# Fourth Grade Math Curriculum Guide

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```					         Fourth Grade Math Curriculum Guide
The North Carolina Mathematics Standard Course of Study provides a set of mathematical
competencies for each grade to ensure rigorous student academic performance standards that
are uniform across the state. It is based on the philosophy of teaching and learning mathematics
that is consistent with current research, exemplary practices, and national standards. The North
Carolina Mathematics Standard Course of Study is organized in five strands for K-5: Number and
operations, Measurement, Geometry, Data Analysis and Probability, and Algebra. This document
describes the mathematical concepts, skills, operations, and relationships that are the significant
components of mathematics instruction that all North Carolina students should learn and
understand. This curriculum should be made available to every child in the Rowan-Salisbury
School System.

Based on 2004 North Carolina Standard Course of Study
2009-2010

Page
North Carolina Standard Course of Study for Mathematics with Sample Essential Questions     3
North Carolina Standard Course of Study Mathematics Strands Grades 3-5                      5
Best Practices in Mathematics                                                               7
Fourth Grade North Carolina Standard Course of Study Mathematics Vocabulary                 9
Fourth Grade Mathematics Pacing Guide                                                      10
Correlation of Week-by-Week Essentials                                                     14
NCDPI Resources for Elementary Mathematics                                                 15
Calculator Requirements for the North Carolina Testing Program                             16
North Carolina End-Of-Grade Sample Items                                                   17
Suggested Children’s Literature                                                            18

2
NORTH CAROLINA STANDARD COURSE OF STUDY FOR MATHEMATICS – 4th GRADE
COMPETENCY GOAL 1: The learner will read, write, model, and compute with non-negative rational numbers.
Objective(s)                                                                Sample Essential Question(s)
1.01 Develop number sense for rational numbers 0.01 through 99,999.                  How can you model numbers in various ways?
a. Connect model, number word, and number using a variety of representations.   How can place value help you determine the value of a number?
b. Build understanding of place value (hundredths through ten thousands).       How do you compare and contrast numbers?
c. Compare and order rational numbers.                                          How do you know when it is appropriate to make estimates?
d. Make estimates of rational numbers in appropriate situations.                What is the difference between the value of a number and the place value?

1.02   Develop fluency with multiplication and division:                                            What are some ways to multiply two digit numbers by two digit numbers?
a. two-digit by two-digit multiplication (larger numbers with calculator).                   What are some ways to divide one, two, or three digit numbers by two digit numbers?
b. up to three-digit by two-digit division (larger numbers with calculator).                 How do you know when to use estimation strategies for products and quotients?
c. strategies for multiplying and dividing numbers.                                          How are multiplication and division related?
d. estimation of products and quotients in appropriate situations.                           How do you use order of operations and basic properties in multi-step problems?
e. relationships between operations.
1.03   Solve problems using models, diagrams, and reasoning about fractions and                     How do you use models, diagrams, and pictures of fractions to understand the relationship
relationships among fractions involving halves, fourths, eighths, thirds, sixths,             and to help you solve problems?
twelfths, fifths, tenths, hundredths, and mixed numbers.
1.04   Develop fluency with addition and subtraction of non-negative rational numbers with          How do you add and subtract fractions and decimals?
like denominators, including decimal fractions through hundredths.                           How do you estimate sums and differences of fractions and decimals?
a. Develop and analyze strategies for adding and subtracting numbers.                        How do you judge if a solution is reasonable?
b. Estimate sums and differences.
c. Judge the reasonableness of solutions.

1.05   Develop flexibility in solving problems by selecting strategies and using mental             How do you know if your chosen problem solving strategy is reasonable?
computation, estimation, calculators or computers, and paper and pencil.                     How do you determine appropriate tools to solve problems?

COMPETENCY GOAL 2: The learner will understand and use perimeter and area.
2.01 Develop strategies to determine the area of rectangles and the perimeter of plane              How do you find the perimeter of various polygons?
figures.                                                                                       How do you find the area of a rectangle?

2.02   Solve problems involving perimeter of plane figures and areas of rectangles.          How do you use perimeter and area to solve problems?
How do you distinguish between when to find perimeter and when to find area in a
problem?
COMPETENCY GOAL 3: The learner will recognize and use geometric properties and relationships.
3.01 Use the coordinate system to describe the location and relative position of points and  How would ordered pairs help you determine location?
draw figures in the first quadrant.                                                     How would you draw figures in the first quadrant?
3.02 Describe the relative position of lines using concepts of parallelism and               How do you create a polygon that has examples of parallelism and perpendicularity?
perpendicularity.
3.03 Identify, predict, and describe the results of transformations of plane figures.        How can you tell if rotations, reflections, and translations have occurred?
a. Reflections.
b. Translations.
c. Rotations.

3
NORTH CAROLINA STANDARD COURSE OF STUDY FOR MATHEMATICS – 4th GRADE
COMPETENCY GOAL 4: The learner will understand and use graphs, probability, and data analysis.
Objective(s)                                                                      Sample Essential Question(s)
4.01 Collect, organize, analyze, and display data (including line graphs and bar graphs) to  How can you collect, organize, analyze, and display data to help you solve problems?
solve problems.

