"
                          of data               MW Range                                                       US: "Mean, Median, Mode,
                                                                                                                 Range, and Overall Distribution"
                                                                                                                WEB: Maths: Handling Data -
                          Determine mode        MW Mode                                                         Mode, median, and mean
                          of a group of                                                                         US: Math Mastery: Graphs and
                          data                                                                                   Statistics
                                                                                                                WEB: BrainPOP: Spelling Test
                                                                                                                 Scores
                          Determine             MW Median
                          median of a
                          group of data




                                                 Writing in Math                                            Other Resources
  Assessments




                                                                    CONCEPT                  MULTIPLE CHOICE              OTHER WAYS TO
                             TRACKING SHEET
                                                                   ASSESSMENT                QUESTION BANK                   ASSESS




        Baltimore City Schools – Office of Mathematics                  Grade 4 Math Curriculum DRAFT                     Page 35
        officeofmath@bcps.k12.md.us
        Unit 6: Concept 3
        Line Plots
                       TIME FRAME: 3-5 days                                                     PREREQUISITE SKILLS
                       Line Plots                                                                   Interpreting tables
                          Create line plots                                                        Ordering numbers
                          Interpret line plots                                                     Range, median, and mode

                       VSC OBJECTIVE (calculators allowed)
                       4.4.B.1.a Interpret line plots
                       ASSESSMENT LIMIT: Use no more than 20 pieces of data with a range no more than 10 and whole numbers (0 to 100)
Knowledge and Skills




                       4.4.A.1.b Organize and display data in line plots and frequency tables using a variety of categories and sets of data
                       ASSESSMENT LIMIT: Use line plots with no more than 20 pieces of unorganized data and a range of no more than 10 and
                       whole numbers (0 – 100)

                       VOCABULARY                   ENDURING UNDERSTANDINGS
                       statistics                       Representation of data depends on the characteristics of that data.
                       graph                            The type of data determines how data sets can be organized, displayed, and analyzed.
                       data                         ESSENTIAL QUESTIONS
                       title                            What data display is appropriate for a given set of data?
                       key                              How does the type of data influence the choice of graph?
                       horizontal axis                  What kinds of questions can be answered using different data displays?
                       median                       CONCEPT KNOWLEDGE AND PROCESS
                       mode                             Line plots show the frequency and spread of data.
                       range
                       outlier                      ERROR INTERVENTION
                       gap                          IF students randomly guess an               THEN consider requiring that students draw the
                       cluster                         answer in a multiple choice                  data in a line plot before matching it with the
                       line plot                       problem or miss a data point                 best answer.
                                                    IF students confuse line plots and line     THEN consider making the connection between a
                                                       graphs                                       line plot and planting seeds in which they plot
                                                                                                    one or more seeds on a direct line.
                                                    IF students confuse the meaning of          THEN consider having students design a large
                                                         the Xs                                        class line plot and then place individual cut-
                                                                                                       out X’s on the plot. They will then see that
                                                                                                       one X represents one person.


        Baltimore City Schools – Office of Mathematics               Grade 4 Math Curriculum DRAFT                          Page 36
        officeofmath@bcps.k12.md.us
Unit 6: Concept 3
Line Plots
                                          IF students have trouble finding the      THEN consider requiring that they translate the Xs
                                             median, mode, and range by                 into a list of numerical data from least to
                                             simply looking at a line plot              greatest.
                                          IF students have trouble                  THEN consider having them circle the data on the
                                             understanding the difference               graph. This helps visual learners understand
                                             between “3 or more” and “more              the meaning of the question.
                                             than 3”
                                          IF students do not understand the         THEN consider having them underline key words
                                             meaning of the question                      and ask themselves: “Is this question asking
                                                                                          me to look at the Xs or to look at the
                                                                                          horizontal axis?”




Baltimore City Schools – Office of Mathematics           Grade 4 Math Curriculum DRAFT                        Page 37
officeofmath@bcps.k12.md.us
        Unit 6: Concept 3
        Line Plots
                                                            LEARNING ACTIVITIES AND STRATEGIES
                                          Activity                                 Description                               Materials
                          Social        Line Up the Kids           The students interpret a line plot that is      Chalkboard or white board
                          Cooperative   SF Grade 4 TE Lesson 4-7   based on class survey results.                  Chalk or dry erase markers
                                        (p. 206B)
Suggested Learning Plan




                          Kinesthetic   How Many Breaths per       The class collects data and displays it on a    Clock with a second hand or
                                        Minute?                    line plot. The students interpret the data        stop watch
                                        SF Grade 4 TE Lesson 4-7   on the line plot by looking at the number
                                        (p. 206B)                  of “Xs” over each number.
                          Verbal        Journal Idea               The students demonstrate that they are          Pencil
                                        SF Grade 4 TE Lesson 4-7   able to create a line plot based on data by     Paper or journal notebook
                                        (p. 207)                   completing a journal assignment where
                                                                   they have to describe the steps to create
                                                                   a line plot.
                          Kinesthetic   Human Line Plot *          The students create a line plot using           Chart paper or large poster
                          Visual                                   information based on themselves and               board
                          Social                                   place their data on the horizontal axis.        1 paper X per student
                                                                                                                   Tape or glue
                                                                                                                   Markers
                                                                                                                   Crayons
                          Kinesthetic   A Handful of Counters      The students create a line plot based on        Counters or
                                        SF Grade 4 TE Lesson 4-7   the number of counters that they grab in        Teaching Tool 14
                                        (p. 206A)                  their hands.




