Township of Union Public Schools s1

TOWNSHIP OF UNION PUBLIC SCHOOLS

College Study Skills Curriculum Guide 2012 Board Members

Francis “Ray” Perkins, President

Versie McNeil, Vice President

David Arminio

Eduardo Espinal

Linda Gaglione

Richard Galante

Thomas Layden

Vito Nufrio

Judy Salazar TOWNSHIP OF UNION PUBLIC SCHOOLS Administration

District Superintendent …………………………………………………………………...…………………….... Dr. Patrick Martin

Assistant Superintendent …………………………………………………………..……………………….….…Mr. Gregory Tatum

Director of Elementary Curriculum ……………………………….………………………………..…………….Ms. Tiffany Moutis

Director of Secondary Curriculum ……………………………….………………………….…………………… Dr. Noreen Lishak

Director of Student Information/Technology ………………………………..………………………….…………. Ms. Ann M. Hart DEPARTMENT SUPERVISORS

Language Arts/Social Studies K-8 ……..………………………………….…………………………………….. Mr. Robert Ghiretti

Mathematics/Science K-8 ………………………………………………….………………………………………. Ms. Deborah Ford

Guidance K-12/SAC …..………………………………………………………………………………….……….Ms. Bridget Jackson

Language Arts/Library Services 9-12 ….………………………………….…………………………………….…Ms. Mary Malyska

Science 9-12 ………………………………………………………….…………………………………...…….Ms. Maureen Guilfoyle

Math 9-12………………………………………………………………………………………………………..…Mr. Jason Mauriello

Social Studies/Business ………………………………………………………………………………………..…….Mr. Jeffery Ballin

World Language/ESL/Career Education>>………………………………………………………………….….Ms. Yvonne Lorenzo

Art/Music …………………………………………………………………………………………………………..….Mr. Ronald Rago

Physical Education/Health ………………………………………………………………………………………...…. Ms. Linda Ionta Curriculum Committee College Study Skills

Sherri Horn—Mathematics, UHS Joseph Kohan—Mathematics, UHS Table of Contents

Title Page

Board Members

Administration

Department Supervisors

Curriculum Committee

Table of Content

District Mission/Philosophy Statement

District Goals

Course Description

Recommended Texts

Course Proficiencies

Curriculum Units

Appendix: New Jersey Core Curriculum Content Standards Mission Statement

The Township of Union Board of Education believes that every child is entitled to an education designed to meet his or her individual needs in an environment that is conducive to learning. State standards, federal and state mandates, and local goals and objectives, along with community input, must be reviewed and evaluated on a regular basis to ensure that an atmosphere of learning is both encouraged and implemented. Furthermore, any disruption to or interference with a healthy and safe educational environment must be addressed, corrected, or when necessary, removed in order for the district to maintain the appropriate educational setting.

Philosophy Statement

The Township of Union Public School District, as a societal agency, reflects democratic ideals and concepts through its educational practices. It is the belief of the Board of Education that a primary function of the Township of Union Public School System is to formulate a learning climate conducive to the needs of all students in general, providing therein for individual differences. The school operates as a partner with the home and community. Statement of District Goals

 Develop reading, writing, speaking, listening, and mathematical skills.  Develop a pride in work and a feeling of self-worth, self-reliance, and self discipline.  Acquire and use the skills and habits involved in critical and constructive thinking.  Develop a code of behavior based on moral and ethical principals.  Work with others cooperatively.  Acquire a knowledge and appreciation of the historical record of human achievement and failures and current societal issues.  Acquire a knowledge and understanding of the physical and biological sciences.  Participate effectively and efficiently in economic life and the development of skills to enter a specific field of work.  Appreciate and understand literature, art, music, and other cultural activities.  Develop an understanding of the historical and cultural heritage.  Develop a concern for the proper use and/or preservation of natural resources.  Develop basic skills in sports and other forms of recreation. Course Description

This course is geared towards test preparation for the mathematics section of the SAT test, used as an admissions requirement by some colleges and universities. The class content has been designed for students wishing to eventually attend a four year post-secondary institution. Students should ideally come into the class having had completed algebra 1 and geometry with a C or better, and currently enrolled in algebra 2 or higher. While numerical, algebraic, geometric, functional analysis and statistical and probability rules and concepts will be highlighted and reviewed, the student is expected to have a certain level of mastery in order to be able to answer SAT style questions. The course’s primary focus is to develop techniques and confidence in reading, interpreting, modeling, answering and checking reasonability of answers to SAT style questions. Real questions from past SAT examinations will be completed and analyzed. By the end of the school year, it is hoped that the student’s will enhance accuracy, speed, and their ability to recognize and complete the most frequently asked questions. Recommended Textbooks

