Investigations

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 -