                                            DIFFERENTIATION                                     CROSS-CURRICULAR CONNECTIONS

                             Accommodations*                G.A.T.E./Enrichment              Artful Teaching             Literacy Integration

        Baltimore City Schools – Office of Mathematics               Grade 4 Math Curriculum DRAFT                        Page 38
        officeofmath@bcps.k12.md.us
                   Unit 6: Concept 3
                   Line Plots
                                                                                                                RESOURCES
Assessments S u g g e s t e d L e a r n i n g P l a n



                                                           Sub-Skills       Teacher Created Materials              Adopted Textbooks                         Technology
                                                        Create line plots    MW Create Line Plots             SF Grade 4 TE Lesson 4-7 (pp.       WEB: Plop It!
                                                                                                                206A-207)




                                                        Interpret line       MW Exploring Interpret
                                                        plots                  Line Plots
                                                                             MW Interpret Line Plots




                                                                              Writing in Math                                                   Other Resources




                                                                                                 CONCEPT                     MULTIPLE CHOICE                 OTHER WAYS TO
                                                            TRACKING SHEET
                                                                                                ASSESSMENT                   QUESTION BANK                      ASSESS




                   Baltimore City Schools – Office of Mathematics                                       Grade 4 Math Curriculum DRAFT                         Page 39
                   officeofmath@bcps.k12.md.us
        Unit 6: Concept 4
        Coordinate Grids
                       TIME FRAME: 1-2 days                                                  PREREQUISITE SKILLS
                       Coordinate Plane                                                         Number lines
                          Identify locations on a coordinate grid given object                 Identifying the X and Y axis
                          Identify objects on a coordinate grid given location

                       VSC OBJECTIVE         (calculators allowed)
Knowledge and Skills




                       4.1.C.1.b Identify positions in a coordinate plane
                       ASSESSMENT LIMIT: Use the first quadrant and ordered pairs of whole numbers (0 to 20)

                       VOCABULARY                      ENDURING UNDERSTANDINGS
                       coordinate grid                    Ordered pairs show an exact location on a coordinate plane.
                       coordinate plane                   Functional relationships can be represented graphically and symbolically.
                       ordered pair                    ESSENTIAL QUESTIONS
                       horizontal                         How is the location of a point on a grid described?
                       vertical                           How are graphs, tables, and symbols used to represent relationships?
                       plot                            CONCEPT KNOWLEDGE AND PROCESS
                       origin                             A coordinate grid describes the location of an object by its distance from a horizontal and
                                                           vertical axis.
                                                       ERROR INTERVENTION
                                                       IF students mistakenly label          THEN consider teaching students a creative mnemonic
                                                           points by writing the vertical               to remember “over, then up.”
                                                           point first and then the
                                                           horizontal point                             Examples: 1.) Superman runs before he flies.
                                                                                                                  2.) In basketball, you dribble the
                                                                                                                      ball before you shoot.

                                                       IF students forget to start at        THEN consider requiring that they put a star at zero
                                                           zero                                         before plotting any points.




        Baltimore City Schools – Office of Mathematics                  Grade 4 Math Curriculum DRAFT                            Page 40
        officeofmath@bcps.k12.md.us
        Unit 6: Concept 4
        Coordinate Grids

                                                             LEARNING ACTIVITIES AND STRATEGIES
                                          Activity                                  Description                             Materials
                          Kinesthetic   Classroom Coordinate Grid   Create a coordinate grid on the classroom     Blue painter’s tape *
                                                                    floor and allow the students to slide         Deck of cards
Suggested Learning Plan




                                                                    horizontally and vertically to the ordered
                                                                    pair that they drew from the deck of
                                                                    cards.
                          Games         Treasure Map Bingo          The students choose five locations on a       1-inch graph paper
                                                                    coordinate grid treasure map and win          Deck of cards
                                                                    BINGO if all of their ordered pairs are       Markers
                                                                    called on their Treasure Map.
                          Visual        What’s the Location?        The students compare a coordinate grid to     Chalkboard or whiteboard
                          Spatial       SF Grade 4 TE Lesson 4-9    a map and describe the ordered pairs as       Chalk or dry erase markers
                                        (p. 212A)                   streets and avenues.                          Ruler