The Official SAT Study Guide by The College Board, New York

Course Proficiencies Students will be able to: 1. Use properties of integers, fractions, exponents and radicals to simplify expressions. 2. Identify factors, multiples, remainders and prime numbers. 3. Correctly order real numbers on a number line. 4. Solve ratio and percent problems. 5. Identify sequences. 6. Find the union and intersection of sets. 7. Use the fundamental counting principle, combinations and permutations. 8. Isolate a variable in an equation and inequality. 9. Factor binomials and trinomials. 10.Use properties of exponents. 11.Understand exponential growth and decay. 12.Find the range of answers for an absolute value equation. 13.Solve systems of equations. 14.Use direct and inverse variation where appropriate. 15.Know graphical behavior of linear and quadratic functions. 16.Utilize properties of quadrilaterals and other polygons. 17.Use area and perimeter formulas of parallelograms and triangles. 18.Find slope, distance and midpoint of two points. 19.Use similarity and congruence. 20.Use properties of right, equilateral and isosceles triangles. 21.Calculate mode, mean, median and weighted average. 22.Calculate elementary and geometric probability. 23.Increase test taking skills. Curriculum Units

Unit 1: Numbers and Operations

Unit 2: Algebra and Functions

Unit 3: Geometry and Measurement

Unit 4: Data Analysis, Statistics and Probability

Unit 5: Test Strategies

Pacing Guide- Course Content Number of Days

The course is not broken into sections by topic. All proficiencies are reviewed or practiced as they arise within the context of a given problem. Class periods spend first and third marking periods in English/Math and second and fourth marking periods in the other discipline.

Unit 1: Numbers and Operations

Unit 2: Algebra and Functions

Unit 3: Geometry and Measurement

Unit 4: Data Analysis, Statistics and Probability

Unit 5: Test Strategies Unit 1; Numbers and Operations

Essential Questions Instructional Objectives/ Activities Assessments Skills and Benchmarks (CPIs) When/why is a number Identify even, odd, Explore positioning real Do consecutive integer excluded from the domain positive, and negative real numbers on a number line and consecutive multiple or range of a problem? numbers and the result when each are in different word problems. when added or multiplied. forms. What is the criteria for a Solve conversion of unit reasonable answer? Compute arithmetic Put regular and improper problems involving more operations with fractions. fractions raised to higher than one proportion. When is it appropriate to powers in order. use a permutation, Find LCM and GCF. Find the sum of the terms combination or the Review long division and in a sequence or the value counting principle? Identify primes. discuss possible of the nth term. remainders given a Identify the union and divisor. Solve problems finding the intersection of sets. correct number given a set (SCP1) Use Venn diagrams to of specifications. demonstrate intersections Find the rule of a and unions. sequence. Demonstrate the Find the probability of 2 difference between independent or dependent combinations and events. permutations using situations involving Calculate the number of people in the class. possible choices using permutations or Make connections combinations or counting between finding roots and principle. (SCP9) raising to a power as inverse operations. Utilize properties of reciprocals.

Unit 2: Algebra and Functions Essential Questions Instructional Objectives/ Activities Assessments Skills and Benchmarks (CPIs) How does the relationship Combine like terms in Have students identify or Translate and solve between quantities solving an equation or write their own equations percent of increase word translate into a function? inequality. that can be solved given problems. parameters for domain What are the key features Use factoring to solve a and range. Practice distance, rate and of a graph over a specified quadratic equation. (FIF8) time problems. interval? Make a chart of key words Evaluate expressions with used in SAT word Calculate what score is How do you distinguish exponents and roots. problems and how they needed to raise an between linear and translate into math average. exponential features? Solve for one variable in symbols. terms of another. Translate the graph of a How do key points on a Using graphing given squareroot, graph answer real life Use substitution and calculators to explore the exponential, quadratic, or problems? linear combination to results of growth and linear equation and solve a system. decay factors in an identify the domain and exponential model. range. Determine when appropriate to use inverse After doing special symbol or direct variation. questions in the SAT book have students create their Understand function own. notation in an equation, table or graph. (FIF1,2) Analyze various graphs for symmetry, intercepts, Locate x and y intercepts slope and extrema through an equation, table or graph. (FIF7)

Find slope, midpoint and distance between 2 points.

