Introduction to the Practice of Statistics Fourth Edition - DOC - DOC by dwc20915


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									                                                                      How Parents Can Help
                                                           As a parent, you are your child's first mathematics
                                                           teacher. In fact, you have probably been doing math
Prince William County Public Schools is pleased to         together since your child was very young. Counting
provide you with an overview of “Investigations in         pictures on a page and singing songs helped your
Number, Data, and Space” mathematics program for           child learn about numbers and counting. Building
the fourth grade.                                          with objects such as blocks and cardboard boxes
                                                           exposed your child to geometric ideas such as shape,
The “Investigations” program is based on years of
research about how children learn mathematics.
                                                           size and symmetry. Chores such as putting away the
                                                           dishes and sorting laundry engaged your child in                in Number,
Each grade level consists of a set of separate units,      sorting and categorizing, which are important
each offering 2–8 weeks of work. These units of            features of data analysis. Games are another way to           Data, and Space
study are presented through investigations that
involve students in the exploration of major
                                                           engage your child in mathematical thinking. Games
                                                           provide meaningful practice whether they are played
                                                                                                                                       2nd Edition
mathematical ideas, and may revolve around related         at home or in school.
areas, for example, addition and subtraction or
geometry and fractions. The students may have a                 Fun Math Activities to Do at Home
                                                           Money: Help grocery shop, compare prices, budget
Student Activity Booklet or they may have Student
                                                           allowance for saving/spending for short/long term
Sheets, Homework Sheets, Game Instructions,                Counting: Practice skip counting – starting at 2, 3, 7, 9;
Practice Pages, and Assessment Tasks to show and           count past 1000 counting by 25, 50, 250
share what they know and are able to do.                   Math Facts: Know addition, subtraction, multiplication
                                                           and division facts fluently and accurately
The Prince William County Mathematics Curriculum           Time: Practice scheduling, time management; determine
covers the same content as the Standards of Learning       elapsed time
(SOL) set by the State of Virginia, and in some cases      Measurement: Participate in cooking, building, measuring
goes beyond state standards. The Prince William            Data: Discuss newspaper graphs or charts; discuss the
County Curriculum is divided into six strands:             probability of likely and unlikely events
 Number and Number Sense
 Computation and Estimation
                                                           Geometry: Discuss 2-D and 3-D shapes you see in your
                                                           environment.                                                       Fourth Grade
                                                                                    School Board
 Measurement                                               Mr. Milton C. Johns                 Mr. Grant Lattin
                                                                                                                                   Parent Edition
 Geometry
                                                            Chairman At-Large                   Vice Chairman
 Patterns, Functions and Algebra
                                                                                                Occoquan District
 Probability and Statistics                                                                                                 Investigations is a crucial part of
                                                           Mrs. Betty D. Covington           Mrs. Denita S. Ramirez          Prince William County Schools’
The complete curriculum guide for mathematics, as          Dumfries District                 Woodbridge District           commitment to enable all children to
well as other useful information is online at the                                                                           understand and use mathematics to
Prince William County Web Mathematics Web Site.            Ms. Julie C. Lucas                Mr. Don Richardson                   solve problems for life.
                          Neabsco District                  Gainesville District