4.02   Describe the distribution of data using median, range and mode.                              How do you use median, range, and mode to help analyze data?
       What does median, range, and mode indicate about a set of data?
4.03   Solve problems by comparing two sets of related data.                                        How do you solve problems by comparing two sets of related data?

4.04 Design experiments and list all possible outcomes and probabilities for an event.  How can you find all of the possible outcomes of an event?
COMPETENCY GOAL 5: The learner will demonstrate an understanding of mathematical relationships.
5.01 Identify, describe, and generalize relationships in which:                         How can you identify and describe patterns and relationships?
a. quantities change proportionally.
b. change in one quantity relates to change in a second quantity.

5.02   Translate among symbolic, numeric, verbal, and pictorial representations of number           How do you show or describe number relationships in various ways?
relationships.

5.03   Verify mathematical relationships using:                                                     How can you determine the mathematical relationships between models, words, and
a. models, words, and numbers.                                                                numbers?
b. order of operations and the identity, commutative, associative, and distributive          How do you use order of operations to determine the mathematical relationships between
properties.                                                                                models, words, and numbers?
       How do you use the identity, commutative, associative, and distributive property to
determine mathematical relationships?

4
PUBLIC SCHOOLS OF NORTH CAROLINA STATE BOARD OF EDUCATION/DEPARTMENT OF PUBLIC INSTRUCTION
North Carolina Standard Course of Study
NUMBER AND OPERATIONS
Students in the intermediate grades represent whole numbers, fractions, and decimals with concrete objects, pictures, and symbols in a variety of
contexts. A firm understanding and use of the place value system and various properties of numbers is developed. Students recognize equivalent
rational numbers and explain the basis for the equivalence. Fractions and decimals are compared and ordered.

A variety of tools are used to model operations with whole numbers and fractions, develop and apply different methods of computing, and relate
models to standard symbolic expressions and algorithms. Students learn the order of operations, explore various properties of operations and are
able to estimate reasonable answers to computations. Students become fluent operating with whole numbers.

MEASUREMENT
Students estimate and measure temperature, length, mass, and capacity in both customary and metric units. They solve problems involving
perimeter of plane figures and area of rectangles and develop the basic formulas for computing these quantities.

GEOMETRY
In the intermediate grades, students compare, describe, classify, and analyze two– and three– dimensional figures. They investigate basic
geometric relationships, such as parallelism, perpendicularity, congruence, and similarity, and recognize geometric transformations. Students plot
points and read graphs on a rectangular grid.

DATA ANALYSIS AND PROBABILITY
Students continue working with the process of statistical investigation, as the techniques for data collection become more sophisticated. The nature
and kinds of representations used include tables, bar and circle graphs, and stem-and leaf-plots. Data are described and compared using median,
mode, and range. Students design experiments and list all possible outcomes and probabilities.

ALGEBRA
Students in the intermediate grades continue to identify and describe patterns in many situations. Tools, such as calculators and computers, are
used to investigate and discover patterns. Patterns are used in geometry and other mathematics to develop new concepts. Tables and graphs are
made to show relationships and then students verbally describe the patterns. Patterns are used to extend student data, suggest rules for
relationships, and make predictions. Students begin to use symbols to represent unknown quantities. They use the symbols in expressions and
open sentences when describing relationships and solving problems. Students begin to identify, describe, and analyze situations with constant or
varying rates of change, and compare them.

5
MAJOR CONCEPTS/SKILLS
•   Number sense 0.001-99,999                                        CONCEPTS/SKILLS to MAINTAIN
•   Multiplication and division of multi-digit numbers               •   Whole number computation
•   Perimeter and area                                               •   Non-negative rational numbers
•   Transformations                                                  •   Length, time, capacity, and mass
•   Line graphs                                                      •   Symmetry and congruence
•   Median, Mode, and Range                                          •   Coordinate grids
•   Variables in number sentences                                    •   Circle graphs
•   Proportional reasoning                                           •   Permutations and combinations – an arrangement of a
•   Students will solve relevant and authentic problems using            given number of objects such as abc, acb, bac
appropriate technology and apply these concepts as well as
those developed in earlier years.

6
BEST PRACTICES IN MATHEMATICS
Evaluations by the U.S. Department of Education, National Science Foundation, American Association for the Advancement of Science, Eisenhower National Consortia, National Diffusion
Network, and the Northwest Regional Educational Laboratory have identified several practices that have proven to be promising in the math classroom. These practices involve active
engagement in problem-solving activities that are built on knowledge of experiences. The ability to reason is a process that grows out of these experiences. Learning is enhanced by connecting
math to the real world through technology and communication of mathematical ideas.

