# Investigations

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```							Grade 5 Pacing/Alignment, Investigations 2nd Edition                                                                                                                       DRAFT 9/09
Unit 1: Number Puzzles and Multiple Towers: Multiplication and Division 22 days
September
In the first of two units about multiplication and division, students continue to develop and practice efficient strategies to solve multiplication problems both in and out of a context.
Students refine and gain fluency in solving two-digit by two-digit multiplication problems, develop strategies for division problems with one- and two-digit divisors, and increase their
knowledge of multiplication relationships by learning about prime factorization (e.g., 36 = 4 x 9 = (2 x 2) x 9 = 2 x 2 x 3 x 3).

Additional Investigations                                      Other Resources:                                            Assessments
Content/Topic                           Content:                                                                                                       Formative/Summative
Flip Chart,                       Bridges to Mathematics                 WA Problem Solving                         Assessments
Student Math Handbook,                                                                                             Content/standards-based: Observing
Mathematics Performance                                                               Supplements                       Notebook (Teacher to                 students at work and paper-pencil
Expectations encountered               www.pearsonsuccessnet.com               www.mathlearningcenter.org                  Teacher, 2006)                  assessments: curriculum, Exam View,
in this unit                     Parent and student access via                                                                                                    SuccessNet
website                                                                                                  Diagnostic/Fluency Asmts located in
CFSD classroom binder
    Multiplication and          In Unit 1, Ten-Minute Math
division                    activities focus on:                                                                5.1 Sports Card                 September – Diagnostic
    Practice efficient                Organizing and analyzing                                                     Probability & Statistics        Assessment:
strategies                             visual images                                                            Solves Problems
    Gain fluency in solving           Developing language and                                                 Organize information
two-digit by two digit                 concepts needed to
DA 46, 47 -- Multiplication
factors 2-10 4.1.A
multiplication problems                communicate spatial                                                       5.3 Baby Bottles
    Develop strategies for                 relationships                                                             Algebraic Sense                DA 46, 48 - Multiplication and
division problems with            Writing equations to                                                          Reasons Logically              division 11s, 12s Fluency not
one- and two-digit                     describe dot patterns                                               Use multiple steps to find cost       required for any PE
divisors                          Identifying prime, square,                                              Sort and organize data                DA 49, 50 - All addition and
    Learn about prime                      a\even, and odd numbers                                             Plan steps                            subtraction combinations 2.2.A
factors                           Determining if one number
is a factor or multiple of                                                   5.5 Can of Worms
another                                                                      Probability & Statistics
    Reasons logically
See Unit 1 pages 14-15

   5.2 Apple Pie (CB)
   Number Sense                 Optional:
   Reasoning                    ExamView (GLE-based)
   Communicates                 End of Unit Asmt (Grade 5
Understanding                Unit 1 Asmt 9-09)
Estimation, mental math
Measuring mass/weight
Organize information
4.1.B   Identify factors and                                                                                                                              Observing students at work:
multiples of a number.                                                                                                                                  Finding Multiplication
Combinations for 18 and
180; Factors of Larger
Numbers
Asmt Activity and Checklist:
Number Puzzles M34

Revised 9/09 mellul CFSD                                                                     -1-
Grade 5 Pacing/Alignment, Investigations 2nd Edition                                                               DRAFT 9/09
End-of-Unit Asmt: Problem 2
M54
5.1.A Represent multi-digit                                                                         Observing students at work:
division using place                                                                         Solving a Division Problem;
value models and                                                                             Practicing Division Strategies
connect the
End-of-Unit Asmt: Shopping
representation to the                                                                        problems M54, 55
related equation.
Limited exposure in Units 1, 7
5.1.B Determine quotients for     SMH 38-39                           A3 – Number and Operations:   Asmt Activity and Checklist:
multiples of 10 and 100                                        Estimating to Multiply and          Number Puzzles M34
by applying knowledge                                          Divide                        End-of-Unit Asmt: Problem 2
of place value and                                                                                 M54
properties of
operations.
5.1.D Estimate quotients to       Ten-Minute Math: Estimation         A3 – Number and Operations:
approximate solutions      and Number Sense                    Estimating to Multiply and
and determine                                                  Divide
reasonableness of                                              A4 – Number and Operations:
answers in problems                                            Long Division
involving up to two-
digit divisors.
5.1.E Mentally divide two-        Ten-Minute Math: Estimation
digit numbers by one-      and Number Sense
digit divisors and
explain the strategies     Online Activity Unit 1 Activity 2
used.
5.1.F Solve single- and multi-                                        A4 – Number and Operations:   End-of-Unit Asmt:
step word problems                                             Long Division                       Problem 3 M55
involving multi-digit
division and verify the
solutions.
5.2.H Solve single- and multi-                                        A5 – Number and Operations:
step word problems                                             Adding and Subtracting
involving addition and                                         Fractions
subtraction of whole                                           A6 – Number and Operations:
numbers, fractions                                             Fraction Concepts
(including mixed
numbers), and
decimals, and verify the
solutions.
5.5.A Classify numbers as         SMH 21-22                                                         Observing students at work:
prime or composite.                                                                                 Ten-Minute Math -
Ten-Minute Math: Number                                                  Number Puzzles

Revised 9/09 mellul CFSD                                                          -2-
Grade 5 Pacing/Alignment, Investigations 2nd Edition                        DRAFT 9/09
Puzzles
5.6.A Determine the
question(s) to be
answered given a
problem situation.
5.6.B Identify information
that is given in a
problem and decide
whether it is essential or
extraneous to the
solution of the problem.
Curriculum Gap
5.6.C Determine whether
additional information
is needed to solve the
problem.
Curriculum Gap
5.6.D Determine whether a
problem to be solved is
similar to previously
solved problems, and
Asmt Activity: What Is the
identify possible                                            Answer? M51
strategies for solving
the problem.
5.6.E Select and use one or
more appropriate
strategies to solve a
problem, and explain
the choice of strategy.
5.6.F Represent a problem                                    End-of-Unit Asmt:
situation using words,                                     Problem 3 M55
numbers, pictures,
physical objects, or
symbols.
5.6.G Explain why a specific
problem-solving
strategy or procedure
was used to determine a
solution.

