MACOPIN MIDDLE SCHOOL
Mathematics 8
Syllabus
I. COURSE TITLE
Mathematics 8
II. TEXTBOOK
Connected Mathematics 2. Glenda Lappan, James T. Fey, et al. Prentice Hall, Boston, MA, 2006.
III COURSE DESCRIPTION
The Connected Mathematics Program, 2nd revision, aims to expand student views of algebra beyond symbolic manipulation and to offer opportunities for students to apply algebraic reasoning to problems in many different contexts throughout the course of the curriculum. Eight units that focus formally on algebra emphasize reasoning and communication while constructing and reinforcing mathematical concepts through practice and application. The Connected Mathematics curriculum is the beginning piece of a comprehensive long-range plan stimulated by New Jersey’s participation in the American Diploma Project, designed to bring larger numbers of students to Algebra II in the high school at a more accelerated pace.
IV. COURSE OBJECTIVES
A. Number Sense and Operations: All students will develop number sense and will perform standard numerical operations and estimations on all types of numbers in a variety of ways.
1. Extend understanding of the number system by constructing meanings for rational numbers, percents, exponents, roots, absolute values, and numbers represented in scientific notation.
2. Demonstrate a sense of the relative magnitudes of numbers
3. Understand and use ratios, proportions, and percents in a variety of situations.
4. Compare and order numbers of all named types.
5. Use whole numbers, fractions, decimals, and percents to represent equivalent forms of the same number.
6. Recognize that repeating decimals correspond to fractions and determine their fractional equivalents.
7. Construct meanings for common irrational numbers, such as pi and the square root of 2.
8. Use and explain procedures for performing calculations involving addition, subtraction, multiplication, division, and exponentiation with integers and all number types named above with pencil-and-paper, mental math, and calculator.
9. Use exponentiation to find whole number powers of numbers.
10. Find square and cube roots of numbers and understand the inverse nature of powers and roots.
11. Solve problems involving proportions and percents.
12. Understand and apply the standard algebraic order of operations, including appropriate use of parentheses.
13. Estimate square and cube roots of numbers.
14. Use equivalent representations of numbers such as fractions, decimals, and percents to facilitate estimation.
15. Recognize the limitations of estimation and assess the amount of error resulting from estimation.
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B. Geometry and Measurement: All students will develop spatial sense and the ability to use geometric properties, relationships, and measurement to model, describe, and analyze phenomena.
1. Understand and apply concepts involving lines, angles, and planes.
2. Understand and apply the Pythagorean Theorem.
3. Understand and apply properties of polygons.
4. Understand and apply the concept of similarity.
5. Use logic and reasoning to make and support conjectures about geometric objects.
6. Understand and apply transformations.
7. Use coordinates in four quadrants to represent geometric concepts.
8. Use a coordinate grid to model and quantify transformations.
9. Recognize that the degree of precision needed in calculations depends on how the results will be used and the instruments used to generate the measurements.
10. Select and use appropriate units and tools to measure quantities to the degree of precision needed in a particular problem-solving situation.
11. Solve problems that involve compound measurement units, such as speed (miles per hour), air pressure (pounds per square inch), and population density (persons per square mile).
12. Develop and apply strategies for finding perimeter and area.
13. Develop and apply strategies and formulas for finding the surface area and volume of a three-dimensional figure.
14. Use formulas to find the volume and surface area of a sphere.
C. Patterns and Algebra: All students will represent and analyze relationships among variable quantities and solve problems involving patterns, functions, and algebraic concepts and processes.
1. Recognize, describe, extend, and create patterns involving whole numbers, rational numbers, and integers.
2. Graph functions, including equations involving two variables, and understand and describe their general behavior.
3. Recognize and describe the difference between linear and exponential growth, using tables, graphs, and equations.
4. Analyze functional relationships to explain how a change in one quantity can result in a change in another, using pictures, graphs, charts, and equations.
5. Use patterns, relations, symbolic algebra, and linear functions to model situations.
6. Use graphing techniques on a number line.
7. Solve simple linear equations informally, graphically, and using formal algebraic methods.
8. Solve simple linear inequalities.
9. Create, evaluate, and simplify algebraic expressions involving variables.
10. Understand and apply the properties of operations, numbers, equations, and inequalities.
D. Data Analysis, Probability, and Discrete Mathematics: All students will develop an understanding of the concepts and techniques of data analysis, probability, and discrete mathematics, and will use them to model situations, solve problems, and analyze and draw appropriate inferences from data.
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1. Select and use appropriate representations for sets of data, and measures of central tendency (mean, median, and mode).
2. Make inferences and formulate and evaluate arguments based on displays and analysis of data.
3. Estimate lines of best fit and use them to interpolate within the range of the data.
4. Use surveys and sampling techniques to generate data and draw conclusions about large groups.
5. Interpret probabilities as ratios, percents, and decimals.
6. Determine probabilities of compound events.
7. Explore the probabilities of conditional events (e.g., if there are seven marbles in a bag, three red and four green, what is the probability that two marbles picked from the bag, without replacement, are both red).
8. Use vertex-edge graphs and algorithmic thinking to represent and find solutions to practical problems.
V. COURSE CONTENT OUTLINE:
A. Thinking With Mathematical Models
1. Recognize linear and non-linear patterns in contexts, tables, and graphs and describe those patterns using words and symbolic expressions.