Bridging the Mathematical Gap Through Best Practices
Begin with the concrete and build toward the abstract.                                            Use of manipulatives
Calculators and computers
Kinesthetic learning
Build communication skills.                                                                       Use of word walls to teach vocabulary
Word problems with a variety of structure and solution paths
Writing journals
Cooperative groups
Discussion
Solve routine and non-routine word problems.                                                      Use of everyday problems and applications
Problem-solving strategies
Investigate problem situations
Problem-solving projects
Build reasoning skills.                                                                           Open-ended problems
Questioning
Making conjectures
Justify thinking
Logic puzzles
Syllogisms
Pattern discernment
Make mathematical connections.                                                                    Concept mapping of mathematical ideas
Relate real world interests
Integrate with other subject matter
To Close the Achievement Gap Mathematics Intervention Strategies Should . . .
•    be used during or before initial instruction to ensure success for at-risk students.         •    include vocabulary activities, higher-order thinking, and problem solving
•    validate the concrete, kinesthetic learner.                                                       strategies.
•    teach concepts moving from manipulatives, to pictures, to symbols.                           •    teach mathematics concepts from the grade-level North Carolina Standard
•    help students transfer “actively learned” concepts to pencil-paper tasks and                      Course of Study on which students will be tested, scaffolding instruction to fill
assessments similar to the end of grade/end-of-course tests.                                      existing “gaps”.
•    be fun, engaging and different than what has already been done!

7
BEST PRACTICES IN MATHEMATICS

To Make Mathematics Work for Closing the Achievement Gap Teachers Must:
•   structure lessons so all students become more actively involved.                                •   continue to improve their knowledge of content so they feel comfortable with the
•   feel comfortable in their use of technology.                                                        curriculum.
•   provide connections to prior knowledge, other subject areas, careers, and student               •   improve their questioning ability by asking higher order questions, allowing for
interests.                                                                                          wait time, and encouraging students to give more than one answer.
•   develop an array of teaching strategies so as to address students with different learning       •   become positive about their ability to teach mathematics to all students.
styles.                                                                                         •   expect students to want to learn, to do homework, to ask questions, and to seek
assistance.

Ten Steps for Solving Mathematics Problems

•   Whisper read the problem at least two times. Make a mental picture of what you are reading.
•   Circle the key words in the question. MAKE SURE YOU UNDERSTAND WHAT THE QUESTION IS ASKING!
•   Identify and circle/underline the key numbers and labels.
•   Eliminate unneeded data by drawing a line through it.
•   Thoroughly study any graphs, charts, or Venn diagrams.
•   Determine the operation(s)/strategies needed to solve the problem.
•   Solve the problem. SHOW YOUR WORK! (Draw a picture, draw a number line, look for a pattern, guess and check, make a table or organized list,
use logical reasoning, work backwards, make it simple, etc.).

8
Fourth Grade North Carolina Standard Course Of Study Mathematics Vocabulary
1.01                  1.02                   1.04                    2.01               2.02               3.01                3.03                         4.02                            5.03
number word               arrays            part-to-whole               triangle           polygon            x-axis              polygon              ordered set of data              order of operations
decimal notation               fact              numerator             quadrilateral          triangle        horizontal             vertices                center/middle                 function machines
expanded notation              share            denominator            parallelogram       quadrilateral          y-axis            clockwise                 least/greatest                        input
expanded form              multiply             like/unlike              trapezoid      parallelogram          vertical      counter clockwise                 spread                            output
standard notation/form          product             fraction bar                square           trapezoid      ordered pairs            vertical                    typical                         pattern
ten thousands place            divide          decimal fractions            rhombus              square             origin           horizontal                                                      table
thousands place             quotient           equal shares               rectangle          rhombus           quadrant                  90°       4.03 – No New Vocabulary                      variable
hundreds place            dividend              equivalent          regular polygon         rectangle          triangle               180°                                                     equations
ones place            remainder           approximately               hexagon            pentagon          rhombus           image (after)                   4.04                             value
tenths place             factors               estimate                 triangle           hexagon      parallelogram              reflect                 probability                         equal
hundredths place           multiples                 ratio                 octagon            triangle         trapezoid                (flip)                 likelihood                 NOTE: multiplication
hundred board          place value                 sum                  decagon             octagon            square             translate                   outcome                  is often written in one
base ten blocks         hundredths              difference                   side            decagon          rectangle              (slide)                     event                   of these three forms:
compose                tenths                                         angles               side           polygon               rotate                 equally likely                         2(3)
decompose                 ones                1.05                vertex/vertices          angles          pentagon                (turn)                 impossible                            2· 3
multiply           hundreds                                     line segment      vertex/vertices       hexagon                  shift                    certain                           2x3
patterns
divide           thousands                                             line       line segment          octagon               move                     less likely
guess and test
product         ten thousands                                           ray                line         decagon                    A                   more likely
make a diagram/chart/graph
quotient              dollars                                   square units               ray           diagonal                  A’                     sample
make an organized list
sum                  cents                                           units       square units             side             4.01                          space
work backwards
difference               about                                         length               units     vertex/vertices                                   permutation
solve a simpler problem                                                                       chart
rational number       approximately                                         width             length              line                                      combination
find a pattern                                                                           tally
factor             estimate                                     dimensions              width       line segment
extra information                                                                          table
multiple            distribute                                    grid paper        dimensions                                                            5.01
representations                                                                   Venn Diagram
fraction            compose                                       geoboards          grid paper          3.02
models                                                                         circle graph              function machines
common fraction         decompose                                            rulers         geoboards
act out the problem                                                right angle         pictograph                      input
decimal fraction                                                                               rulers
90°               line plot                    output
denominator             1.03                                                                              intersecting         bar graph                      T-chart
numerator
part-to-whole                                                                        equal distance    double bar graph                   pattern
mixed numbers
numerator                                                                         non-intersecting       line graph                      table
denominator                                                                             parallel               trend                    variable
approximately
equal shares                                                                         perpendicular     continuous data
equivalent
equivalent                                                                              plane         numerical data                    5.02
number line
comparing                                                                                                                                                    variable
approximately                                                                                               columns
less than <                                                                                                                                                less than <
estimate                                                                                                     rows
less than or equal to ≤                                                                                                                                      less than or equal to ≤
number line                                                                                                   x-axis
greater than >                                                                                                                                             greater than >
y-axis
greater than or equal to                                                                                                                               greater than or equal to ≥ equal to
vertical
≥ equal to =                                                                                                                                                     =
horizontal
not equal to ≠                                                                                                                                             not equal to ≠
labels
equivalent
title
equation
intervals
expression
range of data
scale                       symbol

