ROSE TREE MEDIA SCHOOL DISTRICT
COURSE CURRICULUM
COURSE TITLE: MATH
GRADE LEVEL: GRADE 5
CREATION DATE: November 2003
Essential Question, Concept or Theme: A. Demonstrate knowledge of number systems and number
relationships and use this knowledge to make comparisons.
PA Standards: 2.1.5.A,B,C,D,E,F,G; 2.11.5.A,B,C,D,E,F
Aligned Materials/
Benchmark/Skills
Assessment
Resources/Technology
A. Number Systems/Number Relationships and
Comparisons:
1. Use expanded notation to represent whole
numbers.
2. Apply number theories to rename a number
quantity (eg., six, 6, 3 X 2)
3. Demonstrate that mathematical operations can
represent a variety of problem situations.
4. Use models to represent fractions and decimals.
5. Explain the concepts of prime and composite
numbers.
6. Use simple concepts of negative numbers (eg, on
a number line, temperature).
7. Develop and apply number theory concepts (e.g.
primes, factors, multiples, composites) to
represent numbers in various ways.
8. Make comparisons of numbers (e.g., more, less,
same, least, most, greater than, less than).
9. Identify least and greatest values represented in
graphs and charts.
10. Identify maximum and minimum.
11. Describe the relationship between rates of change
and time.
12. Estimate areas and volumes as sums of areas of
tiles and volumes of cubes.
13. Describe the relationship between the size of the
unit of measurement and the estimate of areas and
volumes.
Math – Grade 5
These May Be Used in Each
Unit:
Computer Software
Investigations Units (Listed
by Appropriate Topic)
SFAW:
Text
Lessons
Performance
Assessments
Problem of the Day
Chapter and
Cumulative Tests
"Daily Math" problems
Observations
Class participation
Math Journal
Group Work
Rubrics
A. Investigations Units:
Mathematical Thinking at
Grade 5 (Introduction to
number theory)
Name the Portion (Fractions,
Decimals and Percents)
Building on Numbers you
Know (Comparisons and
Estimation Strategies)
Page 1
TEXT: Scott ForesmanAddison Wesley Math Grade Five; Scott
Foresman-Addison
Wesley, ©1998.
TEXT: Investigations in
Numbers, Data, and
Space; Dale Seymour
Publications, © 1998.
Approx. Time Allotment:
Instructional Strategies
These strategies and activities
apply to all units:
Activate Prior Knowledge
Problem of the Day
Math Routines
Mental Math
Journals
Vocabulary Development
Written explanation of
strategies
Optional Resources:
Teacher-generated
worksheets and activities
Internet
Literature
Audio Tapes
Calculators
Manipulatives
Calendar Kit
CD ROMs
Daily Transparencies
B. Games
C. Home-School
Connections
E Newspapers,
encyclopedias, magazines,
almanacs
-1-
November 2003
Essential Question, Concept or Theme: A. Demonstrate knowledge of number systems and number
relationships and use this knowledge to make comparisons.
PA Standards: 2.1.5.A,B,C,D,E,F,G; 2.11.5.A,B,C,D,E,F
Adaptations/Inclusion Techniques
SFAW Additional Practice
SFAW Options for Reaching All Learners:
Inclusion and Language Development
Peer Tutors
Computation Aides - manipulatives, number
lines, etc.
Math – Grade 5
Enrichment Strategies
Remediation Strategies
Approx. Time Allotment:
Multicultural/Interdisciplinary
Connection
SFAW Extended
Investigations
SFAW Enrichment
Worksheets
SFAW Problem Solving
Worksheets
Software Programs
Page 2
-2-
November 2003
Essential Question, Concept or Theme: B. Demonstrate a mastery of arithmetic and number concepts and
apply this to estimation strategies
PA Standards: 2.2.5.A,B,C,D,E,F,G,H,I; 2.8.5.A,B,C,D,E,F,G,H,I
Aligned Materials/
Benchmark/Skills
Assessment
Resources/Technology
B. Arithmetic and Number Concepts:
1. Create and solve word problems
involving addition, subtraction,
multiplication and division of
whole numbers.
2. Develop and apply algorithms to
solve word problems that involve
addition, subtraction, and/or
multiplication with decimals with
and without regrouping.