                                            DIFFERENTIATION                                      CROSS-CURRICULAR CONNECTIONS

                             Accommodations*                 G.A.T.E./Enrichment              Artful Teaching           Literacy Integration


        Baltimore City Schools – Office of Mathematics                Grade 4 Math Curriculum DRAFT                      Page 41
        officeofmath@bcps.k12.md.us
        Unit 6: Concept 4
        Coordinate Grids
                                                                                  RESOURCES
Suggested Learning Plan



                             Sub-Skills        Teacher Created Materials             Adopted Textbooks                          Technology
                          Identify locations      MW Exploring Coordinate       SF Grade 4 TE Lesson 4-9 (pp.        US: "Coordinate Mapping"
                          on a coordinate          Grid                           212A-215)                            WEB: Plot Points on a Coordinate
                          grid given object       MW Identify Locations                                                Grid
                                                   Coordinate Grid




                          Identify objects        MW Identify Objects
                          on a coordinate          Coordinate Grid
                          grid given
                          location




                                                   Writing in Math                                                Other Resources
  Assessments




                                                                      CONCEPT                  MULTIPLE CHOICE                  OTHER WAYS TO
                              TRACKING SHEET
                                                                     ASSESSMENT                QUESTION BANK                       ASSESS




        Baltimore City Schools – Office of Mathematics                    Grade 4 Math Curriculum DRAFT                         Page 42
        officeofmath@bcps.k12.md.us
        Unit 6: Concept 5
        Interpret Line Graphs
                       TIME FRAME: 2 - 3 days                                                   PREREQUISITE SKILLS
                       Interpret Line Graphs                                                        Addition
                          Interpret line graphs                                                    Subtraction
                                                                                                    Range, median, mode
                       VSC OBJECTIVE (calculators allowed)
                       4.4.B.1.b Interpret line graphs
Knowledge and Skills




                       ASSESSMENT LIMIT: Use the x-axis representing no more than 6 time intervals, the y-axis consisting of no more than 10
                       intervals with scales as factors of 100 using whole numbers (0 to 100)

                       VOCABULARY                   ENDURING UNDERSTANDINGS
                       statistics                       Representation of data depends on the characteristics of that data.
                       graph                            The type of data determines how data sets can be organized, displayed, and analyzed.
                       data                         ESSENTIAL QUESTIONS
                       title                            What data display is appropriate for a given set of data?
                       scale                            How does the type of data influence the choice of graph?
                       Interval                         What kinds of questions can be answered using different data displays?
                       horizontal axis              CONCEPT KNOWLEDGE AND PROCESS
                       vertical axis                    Line graphs show how data changes over time.
                       Increase                         Horizontal axis will always be time.
                       decrease
                       no change                    ERROR INTERVENTION
                       line graph
                                                    IF students do not see where the            THEN consider having them subtract between each
                                                         greatest increase or decrease is              data point to show the change.


                                                    IF students do not recognize where a        THEN consider using arm signals for up, down, and
                                                         line graph increases, decreases, or           no change and having students draw arrows
                                                         stays the same                                on each segment of the line graph.

                                                    IF students don’t understand the            THEN make a list of typical questions and
                                                         question                                      operations that could be used to answer a
                                                                                                       question.




        Baltimore City Schools – Office of Mathematics               Grade 4 Math Curriculum DRAFT                         Page 43
        officeofmath@bcps.k12.md.us
        Unit 6: Concept 5
        Interpret Line Graphs
                                                            LEARNING ACTIVITIES AND STRATEGIES
                                          Activity                                 Description                               Materials
                          Linguistic    What Story Does the Graph   The students look at a line graph and         Paper or journal notebook
                                        Tell?                       create a story to describe how the data in    Pencil
Suggested Learning Plan




                                        SF Grade 4 TE Lesson 4-10   the graph changed over time.
                                        (p. 216B)
                          Concrete      How Am I Doing?             Students look at their own class work or        Student work samples
                          Visual                                    tests to create a line graph and determine      Graph paper
                                                                    how their grades have changed over the          Rulers
                                                                    school year.                                    Pencils
                          Kinesthetic   Arm Signals                 The students use movements of their           Example of a line graph on the
                          Visual                                    arms to indicate whether the data               overhead
                                                                    increases, decreases or remains the same      Overhead projector
                                                                    as time progresses.
                          Linguistic    What Story Does the Graph   The students look at a line graph and         Paper or journal notebook
                                        Tell?                       create a story to describe how the data in    Pencil
                                        SF Grade 4 TE Lesson 4-10   the graph changed over time.
                                        (p. 216B)




                                           DIFFERENTIATION                                      CROSS-CURRICULAR CONNECTIONS

                              Accommodations*              G.A.T.E./Enrichment               Artful Teaching             Literacy Integration




        Baltimore City Schools – Office of Mathematics               Grade 4 Math Curriculum DRAFT                        Page 44
        officeofmath@bcps.k12.md.us
                          Unit 6: Concept 5
                          Interpret Line Graphs
                                                                                     RESOURCES
Suggested Learning Plan