9
2009-2010 FOURTH GRADE MATHEMATICS PACING GUIDE
Resources: NCDPI Strategies, Indicators, and Week By Week Essentials, enVision Math – Scott Foresman/Addison Wesley, & Teaching Student-Centered
Mathematics 3-5 Volume Two – John Van de Walle
Number & Operations
First Nine Weeks                           Resources                     Second Nine Weeks                     Resources                      Third Nine Weeks                            Resources                Fourth Nine Weeks           Resources
1.01 Develop number sense for        Week by Week Essentials Weeks 1-9 1.02 Develop fluency with              Week by Week Essentials 1.02          Develop fluency with                  Week by Week Essentials       Apply and maintain skills   Week by Week
whole number through                                                       multiplication and                   Weeks 10-18                   multiplication and division:                   Weeks 19-27              previously taught          Essentials
99,999.                            NCDPI Classroom Strategies              division:                                                          a. Two-digit by two-digit                                                  from Goal 1.           Weeks 28-36
a. Connect model, number                       Pages 3-29                a. Two-digit by two-digit     NCDPI Classroom Strategies                multiplication (larger                   NCDPI Classroom
word, and number using                                                    multiplication (larger              Pages 30-56                     numbers with calculator).             Strategies Pages 30-56
a variety of                          Indicators Pages 7-12               numbers with                                                     b. Up to three-digit by two-digit
representations.                                                          calculator).                 Indicators Pages 13-18                 division (larger numbers with         Indicators Pages 13-18
b. Build understanding of                  enVision Topics:              b. Up to three-digit by two-                                            calculator).
place value (hundredths 1 – Numeration                                    digit division (larger           enVision Topics:                c. Strategies for multiplying and           enVision Topics:
through ten thousands). 2 – Adding and Subtracting Whole                  numbers with             7 – Multiplying 2-Digit Numbers            dividing numbers.              1 – Numeration
c. Compare and order              Numbers                                    calculator).             8 – Dividing By 1-Digit Divisors        d. Estimation of products and 2 – Adding and Subtracting
rational numbers.                                                     c. Strategies for                                                       quotients in appropriate           Whole Numbers
d. Make estimates of                                                         multiplying and dividing                                            situations.                    7 – Multiplying 2-Digit Numbers
rational numbers in                                                       numbers.                                                         e. Relationships between          8 – Dividing By 1-Digit Divisors
appropriate situations.                                               d. Estimation of products                                               operations.
and quotients in
1.02 Develop fluency with               NCDPI Classroom Strategies                appropriate situations.                                   1.03   Solve problems using models,         NCDPI Classroom Strategies
multiplication and division:                   Pages 30-56               e. Relationships between                                             diagrams, and reasoning about                 Pages 57-58
a. Two-digit by two-digit                                                   operations.                                                       fractions, and relationships
multiplication (larger               Indicators Pages13-18                                                                                 among fractions involving               Indicators Pages 19-21
numbers with calculator).                                                                                                                  halves, fourths, eighths, thirds,
b. Up to three-digit by two-               enVision Topics:                                                                                   sixths, twelfths, fifths, tenths,          enVision Topic:
digit division (larger     3 – Multiplication Meanings and Facts                                                                           hundredths, and mixed             10 – Understanding Fractions
numbers with calculator). 4 – Division Meanings and Facts                                                                                  numbers.
c. Strategies for multiplying 5 – Multiplying By 1-Digit Numbers
and dividing numbers.                                            1.03 Solve problems using          NCDPI Classroom Strategies 1.04        Develop fluency with addition            NCDPI Classroom
d. Estimation of products                                                models, diagrams, and                   Pages 57-68                  and subtraction of non-negative        Strategies Pages 59-69
and quotients in                                                      reasoning about fractions,                                           rational numbers with like
appropriate                                                           and relationships among          Indicators Pages 19-21              denominators, including decimal        Indicators Pages 22-24
situations.                                                          fractions involving halves,                                          fractions through hundredths.
e. Relationships between                                                 fourths, eighths, thirds,             enVision Topic:                a. Develop and analyze                    enVision Topics:
operations.                                                           sixths, twelfths, fifths,    10 – Understanding Fractions                strategies for adding and   11 – Adding and Subtracting
tenths, hundredths, and                                                  subtracting numbers.             Fractions
1.03 Solve problems using               NCDPI Classroom Strategies            mixed numbers.                      Van de Walle 3-5:                b. Estimate sums and            12 – Understanding Decimals
models, diagrams, and                          Pages 57-68                                            Chapter 5 – Developing Fraction             differences.                13 – Operations With Decimals
reasoning about fractions,                                                                                         Concepts                   c. Judge the reasonableness of
and relationships among                 Indicators Pages 19-21                                        Chapter 6 – Fraction                        solutions.                            Van de Walle 3-5:
fractions involving halves,                                                                                        Computation                                                Chapter 7 – Decimal And Percent
fourths, eighths, thirds,                   enVision Topic:                                                                       .                                                        Concepts And Decimal
sixths, twelfths, fifths,           10 – Understanding Fractions                                                                                                                           Computation
tenths, hundredths, and
mixed numbers.

