Mathematics Department Pre-Algebra Course Syllabus 2015-2016 Instructor: Jarrod Cappello e-mail:[email protected]

A. Grading Policy – course work will be graded as follows: a. Summative Assessments (test, quizzes, projects) – 85% of grade b. Formative Assessments (homework) – 15% of grade c. All grades should be verified in genesis on a regular basis B. Classroom a. Rules of Conduct i. Follow all rules as stated in student handbook ii. Come prepared to class with all required materials iii. No food or drinks in classroom iv. No cell use without teacher consent b. Required Material i. Textbook ii. Pencils iii. Graphing calculator iv. Three ring binder v. Chrome Book c. Homework i. All homework will be posted on the teacher’s school website ii. Homework will not be accepted late unless the student has been absent and/or has a medical excuse iii. As per math MS department policy any homework zero may be made up for full credit during the First Marking period. After 1st marking period each homework missed will be counted as a zero. iv. Missed homework should be made-up for understanding of concepts d. Attendance i. Follow all rules as stated in student handbook ii. One day to make up work for every day absent iii. Work assigned prior to absence(s) will be due on the first day back e. Academic Integrity i. Students are to hand-in their own work 1. Receiving assistance is different from copying ii. Cheating will result in a zero on the assessment and a call home to the parent

f. After School Help i. Available Tuesdays, Wednesdays, Thursdays ii. I Will notify students if I cannot stay on a particular day iii. Morning hours are also available if discussed and agreed upon

C. Course Description This course presents an integrated mathematics curriculum in preparation for Algebra.

In the Connected Math Program, important mathematical ideas are embedded in the context of interesting problems. The mathematical content in Connected Mathematics covers number sense, geometry, measurement, statistics, probability, combinatorics and algebra appropriate for the middle grades.

As students explore a series of connected problems, they discover mathematical content and theories beyond symbolic manipulation as they use problem solving strategies and creative thinking. Students learn mathematics and they learn how to learn mathematics.

D. Course Objectives This course has been designed with respect to and in compliance with the expectations set forth in the New Jersey Core Curriculum Content Standards.

Overarching Objectives - Students will be able to:

a. Linear and Nonlinear Relationships: Recognize and model patterns in bivariate data i. Represent data patterns using graphs, tables, word descriptions, and algebraic expressions ii. Investigate the nature of linear functions in contexts iii. Use mathematical models to answer questions about linear relationships iv. Write linear functions from tables, graphs, and verbal contexts v. Analyze and solve linear equations vi. Model situations with inequalities expressed as “at most” and “at least” situations vii. Investigate the nature of inverse variation in contexts viii. Use mathematical models to answer questions about inverse variation ix. Compare inverse variation relationships with linear relationships b. Data Analysis: Measure variation in data and strength of association in bivariate data i. Use data to make predictions ii. Fit a line to data that show a linear trend and measure closeness of fit iii. Analyze scatter plots of bivariate data to determine the strength of the linear association between two variables iv. Use correlation coefficients informally to describe the strength of the linear association illustrated by scatter plots v. Use standard deviation to measure variability in univariate distributions vi. Distinguish between categorical and numerical variables c. Take square roots and the Pythagorean Theorem, make connections with coordinates, slope, distance, and area i. Relate the area of a square to the length of a side of the square ii. Estimate square roots iii. Develop strategies for finding the distance between two points on a coordinate grid iv. Understand and apply the Pythagorean Theorem v. Use the Pythagorean Theorem to solve a variety of problems d. Recognize and represent exponential growth and decay in tables, graphs, words, and symbols; understand the rules of exponents and scientific notation i. Recognize situations where one variable is an exponential function of another variable ii. Recognize the connections between exponential equations and growth patterns in tables and graphs of those relations iii. Construct equations to express exponential patterns that appear in data tables, graphs, and problem conditions iv. Understand and apply the rules for operating on numerical expressions with exponents v. Solve problems about exponential growth and decay in a variety of situations such as science or business vi. Compare exponential and linear relationships e. Recognize and represent quadratic functions in tables, graphs, words, and symbols and factor simple quadratic expressions i. Recognize the patterns of change for quadratic relationships in a table, graph, equation, and problem situation ii. Construct equations to express quadratic relationships that appear in tables, graphs and problem situations iii. Recognize the connections between quadratic equations and patterns in tables and graphs of those relationships iv. 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. v. Recognize equivalent symbolic expressions for the dependent variable in quadratic relationships vi. Use the distributive property to write equivalent quadratic expressions in factored form or expanded form vii. Use tables, graphs, and equations of quadratic relations to solve problems in a variety of situations from geometry, science, and business viii. Compare properties of quadratic, linear, and exponential relationships f. Use samples to reason about populations and make predictions, compare samples and sample distributions, investigate relationships among attributes in data sets i. Revisit and use the process of statistical investigation to explore problems ii. 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) iii. Explore relationships between paired values of numerical attributes g. Investigate symmetries of designs, perform symmetry transformations and congruency i. Understand important properties of symmetry ii. Recognize and describe symmetries of figures iii. Use tools to examine symmetries and transformations iv. Make figures with specified symmetries v. Identify basic design elements that can be used to replicate a given design vi. Perform symmetry transformations of figures, including reflections, translations, and rotations vii. Examine and describe the symmetries of a design made from a figure and its image(s) under a symmetry transformation viii. Give precise mathematical directions for performing reflections, rotations, and translations ix. Understand that figures with the same shape and size are congruent x. 10. Use symmetry transformations to explore whether two figures are congruent h. Create equivalent expressions, substituted and combined expressions i. Model situations with symbolic statements ii. Write equivalent expressions iii. Determine if different symbolic expressions are mathematically equivalent iv. Interpret the information equivalent expressions represent in a given context v. Determine which equivalent expression to use to answer particular questions; vi. Solve linear equations involving parentheses vii. Use equations to make predictions and decisions viii. Analyze equations to determine the patterns of change in the tables and graphs that the equation represents i. Recognize situations in which various counting techniques apply i. Construct organized lists of outcomes for complex processes and uncover patterns that help in counting the outcomes of those processes ii. Use diagrams, tables, and symbolic expressions to organize examples in listing and counting tasks iii. Analyze the usefulness of counting trees and use counting trees iv. Use mental arithmetic to make estimates in multiplication and division calculations v. Invent strategies for solving problems that involve counting vi. Analyze counting problems involving choices in various contexts vii. Differentiate among situations in which order does and does not matter and in which repeats are and are not allowed viii. Analyze the number of paths through a network ix. Compare the structures of networks with problems involving combinations x. Create networks that satisfy given constraints E. Text(s)/resources/Software: Instructional Resources for all students: Connected Math 2. Glenda Lappan, James T. Fey, et al. Prentice Hall, Boston MA 2013

F. Technology a. TI-84 Graphing Calculator b. SmartBoard c. Smart Calculator d. Chrome Books e. Sumdog f. Math IXL g. Math xl for school