3. Develop and apply algorithms to
solve word problems that involve
addition, subtraction, and/or
multiplication with fractions and
mixed numbers that include like
and unlike denominators.
4. Demonstrate an ability to round
numbers, fractions and decimals.
5. Estimate the reasonableness of
answers for problems involving
addition, subtraction, multiplication
and division of whole numbers.
6. Apply estimation strategies to a
variety of problems.
7. Select a method for computation
and explain why it is appropriate.
Math – Grade 5
These May Be Used in Each
Unit:
Computer Software
Investigations Units (Listed by
Appropriate Topic)
SFAW:
Text
Lessons
Performance
Assessments
Problem of the Day
Chapter and
Cumulative Tests
"Daily Math" problems
Observations
Class participation
Math Journal
Group Work
Rubrics
TEXT: Scott Foresman-Addison
Wesley Math – Grade Five; Scott
Foresman-Addison Wesley,
©1998.
TEXT: Investigations in Numbers,
Data, and Space; Dale Seymour
Publications, © 1998.
B. Investigations Units:
Building on Numbers you
Know (Numerical Strategies,
understanding of operations)
Things That Come in Groups
(Multiplication and Division)
Combining and Comparing
(Addition and Subtraction)
Hands-on Equations Program
B. Games
Page 3
Optional Resources:
Teacher-generated worksheets and
activities
Internet
Literature
Audio Tapes
Calculators
Manipulatives
Calendar Kit
CD ROMs
Daily Transparencies
Approx. Time Allotment:
Instructional Strategies
These strategies and activities
apply to all units:
Activate Prior Knowledge
Problem of the Day
Math Routines
Mental Math
Journals
Vocabulary Development
Written explanation of strategies
C. Home-School Connections
E Newspapers, encyclopedias,
magazines, almanacs
-3-
November 2003
Essential Question, Concept or Theme: B. Demonstrate a mastery of arithmetic and number concepts and
apply this to estimation strategies
PA Standards: 2.2.5.A,B,C,D,E,F,G,H,I; 2.8.5.A,B,C,D,E,F,G,H,I
Adaptations/Inclusion Techniques
SFAW Additional Practice
SFAW Options for Reaching All Learners: Inclusion
and Language Development
Peer Tutors
Computation Aides - manipulatives, number lines,
etc.
Math – Grade 5
Enrichment Strategies
Remediation Strategies
Approx. Time Allotment:
Multicultural/Interdisciplinary
Connection
SFAW Extended
Investigations
SFAW Enrichment
Worksheets
SFAW Problem Solving
Worksheets
Software Programs
Page 4
-4-
November 2003
Essential Question, Concept or Theme: C. Demonstrate knowledge of measurement and time concepts
PA Standards: 2.3.5.A,B,C,D,E
Aligned Materials/
Benchmark/Skills
Assessment
Resources/Technology
Approx. Time Allotment:
C. Measurement and Time Concepts:
These strategies and activities
apply to all units:
1. Select and use appropriate
instruments and units for
measuring quantities (e.g.,
perimeter, volume, area, weight,
time, temperature).
2. Select and use standard tools to
measure the size of figures with
specified accuracy, including
length, width, perimeter and area.
3. Estimate, refine and verify
specified measurements of objects.
4. Convert linear measurements
within the same system (traditional
and metric.)
5. Add and subtract measurements.
These May Be Used in Each
Unit:
Computer Software
Investigations Units (Listed by
Appropriate Topic)
SFAW:
Text
Lessons
Performance
Assessments
Problem of the Day
Chapter and Cumulative
Tests
"Daily Math" problems
Observations
Class participation
Math Journal
Group Work
Rubrics
TEXT: Scott Foresman-Addison
Wesley Math – Grade Five; Scott
Foresman-Addison Wesley,
©1998.
TEXT: Investigations in Numbers,
Data, and Space; Dale Seymour
Publications, © 1998.
