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 8

1.        Review and extend prior learning

2.        Use numbers in a variety of equivalent and interchangeable forms

á         Scientific notation

3.        Demonstrate an initial understanding of how to use numbers in a variety of equivalent and interchangeable forms in problem solving

á         Integers

á         Fractions

á         Decimals

á         Percents

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 8

1.        Review and extend prior learning

2.        Using correct terminology, compute and model all four operations with

á         Real numbers

á         Scientific notation

3.        Apply the order of operations to problems involving

á         Exponents

á         Square roots

á         Absolute value

4.        Create, solve, and justify the solution to multi-step, real-life problems, using

á         Ratio

á         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 8

1.        Review and extend prior learning

2.        Verify by measuring and describe the relationships between vertical angles and angles that are supplementary and complementary

3.        Develop and use concepts that can be measured directly or indirectly (e.g., the concept of rate)

4.        Read and use the scale of a drawing

á         Design and construct a model to scale

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 8

1.        Review and extend prior learning

2.        Investigate and describe functional relationships, including the number of sides of a regular polygon and the maximum number of possible diagonals, expressing the algebraic concept of the number of diagonals of the nth-sided polygon

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 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

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 8

1.        Review and extend prior learning

2.        Follow logical arguments

á         Validate his/her own thinking

á         Demonstrate an understanding of the pervasive use and power of reasoning as part of mathematics

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 8

1.        Review and extend prior learning

2.        Create and solve problems involving the mean, median, mode, and range of a set of data

3.        Use information displayed in various graphical forms to make comparisons, predictions, and inferences

4.        Use a matrix to organize and describe 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 8

1.        Review and extend prior learning

2.        Find all possible combinations and arrangements involving a limited number of variables, i.e., use the Fundamental Counting Principle

3.        Use knowledge of probability to analyze problem situations (e.g., games of chance, board games, grading scales)

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 8

1.        Review and extend prior learning

2.        Use algebraic terms appropriately

á         Term

á         Coefficient

á         Non-linear equation

3.        Manipulate algebraic expressions by

á            Adding

á            Subtracting

á            Multiplying

á            Dividing

4.        Recognize and use algebraic properties

á         Addition property of equality

á         Multiplication property of equality

5.        Demonstrate an initial understanding of how to 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

6.        Solve two-step linear equations and inequalities in one variable, using strategies involving inverse operations and integers

7.        Solve real-life problems requiring the solution of a two-step linear equation

8.        Graph a linear equation in two variables on the coordinate plane, using a table of ordered pairs

9.        Describe and represent relations using tables, graphs, and rules

10.    Create and solve problems using proportions, formulas, and functions

11.    Demonstrate an initial understanding of the laws of exponents

12.    Collect and analyze data to make predictions, write equations, and solve real-life problems

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 8

1.        Review and extend prior learning

2.        Apply transformations (rotate or turn, reflect or flip, translate or slide, dilate or scale) to geometric figures represented on graph paper

3.        Identify real-life applications of transformations (e.g., tiling, fabric design, art, scaling)

4.        Describe, classify, and construct plane and solid figures, using the appropriate geometric tools

5.        Investigate, create, and solve problems involving the volume and surface area of

á         Cones

á         Pyramids

6.        Find the volume and surface area of cones and pyramids, given the appropriate dimensions

Developed 07/17/97

Revised 07/08/98

curr-math-scope-8.doc