Download MATH - Palisades School District

MATH
LENGTH OF TIME:
1 year
GRADE LEVEL:
5
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
 use an array model for multiplication
 solve basic number facts
 identify the factors of a number
 find equivalent names for numbers
 solve addition and subtraction problems with multi-digit numbers for whole
numbers and decimals
 solves extended multiplication and division facts
 identify place value to trillions and thousandths
 use the term numerator and denominator
 identify fractional parts of a set or region
 find equivalent fractions including simplifying
 compare fractions
 use fractions to represent ratios
MATH5\H:
06/28/17






















convert between mixed numbers and fractions
solve addition and subtraction problems for fractions with like and unlike
denominators, as well as mixed numbers
rename easy fractions as decimals and percents
give equivalencies between fractions, decimals and percents
determine prime, composite, odd and even numbers
explain the relationship between multiplication and division
have a successful strategy for adding and subtracting whole multi-digit
numbers
have a successful strategy for multiplying whole multi-digit numbers
use parentheses in number sentences to specify the order of operations
determine whether number sentences containing parentheses are true or false
use negative numbers to represent appropriate situations
have a successful strategy for dividing whole numbers
use exponential notation for square numbers
use exponential notation; convert between exponential, expended and standard
notation
compare and order signed numbers
have a successful strategy for adding and subtracting fractions with like and
unlike denominators
rename fractions in simplest form
have a successful strategy for adding and subtracting mixed numbers
have a successful strategy for adding and subtracting decimals
shade a hundred grid to represent a fraction or a decimal
use a calculator to rename any fraction as a decimal or percent
describe a percent of a region
M2
Geometry and Measurement Concepts
 understand perimeter
 define radius and diameter
 identify and describe parallel lines
 measure and draw angles with a protractor
 identify acute, obtuse, straight, reflect and right angles
 sort polygons according to their properties
 measure lengths in US customary and metric units
 construct and interpret bar graphs
 explain area and use appropriate units when measuring
 use formulas to find the areas of rectangles, parallelograms, triangles and base
of prisms
 identifies and compares properties of geometric solids
M3
Function and Algebraic Concepts
 use an array model for multiplication
MATH5\H:
06/28/17









use parentheses in number sentences to specify the order of operations
determine whether number sentences containing parentheses are true or false
use negative numbers to represent appropriate situations
understand variables in formulas
compare and order signed numbers
add signed numbers
write algebraic expressions to represent situations described in words
use exponential notation for square numbers
convert between exponential, expanded and standard numbers
M4
Statistics and Probability Concepts
 collect, organize and display data using charts, graphs, tables and line plots
 interpret and compare data to draw conclusions and answer questions
 analyze data and make predictions based upon the data
M5
Problem Solving and Mathematical Reasoning
 use strategies for adding and subtracting whole numbers, fractions, decimals
 use and explain strategies to solve number stories
 use strategies for multiplying and dividing whole numbers and multiplying
fractions
 use formulas to solve problems are area, perimeter and volume
 patterns with number or geometric sequences
 rate relationships and tables
 solves problems that make demands on all three aspects of the solution
process - formulation, implementation, and conclusion
M6
Mathematical Skills and Tools
 use a compass and straightedge to construct geometric figures
 use a scale on a map
 use personal references to estimate length and capacity in metric and US
customary units
 use a protractor and a half-circle protractor to measure and draw angles
 use a calculator to rename any fraction as a decimal or percent
 use tables of data to solve problems
 use correct tools to measure length
 create an array model for multiplication
 construct and interpret bar graphs
 use a percent circle to construct and interpret circle graphs
 use a stem and leaf plot to organize and display data
 demonstrate three ways to represent a rate: table, graph and rule
M7
Mathematical Communication
 read, write and solve addition, subtraction, multiplication and division facts
 give equivalent names for fractions
MATH5\H:
06/28/17












M8
read and write numbers to trillions
display data with a line plot, bar graph and tally chart
read and write decimals to thousandths
write ratios as fractions and percents
collect, compare and use tables of data to solve problems
describe properties and classify geometric shapes and solids
make a scale drawing
use appropriate vocabulary to describe the probability of the chance of an
event
translate from scientific notation to standard notation
uses appropriate mathematical vocabulary and language in written and oral
work
shows mathematical work in a variety of ways (example - graphs, charts,
tables)
considers audience and purpose when communicating
Putting Mathematics to Work
 conducts one large scale project drawn from the following:
 data study
 science study
 design a physical structure
 management and planning
 pure mathematical 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
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
MATH5\H:
06/28/17
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 trillions and
thousandths, solve addition and subtraction problems with multi-digit whole numbers and
decimals; solves extended multiplication and division facts; multiplies multi-digit
numbers, renames fractions, decimals and percents, measures using US customary and
metric units; adding and subtracting fractions and decimals; calculate area and perimeter;
collect, interpret, and analyze data; effectively use a calculator, protractor, compass and
computer; with problem solving skills, estimation abilities, and use of technology
integrated throughout the course.
TITLES OF UNITS:
1. Place Value - 3 weeks
2. Addition, Subtraction, Multiplication and Division of Whole Numbers - 8 weeks
3. Addition, Subtraction, and Multiplication of Fractions - 8 weeks
4. Addition, Subtraction, Multiplication and Introductory Division of Decimals - 8
weeks
5. Geometry and Measurement- 5 weeks
MATH5\H:
06/28/17
6. Data and Graphs - 4 weeks
7. Technology, estimation, and problem solving are integrated throughout
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
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
6. Flexible/modified grouping
7. Re-teaching with alternative strategies
8. Extended instructional time
B.
1.
2.
3.
4.
5.
6.
7.
Enrichment
Modified curriculum
Peer tutoring
Modified testing
Math journal and/or projects
Individual mathematical investigations
IST
PAL
PORTFOLIO DEVELOPMENT:
MATH5\H:
06/28/17
1.
2.
3.
4.
5.
6.
7.
Teacher/student assessments
Math journals
Individual/group investigations, projects, and/or activities
Written explanation of problem solving strategies
Student reflections
End of the year assessment task (measure all skills)
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
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
MATH5\H:
06/28/17
-work effectively with others on projects and investigations
-communicate effectively using appropriate mathematical language
MATH5\H:
06/28/17