10
2009-2010 FOURTH GRADE MATHEMATICS PACING GUIDE
Resources: NCDPI Strategies, Indicators, and Week By Week Essentials, enVision Math – Scott Foresman/Addison Wesley, & Teaching Student-Centered
Mathematics 3-5 Volume Two – John Van de Walle
Number & Operations
First Nine Weeks                          Resources                       Second Nine Weeks                      Resources                   Third Nine Weeks                       Resources                 Fourth Nine Weeks           Resources
1.04 Develop fluency with                NCDPI Classroom Strategies                                                                                                                                                 Apply and maintain skills   Week by Week
addition and subtraction of                Pages 59-69                                                                                                                                                         previously taught from        Essentials
non-negative rational                                                                                                                                                                                          Goal 1.                      Weeks 28-36
numbers with like                      Indicators Pages 22-24
denominators, including
decimal fractions through                 enVision Topics:
hundredths.                      11 – Adding & Subtracting Fractions
a. Develop and analyze          12 – Understanding Decimals
strategies for adding and    13 – Operations With Decimals
subtracting numbers.                                                                                                           1.05
b. Estimate sums and                     Van de Walle 3-5:                                                                        1.05
differences.                 Chapter 1 – Foundations of                                                                        1.05
c. Judge the                                Student-Centered                                                                      1.05
reasonableness of                        Instruction
solutions.                   Chapter 2 – Number and Operation
Sense
Chapter 3 – Helping Children Master
The Basic Facts
Chapter 4 – Strategies For Whole
Number Computation

1.05 Develop flexibility in solving      NCDPI Classroom Strategies         1.05 Develop flexibility in solving NCDPI Classroom Strategies 1.05 Develop flexibility in solving      NCDPI Classroom Strategies
problems by selecting                      Pages 70-76                      problems by selecting                 Pages 70-76              problems by selecting                      Pages 70-76
strategies and using mental                                                 strategies and using mental                                    strategies and using mental
computation, estimation,               Indicators Pages 25-27               computation, estimation,         Indicators Pages 25-27        computation, estimation,              Indicators Pages 25-27
calculators, or computers,                                                  calculators, or computers, and                                 calculators, or computers,
and paper and pencil.                     enVision Math                     paper and pencil.                    enVision Math             and paper and pencil.                    enVision Math
embedded in each topic.                                               embedded in each topic.                                             embedded in each topic.

Measurement
2.01 Develop strategies to           NCDPI Classroom Strategies      Apply and maintain
determine the area of                  Pages 77-89              skills previously taught
rectangles and the                                              from Goal 2.
perimeter of plane                Indicators Pages 28-29
figures.
enVision Topic:
14 – Area and Perimeter

2.02 Solve problems involving        NCDPI Classroom Strategies
perimeter of plane figures               Page 90
and areas of rectangles.
Indicators Pages 30-31

enVision Topic:
14 – Area and Perimeter

Van de Walle:
Chapter 9 – Developing
Measurement Concepts

11
2009-2010 FOURTH GRADE MATHEMATICS PACING GUIDE
Resources: NCDPI Strategies, Indicators, and Week By Week Essentials, enVision Math – Scott Foresman/Addison Wesley, & Teaching Student-Centered Mathematics
3-5 Volume Two – John Van de Walle
Geometry
First Nine Weeks                  Resources                 Second Nine Weeks                           Resources                      Third Nine Weeks                            Resources                   Fourth Nine Weeks Resources
3.01 Use the coordinate        NCDPI Classroom Strategies 3.02 Describe the relative position       NCDPI Classroom Strategies      3.01 Use the coordinate system to          NCDPI Classroom Strategies          Apply and maintain
system to describe the            Pages 91-93             of lines using concepts of                  Pages 94-95                   describe the location and                    Pages 91-93                 skills previously taught
location and relative                                     parallelism and                                                           relative position of points and                                          from Goal 3.
position of points and      Indicators Pages 32-33        perpendicularity.                       Indicators Pages 34-35            draw figures in the first                Indicators Pages 32-33
draw figures in the first                                                                                                           quadrant.
quadrant.                       enVision Topic:                                                       enVision Topic:                                                           enVision Topic:
17 – Data and Graphs                                              9 – Lines, Angles, And Shapes                                                  17 – Data and Graphs
Lesson 17-4                                                      Lesson 9-1                                                                      Lesson 17-4

