School Administrative District #4

Unity of purpose

CORE CURRICULUM: SCOPE AND SEQUENCE

Department: Mathematics

CONTENT STANDARD: DISCRETE MATHEMATICS

Students will understand and apply concepts in discrete mathematics. Discrete mathematics studies discrete processes (e.g., all possible bus routes in a school district). This study includes the exploration of diagrams, networks, and flowcharts that students construct to model situations or use for planning, scheduling, and decision making. Three main concerns of discrete mathematics are existence (Is there a solution?), counting (How many solutions are there?), and efficiency (What is the best solution?).

Performance Indicators: The learner will·

Kindergarten

1.        Review and extend prior learning

2.        Demonstrate an initial understanding of possible outcomes when more than one option is available

Grade 1

1.        Review and extend prior learning

2.        Create and use an organized list to determine possible outcomes or to solve problems

á         Three variations of one attribute, e.g., determine the possible arrangements for a triple ice-cream cone given three flavors of ice cream

Grade 2

1.        Review and extend prior learning

2.        Create and use an organized list to determine possible outcomes or to solve problems

á         Two variations of two attributes, e.g., determine the possible arrangements for two differing styles of shirts and two differing styles of pants

Grade 3

1.        Review and extend prior learning

2.        Create and use

á         Organized lists

á         Tree diagrams

3.        Demonstrate an initial understanding of infinity

Grade 4

1.        Review and extend prior learning

2.        Create and use

á         Venn diagrams

á         Networks (e.g., routes, pathways, etc.)

3.        Give examples of infinite and finite solutions

Grade 5

1.        Review and extend prior learning

2.        Identify patterns in the world and express these patterns as rules, e.g., the date one week from any given day

Grade 6

1.        Review and extend prior learning

2.        Create and use networks to explain practical situations or to solve problems

Grade 7

1.        Review and extend prior learning

2.        Analyze and solve problems, including

á         Communication networks

á         Tournament matchings

Grade 8

1.        Review and extend prior learning

2.        Analyze and solve problems, including

á         Production schedules

á         Consumer applications

3.        Investigate sets and relations

á            Union

á            Intersection

á            Empty or null set

4.        Represent finite graphs

Grade 9

1.        Review and extend prior learning

2.        Analyze and solve problems, including

á         Circuit diagrams

á         Math relations

á         Compound interest

á         Home mortgages

á         Annuities

á         Amortization schedules

3.        Apply strategies from game theory to problem-solving strategies

Grade 10

1.        Review and extend prior learning

2.        Given a property of points and lines, determine the truth of that property in graph theory

Grade 11

1.        Review and extend prior learning

Grade 12

1.        Review and extend prior learning