2. Write equations to express linear patterns appearing in tables, graphs, and verbal contexts
3. Write linear equations when specific information, such as two points or a point and a slope, is given for a line
4. Approximate linear data patterns with graph and equation models
5. Solve linear equations
6. Interpret inequalities
7. Write equations describing inverse variation
8. Use linear and inverse variation equations to solve problems and to make predictions and decisions
B. Looking For Pythagoras
1. Relate the area of a square to the length of a side of the square
2. Estimate square roots
3. Develop strategies for finding the distance between two points on a coordinate grid
4. Understand and apply the Pythagorean Theorem
5. Use the Pythagorean Theorem to solve a variety of problems
C. Growing, Growing, Growing
1. Recognize situations where one variable is an exponential function of another variable
2. Recognize the connections between exponential equations and growth patterns in tables and graphs of those relations
3. Construct equations to express exponential patterns that appear in data tables, graphs, and problem conditions
4. Understand and apply the rules for operating on numerical expressions with exponents
5. Solve problems about exponential growth and decay in a variety of situations such as science or business
6. Compare exponential and linear relationships
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D. Frogs, Fleas, and Painted Cubes
1. Recognize the patterns of change for quadratic relationships in a table, graph, equation, and problem situation
2. Construct equations to express quadratic relationships that appear in tables, graphs and problem situations
3. Recognize the connections between quadratic equations and patterns in tables and graphs of those relationships
4. Use tables, graphs, and equations of quadratic relationships to locate maximum and minimum values of a dependent variable and the x- and y-intercepts and other important features of parabolas.
5. Recognize equivalent symbolic expressions for the dependent variable in quadratic relationships
6. Use the distributive property to write equivalent quadratic expressions in factored form or expanded form
7. Use tables, graphs, and equations of quadratic relations to solve problems in a variety of situations from geometry, science, and business
8. Compare properties of quadratic, linear, and exponential relationships
E. Kaleidoscopes, Hubcaps, and Mirrors
1. Understand important properties of symmetry
2. Recognize and describe symmetries of figures
3. Use tools to examine symmetries and transformations
4. Make figures with specified symmetries
5. Identify basic design elements that can be used to replicate a given design
6. Perform symmetry transformations of figures, including reflections, translations, and rotations
7. Examine and describe the symmetries of a design made from a figure and its image(s) under a symmetry transformation
8. Give precise mathematical directions for performing reflections, rotations, and translations
9. Draw conclusions about a figure, such as measures of sides and angles, lengths of diagonals, or intersection points of diagonals, based on symmetries of the figure
10. Understand that figures with the same shape and size are congruent
11. Use symmetry transformations to explore whether two figures are congruent
12. Give examples of minimum sets of measures of angles and sides that will guarantee that two triangles are congruent
13. Use congruence of triangles to explore congruence of two quadrilaterals
14. Use symmetry and congruence to deduce properties of figures
15. Write coordinate rules for specifying the image of a general point (x, y) under particular transformations
16. Use transformational geometry to describe motions, patterns, designs, and properties of shapes in the real world
F. Say It With Symbols
1. Model situations with symbolic statements
2. Write equivalent expressions
3. Determine if different symbolic expressions are mathematically equivalent
4. Interpret the information equivalent expressions represent in a given context
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5. Determine which equivalent expression to use to answer particular questions;
6. Solve linear equations involving parentheses
7. Solve quadratic equations by factoring
8. Use equations to make predictions and decisions
9. Analyze equations to determine the patterns of change in the tables and graphs that the equation represents
10. Understand how and when symbols should be used to display relationships, generalizations, and proofs
G. The Shapes of Algebra
1. Write and use equations of circles
2. Determine lines are parallel or perpendicular by looking at patterns in their graphs, coordinates, and equations
3. Find coordinates of points that divide line segments in various ratios
4. Write inequalities that satisfy given situations
5. Find solutions to inequalities represented by a graph or an equation
6. Solve systems of linear equations by graphing, combining equations, and by substitution
7. Write linear inequalities in two variables to match constraints in problem conditions
8. Graph linear inequalities and systems of inequalities and use the results to solve problems
H. Samples and Populations
1. Revisit and use the process of statistical investigation to explore problems
2. Distinguish between samples and populations and use information drawn from samples to draw conclusions about populations
3. Explore the influence of sample size and of random or nonrandom sample selection
4. Apply concepts from probability to select random samples from populations
5. Compare sample distributions using measures of center (mean or median), measures of dispersion (range or percentiles), and data displays that group data (histograms and box-and-whisker plots)
6. Explore relationships between paired values of numerical attributes
VI. EVALUATION OF STUDENT LEARNING
A. The evaluation of student performance is based upon tests, quizzes, assignments, alternate assignments, and class participation. Each student is responsible for daily preparation; i.e., pencil, notebook/binder, textbook, homework, etc. Homework is usually assigned daily. A minimum of 30 minutes should be spent at home each day preparing assignments and reviewing class work. Daily attendance is an important factor for the continuity of the course. Students are responsible for making up all work missed due to an absence from class. The student is expected to take an active role in the learning process by participating in class and by taking the initiative to seek extra help when difficulties arise.
B. Grade development
1. Tests, quizzes, and alternate assessment - 80%
2. Homework and class work - 20%
C. Comprehensive Final Exam (one-ninth of final grade)