3.03 Identify, predict, and describe      NCDPI Classroom Strategies                                                       Van de Walle 3-5:
the results of transformations              Pages 96-102                                                    Chapter 8 - Geometric Thinking And
of plane figures through                                                                                                Geometric Concepts
reflections, translations, and          Indicators Pages 36-37
rotations.
enVision Topic:
19 – Transformations,
Congruence, and Symmetry

Van de Walle 3-5:
8 – Geometric Thinking And
Geometric Concepts

Data Analysis & Probability
4.01 Collect, organize, analyze,          NCDPI Classroom Strategies      4.02 Describe the distribution of                NCDPI Classroom               Apply and maintain
and display data (including                Pages 103-108                  data using median, range, and           Strategies Pages 109-111          skills previously taught
line graphs and bar graphs) to                                            mode.                                                                     from Goal 4.
solve problems.                         Indicators Pages 38-41                                                     Indicators Pages 42-43

enVision Topic:                                                            enVision Topic:
17 – Data and Graphs                                                       17 – Data and Graphs
4.04 Design experiments and list
4.02 Describe the distribution of               NCDPI Classroom                all possible outcomes and             NCDPI Classroom Strategies
data using median, range, and          Strategies Pages 109-111           probabilities for an event.                 Pages 114-115
mode.
Indicators Pages 42-43                                                     Indicators Pages 46-47

enVision Topic:                                                            enVision Topics:
17 – Data and Graphs                                                    1 – Numeration, Lesson 1-7
Lesson 17-7                                                       20 – Probability

4.03 Solve problems by comparing          NCDPI Classroom Strategies                                                        Van de Walle 3-5:
two sets of related data.                  Pages 112-113                                                    Chapter 11 – Exploring Data Analysis
Chapter 12 – Exploring Concepts of
Indicators Pages 44-45                                              Probability

enVision Topic:
17 – Data and Graphs,
Lesson 17-10

Van de Walle 3-5:
Chapter 11 – Exploring Data
Analysis
Chapter 12 – Exploring Concepts
of Probability

12
2009-2010 FOURTH GRADE MATHEMATICS PACING GUIDE
Resources: NCDPI Strategies, Indicators, and Week By Week Essentials, enVision Math – Scott Foresman/Addison Wesley, & Teaching Student-Centered
Mathematics 3-5 Volume Two – John Van de Walle
Algebra
First Nine Weeks                    Resources                    Second Nine Weeks                    Resources                 Third Nine Weeks                             Resources                  Fourth Nine Weeks           Resources
5.02 Translate among              NCDPI Classroom Strategies 5.02 Translate among symbolic,              NCDPI Classroom      5.01 Identify, describe, and                 NCDPI Classroom Strategies        Apply and maintain skills
symbolic, numeric, verbal,         Pages 133-135             numeric, verbal, and pictorial            Strategies             generalize relationships in                   Pages 127-132               previously taught from
and pictorial representations                                 representations of the number           Pages 133-135            which:                                                                    Goal 5.
of the number relationships.    Indicators Pages 50-51        relationships.                                                   •      quantities change                   Indicators Pages 48-49
Indicators Pages 50-51             proportionally.
enVision Topic:                                                                            •      change in one quantity                  enVision Topic:
6 – Patterns and Expressions                                            enVision Topic:                 relates to change in a            6 – Patterns And Expressions
6 – Patterns And                second quantity.
Expressions
5.02 Translate among symbolic,               NCDPI Classroom Strategies
5.03 Verify mathematical                NCDPI Classroom           numeric, verbal, and pictorial                Pages 133-135
relationships using:                   Strategies            representations of the number
• models, words, and                 Pages 136-144           relationships.                             Indicators Pages 50-51
numbers.
• order of operations and       Indicators Pages 52-54                                                      enVision Topic:
the identity, commutative,                                                                       6 – Patterns And Expressions
associative, and               enVision Topic:
distributive properties.        18 – Equations     5.03 Verify mathematical relationships       NCDPI Classroom Strategies
using:                                        Pages 136-144
Van de Walle 3-5:         •      models, words, and
Chapter 10 – Algebraic             numbers.                            Indicators Pages 52-54
Reasoning             •      order of operations and
the identity, commutative,            enVision Topics:
associative, and           2–  Adding And Subtracting Whole
distributive properties.       Numbers, Lesson 2-1
4–  Division Meanings And Facts,
Lesson 4-1
5 – Multiplying By 1-Digit Numbers,
Lesson 5-5
13 – Operations With Decimals,
Lesson 13-4
18 – Equations, Lesson 18-1

Van de Walle 3-5:
Chapter 10 – Algebraic Reasoning

13
Correlation of Week-by-Week Essentials
Number &            Measurement         Geometry     Data Analysis &   Algebra
Operations                                             Probability
1st Quarter    1.01, 1.05                               3.01          4.01, 4.02        5.02
4.03
2nd Quarter    1.02, 1.05           2.01, 2.02        3.02, 3.03                     5.02, 5.03

3rd Quarter    1.01, 1.02                                                            5.01, 5.02,
1.03, 1.04,                                                              5.03
1.05
4th Quarter       1.05                                                  4.04            5.02