Revised 9/09 mellul CFSD                               -3-
Grade 5 Pacing/Alignment, Investigations 2nd Edition                                                                                                              DRAFT 9/09
Unit 2: Prisms and Pyramids: 3D Geometry and Measurement 16 days
October
Students investigate concepts of volume by finding the volume of prisms, pyramids, cylinders, and cones. They use patterns of open boxes and build prisms from cubes
to develop a strategy for finding the volume of any rectangular prism. Using concrete materials, they also examine the 3-to-1 volume relationship between related
(having the same base and height) prisms and pyramids, and related cylinders and cones. Geometry work includes naming geometric solids and their attributes.

Additional Investigations                                 Other Resources:                                       Assessments
Content/Topic                            Content:                                                                                            Formative/Summative
Flip Chart,                                                                                               Assessments
Mathematics Performance                   Student Math Handbook,
Bridges to Mathematics         WA Problem Solving
Content/standards-based: Observing
Expectations encountered in             www.pearsonsuccessnet.com                      Supplements               Notebook (Teacher to               students at work and paper-pencil
this unit                      Parent and student access via            www.mathlearningcenter.org         Teacher, 2006)                assessments: curriculum, Exam View,
SuccessNet
website                                                                                         Diagnostic/Fluency Asmts located in
CFSD classroom binder
    Concepts of volume          In Unit 2, Ten-Minute Math                                                        5.2 Clowning Around
    Prisms, pyramids, cones     activities focus on:                                                              Geometric Sense
    Develop strategy for              Organizing and analyzing                                                   Communicates
finding volume of any                  visual images                                                           Understanding
rectangular prism                 Developing language and                                          Reflection, congruence, spatial
    Examine 3-to-1                         concepts needed to                                           visualization
See Unit 2 pages 14-15
relationship between                   communicate agout spatial
prisms and pyramids, and               relationships                                                          5.4 Pattern Block
cylinders and cones               Decomposing images of 3-                                                    Trains
    Name geometric solids                  D shapes and them                                                      Number Sense
and their attributes                   recombining them to make a                                             Algebraic Sense
given building                                                         Solves Problems
Correlation of PEs with the                 Estimating solutions to 2-                                       Area
content of this unit is not strong.              and 3-digit multiplication an
PEs listed below are practiced in                division problems                                                      5.A Transforming
the Student Activity Book. (For             Breaking apart, reordering,                                                 Puzzle
specific page numbers refer to                   or changing numbers                                                Geometric Sense
Pearson correlation document:                    mentally to determine a                                            Solves Problems
WA_Investigations_Grade5_2ndEd_                  reasonable estimate                                          Translation
2008_0608_Final.pdf)                                                                                          Reflection
 5.B Inside a Tangram
 Geometric Sense
 Communicates
Understanding
Parallel, perpendicular

5.5 A Weighty Problem
(CBES)
 Measurement
 Solves Problems
Volume, weight

   5.12 Transforming Cats
Revised 9/09 mellul CFSD                                                                    -4-
Grade 5 Pacing/Alignment, Investigations 2nd Edition                                                                                                DRAFT 9/09
(CBES)
   Geometric Sense
   Communicates
Understanding

     5.A Rotations (CBES)
     Geometric Sense
     Communicates
Understanding Rubric
Rotation, symmetry
5.1.D Estimate quotients to         Ten-Minute Math: Estimation   A3 – Number and Operations:
approximate solutions         and Number Sense              Estimating to Multiply and
and determine                                               Divide
reasonableness of                                           A4 – Number and Operations:
answers in problems                                         Long Division
involving up to two-
digit divisors.
5.1.F Solve single- and multi-                                    A4 – Number and Operations:
step word problems                                          Long Division
involving multi-digit
division and verify the
solutions.
5.6.A Determine the                                               E1 – Data Analysis: Probability                                    Observing students at work:
question(s) to be                                           and Technology                                                            Finding the Volume of
answered given a                                                                                                                      Boxes, Doubling the
problem situation.                                                                                                                    Cubes, Doubling and
Halving
5.6.B Identify information
that is given in a
problem and decide
whether it is essential or
extraneous to the
solution of the problem.
Curriculum Gap
5.6.C Determine whether
additional information
is needed to solve the
problem.
Curriculum Gap
5.6.E Select and use one or
more appropriate
strategies to solve a
problem, and explain
the choice of strategy.
5.6.F Represent a problem                                                                                                            Asmt Activity and Checklist:
Measuring Volume in
Revised 9/09 mellul CFSD                                                       -5-
Grade 5 Pacing/Alignment, Investigations 2nd Edition               DRAFT 9/09
situation using words,                                Cubic Centimeters? M24-
numbers, pictures,                                    25
physical objects, or
symbols.

Revised 9/09 mellul CFSD                               -6-
Grade 5 Pacing/Alignment, Investigations 2nd Edition                                                                                                             DRAFT 9/09
Unit 3: Thousands of Miles, Thousands of Seats: Addition, Subtraction, and the Number System 15 days
November
Students study place value in large numbers by building a 10,000 chart and by adding multiples of 10 to and subtracting multiples of 10 from four- and five-digit
numbers. Students finalize their study of subtraction by refining and gaining fluency in solving subtraction problems, including a study of the U.S. algorithm for
subtraction. Using a context of the capacities of stadiums and arenas, they solve addition and subtraction problems involving four- and five-digit numbers. Students also
demonstrate fluency with the division facts up to 144 ÷ 12.