                             Sub-Skills         Teacher Created Materials              Adopted Textbooks                       Technology
                          Interpret line         MW Interpret Line Graphs         SF Grade 4 TE Lesson 4-10         WEB: Create A Graph
                          graphs                                                    (pp. 216A-221)                    WEB: Print Your Own Graph
                                                                                                                       Paper




                                                    Writing in Math                                               Other Resources
  Assessments




                                                                        CONCEPT                  MULTIPLE CHOICE               OTHER WAYS TO
                              TRACKING SHEET
                                                                       ASSESSMENT                QUESTION BANK                    ASSESS




                          Baltimore City Schools – Office of Mathematics          Grade 4 Math Curriculum DRAFT                     Page 45
                          officeofmath@bcps.k12.md.us
                                 Grade 4: Unit 7

                                          Algebra 2

                                                      Unit Resources

                              Unit Vocabulary                                    Unit Assessment




Baltimore City Schools – Office of Mathematics   Grade 4 Math Curriculum DRAFT                     Page 46
officeofmath@bcps.k12.md.us
        Unit 7: Concept 1
        Write Expressions
                       TIME FRAME: 2 - 3 days                                               PREREQUISITE SKILLS
                       Write Expression                                                        Writing expressions using addition
                          Write expressions using addition and subtraction                    Writing expressions using subtraction
                          Write expressions using multiplication and division

                       VSC OBJECTIVE         (calculators allowed)
                       4.1.B.1.a Represent numeric quantities using operational symbols (+, -, ×, ÷ with no remainders)
Knowledge and Skills




                       ASSESSMENT LIMIT: Use whole numbers (0 to 100)

                       VOCABULARY                     ENDURING UNDERSTANDINGS
                       operation                         Mathematical expressions and equations represent relationships among quantities.
                       operational symbols               Symbolic notation is used to represent mathematical relationships.
                                                      ESSENTIAL QUESTIONS
                                                         How does a mathematical expression differ from a number sentence?
                                                         How is a number sentence like a balance scale?
                                                         How are symbols used to represent mathematical relationships including operations,
                                                          equality, and inequality?
                                                      CONCEPT KNOWLEDGE AND PROCESS
                                                       An expression names an amount.
                                                      ERROR INTERVENTION
                                                      IF students do not understand         THEN consider making a list of addition, subtraction,
                                                          which operation to use to             multiplication, and division clue words. Students
                                                          write or solve the problem            should then circle important numbers and
                                                                                                underline clue words before determining the
                                                                                                operation needed.
                                                      IF students do not understand         THEN consider having them draw a picture to represent
                                                         which operation to use to              the problem. They can then usually identify the
                                                         write or solve the problem             correct operation.
                                                      IF students do not understand         THEN consider having them visualize the problem,
                                                         which operation to use to              determine if the answer is increasing (+ or x) or
                                                         write or solve the problem             decreasing (- or ÷) in equal groups or non-equal
                                                                                                groups, and then identify the correct operation.


        Baltimore City Schools – Office of Mathematics                 Grade 4 Math Curriculum DRAFT                        Page 47
        officeofmath@bcps.k12.md.us
        Unit 7: Concept 1
        Write Expressions
                                                            LEARNING ACTIVITIES AND STRATEGIES
                                          Activity                                 Description                                Materials
                          Verbal        Develop Clue Words *        The students create an ongoing list of clue      Chart paper
                                                                    words that will aid them in choosing the         Markers
Suggested Learning Plan




                                                                    appropriate operational symbol to                Teacher clue word sheet
                                                                    complete the expression.                         Student clue words sheets

                          Auditory      Name That Expression        The students use clue words to determine         White board
                          Kinesthetic                               if the solution to an expression will be         White board markers
                          Visual                                    bigger or smaller and to determine the           Overhead
                                                                    appropriate operational symbol to use in         Pre-prepared word problems
                                                                    the expression.
                          Linguistic    Read to Understand          Students identify clue words and record        Chart paper
                          Auditory      SF Grade 4 TE Lesson 2-10   them on a chart as they read different
                                        (p. 94B)                    phrases.




