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Roselle Park Middle School Mathematics Department Course of Study Math Problem Solving Grade 7 MATH PROBLEM SOLVING GRADE 7 In order to understand how these objectives are to be achieved, a sequence of topics is listed for each unit. Space is provided on each page to allow for notes and recommendations. The New Jersey Core Curriculum Content Standards and the New Jersey Core Course Proficiencies are infused throughout the units. The objective of the sixth grade math problem solving is to aid students in further exploring problem solving skills related to standardized testing. This guide applies to all students and meets the Affirmative Action guidelines. Written by: Kimberly Guercio Patricia Mawer July 2008 Edited by: Frances Kenny Director of Math, Science & Talented and Gifted Education 1 ROSELLE PARK PUBLIC SCHOOLS MATHEMATICS PHILOSOPHY Our children need to be well prepared for lives and careers in a technological world and in a global economy. They need to be able to solve problem and reason effectively. They need to use complex information and advanced tools. They need to know and understand how to use and apply mathematics. These high standards will benefit both our children and our society. The Roselle Park High School Mathematics Curriculum will develop students’ understanding of concepts and help them to acquire essential skills. Their philosophy is based upon the fact that all students possess the ability to be rational thinkers, independent problem solvers, and efficient users of technology. Each student can achieve success and pride while developing these skills. A comprehensive program has been developed in a spiral and sequential format so those students will learn the many aspects of mathematics and its applications. Emphasis will be placed on being actively involved in learning mathematics, writing and talking about math, using critical thinking skills in problem solving, using calculators, computers, and other mathematical tools of learning, and achieving at a high level. Consideration will be given to the individual student’s needs, interests, and abilities. All students must develop and sharpen their skills, deepen their understanding of mathematical concepts and processes, and hone their problem-solving, reasoning, and communication abilities while using mathematics to make sense of, and solve, compelling problem. For this to occur, rigorous mathematical content must be organized, taught, and assessed in a problem-solving environment. The students will be challenged to use math in meaningful ways, so that they come to realize how useful mathematics will be in their lives. Moreover, the curriculum will also encourage the development of positive attitudes and interests in mathematics, which will last a lifetime. 2 Roselle Park Public Schools Educational Goals GOALS 1. Communicate mathematically through written, oral, symbolic, and visual forms of expression. 2. Understand the interrelationships of mathematical ideas and the roles that mathematics plays in other disciplines and in life. 3. Use calculators, computers, manipulatives, and other mathematical tools to enhance mathematical thinking and understanding. 4. Develop the ability to pose and solve mathematical problems in mathematics, other disciplines, and everyday experiences. 5. Develop reasoning ability and become self-reliant, independent mathematical thinkers. 6. Demonstrate high levels of mathematical thought through experiences which extend beyond traditional computation, algebra, and geometry. 7. Develop an understanding of patterns, relationships, and functions, and use them to represent and explain real world phenomena. 3 MATHEMATICS DEPARTMENT COURSE PROFICIENCIES Math 7 I. Descriptions: The objective of the seventh grade math problem solving class is to aid students in further exploring problem solving skills related to standardized testing. The curriculum lays the foundations for the studies of algebra, geometry, and probability. Basic operations with whole numbers, fractions, decimals, and percents are reinforced and built upon. Students will also use explorations, manipulatives, and technology to further understand concepts such as solving equations and inequalities, graphing, geometry, and probability. Students will develop fluency with operations involving integers. A basic goal is to improve problem-solving strategies while maintaining real-world relevance. The pace of the course and the depth of topics covered will vary in accordance to the level of the class. Students are identified in Grade 7 through tests and teacher recommendation. II. Unit Topics: Tools for Algebra and Geometry Test Taking Strategies Number Sense, Patterns, and Algebraic Thinking Decimal Operations Data Statistics Number Patterns and Fractions Fractions Operations Integers Equations, Inequalities, and Functions Ratios and Proportions Percents Probability Geometric Figures Measurement and Area Surface Area and Volume 4 III Objectives: Grade 7 Number and Numerical 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. All students will be able to: Express ratios as a fraction Determine whether two ratios are equivalent Find a ratio that is equivalent to a given ratio Calculate the value of a variable as presented within a ratio Write a proportion to model a given situation and then solve the proportion Convert fractions to equivalent decimals and percents Understand the concept of a percent greater than 100 and less than 1 Solve percent problems using the percent equation Write and solve percent equations to model real life applications that include but are not limited to interest, sales tax, discount, commission, and percent of increase or decrease Create a graphical model of a situation that will total 100 percent Geometry and Measurement All students will develop spatial sense and the ability to use geometric properties, relationships, and measurements to model, describe and analyze phenomena. Recognize the properties that make two figures similar Use the properties of similarity to find the value of sides and angles in a pair of