School Administrative District #4
Unity of purpose
CORE CURRICULUM: SCOPE AND SEQUENCE
Department: Mathematics
CONTENT STANDARD: NUMBERS AND NUMBER SENSE
Students will understand and demonstrate a sense of what numbers mean and how they are used. Numbers are used to describe and interpret phenomena. Building a sense of number relationships is essential for developing the ability to deal with any set of numbers. Number sense involves understanding the meaning of numbers, relationships among numbers, relative number magnitudes, and the effects of operations on numbers. Skilled estimation is also an important component of number sense.
Performance Indicators: The learner will·
|
Grade 9 |
1. Review and extend prior learning
2. Describe the structure of the real number system and identify its appropriate applications and limitations
3. Use numbers in a variety of equivalent and interchangeable forms in problem solving
á Integers
á Fractions
á Decimals
á Percents
á Exponents
á Scientific notation
á Irrational numbers
CONTENT STANDARD: COMPUTATION
Students will understand and demonstrate computation skills. Computation involves understanding the fundamental operations of and relationships between and among addition, subtraction, multiplication, and division. Proficiency in computational skills requires that students learn to evaluate the reasonableness of an answer and to obtain accuracy in calculations with ever-increasing ease and confidence, with and without technological tools.
Performance Indicators: The learner will·
|
Grade 9 |
1. Review and extend prior learning
2. Use a variety of materials, strategies, and symbols to manipulate
á Real numbers
3. Create, solve, and justify the solution to multi-step, real-life problems, using
á Inverse proportion
CONTENT STANDARD: MEASUREMENT
Students will understand and demonstrate measurement skills. Measurement is valuable as an integrating skill throughout the curriculum and in everyday life. The use of estimation is vital in determining the reasonableness of measurement. Measurement attributes (e.g., length, volume, time), U.S. customary and metric units, and tools enhance the ability to describe and understand the world.
Performance Indicators: The learner will·
|
Grade 9 |
1. Review and extend prior learning
2. Convert from one measurement system to another, using unit multipliers
á Metric to U.S. customary units
á U.S. customary units to metric
3. Demonstrate an initial understanding of how to use measurement tools and units appropriately and recognize limitations in the precision of the measurement tools
á Vernier caliper
á Graphing calculator
4. Show magnitude and direction, using vectors
CONTENT STANDARD: PATTERNS, RELATIONS, AND FUNCTIONS
Students will understand that mathematics is the science of patterns, relationships, and functions. Relationships are central to mathematical understanding. A study of patterns often reveals regularity, indicating the presence of a mathematical relationship. Studying relationships allows students to make generalizations and predictions about phenomena and occurrences.
Performance Indicators: The learner will·
|
Grade 9 |
1. Review and extend prior learning
2. Create a graph to explain a real-life situation and draw inferences from it
3. Translate and solve a real-life problem using symbolic language
4. Apply techniques to fit functions (model) to collected data and make predictions from the function of best fit
á Median-fit line
5. Identify and use the different types of functions and their descriptions
á Constant
á Linear
á Quadratic
á Polynomial
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·
|
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
CONTENT STANDARD: MATHEMATICAL REASONING
Students will understand and apply concepts of mathematical reasoning. Reasoning is fundamental to the knowing and doing of mathematics. To give more students access to mathematics as a powerful way of making sense of the world, it is essential that an emphasis on reasoning pervade all mathematics. Students need a great deal of time and many experiences to develop their ability to construct and evaluate valid arguments in problem settings and to evaluate the arguments of others.
Performance Indicators: The learner will·
|
Grade 9 |
1. Review and extend prior learning
2. Follow logical arguments
á Formulate counterexamples
á Derive properties and other mathematical models
CONTENT STANDARD: DATA ANALYSIS AND STATISTICS
Students will understand and apply concepts of data analysis. Individuals are faced with massive quantities of information which must be selected, sorted, and analyzed to reach conclusions. Sound decision making requires the ability to collect data effectively, organize data, discover patterns, summarize trends, make inferences, draw conclusions, and make predictions. The ethical use of statistics is a paramount concern in the Information Age.