                                           DIFFERENTIATION                                      CROSS-CURRICULAR CONNECTIONS

                              Accommodations*               G.A.T.E./Enrichment              Artful Teaching              Literacy Integration



        Baltimore City Schools – Office of Mathematics               Grade 4 Math Curriculum DRAFT                         Page 48
        officeofmath@bcps.k12.md.us
        Unit 7: Concept 1
        Write Expressions
                                                                               RESOURCES
Suggested Learning Plan



                             Sub-Skills     Teacher Created Materials             Adopted Textbooks                     Technology
                          Write                MW Exploring Write            SF Grade 4 TE Lesson 2-10       WEB: Math Playground: Various
                          expressions           Expression                     (pp. 94A-95)                     Word Problems
                          using addition       MW Write Expressions          SF Grade 4 TE lesson 3-12       WEB: Four Square for Story
                          and subtraction       Addition and Subtraction       (pp. 160A-163)                   Problems




                          Write                MW Write Expressions
                          expressions           Multiplication and
                          using                 Division
                          multiplication
                          and division




                                                Writing in Math                                            Other Resources
  Assessments




                                                                   CONCEPT                  MULTIPLE CHOICE             OTHER WAYS TO
                              TRACKING SHEET
                                                                  ASSESSMENT                QUESTION BANK                  ASSESS




        Baltimore City Schools – Office of Mathematics                 Grade 4 Math Curriculum DRAFT                    Page 49
        officeofmath@bcps.k12.md.us
        Unit 7: Concept 2
        Equivalent Expressions
                       TIME FRAME: 1 - 2 days                                                 PREREQUISITE SKILLS
                       Equivalent Expressions                                                    Writing expressions for addition
                          Write equivalent expressions                                          Writing expressions for subtraction

                       VSC OBJECTIVE         (calculators allowed)
Knowledge and Skills




                       4.1.B.1.b Determine equivalent expressions
                       ASSESSMENT LIMIT: Use whole numbers (0 to 100)

                       VOCABULARY                    ENDURING UNDERSTANDINGS
                       equivalent                        Mathematical expressions and equations represent relationships among quantities.
                       expression                        Symbolic notation is used to represent mathematical relationships.
                       equal                         ESSENTIAL QUESTIONS
                       fact family                       How does a mathematical expression differ from a number sentence?
                                                         How is a number sentence like a balance scale?
                                                         How are symbols used to represent mathematical relationships including operations,
                                                          equality, and inequality?
                                                     CONCEPT KNOWLEDGE AND PROCESS
                                                         An expression names an amount.

                                                     ERROR INTERVENTION
                                                     IF students assume that because          THEN consider requiring students to solve each
                                                        two problems have the same                    expression before determining the correct
                                                        numbers, they are equivalent                  answer. They will then see that 5 + 3 ≠ 5 x 3.
                                                        (Example: students think that 5
                                                        + 3 = 5 x 3)
                                                     IF students do not understand            THEN consider underlining the “equ” in equivalent,
                                                        what equivalent means                         equal, and equation.




        Baltimore City Schools – Office of Mathematics                Grade 4 Math Curriculum DRAFT                          Page 50
        officeofmath@bcps.k12.md.us
        Unit 7: Concept 2
        Equivalent Expressions
                                                            LEARNING ACTIVITIES AND STRATEGIES
                                        Activity                                   Description                              Materials
                          Visual        Balancing Act              The students use a number balance to           Number balance *
                          Kinesthetic                              determine whether their expressions are        Calculator *
Suggested Learning Plan




                          Cooperative                              equivalent to their partner’s expression.

                          Kinesthetic   Equal Expressions          The students use white boards to compose       Whiteboards
                          Visual                                   an expression equivalent to an expression      Dry erase markers
                                                                   that is given.

                          Concrete      How Many Ways to 12        The students learn about writing               Pencil
                                                                   equivalent expressions by finding how          Paper
                                                                   many different ways they can make 12           Calculator *
                                                                   using addition, subtraction, multiplication
                                                                   and division.




                                         DIFFERENTIATION                                        CROSS-CURRICULAR CONNECTIONS

                             Accommodations*                G.A.T.E./Enrichment              Artful Teaching            Literacy Integration




        Baltimore City Schools – Office of Mathematics               Grade 4 Math Curriculum DRAFT                       Page 51
        officeofmath@bcps.k12.md.us
        Unit 7: Concept 2
        Equivalent Expressions
                                                                                  RESOURCES
Suggested Learning Plan



                             Sub-Skills      Teacher Created Materials               Adopted Textbooks                     Technology
                          Write equivalent      MW Exploring Write              SF Grade 4 TE Lesson 2-11       WEB: Can You Balance?
                          expressions            Equivalent Expressions           (pp. 96A-97)                    WEB: Match Equivalent
                                                MW Write Equivalent             SF Grade 4 TE Lesson 2-12        Expressions
                                                 Expressions                      (pp. 98A-99)                    WEB: Cyberchase – Poodle Weigh
                                                                                                                   In




                                                 Writing in Math                                              Other Resources
  Assessments




                                                                    CONCEPT                    MULTIPLE CHOICE             OTHER WAYS TO
                             TRACKING SHEET
                                                                   ASSESSMENT                  QUESTION BANK                  ASSESS