Additional Investigations                                 Other Resources:                                       Assessments
Content/Topic                            Content:                                                                                            Formative/Summative
Flip Chart,                                                                                               Assessments
Student Math Handbook,
Bridges to Mathematics          WA Problem Solving
Mathematics Performance                                                                                                                          Content/standards-based: Observing
www.pearsonsuccessnet.com                      Supplements                Notebook (Teacher to              students at work and paper-pencil
Expectations encountered in
Parent and student access via           www.mathlearningcenter.org           Teacher, 2006)               assessments: curriculum, Exam View,
this unit                                                                                                                                             SuccessNet
website                                                                                         Diagnostic/Fluency Asmts located in
CFSD classroom binder
   Place value to 10,000        In Unit 3, Ten-Minute Math                                                   5.6 S’Mores
   Add and subtract             activities focus on:                                                         Number Sense                  November (first week) –
multiples of 10 to and             Recognizing and                                                       Solves Problems
from four- and five-digit               interpreting the value of                                    Multiples, patterns                 Diagnostic Assessment:
numbers                                 each digit in 4- and 5-digit

DA 45 and DA 48 --
Solve addition and                      numbers                                                              5.7 Outfits
subtraction problems               Finding different                                                        Probability & Statistics   Multiplication to 12x12
with four- and five- digit              combinations of a number,                                            Communicates               DA 52 -- Division, divisors
numbers                                 using only 1,000s, 100s,                                              Understanding              11,12, through dividend of 144
   Demonstrate fluency                     10s, and 1s and recognizing                                  Organizing data                     Fluency Assessment:
with division facts up to               their equivalency (i.e., 1                                                                       FA 46, 47 -- Multiplication and
144 ÷ 12                                hundred, 3 tens, and 7 ones                                          5.21 School Clothes        division 4.1.A
= 12 tens and 17 ones, etc.)                                         Number Sense               FA 49, 50 -- Addition and
 Reading and writing                                              Money                                       subtraction 2.2.A
numbers up to 100,000
 Adding multiples of 10 to,                                                5.8 Shape Up (CB)
and subtracting multiples of                                          Geometric Sense
10 from, 4- and 5-digit                                               Communicates              See Unit 3 pages 14-15
numbers                                                                Understanding
 Estimating solutions to 2-                                       Visualize shape and size
and 3-digit multiplication                                   Congruence
and division problems
 Breaking apart, reordering,
or changing numbers
mentally to determine a
reasonable estimate

3.1.C Fluently and accurately                                                  (Grade 3)
add and subtract whole                                                   A3 – Number and Operations:
numbers using the                                                        Multi-Digit Addition and                                          End-of-Unit Asmt: Solve two

Revised 9/09 mellul CFSD                                                                   -7-
Grade 5 Pacing/Alignment, Investigations 2nd Edition                                                                   DRAFT 9/09
standard regrouping                                           Subtraction                      problems M20
algorithm.                                                    A6 – Number and Operations:
3.1.E   Solve single- and multi-                                       Estimating to Add and Subtract
step word problems
involving addition and                                        (Grade 3
subtraction of whole                                          A3 – Number and Operations:
numbers and verify the                                        Multi-Digit Addition and
solutions.                                                    Subtraction
4.1.A   Quickly recall                                                                                  Asmt Activity: Division Facts
multiplication facts                                                                                  M18
through 10 x 10 and the
related division facts.
5.1.F    Solve single- and multi-                                      A4 – Number and Operations:
step word problems                                            Long Division
involving multi-digit
division and verify the
solutions.
5.2.G    Estimate sums and           Ten-Minute Math: Practicing       A6 – Number and Operations:      Observing students at work:
differences of fractions,   Place Value                       Fraction Concepts                       Close to 1,000
mixed numbers, and          Online Activity Unit 6 Activity
decimals to
approximate solutions
to problems and
determine
reasonableness of
answers.
5.6.D    Determine whether a
problem to be solved is
similar to previously
solved problems, and
identify possible
strategies for solving
the problem.
5.6.E    Select and use one or                                                                          Observing students at work:
more appropriate                                                                                      More Numbers on the
strategies to solve a                                                                                 Chart; Practicing Place
problem, and explain                                                                                  Value; Practicing
Subtraction; Starter
the choice of strategy.                                                                               Problems
Asmt Checklist: Reading,
Writing, and Sequencing
Numbers to 100,000 M3
5.6.F   Represent a problem
situation using words,
numbers, pictures,
Revised 9/09 mellul CFSD                                                            -8-
Grade 5 Pacing/Alignment, Investigations 2nd Edition         DRAFT 9/09
physical objects, or
symbols.
5.6.G Explain why a specific
problem-solving
strategy or procedure
was used to determine a
solution.

Revised 9/09 mellul CFSD                               -9-
Grade 5 Pacing/Alignment, Investigations 2nd Edition                                                                                                         DRAFT 9/09
Unit 4: What’s That Portion?: Fractions and Percents 21 days
December
Students study the relationship among fractions and between fractions and percents and use this knowledge to find equivalent fractions, order fractions, and add
commonly used fractions. They use a variety of contexts and models, including area, number lines, and rotation, to further understand the meaning of fractions and
model their strategies. This is the first of two units in Grade 5 about rational numbers.