similar figure Prove two figures are similar Create a mapping given a figure by applying various transformations including rotation, translation, dilation and reflection Graph figures on a coordinate plane Create an image of a given figure using transformations and name the coordinates of the image Identify the sequence of transformations needed to map one figure into another Determine the scale factor and find a specified measure on a scale drawing Create a diagram that is a scale drawing of and actual location Calculate the area of a triangle Calculate the area of a trapezoid Determine the perimeter and area of an irregular figure Determine the complement and supplement of a given angle 5 Identify the relationship between vertical angles and use that relationship to find the value of various angles. Draw the next stage in a given fractal Solve problems requiring calculations that involve different units of measure within a measurement system Utilize the reference sheet provide by the state of New Jersey to solve problems Patterns and Algebra All students will represent and analyze relationships among variable quantities and solve problems involving functions, and algebraic concepts and processes. Represent patterns on tables and graphs Describe in words the behavior of a function Graph equations in two variables Analyze functional relationships Create formulas for patterns in the form of Next = Analyze growth patterns of a function including both exponential and geometric growth Graph integers on a number line Determine the absolute value of an integer and explain how this is related to its location on the number line Perform operations with integers included addition, subtraction, multiplication and division through the use of a number line, vectors and mental computation Solve multi-step equations involving integers Simplify all forms of algebraic expressions Use the order of operations, including exponents and parenthesis to simplify expression Demonstrate the distributive property Use the distributive property when simplifying expressions and solving equations 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. Select appropriate representation for given data Interpret and answer questions about box and whisker plots Display data on a scatter plot and identify correlations and outliers Draw inference from a given graph Model situation involving a simulation, using such things as a table of sums, to differentiate between theoretical and experimental probability 6 Apply the multiplication principle to determine the number of possible outcomes given a situation Use permutation with and without replacement Explore counting problems involving Venn Diagrams with three attributes Apply techniques of systematic listing, counting and reasoning in a variety of contexts Mathematical Process All students will use mathematical processes of problem solving, communication, reasoning, representation and technology to solve problems and communicate mathematical idea as described in the appropriate grade level New Jersey Core Curriculum Content Standards. IV Types of Evaluations: 1. 2. 3. 4. 5. 6. 7. 8. V Tests Quizzes Class work/Notebooks Class participation Homework Open ended questions Rubric based assessment Benchmark student assessments Standards of Evaluation: 1. 2. 3. 4. 5. 6. 7. 8. Tests Quizzes Class notes/Notebooks Class participation Homework Open ended questions Rubric based assessment Benchmark student assessment 7 VI Expectations: 1. Students will be responsible for textbooks and other supplies necessary to complete a class work. 2. Students will maintain notes required by the teacher. 3. Students will be expected to list and follow all directions necessary to complete assignments. 4. Students will be responsible for acceptable performance such as class attendance, make up work, and testing. 5. Students will be responsible for efficient use of calculators, computers, manipulatives, and other mathematical tools. 6. Students will review daily homework and concepts. 7. Students will organize review for tests including test-taking and testpreparation strategies. 8. Students will work effectively to complete group/individual assignments. 9. Students will review /take a mid-term and final exam. 8 STATE STANDARDS MATHEMATICS STANDARDS AND PROGRESS INDICATORS GRADE 7 STANDARD 4.1 (Number and numerical 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. Strands and Cumulative Progress Indicators Building upon knowledge and skills gained in preceding grades, by the end of Grade 7, students will: A. Number Sense 1. Extend understanding of the number system by constructing meanings for the following (unless otherwise noted, all indicators for grade 7 pertain to these sets of numbers as well): Rational numbers Percents Whole numbers with exponents 2. Demonstrate a sense of the relative magnitudes of numbers. 3. Understand and use ratios, proportions, and percents (including percents greater than 100 and less than 1) 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. Understand that all fractions can be represented as repeating or terminating decimals. 9 B. Numerical Operations 1. Use and explain procedures for performing calculations with integers and all number types named above with: Pencil-and-paper Mental math Calculator 2. Use exponentiation to find whole number powers of numbers. 3. Understand and apply the standard algebraic order of operations, including appropriate use of parentheses. C. Estimation 1. Use equivalent representations of numbers such as fractions, decimals, and percents to facilitate estimation. 10 STANDARD 4.2 (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. Strands and Cumulative Progress Indicators Building upon knowledge and skills gained in preceding grades, by the end of Grade 7, students will: A. Geometric Properties 1. Understand and apply properties of polygons. Quadrilaterals, including squares, rectangles, parallelograms, trapezoids, rhombi Regular polygons 2. Understand and apply the concept of similarity. Using proportions to find missing measures Scale drawings Models of 3D objects 3. Use logic and reasoning to make and support conjectures about geometric objects. B. Transforming Shapes 1. Understand and apply transformations. Finding the image, given the pre-image, and vice-versa Sequence of transformations needed to map one figure onto another Reflections, rotations, and translations result in images congruent to the pre-image Dilations (stretching/shrinking) result in images similar to the pre-image C. Coordinate Geometry 1. Use coordinates in four quadrants to represent geometric concepts. 