Performance Indicators: The learner will·
|
Grade 9 |
1. Review and extend prior learning
2. Manipulate large, realistic sets of data
CONTENT STANDARD: PROBABILITY
Students will understand and apply concepts of probability. Probability is the study of uncertainty. Informed consumers of information understand the basic principles of probability. People need to understand the uncertainties and limitations involved when drawing conclusions from data.
Performance Indicators: The learner will·
|
Grade 9 |
1. Review and extend prior learning
2. Find the quotient of numbers given factorial notation
3. Find probability when the event always occurs
4. Distinguish between probability of simple, independent, dependent, inclusive, and mutually exclusive events
5. Find the probability of a
á Simple event
á Compound event, using
á A sample space
CONTENT STANDARD: ALGEBRA CONCEPTS
Students will understand and apply algebraic concepts. Algebra and analytic thinking are fundamental tools for working in and thinking about mathematics. These tools provide ways to generalize and predict problem solutions when not all information is known. Taught within the context of mathematical and practical applications, the concept of functions is a unifying theme for algebraic concepts.
Performance Indicators: The learner will·
|
Grade 9 |
NOTE: The following performance indicators also apply to those students taking eighth-grade Algebra I.
1. Review and extend prior learning
2. Distinguish and compute between the various sets of complex numbers, including
á Real numbers
á Rational numbers
á Whole numbers
á Integers
á Fractions and decimals
á Irrational numbers
3. Apply scientific notation to algebraic situations
4. Compute with integers, using
á Absolute value
á Exponents
5. Solve and graph exponential situations, involving
á Growth
á Decay
á Simple interest
á Compound interest
6. Understand and apply the laws of exponents
7. Understand and manipulate polynomials
á Determine degree of polynomials
á Classify polynomials
á Simplify polynomials
á Add, subtract, and multiply polynomials
8. Factor polynomials by
á Finding the greatest common factor
á Grouping
á Using the Difference of Two Squares Theorem
á Trinomial factoring
á Using the Factor Theorem
á Using the Quadratic Formula to find roots
9. Solve quadratic equations by
á Factoring
á Using the Quadratic Formula
á Finding the nature of roots using the discriminant
á Graphing (e.g., calculator, computer, graph paper)
á Using the Difference of Two Squares Theorem
10. Manipulate rational expressions by
á Simplifying by adding, subtracting, multiplying, and dividing rational expressions
á Simplifying complex rational expressions
11. Solve multi-step linear equations involving
á One variable
á Multi-variables
á Proportions
á Absolute value
á Rational expressions
á Radical expressions
12. Solve linear systems of equations and inequalities by
á Graphing
á Substitution
13. Find the distance between two points on a coordinate plane, using the
á Pythagorean Theorem
á Distance Formula
14. Write and graph linear equations by
á Finding slope and intercepts
á Recognizing the slope-intercept form
á Recognizing point-slope form
á Recognizing general form
á Recognizing standard form
á Finding the equations of horizontal and vertical lines
15. Solve word problems, involving
á Distance
á Cost
á Motion
á Consecutive integers
á Even
á Odd
á Age
á Percent
16. Justify steps used in simplifying expressions and solving equations and inequalities
CONTENT STANDARD: GEOMETRY
Students will understand and apply concepts from geometry. Geometry is the study of the spatial world and its symmetries. The ideas of geometry are used to describe, interpret, represent, and change the spatial world in which people live. The understanding and development of spatial and visual skills strengthens problem-solving abilities.
Performance Indicators: The learner will·
|
Grade 9 |
1. Review and extend prior learning
2. Derive and use formulas for perimeter, area, surface area, and volume of many types of figures; and apply the appropriate unit labels (i.e., units, square units, cubic units)
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Developed 07/17/97 Revised 07/08/98 |
curr-math-scope-9.doc |