Additional Investigations                                 Other Resources:                                   Assessments
Content/Topic                            Content:                                                                                        Formative/Summative
Flip Chart,                                                                                           Assessments
Mathematics Performance                  Student Math Handbook,
Bridges to Mathematics          WA Problem Solving
Content/standards-based: Observing
Expectations encountered in            www.pearsonsuccessnet.com                    Supplements                Notebook (Teacher to            students at work and paper-pencil
this unit                     Parent and student access via         www.mathlearningcenter.org           Teacher, 2006)             assessments: curriculum, Exam View,
SuccessNet
website                                                                                     Diagnostic/Fluency Asmts located in
CFSD classroom binder
   Study the relationship       In Unit 4, Ten-Minute Math                                                  5.8 Coins
among fractions and          activities focus on:                                                        Probability & Statistics
between fractions and              Estimating solutions to 3-,                                          Solves problems
percents                                4-and 5-digit addition and                                 Finding all possibilities
   Find equivalent fractions               subtraction problems
   Use variety of contexts            Breaking apart, reordering,                                          5.9 Leap Frog
and models (area,                       or changing numbers                                              Number Sense               See Unit 4 pages 14-15
number lines, rotation) to              mentally to determine a                                          Solves Problems
further understand the                  reasonable estimate                                        Fractions
meaning of fractions and           Identifying fractions of a                                     Careful reading
model their strategies                  group
   The first of two units             Using evidence and                                                  5.11 Party Hearty
about rational numbers                  formulating questions to                                        Number Sense
make hypotheses about the                                       Solves Problems
common characteristics of                                  Doubling fractions to simplify
groups of people
 Systematically eliminating                                             5.1 Sharing Cookies
possibilities                                                       (CB)
    Number Sense
    Communicates
Understanding
Ratio
One-half, one-fourth
5.2.A Represent addition and         SMH 52-53                               A5 – Number and Operations:                                     Asmt Activity: School Days SE
subtraction of fractions                                               Adding and Subtracting                                                 15-16
and mixed numbers              Online Activity Unit 4: Activity        Fractions                                                       Asmt Checklist: Solving
using visual and               61                                                                                                             Problems with Fractions
and Percents M11
numerical models, and                                                                                                                  Asmt Activity: Adding and
connect the                                                                                                                                   Subtracting Fractions SE
representation to the                                                                                                                         46
related equation.                                                                                                                      Asmt Checklist: Adding
Fractions? M24
Revised 9/09 mellul CFSD                                                                 - 10 -
Grade 5 Pacing/Alignment, Investigations 2nd Edition                                                              DRAFT 9/09
5.2.D Determine the greatest      Online Activity Unit 4 Activity     A6 – Number and Operations:
common factor and the      6, 8                                Fraction Concepts
least common multiple
of two or more whole
numbers.
Curriculum Gap
5.2.E Fluently and accurately     Online Activity Unit 4 Activity 7   A5 – Number and Operations:
add and subtract                                               Adding and Subtracting
fractions, including                                           Fractions
mixed numbers.                                                 A6 – Number and Operations:
Fraction Concepts
5.2.G Estimate sums and           Ten-Minute Math: Practicing         A6 – Number and Operations:
differences of fractions,   Place Value                         Fraction Concepts
mixed numbers, and          Online Activity Unit 6 Activity
decimals to                 33
approximate solutions
to problems and
determine
reasonableness of
answers.
5.2.H Solve single- and multi-                                        A5 – Number and Operations:   Asmt Activity: School Days SE
step word problems                                              Adding and Subtracting               15-16
involving addition and                                          Fractions                     Asmt Checklist: Solving
subtraction of whole                                            A6 – Number and Operations:          Problems with Fractions
and Percents M11
numbers, fractions                                              Fraction Concepts
(including mixed
numbers), and
decimals, and verify the
solutions.
5.6.A Determine the               E1 – Data Analysis: Probability
question(s) to be           and Technology
answered given a
problem situation.
5.6.D Determine whether a
problem to be solved is
similar to previously
solved problems, and
identify possible
strategies for solving
the problem.
5.6.E Select and use one or
more appropriate
strategies to solve a
problem, and explain
Revised 9/09 mellul CFSD                                                          - 11 -
Grade 5 Pacing/Alignment, Investigations 2nd Edition                           DRAFT 9/09
the choice of strategy.
5.6.F Represent a problem                                       Observing students at work:
situation using words,                                           Which is Greater?
numbers, pictures,                                        End-of-Unit Asmt: Problem 2
physical objects, or                                             Compare fractions M33
symbols.
5.6.G Explain why a specific                                    Observing students at work:
problem-solving                                                  Which is Greater?; Roll
strategy or procedure                                            Around the Clock;
was used to determine a                                          Fraction Track Game
End-of-Unit Asmt: Problem 3
solution.                                                        Solve and explain M33

Revised 9/09 mellul CFSD                               - 12 -
Grade 5 Pacing/Alignment, Investigations 2nd Edition                                                                                                               DRAFT 9/09
Unit 5: Measuring Polygons: 2D Geometry and Measurement 18 days
January
Students create polygons using “power polygon” pieces and discuss, apply, and evaluate definitions of these polygons. They focus on properties of quadrilaterals and
also study similarity of 2D shapes. Measurement work includes finding measures of angles using known angles and finding perimeter and area of rectangles.

LogoPaths, a Logo programming environment designed for Investigations students in 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, and characteristics of specific shapes. (Introduced in grade three.)

Additional Investigations                                    Other Resources:                                     Assessments
Content/Topic                             Content:                                                                                             Formative/Summative
Flip Chart,                                                                                                Assessments
Mathematics Performance                   Student Math Handbook,
Bridges to Mathematics          WA Problem Solving
Content/standards-based: Observing
Expectations encountered in             www.pearsonsuccessnet.com                       Supplements                Notebook (Teacher to              students at work and paper-pencil
this unit                      Parent and student access via            www.mathlearningcenter.org           Teacher, 2006)               assessments: curriculum, Exam View,
SuccessNet
website                                                                                          Diagnostic/Fluency Asmts located in
CFSD classroom binder
    Create polygons with         In Unit 5, Ten-Minute Math                                                     5.10 Tree House
“power polygon” pieces       activities focus on:                                                           Number Sense                 January (last week) --
    Discuss, apply, evaluate           Decomposing images of 2-                                                Measurement                  Diagnostic Assessment:
definitions of these                    D     shapes      and    then                                       Solves Problems              Addition and subtraction, sums
polygons                                recombining them to make a                                    Conversion of meters and
    Properties of                           given design                                                  centimeters
to 20 – choose from resources
quadrilaterals                     Developing language and                                                                               Select multiplication and
    Similarity of 2D shapes                 concepts to communicate                                             5.15 Bulletin Boards         division combinations as
    Measure angles using                    about spatial relationships                                         Measurement                  needed – choose from resources
known angles                       Organizing and analyzing                                                Solves Problems
    Find perimeter and area                 visual images                                                 Spatial visualization               Fluency Assessment:
of rectangles                      Describing features of the                                                                            FA 49, 50, 51, 53 -- Addition
    LogoPaths – geometrical                 data                                                              5.22 Lines and Angles                 and subtraction 2.2.A,
relationships: angle,              Interpreting and posing                                               Geometric Sense                       multiplication and
length, perimeter,                      questions about the data                                          Measurement
patterns in sides and                                                                                 Geometry terms
division
angles, characteristics of
specific shapes
 5.24 Treasure Hunt
 Measurement                   See Unit 5 pages 14-15
Use protractor to measure degrees