C. Investigations Unit:
Measurement Benchmarks at
Grade 5 (Measurement)
B. Games
Optional Resources:
Teacher-generated worksheets and
activities
Internet
Literature
Audio Tapes
Calculators
Manipulatives
Calendar Kit
CD ROMs
Daily Transparencies
Instructional Strategies
Activate Prior Knowledge
Problem of the Day
Math Routines
Mental Math
Journals
Vocabulary Development
Written explanation of strategies
C. Home-School Connections
E Newspapers, encyclopedias,
magazines, almanacs
Math – Grade 5
Page 5
-5-
November 2003
Essential Question, Concept or Theme: C. Demonstrate knowledge of measurement and time concepts
PA Standards: 2.3.5.A,B,C,D,E
Adaptations/Inclusion Techniques
SFAW Additional Practice
SFAW Options for Reaching All Learners:
Inclusion and Language Development
Peer Tutors
Computation Aides - manipulatives, number
lines, etc.
Math – Grade 5
Enrichment Strategies
Remediation Strategies
Approx. Time Allotment:
Multicultural/Interdisciplinary
Connection
SFAW Extended
Investigations
SFAW Enrichment
Worksheets
SFAW Problem Solving
Worksheets
Software Programs
Page 6
-6-
November 2003
Essential Question, Concept or Theme: D. Students will apply mathematical reasoning to make connections,
and to solve problems involving everyday situations
PA Standards: 2.4.5.A,B,C,D,E,F; 2.5.5.A,B,C,D,E,F
Aligned Materials/
Benchmark/Skills
Assessment
Resources/Technology
D. Mathematical Reasoning and
Problem-Solving:
1. Compare quantities and
magnitudes of numbers.
2. Use models, number facts,
properties and relationships to
check and verify predictions and
explain reasoning.
3. Draw inductive and deductive
conclusions within mathematical
contexts.
4. Distinguish between relevant and
irrelevant information in a
mathematical problem.
5. Interpret statements made with
precise language of logic (e.g.,
"all", "or", "every", "none",
"some", "or", "many).
6. Develop a plan to analyze a
problem, identify the information
needed to solve the problem,
carry out the plan, check whether
an answer makes sense and
explain how the problem was
solved in writing.
7. Use appropriate mathematical
terms, vocabulary, language
symbols and graphs to explain
clearly and logically solutions to
Math – Grade 5
These May Be Used in Each
Unit:
Computer Software
Investigations Units (Listed by
Appropriate Topic)
SFAW:
Text
Lessons
Performance
Assessments
Problem of the Day
Chapter and Cumulative
Tests
"Daily Math" problems
Observations
Class participation
Math Journal
Group Work
Rubrics
TEXT: Scott Foresman-Addison
Wesley Math - Grade Five; Scott
Foresman-Addison Wesley,
©1998.
TEXT: Investigations in Numbers,
Data, and Space; Dale Seymour
Publications, © 1998.
D. Investigations Units
B. Games
Optional Resources:
Teacher-generated worksheets and
activities
Internet
Literature
Audio Tapes
Calculators
Manipulatives
Calendar Kit
CD ROMs
Daily Transparencies
Approx. Time Allotment:
Instructional Strategies
These strategies and activities
apply to all units:
Activate Prior Knowledge
Problem of the Day
Math Routines
Mental Math
Journals
Vocabulary Development
Written explanation of strategies
C. Home-School Connections
E Newspapers, encyclopedias,
magazines, almanacs
Page 7
-7-
November 2003
Essential Question, Concept or Theme: D. Students will apply mathematical reasoning to make connections,
and to solve problems involving everyday situations
PA Standards: 2.4.5.A,B,C,D,E,F; 2.5.5.A,B,C,D,E,F
Aligned Materials/
Benchmark/Skills
Assessment
Resources/Technology
problems.
8. Show ideas in a variety of ways,
including words, numbers,
symbols, pictures, charts, graphs,
tables, diagrams and models.
9. Connect, extend and generalize
problem solutions to other
concepts, problems and
circumstances in mathematics.
10. Select, use and justify the
methods, materials and strategies
used to solve problems.
11. Use appropriate problem-solving
strategies (e.g., solving a simpler
problem, drawing a picture or
diagram).
Math – Grade 5
Page 8
Approx. Time Allotment:
Instructional Strategies
-8-
November 2003
Essential Question, Concept or Theme: D. Students will apply mathematical reasoning to make connections,
and to solve problems involving everyday situations
PA Standards: 2.4.5.A,B,C,D,E,F; 2.5.5.A,B,C,D,E,F
Adaptations/Inclusion Techniques
SFAW Additional Practice
SFAW Options for Reaching All Learners:
Inclusion and Language Development
Peer Tutors
Computation Aides - manipulatives, number
lines, etc.