        Baltimore City Schools – Office of Mathematics                    Grade 4 Math Curriculum DRAFT                    Page 52
        officeofmath@bcps.k12.md.us
        Unit 7: Concept 3
        Write Relationships
                       TIME FRAME: 2 – 4 days                                                     PREREQUISITE SKILLS
                       Write Relationships                                                            Comparing expressions
                          Evaluate relationships with missing relational symbols                     Evaluate relationships with addition and
                          Represent relationships in word problems                                    subtraction
                                                                                                      Represent relationships in addition and
                                                                                                       subtraction word problems
                       VSC OBJECTIVE         (calculators allowed)
                        4.1.B.2.a Represent relationships using relational symbols (>, <, =) and operational symbols (+, -, ×, ÷) on either side
Knowledge and Skills




                       Assessment Limit: Use operational symbols (+, -, ×) and whole numbers (0 to 200)

                       VOCABULARY                     ENDURING UNDERSTANDINGS
                       expression                        Mathematical expressions and equations represent relationships among quantities.
                       relational symbols                Symbolic notation is used to represent mathematical relationships.
                       operational symbols            ESSENTIAL QUESTIONS
                       equal                             How does a mathematical expression differ from a number sentence?
                       balance                           How is a number sentence like a balance scale?
                       not equal                         How are symbols used to represent mathematical relationships including operations,
                       Inequality                         equality, and inequality?
                       equivalent                     CONCEPT KNOWLEDGE AND PROCESS
                                                         A relationship where two expressions have the same value has an = sign.
                                                         A relationship where two expressions do not have the same value has a > or < sign.

                                                      ERROR INTERVENTION
                                                      IF students become overwhelmed by           THEN consider having them highlight the first
                                                          the wordiness of the problem                expression in one color and the second
                                                                                                      expression in another color; write the first
                                                                                                      expression, then write the second
                                                                                                      expression; finally, compare the expressions.
                                                      IF students rush to input operational       THEN consider requiring that they plug in all
                                                          symbols                                     possible operational symbols before
                                                                                                      determining the correct answer.

                                                      IF students choose a relationship as        THEN consider requiring that they solve each
                                                          correct just by looking at the                  expression before determining the correct
                                                          numbers                                         answer.

        Baltimore City Schools – Office of Mathematics                 Grade 4 Math Curriculum DRAFT                          Page 53
        officeofmath@bcps.k12.md.us
        Unit 7: Concept 3
        Write Relationships
                                                             LEARNING ACTIVITIES AND STRATEGIES
                                         Activity                                   Description                                   Materials
                          Verbal        Develop Clue Words          The students create an ongoing list of clue        Chart paper
                                                                    words that will aid them in choosing the           Markers
                                                                    appropriate operational symbol to                  Student clue words sheets
Suggested Learning Plan




                                                                    complete the expression.

                          Auditory      Name That Expression      The students use clue words to determine               White board
                          Kinesthetic                             if the solution to an expression will be               White board markers
                          Visual                                  bigger or smaller and to determine the                 Overhead
                                                                  appropriate operational symbol to use in               Pre-prepared word problems
                                                                  the expression.
                          Linguistic    Read to Understand        Students identify clue words and record                Chart paper
                          Auditory      SF Grade 4 TE Lesson 2-10 them on a chart as they read different
                                        (p. 94B)                  phrases.

                          Kinesthetic   Pinch Cards                 The students use an index card with                  Index Cards with    > < = on
                          Visual                                    relational symbols on it to indicate the              them
                                                                    appropriate relationship between two                 Markers
                                                                    expressions.




                                           DIFFERENTIATION                                       CROSS-CURRICULAR CONNECTIONS

                              Accommodations*                G.A.T.E./Enrichment              Artful Teaching                 Literacy Integration


        Baltimore City Schools – Office of Mathematics                Grade 4 Math Curriculum DRAFT                            Page 54
        officeofmath@bcps.k12.md.us
   Unit 7: Concept 3
   Write Relationships
                                                                         RESOURCES
Suggested Learning



                     Sub-Skills            Teacher Created Materials           Adopted Textbooks                   Technology
               Evaluate                    MW Exploring Relationships        SF Grade 4 TE Lesson       WEB: BrainPOP: Inequalities
               relationships with          MW Evaluate Relationships          2-11 (pp. 96A-97)           Movie
               missing relational           Missing Relationships
               symbols

               Represent                   MW Represent Relationships
       Plan




               relationships in word        in word problems
               problems




                                       Writing in Math                                                Other Resources
Assessments




                                                          CONCEPT                   MULTIPLE CHOICE                OTHER WAYS TO
                     TRACKING SHEET
                                                         ASSESSMENT                 QUESTION BANK                     ASSESS




   Baltimore City Schools – Office of Mathematics              Grade 4 Math Curriculum DRAFT                       Page 55
   officeofmath@bcps.k12.md.us
                                 Grade 4: Unit 8