 5.26 Growing Taller
 Geometric Sense
 Number Sense
Use yardstick to measure
Fractions
5.1.F   Solve single- and multi-                                                 A4 – Number and Operations:
step word problems                                                       Long Division
involving multi-digit
Revised 9/09 mellul CFSD                                                                     - 13 -
Grade 5 Pacing/Alignment, Investigations 2nd Edition                                                                DRAFT 9/09
division and verify the
solutions.
5.2.A Represent addition and      SMH 52-53                           A5 – Number and Operations:
subtraction of fractions                                        Adding and Subtracting
and mixed numbers           Online Activity Unit 4: Activity    Fractions
using visual and            61
numerical models, and
connect the
representation to the
related equation.
5.2.E Fluently and accurately     Online Activity Unit 4 Activity 7   A5 – Number and Operations:
add and subtract                                                Adding and Subtracting
fractions, including                                            Fractions
mixed numbers.                                                  A6 – Number and Operations:
Fraction Concepts
5.2.G Estimate sums and           Ten-Minute Math: Practicing         A6 – Number and Operations:
differences of fractions,   Place Value                         Fraction Concepts
mixed numbers, and          Online Activity Unit 6 Activity
decimals to                 33
approximate solutions
to problems and
determine
reasonableness of
answers.
5.2.H Solve single- and multi-                                        A5 – Number and Operations:
step word problems                                              Adding and Subtracting
involving addition and                                          Fractions
subtraction of whole                                            A6 – Number and Operations:
numbers, fractions                                              Fraction Concepts
(including mixed
numbers), and
decimals, and verify the
solutions.
5.3.A Classify quadrilaterals.    SMH 96-98                           C1 – Geometry: Triangles and   Observing students at work:
Quadrilaterals                        Classifying Polygons
Asmt Activity: Quadrilaterals
and Angles M17
End-of-Unit Asmt: Problem 1
Angles in a pentagon
M20
5.3.B Identify, sketch, and       SMH 99-101
measure acute, right,
and obtuse angles.          Online Activity Unit 5: Activity
14

Revised 9/09 mellul CFSD                                                          - 14 -
Grade 5 Pacing/Alignment, Investigations 2nd Edition                                                                   DRAFT 9/09
Grade 4, Unit 4: 95-96, 99-101,
103-104; SMH 112
5.3.C Identify, describe, and       SMH 95                                C1 – Geometry: Triangles and
classify triangles by                                              Quadrilaterals
angle measure and
number of congruent
sides.
5.3.D Determine the formula         Online Activity Unit 5: Activity      C1 – Geometry: Triangles and
for the area of a            20                                    Quadrilaterals
parallelogram by
relating it to the area of
a rectangle.
Curriculum Gap
5.3.E Determine the formula         Online Activity Unit 5: Activity      C1 – Geometry: Triangles and
for the area of a triangle   20                                    Quadrilaterals
by relating it to the area
of a parallelogram.
Curriculum Gap
5.3.F Determine the                 Online Activity Unit 5: Activity 18   C1 – Geometry: Triangles and   Observing students at work: A
perimeters and areas of                                            Quadrilaterals                        Sequence of Rectangles;
triangles and                Grade 4 Unit 4: 142-143                                                     Fencing a Garden;
parallelograms.                                                                                          LogoPaths tasks
Asmt Activity: Perimeter and
Area of Rectangles M19
5.3.G Draw quadrilaterals and       SMH 54-55, 79, 116-119                C1 – Geometry: Triangles and
triangles from given                                               Quadrilaterals
information about sides
and angles.
Limited practice?
5.3.H Determine the number          Online Activity Unit 5: Activity
and location of lines of     27
symmetry in triangles
and quadrilaterals.          Grade 4, Unit 4: 113-114; SMH
117

5.3.I Solve single- and multi-      SMH 102                               C1 – Geometry: Triangles and
step word problems                                                  Quadrilaterals
about the perimeters
and areas of
quadrilaterals and
triangles and verify the
solutions.
5.4.A Describe and create a         SMH 77-78
rule for numerical and

Revised 9/09 mellul CFSD                                                              - 15 -
Grade 5 Pacing/Alignment, Investigations 2nd Edition                                                   DRAFT 9/09
geometric patterns and
extend the patterns.
5.5.C   Construct and interpret
line graphs.
5.6.D   Determine whether a
problem to be solved is
similar to previously
solved problems, and
identify possible
strategies for solving
the problem.
5.6.E   Select and use one or
more appropriate
strategies to solve a
problem, and explain
the choice of strategy.
5.6.F   Represent a problem                                                              End-of-Unit Asmt: Problem 3
situation using words,                                                                  Similar rectangles? M22
numbers, pictures,
physical objects, or
symbols.
5.6.G   Explain why a specific                                                           Observing students at work:
problem-solving                                                                         LogoPaths Angle and
strategy or procedure                                                                   Turn Game
was used to determine a
solution.
5.6.H   Analyze and evaluate                           A3 – Number and Operations:
whether a solution is                          Estimating to Multiply and
reasonable, is                                 Divide
mathematically correct,
and answers the
question.
5.6.I   Summarize                                      E1 – Data Analysis: Probability
mathematical                                   and Technology
information, draw
conclusions, and
explain reasoning.

Revised 9/09 mellul CFSD                                            - 16 -
Grade 5 Pacing/Alignment, Investigations 2nd Edition                                                                                                         DRAFT 9/09
Unit 6: Decimals on Grids and Number Lines: Decimals, Fractions, and Percents 18 days
February
In this unit, students focus primarily on decimals and how the number system extends to numbers less than one. Students use their understanding of fractions and
percents and their relationship to decimals to solve computation problems involving decimals. Students use contexts (time and precipitation) and models (area and
number lines) to order and add decimals. This is the second of two rational number units in Grade 5.