Math – Grade 5
Enrichment Strategies
Remediation Strategies
Approx. Time Allotment:
Multicultural/Interdisciplinary
Connection
SFAW Extended
Investigations
SFAW Enrichment
Worksheets
SFAW Problem Solving
Worksheets
Software Programs
Page 9
-9-
November 2003
Essential Question, Concept or Theme: E. Students will collect and analyze data to make pictorial
representations of information and make interpretations based upon these representations.
PA Standards: 2.6.5.A,B,C,D,E
Aligned Materials/
Benchmark/Skills
Assessment
Resources/Technology
E. Collecting and Analyzing Data
and Statistcs:
1. Organize and display data using
pictures, tallies, tables, charts, bar
graphs, line graphs, and
pictographs.
2. Describe data sets using the terms
mean, median, mode and range.
3. Sort data using graphic
representations including Venn
diagrams.
4. Predict the likely number of times
a condition will occur based on
analyzed data.
5. Construct and defend simple
conclusions based on data.
These May Be Used in Each
Unit:
Computer Software
Investigations Units (Listed by
Appropriate Topic)
SFAW:
Text
Lessons
Performance
Assessments
Problem of the Day
Chapter and Cumulative
Tests
"Daily Math" problems
Observations
Class participation
Math Journal
Group Work
Rubrics
TEXT: Scott Foresman-Addison
Wesley Math - Grade Five; Scott
Foresman-Addison Wesley,
©1998.
TEXT: Investigations in Numbers,
Data, and Space; Dale Seymour
Publications, © 1998.
E. Investigations Units:
Data Kids and Cats (Statistics
and Analysis)
B. Games
Optional Resources:
Teacher-generated worksheets and
activities
Internet
Literature
Audio Tapes
Calculators
Manipulatives
Calendar Kit
CD ROMs
Daily Transparencies
Approx. Time Allotment:
Instructional Strategies
These strategies and activities
apply to all units:
Activate Prior Knowledge
Problem of the Day
Math Routines
Mental Math
Journals
Vocabulary Development
Written explanation of strategies
C. Home-School Connections
E Newspapers, encyclopedias,
magazines, almanacs
Math – Grade 5
Page 10
- 10 -
November 2003
Essential Question, Concept or Theme: E. Students will collect and analyze data to make pictorial
representations of information and make interpretations based upon these representations.
PA Standards: 2.6.5.A,B,C,D,E
Adaptations/Inclusion Techniques
SFAW Additional Practice
SFAW Options for Reaching All Learners:
Inclusion and Language Development
Peer Tutors
Computation Aides - manipulatives, number
lines, etc.
Math – Grade 5
Enrichment Strategies
Remediation Strategies
Approx. Time Allotment:
Multicultural/Interdisciplinary
Connection
SFAW Extended
Investigations
SFAW Enrichment
Worksheets
SFAW Problem Solving
Worksheets
Software Programs
Page 11
- 11 -
November 2003
Essential Question, Concept or Theme: F. Students will develop an understanding of probability concepts.
PA Standards: 2.7.5.A,B,C,D,E,F,G,H,I,J
Aligned Materials/
Benchmark/Skills
Assessment
Resources/Technology
Approx. Time Allotment:
Probability Concepts:
These strategies and activities
apply to all units:
1. Perform simulations with
concrete devices (e.g. number
cubes, spinners) to predict the
chance of an event occuring.
2. Determine the fairness of a
spinner.
3. Express probabilities as fractions
and decimals.
4. Compare predictions based on
theoretical probability and
experimental results.
5. Calculate the probability of a
simple event.
6. Determine patterns generated as a
result of an experiment.
7. Determine the probability of an
event involving "and", "or" "not".
8. Predict and determine why some
outcomes are certain, more likely,
less likely, equally likely or
impossible.
9. Find all possible combinations
and arrangements involving a
limited number of variables.
Math – Grade 5
These May Be Used in Each
Unit:
Computer Software
Investigations Units (Listed by
Appropriate Topic)
SFAW:
Text
Lessons
Performance
Assessments
Problem of the Day
Chapter and Cumulative
Tests
"Daily Math" problems
Observations
Class participation
Math Journal
Group Work
Rubrics
TEXT: Scott Foresman-Addison
Wesley Math - Grade Five; Scott
Foresman-Addison Wesley,
©1998.