                                  Geometry 1
                                                    Unit Resources

                             Unit Vocabulary                                     Unit Assessment




Baltimore City Schools – Office of Mathematics   Grade 4 Math Curriculum DRAFT                     Page 56
officeofmath@bcps.k12.md.us
          Unit 8: Concept 1
          Angles
                       TIME FRAME: 2-4 days                                                PREREQUISITE SKILLS
                       Angles                                                                 Rays, lines, and line segments
                          Identify right angles
                          Identify acute and obtuse angles
                          Identify angles in shapes and objects
                       VSC OBJECTIVE          (calculators allowed)
                       4.2.A.1.b Identify, compare, classify, and describe angles in relationship to another angle
Knowledge and Skills




                       ASSESSMENT LIMIT: Use acute, right, or obtuse angles

                       VOCABULARY                 ENDURING UNDERSTANDINGS
                       geometry                      Objects can be described and compared using geometric attributes.
                       point                         A three dimensional figure can be analyzed in terms of its two-dimensional parts.
                       Line                       ESSENTIAL QUESTIONS
                       ray                           How are angles classified?
                       line segment                  What makes one angle different from another?
                       vertex                     CONCEPT KNOWLEDGE AND PROCESS
                       angle                         An angle is created from two rays that share an endpoint.
                       endpoint                      A right angle forms the corner of a square.
                       right angle                   An acute angle is smaller than a right angle.
                       acute angle                   An obtuse angle is bigger than a right angle.
                       obtuse angle
                                                  ERROR INTERVENTION
                                                  IF students confuse acute angles,        THEN consider using a mnemonic to distinguish between
                                                      right angles, and obtuse angles          the types of angles:
                                                                                               An acute angle is “a cute” little baby angle.
                                                                                               An obtuse angle looks like an open book.
                                                                                               A right angle is “just right.” It makes a perfect L.
                                                   IF students have trouble identifying    THEN consider having students highlight the rays to
                                                      angles within shapes                     better see the angle.
                                                   IF students have trouble identifying    THEN consider having them put a square in the angle.
                                                      angles within shapes
                                                   IF students have trouble identifying    THEN consider encouraging students to turn their paper
                                                      angles that are turned                      so that the angle looks “right side up.”

          Baltimore City Schools – Office of Mathematics              Grade 4 Math Curriculum DRAFT                         Page 57
          officeofmath@bcps.k12.md.us
        Unit 8: Concept 1
        Angles
                                                              LEARNING ACTIVITIES AND STRATEGIES
                                         Activity                                    Description                               Materials
                          Visual        Geometry on the              The students use Geoboards to represent         Geoboard or
                          Spatial       Geoboard                     different types of angles by intersecting       Geoboard paper
Suggested Learning Plan




                                        SF Grade 4 TE Lesson 8-3     lines.                                          Rubber bands
                                        (p. 440a)

                          Visual        Angles on the Floor          The students work in pairs to identify          Blue painter’s tape
                          Kinesthetic                                types of angles using a index card to see       Index cards *
                          Cooperative                                if the angle is bigger, smaller, or equal to
                                                                     a right angle.
                          Visual        I Spy Right Angles           The students identify right angles that         Blue painters tape
                          Kinesthetic                                they see within the classroom and mark
                                                                     them by creating a square inside the
                                                                     angle with blue painter’s tape.
                          Visual        Geometry Simon Says          The students play a game of Simon Says
                          Kinesthetic                                where they have to create angles and
                          Game                                       lines using arm signals.




                                           DIFFERENTIATION                                        CROSS-CURRICULAR CONNECTIONS

                             Accommodations*                  G.A.T.E./Enrichment              Artful Teaching             Literacy Integration




        Baltimore City Schools – Office of Mathematics                 Grade 4 Math Curriculum DRAFT                        Page 58
        officeofmath@bcps.k12.md.us
        Unit 8: Concept 1
        Angles
                                                                                   RESOURCES
Suggested Learning Plan



                             Sub-Skills        Teacher Created Materials              Adopted Textbooks                         Technology
                          Identify right          MW Exploring Angles            SF Grade 4 TE Lesson 8-3 (pp.       WEB: Alphabet Geometry: Right
                          angles                  MW Identify Right Angles        440A-443)                            Angles
                                                                                                                       WEB: Alphabet Geometry: Acute
                                                                                                                        Angles
                                                                                                                       WEB: Alphabet Geometry: Obtuse
                          Identify acute          MW Identify Acute                                                    Angles
                          and obtuse               Obtuse Angles
                          angles



                          Identify angles in      MW Identify Angles in
                          shapes and               Objects
                          objects




                                                   Writing in Math                                                 Other Resources
  Assessments




                                                                      CONCEPT                   MULTIPLE CHOICE                 OTHER WAYS TO
                              TRACKING SHEET
                                                                     ASSESSMENT                 QUESTION BANK                      ASSESS