14
Rowan-Salisbury School System Elementary Mathematics Resources

MATH RENAISSANCE
Math Renaissance gives you the tools and information you need to improve student achievement in math.
These resources are aligned to the state standards of North Carolina. Each elementary school has
Accelerated Math, STAR Math and MathFacts in a Flash. (http://renlearn.com/math.htm)

Generates personalized math assignments at each student’s        Now assessing student’s math progress in grades 1-12 is     Help your students master all their math
level and scores automatically. Educators can use these          fast, accurate, and easy. STAR Math helps you determine     facts. . . MathFacts is an innovative way to improve
reports to identify specific problem areas.                      the math level of each student and measure individual and   students’ computational skills.
•     Generates unlimited practice assignments                   class growth. Students can complete the computer adaptive   •    Allows students to work at their own levels to
tailored to each student’s level                          assessment in less that 12 minutes.                              maximize learning
•     Gives immediate and individualized feedback                •     Determine placement of levels for all students        •    Motivates students in all grades to practice and
•     Lets you see at a glance how each student is progressing   •     Deliver time-saving data within seconds                    improve their math skills
with each math objective                                   •     Measure student growth with specific objectives       •    Addresses 44 levels in addition, subtraction,
•     Automatically scores all assignments                       •     Assess student progress when needed                        multiplication, division, sequencing, and more
•     Helps each student practice the precise skills necessary                                                               •    Improve students’ computational skills
to move ahead at their own pace                                                                                        •    Monitors student and class progress
•    Encourages students to get additional math facts
practice by using Home Practice Programs

15
NCDPI RESOURCES FOR MATHEMATICS
RESOURCES FOR MATHEMATICS
Week by Week Essentials
Week by Week Mathematics Essentials are written to reflect the North Carolina Standard Course of Study in mathematics. Each week (1-36) focuses on the five strands of mathematics with integration of
reading and writing. Students will benefit more from hands-on involvement than from paper and pencil. Effective learning takes place when a child has the opportunity to experience how numbers work
as they build number concepts. Week by Week Essentials can be located on the Rowan-Salisbury Elementary website http://www.rss.k12.nc.us/eled/handouts.html).

Classroom Strategies
Classroom Strategies provide activities for the classroom that focus on the Five Strands (Numbers and Operations, Measurement, Geometry, Data Analysis and Probability and Algebra). Black line
masters are also located on this website. These can be located on the Rowan-Salisbury Elementary web-site. (http://www.rss.k12.nc.us/eled/handouts.html).

Indicators
Indicators are measures to determine mastery of a concept, procedure, or application within a specific objective or group of objectives. The Indicators illustrate and elaborate each objective with sample
problems and tasks, vocabulary and related concepts and skills. Indicators are summative in nature, that is, they are intended to show the kind of mathematical problem-solving that is appropriate to
indicate a student’s mastery of the curriculum after an extended period of instruction and practice. The items contained in this document are intended to represent sample end-of-grade test questions.
These can be located on the Rowan-Salisbury Elementary website (http://rss.k12.nc.us/eled/handouts.html).

Teachers should utilize these NCDPI Resources in classroom mathematics instruction and assessment.

North Carolina Manipulative Kits                                                                               2009 Summer Calendars
The North Carolina Manipulative Kits have been revised and                                       The teachers in the Teaching Excellence and Mathematics project worked
updated to reflect changes in both curriculum and assessment                                     together to create summer calendars with mathematics activities that reinforce
what was learned in school during the previous year. We hope that you will enjoy
since 2003. The consistent use of manipulatives with hands-
doing these activities each day. Because calendar space is limited, some of the
on activities is mandated as a component of math instruction                                     directions are abbreviated. You may want to include the Math Calendars as a
in North Carolina. A new contract for the purchase of these                                      warm-up activity or as a brain teaser during your daily instruction. We suggest
kits has been awarded to ETA Cuisenaire.                                                         you use the previous grade’s calendar for the first and second quarter then utilize

Calendars can be located on the Rowan-Salisbury Elementary Website

16
CALCULATOR REQUIREMENTS FOR THE NORTH CAROLINA TESTING PROGRAM

CALCULATOR USE
Calculators are useful tools, beyond paper and pencil, which students use to demonstrate their understanding of complex problems. Several tests in the North
Carolina Testing Program require students to use calculators. These tests include the Pre-test ~ Grade 3, the End of Grade Tests at Grades 3-5 of Mathematics and

STATE POLICY
All students must have access to calculators that meet the minimum (at least) requirements during the administration of North Carolina tests, when applicable.
Students are to use calculators that are similar to those used during classroom instruction in the current school year. Students who regularly use more than one
calculator during classroom instructional activities may be permitted to use more than one calculator during the test administration. Students may use calculators with
fraction keys; however, school systems should use caution as the use of fraction keys without prior training may confuse students. This may adversely affect their
performance during the test administration. Students are NOT allowed to share calculators during the test administration.

TEST                                                  Minimum (at least) CALCULATOR REQUIREMENTS
Mathematics                                                        Four-function calculator with memory key

Mathematics & Science                                                   Four-function calculator with memory key

17
NORTH CAROLINA END OF GRADE SAMPLE ITEMS
BY THE NORTH CAROLINA DEPARTMENT OF EDUCATION
The following website was developed for educational and instructional purpose.
The sample items focus on the following...

http://www.dpi.state.nc.us/accountability/testing/eog/sampleitems

MATHEMATICS COMPETENCY GOAL 1
The learner will read, write, model, and compute with non-negative rational numbers.