TEXT: Investigations in Numbers,
Data, and Space; Dale Seymour
Publications, © 1998.
F. Investigations Units:
Between Never and Always
(Probability)
B. Games
Optional Resources:
Teacher-generated worksheets and
activities
Internet
Literature
Audio Tapes
Calculators
Manipulatives
Calendar Kit
CD ROMs
Daily Transparencies
Instructional Strategies
Activate Prior Knowledge
Problem of the Day
Math Routines
Mental Math
Journals
Vocabulary Development
Written explanation of strategies
C. Home-School Connections
E Newspapers, encyclopedias,
magazines, almanacs
Page 12
- 12 -
November 2003
Essential Question, Concept or Theme: F. Students will develop an understanding of probability concepts.
PA Standards: 2.7.5.A,B,C,D,E,F,G,H,I,J
Adaptations/Inclusion Techniques
SFAW Additional Practice
SFAW Options for Reaching All Learners:
Inclusion and Language Development
Peer Tutors
Computation Aides - manipulatives, number
lines, etc.
Math – Grade 5
Enrichment Strategies
Remediation Strategies
Approx. Time Allotment:
Multicultural/Interdisciplinary
Connection
SFAW Extended
Investigations
SFAW Enrichment
Worksheets
SFAW Problem Solving
Worksheets
Software Programs
Page 13
- 13 -
November 2003
Essential Question, Concept or Theme: G. Students will demonstrate an understanding of algebraic and
pattern thinking.
Approx. Time Allotment:
PA Standards: 2.8.5.A,B,C,D,E,F,G,H,I
Benchmark/Skills
Aligned Materials/
Resources/Technology
Assessment
G. Algebra and Patterns:
1.
2.
3.
4.
5.
6.
7.
8.
These May Be Used in Each
Unit:
Recognize, reproduce, extend,
Computer Software
create and describe patterns,
Investigations Units (Listed by
sequences and relationships
Appropriate Topic)
verbally, numerically,
SFAW:
symbolically and graphically,
Text
using a variety of materials.
Lessons
Connect patterns to geometric
Performance
relations and basic number skills. Assessments
Form rules based on patterns.
Problem of the Day
Use concrete objects and
Chapter and Cumulative
combinations of symbols to create Tests
expressions that model
"Daily Math" problems
mathematical situations.
Observations
Explain the use of combinations
Class participation
of symbols and numbers in
Math Journal
expressions, equations and
Group Work
inequalities.
Rubrics
Describe a realistic situation using
information given in equations,
G. Investigations Units:
inequalities, tables or graphs.
Picturing Polygons (coordinate
Select and use appropriate
grids)
strategies, including concrete
Mathematical Thinking at Grade
materials, to solve number
5 (Algebraic thinking)
sentences and explain the method Building on Numbers You Know
of solution.
(Patterns)
Locate and identify points on a
coordinate grid system.
Math – Grade 5
Page 14
TEXT: Scott Foresman-Addison
Wesley Math - Grade Five; Scott
Foresman-Addison Wesley,
©1998.
TEXT: Investigations in Numbers,
Data, and Space; Dale Seymour
Publications, © 1998.
Optional Resources:
Teacher-generated worksheets and
activities
Internet
Literature
Audio Tapes
Calculators
Manipulatives
Calendar Kit
CD ROMs
Daily Transparencies
Instructional Strategies
These strategies and activities
apply to all units:
Activate Prior Knowledge
Problem of the Day
Math Routines
Mental Math
Journals
Vocabulary Development
Written explanation of strategies
B. Games
C. Home-School Connections
E Newspapers, encyclopedias,
magazines, almanacs
- 14 -
November 2003
Essential Question, Concept or Theme: G. Students will demonstrate an understanding of algebraic and
pattern thinking.
PA Standards: 2.8.5.A,B,C,D,E,F,G,H,I
Adaptations/Inclusion Techniques
SFAW Additional Practice
SFAW Options for Reaching All Learners:
Inclusion and Language Development
Peer Tutors
Computation Aides - manipulatives, number
lines, etc.