Additional Investigations                                   Other Resources:                                 Assessments
Content/Topic                            Content:                                                                                        Formative/Summative
Flip Chart,                                                                                           Assessments
Mathematics Performance                  Student Math Handbook,
Bridges to Mathematics         WA Problem Solving
Content/standards-based: Observing
Expectations encountered in            www.pearsonsuccessnet.com                      Supplements               Notebook (Teacher to           students at work and paper-pencil
this unit                     Parent and student access via           www.mathlearningcenter.org          Teacher, 2006)            assessments: curriculum, Exam View,
SuccessNet
website                                                                                     Diagnostic/Fluency Asmts located in
CFSD classroom binder
   Focus on decimals and        In Unit 6, Ten-Minute Math                                                    5.9 Leap Frog
how the number system        activities focus on:                                                          Number Sense
extends to numbers less            Reading and writing                                                    Solves Problems
than one                                numbers up to 100,000                                        Fractions
   Use understanding of               Adding multiples of 10 to,                                       Careful reading
See Unit 6 pages 14-15
fractions and percents                  and subtracting multiples of
and their relationship to               10 from 4- and 5-digit                                             5.13 What is the
decimals                                numbers                                                             Chance
   Solve computation                  Reading and writing                                                  Probability & Statistics
problems involving                      decimal fractions and                                        Communicates Understanding
decimals                                decimal numbers
   Order and add decimals             Adding tenths or hundredths
in the context of time and              to, and subtracting them
precipitation; using the                from, decimal fractions and
models of area and                      decimal numbers
number lines
5.1.E Mentally divide two-           Ten-Minute Math: Estimation
digit numbers by one-          and Number Sense
digit divisors and
explain the strategies         Online Activity Unit 1 Activity 2
used.
5.1.F Solve single- and multi-                                                 A4 – Number and Operations:
step word problems                                                       Long Division
involving multi-digit
division and verify the
solutions.
5.2.B Represent addition and         SMH 63-65                                                                                               ? End-of-Unit Asmt:
subtraction of decimals                                                                                                                      Problem 1
using place value              Grade 4, Unit 6: 117-118, 121-                                                                                Order decimals M27
models and connect the         126, 130-131; SMH 70-71
representation to the
Revised 9/09 mellul CFSD                                                                   - 17 -
Grade 5 Pacing/Alignment, Investigations 2nd Edition                                                                    DRAFT 9/09
related equation.
Limited exposure?
5.2.F Fluently and accurately                                                                            End-of-Unit Asmt:
add and subtract                                                                                       Problem 2 Add decimals
decimals.                                                                                                M28
5.2.G Estimate sums and              Ten-Minute Math: Practicing       A6 – Number and Operations:       Observing students at work:
differences of fractions,     Place Value                       Fraction Concepts                        Decimals on Grids;
mixed numbers, and            Online Activity Unit 6 Activity                                            Representing Hundredths
decimals to                   33                                                                         and Thousandths;
Decimal In Between
approximate solutions                                                                                    Game; Smaller to Larger
to problems and
determine
reasonableness of
answers.
5.2.H Solve single- and multi-                                         A5 – Number and Operations:        Asmt Activity:
step word problems                                              Adding and Subtracting                 SE 23-25
involving addition and                                          Fractions                         Asmt Checklist: Decimal
subtraction of whole                                            A6 – Number and Operations:              Problems M18
Observing students at work:
numbers, fractions                                              Fraction Concepts                        Close to 1 game
(including mixed                                                                                   End-of-Unit Asmt:
numbers), and                                                                                          Problem 2 Add decimals
decimals, and verify the                                                                                 M28
solutions.
5.4.A Describe and create a          SMH 77-78
rule for numerical and
geometric patterns and
extend the patterns.
5.6.A Determine the question(s)                                        E1 – Data Analysis: Probability   End-of-Unit Asmt:
to be answered given a                                         and Technology                         Problem 2 Add decimals
problem situation.                                                                                      M28
5.6.E   Select and use one or more
appropriate strategies to
solve a problem, and
explain the choice of
strategy.
5.6.F   Represent a problem
situation using words,
numbers, pictures,
physical objects, or
symbols.
5.6.G   Explain why a specific                                                                           Observing students at work:
problem-solving strategy                                                                                Strategies for Adding
or procedure was used to                                                                                Decimals
determine a solution.

Revised 9/09 mellul CFSD                                                            - 18 -
Grade 5 Pacing/Alignment, Investigations 2nd Edition                                                                                                            DRAFT 9/09
Unit 7: How Many People? How Many Teams?: Multiplication and Division 20 days
March
In the second unit on multiplication and division, students find and study equivalent expressions for multiplication and division problems (e.g., 112 ÷ 8 = 28 ÷ 2).
Students practice solving larger multiplication problems (3 digit x 2 digit) accurately and efficiently and study the U.S. algorithm for multiplication. Students gain
fluency solving division problems with one-, two-, and three-digit divisors.
Additional Investigations                             Other Resources:                                        Assessments
Content/Topic                         Content:                                                                                         Formative/Summative
Flip Chart,                                                                                            Assessments
Mathematics Performance                Student Math Handbook,            Bridges to Mathematics               WA Problem Solving
Content/standards-based: Observing
Expectations encountered in          www.pearsonsuccessnet.com                 Supplements                  Notebook (Teacher to            students at work and paper-pencil
this unit             Parent and student access via website www.mathlearningcenter.org              Teacher, 2006)             assessments: curriculum, Exam View,
SuccessNet
Diagnostic/Fluency Asmts located in
CFSD classroom binder
    Second unit on               In Unit 7, Ten-Minute Math                                                   5.20 Follow the Clues
multiplication and           activities focus on:                                                         Algebraic Sense
division                           Identifying prime, square,                                      Mathematical equality and
    Find and study                          even, and odd numbers                                       inequality symbols
equivalent expressions             Determining if one number                                       1
See Unit 7 pages 14-15
for multiplication and                  is a factor or multiple of
division problems                       another                                                          5.27 On the Move
    Solve larger                       Estimating solutions to 2-                                           Geometric Sense
multiplication problems                 digit to 4-digit                                            Longitude, latitude
accurately; three-digit by              multiplication and division                                 Translations
two digit                               problems
    Use algorithm for                  Estimating solutions to
multiplication                          addition and subtraction
    Gain fluency solving                    problems with fractions and
division problems with                  mixed numbers
one-, two-, and three-             Breaking apart, reordering,
digit divisors                          or changing numbers
mentally to determine a
reasonable estimate
5.1.A Represent multi-digit
division using place
value models and
connect the
representation to the
related equation.
Limited exposure in Units 1, 7

5.1.B Determine quotients for         SMH 38-39                                A3 – Number and Operations:                                    Observing students at work:
multiples of 10 and 100                                                  Estimating to Multiply and                                            Dividing by Multiples of
by applying knowledge                                                    Divide                                                                10 SE 31
of place value and
properties of

Revised 9/09 mellul CFSD                                                                   - 19 -
Grade 5 Pacing/Alignment, Investigations 2nd Edition                                                                     DRAFT 9/09
operations.