        Baltimore City Schools – Office of Mathematics                     Grade 4 Math Curriculum DRAFT                        Page 59
        officeofmath@bcps.k12.md.us
        Unit 8: Concept 2
        Transformations
                       TIME FRAME: 2-4 days                                                PREREQUISITE SKILLS
                       Transformations                                                        Flips
                          Identify translations                                              Turns
                          Identify reflections                                               Slides
                          Identify rotations                                                 Congruence
                                                                                              Symmetry
                       VSC OBJECTIVE            (calculators allowed)
                       4.2.E. 1.a Identify and describe the results of translations, reflections, and rotations
                       ASSESSMENT LIMIT: Use a horizontal line translation, reflection over a vertical line, or rotation of 90° clockwise around a
Knowledge and Skills




                       given point of a geometric figure or picture
                       4.2.D.1.a Identify and describe geometric figures as congruent
                       ASSESSMENT LIMIT: Identify the result in a transformation as being congruent to the original figure

                       VOCABULARY           ENDURING UNDERSTANDINGS
                       geometry                   A transformation is a specific movement of an object.
                       congruent                  Changing the position of an object does not affect its attributes.
                       transformation       ESSENTIAL QUESTIONS
                       translation                In what ways can the position of geometric figures be changed?
                       reflection                 What are translations, rotations, and reflections?
                       rotation             CONCEPT KNOWLEDGE AND PROCESS
                                                  A transformation moves a shape to a new spot without changing its size or shape
                                                  You can transform (move) a shape three ways: by flipping it, sliding it, or turning it.
                                                  A flip, or reflection, is a mirror image of a figure on the opposite side of a line.
                                                  A slide, or translation, is a figure moved a certain distance in a given direction.
                                                  A turn, or rotation, moves a figure around a point.
                                            ERROR INTERVENTION
                                            IF students confuse translations,              THEN consider emphasizing the similar letters
                                                   reflections, and rotations                SLide is a tranSLation.
                                                                                             TuRn is a RoTation.
                                                                                             FLip is a reFLection.
                                            IF students confuse translations,              THEN consider doing hand movements to help them identify
                                               reflections, and rotations                      the transformations.
                                            IF students have trouble identifying a         THEN consider having them actually turn their paper and
                                               rotation                                        observe how the figure looks as it turns.
                                            IF students forget that transformations        THEN consider requiring that they trace the initial figure and
                                                   must be congruent                              then translate, rotate, or reflect it to check their work
        Baltimore City Schools – Office of Mathematics                     Grade 4 Math Curriculum DRAFT                          Page 60
        officeofmath@bcps.k12.md.us
        Unit 8: Concept 2
        Transformations
                                                            LEARNING ACTIVITIES AND STRATEGIES
                                         Activity                                   Description                              Materials
                          Visual        Finger Painting *           The students learn about translations by        Three large pieces of paper
                          Kinesthetic                               using finger paints and their hands as           folded in half (per student)
Suggested Learning Plan




                                                                    the object being transformed.                   Finger paints

                          Visual        Letter Cut Outs *           The students use letter cut-outs to             Large pieces of construction
                          Kinesthetic                               translate, reflect, and rotate over a            paper
                          Spatial                                   dotted line.                                    Letter cut outs of the first
                                                                                                                     letter of the first name of
                                                                                                                     each student in the class.
                          Kinesthetic   “Transformation Shuffle”    The students translate, reflect and rotate      Words to transformation
                          Auditory                                  to the tune of a popular hip-hop song.           shuffle
                                                                                                                    Song “Cupid Shuffle” by
                                                                                                                     Cupid




                                          DIFFERENTIATION                                       CROSS-CURRICULAR CONNECTIONS

                             Accommodations*                G.A.T.E./Enrichment              Artful Teaching             Literacy Integration




        Baltimore City Schools – Office of Mathematics               Grade 4 Math Curriculum DRAFT                        Page 61
        officeofmath@bcps.k12.md.us
        Unit 8: Concept 2
        Transformations
                                                                                    RESOURCES
Suggested Learning Plan


                             Sub-Skills        Teacher Created Materials               Adopted Textbooks                         Technology
                          Identify              MW Identify Translations          SF Grade 4 TE Lesson 8-6 (pp.       WEB: NLVM - Playing with
                          translations                                              452A-455)                            Translations
                                                                                                                        WEB: NLVM - Playing with
                                                                                                                         Reflections
                                                                                                                        WEB: NLVM - Playing with
                          Identify              MW Identify Reflections                                                 Rotations
                          reflections                                                                                   WEB: Alphabet Geometry:
                                                                                                                         Transformations

                          Identify rotations    MW Identify Rotations




                                                 Writing in Math                                                    Other Resources
  Assessments




                                                                    CONCEPT                      MULTIPLE CHOICE                 OTHER WAYS TO
                              TRACKING SHEET
                                                                   ASSESSMENT                    QUESTION BANK                      ASSESS




        Baltimore City Schools – Office of Mathematics                      Grade 4 Math Curriculum DRAFT                        Page 62
        officeofmath@bcps.k12.md.us

				
DOCUMENT INFO
Shared By:
Categories:
Tags:
Stats:
views:20
posted:7/26/2011
language:English
pages:63