Download Math - Palisades School District

MATH
LENGTH OF TIME:
One year
GRADE LEVEL:
4
COURSE STANDARDS:
Students will:
1. Use numbers, number systems, and equivalent forms (including numbers, words,
objects, and graphics) to represent theoretical and practical situations. (M1a-f, M2ak)
2. Compute, measure, and estimate to solve theoretical and practical problems using
appropriate tools which include modern technology such as calculators and
computers. (M1a-f, M2a-k, M6a-h)
3. Apply the concepts of patterns, functions, and relations to solve theoretical and
practical problems. (M3a-d, M6a-h)
4. Formulate and solve problems while being able to communicate the mathematical
processes used and the reasons for using them. (M5a-c, M6a-h, M7a-e)
5. Understand and apply the basic concepts of algebra, geometry, probability, and
statistics to solve theoretical and practical problems. (M2a-k, M3a-d)
6. Evaluate and draw references from charts, tables, and graphs showing the
relationships between data and real-world situations. (M4a-f, M5a-c, M6a-h)
7. Make decisions based upon the collection, organization, analysis, and interpretation of
statistical data and predictions of outcomes based upon the application of probability.
(M4a-f, M5a-c, M6a-h)
8. Conducts one large scale mathematical investigation and communicates the
mathematical processes used, the reasoning, and the results found. (M7a-e, M8a-e)
RELATED NEW STANDARDS
M1
Arithmetic and Number Concepts
 solves addition and subtraction facts with multi-digit numbers
 gives equivalent names for numbers
 reads and writes numbers to millions
 gives values of digits in numerals to millions
 identifies and uses square numbers
 identifies fractional parts of a region and collections of objects
 makes magnitude estimates for multiplication problems
 identify place value to trillions and thousandths
 have a successful strategy for adding multi-digit numbers
 have a successful strategy for subtracting multi-digit numbers
 explain the relationship between multiplication and division
 solve basic multiplication facts
 solve extended multiplication facts
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use and explain strategies for solving multiplication and division stories
have a successful strategy for solving multi-digit multiplication problems
identify fractional parts of regions
identify fractional parts of collections of objects
use a map scale to estimate distances
M2
Geometry and Measurement
 names, draw and labels line segments, lines and rays
 names and draws angles, triangles and quadrangles
 identifies and describes right angles and parallel lines
 uses personal references to estimate lengths in US customary units
 identified lines of symmetry
 draws the reflection of a figure using appropriate tools
 measures feet and inches
 describes properties of parallelograms
 uses two dimensional coordinate system to find locations on map or grid
 estimates and measures length, width, perimeter, and area
 calculates simple unit conversions (examples - between cm and m, hours and
minutes)
 uses scales on maps
M3
Function and Algebra
 finds missing numbers on a number line
 uses rate tables to solve problems
 uses linear equations (repeated patterns and functional relationships)
 recognizes that an equality remains the same, when the same change is made
to both quantities
 uses letters, boxes, or symbols to stand for any number in an equation
 recognizes simple non-linear patterns (example - growing patterns, squaring,
etc.)
M4
Statistics and Probability Concepts
 finds the median of a set of data
 collects and organizes data to create line plots, graphs, tables and charts
 finds statistical landmarks for a set of data
 uses appropriate vocabulary to describe the probability of chance events
 uses statistical landmarks maximum and minimum
 calculates the probability of a simple event
 determine the fairness of the design of a spinner
 determine the patterns generated as a result of an experiment
 list all possible combinations within a limited number of variables
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M5
Problem Solving and Mathematical Reasoning
 has a successful strategy for solving multi-digit multiplication problems
 has a successful strategy for solving multi-digit addition problems
 has a successful strategy for solving multi-digit subtraction problems
 explains the relationship between multiplication and division
 uses and explains strategies for solving multiplication and division stories
 uses tables to solve problems
 solves elapsed time problems
 uses appropriate mathematical terms, vocabulary, symbols and graphs to
clearly and logically explain solutions to problems
 solves problems that make demands on all three aspects of the solution
process - formulation, implementation, and conclusion
M6
Math Skills and Tools
 uses a map scale to estimate distances
 uses a calculator to rename any fraction as a decimal
 measure and draws angles with a protractor
 uses recall, mental computations, pencil and paper, measuring devices,
manipulatives, calculators, and computers to achieve solutions
M7
Math Communication
 uses and explain strategies for solving multiplication and division number
stories
 describes properties of a parallelogram
 uses appropriate mathematical vocabulary and language in written and oral
work
 shows mathematical work in a variety of ways (example - graph, chart, table)
 considers audience and purpose when communicating
M8
Putting Mathematics to Work
 conducts one large scale project, drawn from the following:
 data study
 science study
 design of a physical structure
 management and planning
 pure mathematics investigation
RELATED PENNSYLVANIA STATE STANDARDS
1. Number Sense, Properties, Operations
A. Decimals
B. Fractions
C. Estimation and Rounding
D. Multiples and Factors
E. Whole Number Operations
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2. Measurement
A. Area, Perimeter and Volume
B. Customary and Metric Conversion
C. Reasonable Measurement Units and Estimates
D. Solving Problems Involving Measurement Units
3. Geometry
A. Identification and Properties of Geometric Shapes
B. Lines and Angles
C. Visualizing Constructed and Changed Shapes
4. Data Analysis, Statistics and Probability
A. Interpreting Graphs
B. Interpreting Tables
C. Probability and Statistics
5. Algebra and Functions
A. Finding Unknown
B. Patterns
PERFORMANCE ASSESSMENTS:
Students will demonstrate achievement of the standards by:
1. Objective tests using pencil, paper, and calculator activities with/without rubrics.
(Course Standards 1-7)
2. Demonstration of the problem solving process with routine and non-routine problems.
(Course Standards 1-7)
3. Oral questioning and interviewing. (Course Standards 1-7)
4. Self and peer assessment. (Course Standards 1-7)
5. Teacher observation at completion of task or activity. (Course Standards 1-7)
6. Student portfolio to maintain student work. (Course Standards 1-7)
7. Math journal. (Course Standards 1-7)
8. Oral or written presentation to demonstrate a solution, concept, project, survey, etc.
with/without rubrics. (Course Standards 1-7)
9. Group and individual mathematical investigations. (Course Standards 8)
10. Free response questions with/without rubrics. (Course Standards 1-7)
11. Class and homework assignments. (Course Standards 1-7)
DESCRIPTION OF COURSE:
This course stresses the fundamentals, application, and appreciation of mathematics.
Students will solve problems using skills commensurate to those standards indicated
above and communicate effectively using mathematical language. Students will
demonstrate number sense, problem solving skills, reasoning abilities, and technological
skills throughout the course.
Instruction will include, but not be limited to: Numeration through the million’s period;
addition of 2, 3, or more addends into the thousand’s period with regrouping to include
money; subtraction into the thousand’s period with regrouping to include money;
multiplication and division facts through the nine’s table; multiplication of three-digit
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factors by two-digit factors with regrouping; division with two-digit divisors and threedigit dividends; adding and subtracting decimals to the hundredth’s place value; renaming
fractions to lowest terms; addition and subtraction of fractions with unlike denominators;
tell time to the nearest minute; metric and standard measurements in length, capacity, and
weight; find perimeter, area, and volume of geometric figures; with problem solving
skills, estimation abilities, and technology integrated throughout the course.
TITLES OF UNITS:
1. Place Value
2 weeks
2. Whole Number Sense and Operations
18 weeks
3. Measurement
4 weeks
4. Decimals
3 weeks
5. Geometry
4 weeks
6. Fractions
5 weeks
Technology, estimation, and problem solving (including algebra, graphs, charts, patterns,
and interpretation of data) are integrated throughout the year.
SAMPLE INSTRUCTIONAL STRATEGIES:
1. Teacher/student made activities
2. Teacher/student led discussions and activities
3. Problem solving strategies
4. Calculators and computers
5. Individual and group explorations and investigations
6. Games and manipulatives
7. Written explanations and journal activities
8. Teacher/peer modeling
9. Math Word Wall
MATERIALS:
1. Everyday Mathematics: The University of Chicago School Mathematics Project,
Everyday Learning Corporation, 1999, Chicago, Illinois.
2. Calculators
3. Computers
4. Enrichment materials
5. Computer software
6. Standard related games and manipulatives
7. Base 10 blocks
METHODS OF ASSISTANCE AND ENRICHMENT:
A.
Assistance
1. IST
2. Cooperative groups
3. ADAPT
4. Peer helpers
5. Volunteer tutors
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6. Flexible/modified grouping
7. Re-teaching with alternative strategies
8. Extended instructional time
B.
1.
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7.
Enrichment
Modified curriculum
Peer tutoring
Modified testing
Math journal and/or projects
Individual mathematical investigations
IST
PAL
PORTFOLIO DEVELOPMENT:
1. Teacher/student assessments
2. Math journals
3. Individual/group investigations, projects, and/or activities
4. Written explanation of problem solving strategies
5. Student reflections
6. End of the year assessment task (measure all skills)
7. District developed four problem solving tasks (measure all focused problem solving
strategies)
METHODS OF EVALUATION:
1. Teacher/student checklists
2. Individual/group tests
3. Investigations, projects, and/or journals
4. Problem solving activities
5. Written and oral presentations
6. End of the year assessment task
7. District developed four problem solving tasks
INTEGRATED ACTIVITIES:
1.
Concepts
-demonstrate knowledge of the basic concepts and principles for the above
mentioned standards
2.
Communication
-compose and make oral presentations using appropriate mathematical language
-written entries in math journal using appropriate mathematical terms and
vocabulary
-explains solutions and strategies clearly and logically with supporting evidence
-listen to, and understand, oral math presentations
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3.
Thinking/Problem Solving
-apply the concepts of the above mentioned standards to formulate and solve
problems
-make critical judgments using the learned skills
-draw conclusions and show relationships in mathematical settings
-make decisions and predictions based upon the application of learned skills
4.
Application of Knowledge
-use learned skills to solve authentic problems
-exhibit skills with calculators and computers
-examine, evaluate, and solve routine and non-routine problems
5.
Interpersonal Skills
-work cooperatively with others on projects and investigations
-work effectively with others on projects and investigations
-communicate effectively using appropriate mathematical language
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