5.1.C Fluently and accurately       Online Activity Unit 7 Activity     A4 – Number and Operations:       Observing students at work:
divide up to a four-digit    59                                  Long Division                            Division Practice SE 29
number by one- or two-                                                                             Asmt Activity: Solve M29
digit divisors using the
End-of-Unit Asmt:
standard long-division                                                                                  Problem 2 Divide 4-digit by
algorithm.                                                                                                2-digit M32
Curriculum Gap
5.1.D Estimate quotients to         Ten-Minute Math: Estimation         A3 – Number and Operations:       Observing students at work:
approximate solutions        and Number Sense                    Estimating to Multiply and               Estimation and Number
and determine                                                    Divide                                   Sense T75
reasonableness of                                                A4 – Number and Operations:
answers in problems                                              Long Division
involving up to two-
digit divisors.
5.1.E Mentally divide two-          Ten-Minute Math: Estimation
digit numbers by one-        and Number Sense
digit divisors and
explain the strategies       Online Activity Unit 1 Activity 2
used.
5.1.F Solve single- and multi-                                          A4 – Number and Operations:
step word problems                                               Long Division
involving multi-digit
division and verify the
solutions.
5.6.A Determine the                                                     E1 – Data Analysis: Probability   End-of-Unit Asmt:
question(s) to be                                                and Technology                         Problem 1 Digit card
answered given a                                                                                          problem M31
problem situation.
5.6.B Identify information                                                                                End-of-Unit Asmt:
that is given in a                                                                                      Problem 1 Digit card
problem and decide                                                                                        problem M31
whether it is essential or
extraneous to the
solution of the problem.
Curriculum Gap
5.6.C Determine whether
additional information
is needed to solve the
problem.
Curriculum Gap
5.6.D Determine whether a
problem to be solved is
Revised 9/09 mellul CFSD                                                             - 20 -
Grade 5 Pacing/Alignment, Investigations 2nd Edition                                                    DRAFT 9/09
similar to previously
solved problems, and
identify possible
strategies for solving
the problem.
5.6.E Select and use one or
more appropriate
strategies to solve a
problem, and explain
the choice of strategy.
5.6.F Represent a problem                                                                Observing students at work:
situation using words,                                                                    Equivalence in Division
numbers, pictures,                                                                        SE 11
physical objects, or
symbols.
5.6.G Explain why a specific                                                             Observing students at work:
problem-solving                                                                           Finding Many
strategy or procedure                                                                     Equivalents; Equivalence
was used to determine a                                                                   in Division
Asmt Checklist: Equivalence in
solution.                                                                                 Multiplication M15
5.6.I   Summarize                                      E1 – Data Analysis: Probability
mathematical                                   and Technology
information, draw
conclusions, and
explain reasoning.
5.6.J   Make and test                                  E1 – Data Analysis: Probability
conjectures based on                           and Technology
data (or information)
collected from
explorations and
experiments.

Revised 9/09 mellul CFSD                                            - 21 -
Grade 5 Pacing/Alignment, Investigations 2nd Edition                                                                                                            DRAFT 9/09
Unit 8: Growth Patterns: Patterns, Functions, and Change 13 days
April
Students investigate situations in which two quantities change in relation to each other. Students describe data about functional relationships, develop an overall sense
of change from a graph, and understand how the changes and totals are related. They also compare two linear functions with different rates of change..
Additional Investigations                            Other Resources:                                         Assessments
Content/Topic                           Content:                                                                                         Formative/Summative
Flip Chart,                                                                                            Assessments
Mathematics Performance                 Student Math Handbook,            Bridges to Mathematics            WA Problem Solving
Content/standards-based: Observing
Expectations encountered in           www.pearsonsuccessnet.com               Supplements                  Notebook (Teacher to              students at work and paper-pencil
this unit               Parent and student access via website www.mathlearningcenter.org            Teacher, 2006)               assessments: curriculum, Exam View,
SuccessNet
Diagnostic/Fluency Asmts located in
CFSD classroom binder
    Investigate situations in    In Unit 8, Ten-Minute Math                                                   5.12 Probably Plants
which two quantities         activities focus on:                                                         Probability & Statistics   April (first week) –
change in relation to each         Estimating solutions to 3- to                                         Solves Problems            Fluency Assessment:
other                                   5- digit addition and                                       Pre-algebra techniques
    Describe data                           subtraction problems
                                       Breaking apart, reordering,
FA 49, 50 -- All addition and
Develop overall sense of                                                                                 5.14 Post It
change from a graph                     or changing numbers                                              Number Sense                subtraction combinations
    Understand how the                      mentally to determine a                                          Algebraic Sense             through 10+10
changes and totals are                  reasonable estimate                                              Solves Problems             FA 45 and FA 48 --
related                            Reading and writing                                             Read and interpret data           Multiplication to 12x12 4.1.A
    Compare two linear                      numbers up to 100,000                                       Discover pattern                  FA 53 -- Division to 144 4.1.A
functions with different           Adding multiples of 10 to,
rates of change                         and subtracting multiples of                                         5.28 Building Global
10 from, 3- to 5-digit                                                Awareness
numbers                                                          Probability & Statistics
See Unit 8 pages 16-17
 Reading and writing                                             Create line graph using data
decimal fractions and
decimal numbers                                                  5.29 Lake Washington
 Adding tenths or hundredths                                          Algebraic Sense
to, and subtracting them                                    Double or Add Game
from, decimal fractions and                                 Guess My Rule
decimal numbers                                             Apply a pattern to develop
5.4.A Describe and create a           SMH 77-78                                                                                                Observing students at work: 4,
rule for numerical and                                                                                                                         5, and 6 Tiles Across
geometric patterns and
extend the patterns.
5.4.B Write a rule to describe        SMH 77
the relationship                                                                                                                        Asmt Activity: Comparing
between two sets of                                                                                                                            Animals’ Growth SE 15-
data that are linearly                                                                                                                         16, M17
related.
5.4.C Write algebraic                 Online Activity Unit 8: Activity          B1 – Algebra: Diagrams and                                     End-of-Unit Asmt: Problem 3
expressions that               43, 65                                    Equations                                                             Write an expression using
represent simple                                                                                                                               n M23
Revised 9/09 mellul CFSD                                                                    - 22 -
Grade 5 Pacing/Alignment, Investigations 2nd Edition                                                    DRAFT 9/09
situations and evaluate
the expressions, using
substitution when
variables are involved.
5.4.D Graph ordered pairs in     SMH 67-69                                               End-of-Unit Asmt: Problem 4
the coordinate plane for                                                                  Tom and Sophie M24
two sets of data related
by a linear rule and
draw the line they
determine.
5.5.C Construct and interpret                                                            Observing students at work: The
line graphs.                                                                              Krink, the Trifoot and the
Water Weasel
End-of-Unit Asmt: Problem 4
Tom and Sophie M24
5.6.D Determine whether a
problem to be solved is
similar to previously
solved problems, and
identify possible
strategies for solving
the problem.
5.6.E Select and use one or
more appropriate
strategies to solve a
problem, and explain
the choice of strategy.
5.6.F Represent a problem
situation using words,
numbers, pictures,
physical objects, or
symbols.
5.6.G Explain why a specific
problem-solving
strategy or procedure
was used to determine a
solution.
5.6.H Analyze and evaluate                             A3 – Number and Operations:
whether a solution is                            Estimating to Multiply and
reasonable, is                                   Divide
mathematically correct,
and answers the
question.
5.6.I Summarize                                        E1 – Data Analysis: Probability   End-of-Unit Asmt: Problem 5