          Other math web sites of interest:                Dr. Michael I. Otaigbe            Mr. Gil Trenum
                   Coles District                    Brentsville District       The Prince William County Public School Division does                                                                        not discriminate in employment or in its educational                   Superintendent of Schools                     programs and activities against qualified individuals on
 (SuccessNet: Contact your child’s teacher for user name                                                                 the basis of race, color, national origin, religion, sex,
                                                                              Dr. Steven L. Walts                             pregnancy, age, veteran status, or disability.
                and password information)
                                                                    Supervisor of Mathematics, Carol Knight
               Fourth Grade                                              Size, Shape, and Symmetry:                                Moving Between Solids and Silhouettes:
              Unit Descriptions                                         2D Geometry and Measurement                                   3D Geometry and Measurement
                                                                This first geometry and measurement unit focuses on               In this second geometry and measurement unit, students
                                                                classifying two-dimensional shapes, comparing the size of         examine the relationships between 3D solids and their 2D
       Factors, Multiples, and Arrays:                          angles, and working with linear and area measurement.             representations. They learn and use the mathematical
                Multiplication                                  Students define and categorize polygons by identifying            terminology for these solids and their attributes. They
In this first unit in the multiplication and division strand,   sets of shapes that have a common attribute and use 90            translate between 3D shapes and their 2D representations as
students deepen their understanding of the operation of         degrees as a reference for finding the measurement of             they build cube configurations from pictures and mental
multiplication. Students use rectangular arrays to represent    other angles. They continue their measurement work from           images and investigate silhouettes of solids from several
the relationship between factors and multiples, use what        earlier grades by measuring distance and perimeter,               different perspectives. Students build an understanding of
they know to solve problems that increase in size, and          using both U.S. and metric units and finding the area of          measuring volume as they examine the structure of
focus on solving problems efficiently. They continue to         polygons in square units. LogoPaths, a Logo programming           rectangular prisms and determine the number of cubes that
develop fluency with multiplication combinations (facts up      environment designed for “Investigations” students in             fit inside given box patterns.
to 12 x 12).                                                    Grades 3–5 is introduced in this unit. It allows students to
                                                                explore geometrical relationships, especially focusing on
                                                                angle, length, and perimeter, patterns in sides and angles,                   How Many Packages?
  Describing the Shape of the Data: Data                        and characteristics of specific shapes.                                        How Many Groups?
         Analysis and Probability                                                                                                            Multiplication and Division
This unit develops ideas about collecting, describing, and            Landmarks and Large Numbers:                                In this last multiplication and division unit in Grade 4,
representing data. Students collect data through counting                                                                         students continue to develop efficient strategies for solving
and measuring and use bar graphs and line plots to                     Addition, Subtraction, and the                             multiplication problems by breaking problems into smaller
represent their data involving one group and compare data                     Number System                                       parts or changing one or both numbers to create an easier
of two groups. They interpret the data and draw                 Students extend their knowledge of the number system by           problem. Students also focus on recording their work with
conclusions based on the data using terms such as mode,         examining the structure of 10,000 and practice and refine         clear and concise notation. Students develop strategies for
median, range, and outlier. Students begin their study of       strategies for adding and subtracting whole numbers up to         solving division problems (three-digit divided by two-
probability by placing events on a “likelihood line” that       10,000. They continue to study place value by adding and          digit), which involve making groups of the divisor. These
goes from impossible to certain and work with mixtures of       subtracting multiples of 10 and 100 to numbers in the             problems are presented both in story contexts and
colored cubes to describe the probability of different          thousands, and they consolidate their understanding of the        numerically.
outcomes.                                                       operation of addition by studying a variety of addition
                                                                strategies and algorithms, including the U.S. algorithm for
                                                                addition. Students continue their study of subtraction by          Penny Jars and Plant Growth: Patterns,
   Multiple Towers and Division Stories:                        solving, representing, and discussing their strategies for a              Functions, and Change
        Multiplication and Division                             variety of subtraction problems.
                                                                                                                                  Students explore situations in which two quantities change
Students develop strategies for solving multiplication                                                                            in relation to each other. They work with changes over
problems with two-digit numbers and deepen their                                                                                  time, such as increasing or decreasing speed or the growth
understanding of the operation of division by focusing on          Fraction Cards and Decimal Squares:                            of a plant, and situations of constant change, such as how
the relationship between multiplication and division. Using                  Rational Numbers                                     the number of windows in a building depends on the height
story contexts and multiple towers, students continue their     Students develop ideas about fractions by identifying             of the building if every floor has the same number of
investigation of the relationship between numbers and their     fractions of an area (3/4 of a rectangle), fractions of a group   windows. Students create and interpret graphs and tables
factors. Students practice multiplying by 10 and multiples      of objects (3/4 of 24), and decimal fractions (.75). They         for these linear and nonlinear functions and connect these
of 10, break problems into smaller parts that can be            compare fractions of different wholes (1/3 of a 6 x 4             graphs to the situations they represent.
multiplied easily, and find the multiples of two-digit          rectangle and 1/3 of a 10 x 10 rectangle), and combine
numbers. They gain fluency with all multiplication              fractions using models and reasoning. Students use
combinations to 12 x 12. Students solve, represent, and         10 x 10 grids to represent, compare, and combine common
discuss division story problems, including remainders.          decimals in the tenths and hundredths.

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