Identify graph transformations (FBF3)

Locate algebraically and geometrically the vertex of a quadratic function. (FIF7)

Identify growth or decay (FIF8)

Unit 3: Geometry and Measurement Essential Questions Instructional Objectives/ Activities Assessments Skills and Benchmarks (CPIs) How do the properties of Recognize when to apply Draw and translate a Prove the sum of the 2 similarity and congruence the following theorems in geometric shape on a remote angle in a triangle help in solving a a problem: coordinate plane and are equal to the exterior geometric problem? Sides of a triangle are compute area and angle. congruent if and only if perimeter. How can a 2 dimensional opposite angles are If the radius of a circle is picture aid in visualizing a A radius forms a right Demonstrate using straws 10 and the arc length of 3D problem? angle with a tangent. that the third side of a arcAB is 2pi what is the (GC2) triangle must be between measure of the central Which theorems from the sum and difference of angle intersecting the geometry are most used Find the missing side in a the other two. circle at A and B? on the SAT? special triangle. Have students make flash Find the largest pencil that Use ratos in finding parts cards with the definitions can fit in a cylinder of in congruent triangles. of commonly used radius 1 and height 7. (GSRT6) geometry words: bisect, trisect, vertical, What are the coordinates Recognize Pythagorean supplementary, after a point has been triple. complimentary, straight translated after both axes? angle, adjacent. Use the formula for the sum of the interior angles Cut various polygons into of a polygon. triangles to develop the sum of interior angles Use volume area and formula. perimeter formulas. (GGMD3) Do review lesson on angles formed by a Make a proportional transversal. connection between arc length to circumference, Develop the formula for sector area to total area finding the diagonal of a and central angle to 360. rectangular prism by (GC5) using the Pythagorean theorem twice. Utilize properties of polygons. (GCO8&GSRT2,3)

Distinguish between surface area and volume.

Use properties of perpendicular and parallel lines.

Recognize properties of a parallelogram. (GCO11)

Unit 4: Data Analysis, Statistics andProbabilty Essential Questions Instructional Objectives/ Activities Assessments Skills and Benchmarks (CPIs) What inferences can be Read circle, bar, line and Find graphs in Calculate mode median made from a table, circle picot graphs. (SID1) newspapers and and mean from various graph or bar graph? magazines and draw graphs. Find mean, mode and appropriate conclusions. Which measure of central median. The average of a list of 10 tendency is most useful Use a dart board to find numbers is 15. If one under given Understand how to use geometric probability. number is removed the circumstances? weighted average. average is 14. What was the number removed. How are area formulas Find probability of used in calculating dependent and What is the probability of probability? independent events. randomly choosing a point (SCP2) outside a square with side 4 but inside a circle of Compute geometric radius 4? probability on circles and rectangles. Unit 5: Test Strategies

Essential Questions Instructional Objectives/ Activities Assessments Skills and Benchmarks (CPIs) When is it beneficial to Locate and use when Experiment with the order X 2/Y = integer and X/Y guess at or skip a appropriate the formula of answering questions in does not equal an integer, question on the SAT? page of the test. the section of combined which of the following multiple choice and open could be X and Y? (2,1) or How is the test scored? Understand the difference ended questions. (6,9) or (2,3) between the scoring of a How much time should be multiple choice and open As students do practice Which of the following spent on each question? ended question. tests have them keep a proves the statement journal of common FALSE: If the sum of the How are parts of a Understand the difference questions that repeat each digits is odd the number problem inputted into a between a question test. itself is odd? 1011 or 2024 calculator? containing must as or 1023 or 1022? opposed to could. Time students and have them self score X = Y 2 and W = X 2 + X, what Utilize the technique of successive practice tests. is the value of W in terms plugging in real numbers of Y? Y 4 + Y 2 or Y 6 or Y 8 to find the correct answer Explore to a variable problem. hypothesis/conclusion problems to discover one Recognize when is false only when substituting the multiple hypothesis is true and choice answers in will aid conclusion is false. in finding the solution.

Recognize when a problem can be solved backwards.

Enter negatives and fractions into the calculator with the appropriate parentheses.

Recognize the contrapositive answer to an equivalence question.

Use a proportion to solve an if/then question.

Use lists and pictures to aid in solving a problem.

New Jersey Core Curriculum Content Standards Acedemic Area New Jersey Scoring Rubric