Revised 9/09 mellul CFSD                                            - 23 -
Grade 5 Pacing/Alignment, Investigations 2nd Edition                                                    DRAFT 9/09
mathematical                                   and Technology                            Summarize Sophie/Tom
information, draw                                                                        graph M25
conclusions, and
explain reasoning.
5.6.J   Make and test                                  E1 – Data Analysis: Probability   End-of-Unit Asmt: Problem 2
conjectures based on                           and Technology                           Write a division story
data (or information)                                                                   problem M22
collected from
explorations and
experiments.

Revised 9/09 mellul CFSD                                            - 24 -
Grade 5 Pacing/Alignment, Investigations 2nd Edition                                                                                                              DRAFT 9/09
Unit 9: How Long Can You Stand on One Foot?: Data Analysis and Probability 16 days
May - June
Students describe major features of a set of data, represented in a line plot or bar graph, and quantify the description by using medians or fractional parts of the
data. Students draw conclusions about how two groups compare based on summarizing the data for each group. They conduct their own data experiment. Students
also look at the probability of various events. They express the probabilities of the possible outcomes (e.g., landing on the green part of the spinner, landing on the white
part of the spinner) by using numbers from 0 to 1. Then they conduct experiments to see what actually occurs. Students also consider the notion of fairness in the
context of probability by playing fair and unfair games, that is, games in which players do or do not have equal chances of winning.
Additional Investigations                              Other Resources:                                         Assessments
Content/Topic                           Content:                                                                                           Formative/Summative
Flip Chart,                                                                                              Assessments
Mathematics Performance                  Student Math Handbook,            Bridges to Mathematics              WA Problem Solving
Content/standards-based: Observing
Expectations encountered in            www.pearsonsuccessnet.com                Supplements                   Notebook (Teacher to              students at work and paper-pencil
this unit              Parent and student access via website www.mathlearningcenter.org               Teacher, 2006)              assessments: curriculum, Exam View,
SuccessNet
Diagnostic/Fluency Asmts located in
CFSD classroom binder
    Describe major features      In Unit 9, Ten-Minute Math                                                    5.23 Want to Win?
of a set of data,            activities focus on:                                                          Probability & Statistics    June (second week) –
represented in a line plot         Describing features of data                                      “Difference”                        Fluency Assessment:
or bar graph                       Interpreting and posing                                          Possible solutions
    Quantify description                    questions about data
 Estimating 2-, 3-, and 4-
FA 49, 50 -- All addition and
using medians or                                                                                          5.25 Soccer Game
fractional parts of the                 digit multiplication and                                          Probability & Statistics     subtraction combinations
data                                    division problems                                            Visual model of mean, median,      through 10+10
    Draw conclusions about             Breaking apart, reordering,                                      mode                               DA/FA 51.53 --Multiplication
how two groups compare                  or changing numbers                                                                                     and division to 12x12
    Summarize data for each                 mentally to determine a                                                                                 4.1.A
group                                   reasonable estimate
    Conduct own data
experiment                                                                                                                              See Unit 9 pages 14-15
    Probability of various
events
    Express probabilities of
possible outcomes, using
numbers from 0-1
    Consider notion of
fairness in context of
probability (Do players
have equal chances of
winning?)
5.1.E   Mentally divide two-          Ten-Minute Math: Estimation
digit numbers by one-         and Number Sense
digit divisors and
explain the strategies        Online Activity Unit 1 Activity 2
used.
5.1.F   Solve single- and multi-                                            A4 – Number and Operations:
step word problems                                                  Long Division
Revised 9/09 mellul CFSD                                                                - 25 -
Grade 5 Pacing/Alignment, Investigations 2nd Edition                                                   DRAFT 9/09
involving multi-digit
division and verify the
solutions.
5.5.C Construct and interpret                                                            End-of-Unit Asmt: Problem 1
line graphs.                                                                               Represent data M35-36
5.6.E Select and use one or                                                              Asmt Checklist: Students’
more appropriate                                                                           Experiment Projects
strategies to solve a                                                                      M22
problem, and explain
the choice of strategy.
5.6.F Represent a problem                                                                End-of-Unit Asmt: Problem 1
situation using words,                                                                    Represent data M35-36
numbers, pictures,
physical objects, or
symbols.
5.6.I Summarize                                        E1 – Data Analysis: Probability   End-of-Unit Asmt: Problem 1
mathematical                                     and Technology                           Represent data M35-36
information, draw
conclusions, and
explain reasoning.
5.6.J Make and test                                    E1 – Data Analysis: Probability   End-of-Unit Asmt: Problem 2
conjectures based on                             and Technology                           Spinner Game M37-38
data (or information)
collected from
explorations and
experiments.

Revised 9/09 mellul CFSD                                            - 26 -

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