Math – Grade 5
Enrichment Strategies
Remediation Strategies
Approx. Time Allotment:
Multicultural/Interdisciplinary
Connection
SFAW Extended
Investigations
SFAW Enrichment
Worksheets
SFAW Problem Solving
Worksheets
Software Programs
Page 15
- 15 -
November 2003
Essential Question, Concept or Theme: H. Students will further develop their knowledge of geometry
concepts to include two and three dimensional types.
PA Standards: 2.9.5.A,B,C,D,E,F,G,H,I,J,K,L; 2.10.5.A,B
Aligned Materials/
Benchmark/Skills
Assessment
Resources/Technology
H. Geometry Concepts:
1. Give formal definitions of
geometric figures.
2. Classify and compare triangles
and quadrilaterals according to
sides and/or angles.
3. Identify and measure circles, their
diameters and radii.
4. Describe in words how geometric
shapes are constructed.
5. Construct two- and threedimensional shapes and figures
using manipulatives, geoboards
and computer software
6. Find familiar solids in the
environment and describe them.
7. Describe the relationship between
the perimeter and area of
triangles, quadrilaterals and
circles.
8. Represent and use the concepts of
line, point and plane.
9. Define the basic properties of
squares, pyramids,
parallelograms, quadrilaterals,
trapezoids, polygons, rectangles,
rhombi, circles, triangles, cubes,
prisms, spheres and cylinders.
10. Analyze simple transformations
Math – Grade 5
These May Be Used in Each
Unit:
Computer Software
Investigations Units (Listed by
Appropriate Topic)
SFAW:
Text
Lessons
Performance
Assessments
Problem of the Day
Chapter and Cumulative
Tests
"Daily Math" problems
Observations
Class participation
Math Journal
Group Work
Rubrics
TEXT: Scott Foresman-Addison
Wesley Math - Grade Five; Scott
Foresman-Addison Wesley,
©1998.
TEXT: Investigations in Numbers,
Data, and Space; Dale Seymour
Publications, © 1998.
H. Investigations Units:
Picturing Polygons (2-D
Geometry)
Containers and Cubes (3-D
Geometry)
B. Games
Optional Resources:
Teacher-generated worksheets and
activities
Internet
Literature
Audio Tapes
Calculators
Manipulatives
Calendar Kit
CD ROMs
Daily Transparencies
Approx. Time Allotment:
Instructional Strategies
These strategies and activities
apply to all units:
Activate Prior Knowledge
Problem of the Day
Math Routines
Mental Math
Journals
Vocabulary Development
Written explanation of strategies
C. Home-School Connections
E Newspapers, encyclopedias,
magazines, almanacs
Page 16
- 16 -
November 2003
Essential Question, Concept or Theme: H. Students will further develop their knowledge of geometry
concepts to include two and three dimensional types.
PA Standards: 2.9.5.A,B,C,D,E,F,G,H,I,J,K,L; 2.10.5.A,B
Aligned Materials/
Benchmark/Skills
Assessment
Resources/Technology
of geometric figures and rotations
of line segments.
11. Identify properties of geometric
figures (e.g., parallel,
perpendicular, similar, congruent,
symmetrical.)
12. Identify and compare parts of
right triangles, including right
angles, acute angles, hypotenuse
and legs.
13. Create right triangles on
geoboards.
Math – Grade 5
Page 17
Approx. Time Allotment:
Instructional Strategies
- 17 -
November 2003
Essential Question, Concept or Theme: H. Students will further develop their knowledge of geometry
concepts to include two and three dimensional types.
PA Standards: 2.9.5.A,B,C,D,E,F,G,H,I,J,K,L; 2.10.5.A,B
Adaptations/Inclusion Techniques
SFAW Additional Practice
SFAW Options for Reaching All Learners:
Inclusion and Language Development
Peer Tutors
Computation Aides - manipulatives, number
lines, etc.
Math – Grade 5
Enrichment Strategies
Remediation Strategies
Approx. Time Allotment:
Multicultural/Interdisciplinary
Connection
SFAW Extended
Investigations
SFAW Enrichment
Worksheets
SFAW Problem Solving
Worksheets
Software Programs
Page 18
- 18 -
November 2003
Math – Grade 5
Page 19
- 19 -
November 2003