MATHEMATICS COMPETENCY GOAL 2
The learner will understand and use perimeter and area.

MATHEMATICS COMPETENCY GOAL 3
The learner will recognize and use geometric properties and relationships.

MATHEMATICS COMPETENCY GOAL 4
The learner will understand and use graphs, probability, and data analysis.

MATHEMATICS COMPETENCY GOAL 5
The learner will demonstrate an understanding of mathematical relationships.

18
SUGGESTED CHILDREN’S LITERATURE

Counting Books                                          Geometry                          Number Relationships
One Crow                                           Picture Pie                     One, Two, Three Going to Sea
Ten, Nine, Eight                                 Shapes and Things                   Anno’s Mysterious Multiplying Jar
One Bear All Alone                              Shapes, Shapes, Shapes                       Anno’s Counting House
Six Little Ducks                           Circles, Triangles, and Squares                      Too Many Eggs
Ten Black Dots                                   Changes, Changes                               Millions of Cats
Fish Eyes (A Book You Can Count On)                            Square is a Shape                       Don’t Count Your Chicks
Moja Means One (Swahili Counting Book)                           Straight is a Line             One, Two, Three, and Four. No More?
Ross Over                                            Shapes                                  More Than One
How Many Snails?                                    A Light in the Attic                        The Doorbell Rang
Ten Green Bottles                                                                          The Wolf’s Chicken Stew
Count Your Way Through China                                 Graphing                                One Watermelon Seed
Count and See                            Guess Who My Favorite Person Is             Bunches & Bunches of Bunnies
More Than One                                 The Mysterious Tadpole                      The Hundred Penny Box
Seven Eggs                                       Stone Soup                                   Billions of Bugs
1 Hunter                                       Red is Best                                  A Grain of Rice
One Bear At Bedtime                                  Whose Shoes                                    So Many Cats
Two, Four, Six, Eight (A book about legs)                                                                 How Much is a Million
When Sheep Cannot Sleep                                                                            If You Made a Million
The Twelve Days of Christmas                                  Money                           Millions and Millions and Millions
Ocean Parade                                  \$1.00 Word Riddle Book                    Where the Sidewalk Ends
Counting Wildflowers                             Where the Sidewalk Ends             The 500 Hats of Bartholomew Cubbins
Farm Counting Book                      Alexander, Who Used to be Rich Last Sunday    I Can Count the Petals of the Flower
Monster Bubbles                                                                                The 329th Friend
Numbers of Things                                  Measurement
A Farmer’s Dozen                                    Ten Beads Tall
One Was Johnny                                  Mr. Archimedes’ Bath
Who Wants One?                                    The King’s Flower
A Light in the Attic                      The Chocolate Chip Cookie Contest
One Sun, Two Eyes, and a Million Stars                      Jim and the Beanstalk                 Volume 1 (TS4-TS5) (T50-T56)
One Woolly Wombat                                Much Bigger Than Martin                     Volume 2 (T50-T56)
1 is One                                      The Carrot Seed
Who’s Counting?                                      Inch By Inch
1 is No Fun But 20 is Plenty                      The Biggest House in the World
An Invitation to the Butterfly Ball                         How Big is a Foot
The Borrowers

19
SUGGESTED CHILDREN’S LITERATURE
Patterns                                     Miscellaneous                Well-Known Authors
The Very Busy Spider                              Anno’s Math Games            Of Math Literature
Round Trip                                 Anno’s Math Games II               David Schwartz
Reflections                             Socrates and the Three Pigs             Greg Tang
A Light in the Attic (“Reflections”, p29)               First Grade Takes a Test             Loreen Leedy
The Mirror Puzzle Book                              Changes, Changes                  Marilyn Burns
Numblers                     Stuart Murphy
Probability                                     Pumpkin, Pumpkin                Shel Silverstein
Anno’s Hat Tricks                           Each Orange Had 8 Slices          Cindy Neuschwander
Journey                                  Grandfather Tang’s Story
Mouse Tales                               17 Kings and 42 Elephants
Caps For Sale
Elephant Buttons                                     Time
Anno’s Sundial
Sorting                                     Anno’s Counting Book
The Baby’s Cantaloupe                       Caps, Hats, Socks, and Mittens
Harriet’s Halloween Candy                        This is a Book About Time
Is it Red? Is it Smooth? Is it Blue?                    The Grouchy Ladybug
A House is a House For Me                        The Very Hungry Caterpillar
Growing Colors                                 Ramona the Pest
People                              Season of Arnold’s Apple Tree
Those Green Things                                 Boss for a Week
Frederick
Fractions                                       Knots on a Rope
Pezzettino                                        Time To . . .
Gator Pie                                 Monday I Was An Alligator
Time
One Hundred Years Ago
On Friday Something Funny Happened
Only Six More Days
This Year’s Garden
The Tomorrow Book
Chicken Soup With Rice
One Monday Morning
All Year Long
You’ll Grow Into It

20

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