11 2. Use a coordinate grid to model and quantify transformations (e.g., translate right 4 units). D. Units of Measurement 1. Solve problems requiring calculations that involve different units of measurement within a measurement system (e.g., 4'3" plus 7'10" equals 12'1"). 2. Select and use appropriate units and tools to measure quantities to the degree of precision needed in a particular problem-solving situation. 3. Recognize that all measurements of continuous quantities are approximations. E. Measuring Geometric Objects 1. Develop and apply strategies for finding perimeter and area. Geometric figures made by combining triangles, rectangles and circles or parts of circles Estimation of area using grids of various sizes 2. Recognize that the volume of a pyramid or cone is one-third of the volume of the prism or cylinder with the same base and height (e.g., use rice to compare volumes of figures with same base and height). 12 STANDARD 4.3 (Patterns and algebra) All students will represent and analyze relationships among variable quantities and solve problems involving patterns, functions, and algebraic concepts and processes. Strands and Cumulative Progress Indicators Building upon knowledge and skills gained in preceding grades, by the end of Grade 7, students will: A. Patterns 1. Recognize, describe, extend, and create patterns involving whole numbers, rational numbers, and integers. Descriptions using tables, verbal and symbolic rules, graphs, simple equations or expressions Finite and infinite sequences Generating sequences by using calculators to repeatedly apply a formula B. Functions and Relationships 1. Graph functions, and understand and describe their general behavior. Equations involving two variables C. Modeling 1. Analyze functional relationships to explain how a change in one quantity can result in a change in another, using pictures, graphs, charts, and equations. 2. Use patterns, relations, symbolic algebra, and linear functions to model situations. Using manipulatives, tables, graphs, verbal rules, algebraic expressions/equations/inequalities Growth situations, such as population growth and compound interest, using recursive (e.g., NOW-NEXT) formulas (cf. science standard 5.5 and social studies standard 6.6) 13 D. Procedures 1. Use graphing techniques on a number line. Absolute value Arithmetic operations represented by vectors (arrows) (e.g., "-3 + 6" is "left 3, right 6") 2. Solve simple linear equations informally and graphically. Multi-step, integer coefficients only (although answers may not be integers) Using paper-and-pencil, calculators, graphing calculators, spreadsheets, and other technology 3. Create, evaluate, and simplify algebraic expressions involving variables. Order of operations, including appropriate use of parentheses Substitution of a number for a variable 4. Understand and apply the properties of operations, numbers, equations, and inequalities. Additive inverse Multiplicative inverse 14 STANDARD 4.4 (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. Strands and Cumulative Progress Indicators Building upon knowledge and skills gained in preceding grades, by the end of Grade 7, students will: A. Data Analysis (or Statistics) 1. Select and use appropriate representations for sets of data, and measures of central tendency (mean, median, and mode). Type of display most appropriate for given data Box-and-whisker plot, upper quartile, lower quartile Scatter plot Calculators and computer used to record and process information 2. Make inferences and formulate and evaluate arguments based on displays and analysis of data. B. Probability 1. Interpret probabilities as ratios, percents, and decimals. 2. Model situations involving probability with simulations (using spinners, dice, calculators and computers) and theoretical models. Frequency, relative frequency 3. Estimate probabilities and make predictions based on experimental and theoretical probabilities. 4. Play and analyze probability-based games, and discuss the concepts of fairness and expected value. 15 C. Discrete Mathematics—Systematic Listing and Counting 1. Apply the multiplication principle of counting. Permutations: ordered situations with replacement (e.g., number of possible license plates) vs. ordered situations without replacement (e.g., number of possible slates of 3 class officers from a 23 student class) 2. Explore counting problems involving Venn diagrams with three attributes (e.g., there are 15, 20, and 25 students respectively in the chess club, the debating team, and the engineering society; how many different students belong to the three clubs if there are 6 students in chess and debating, 7 students in chess and engineering, 8 students in debating and engineering, and 2 students in all three?). 3. Apply techniques of systematic listing, counting, and reasoning in a variety of different contexts. D. Discrete Mathematics—Vertex-Edge Graphs and Algorithms 1. Use vertex-edge graphs to represent and find solutions to practical problems. Finding the shortest network connecting specified sites Finding the shortest route on a map from one site to another Finding the shortest circuit on a map that makes a tour of specified sites 16 STANDARD 4.5 (Mathematical processes) All students will use mathematical processes of problem solving, communication, connections, reasoning, representations, and technology to solve problems and communicate mathematical ideas. Strands and Cumulative Progress Indicators Building upon knowledge and skills gained in preceding grades, by the end of Grade 7, students will: A. Problem Solving 1. Learn mathematics through problem solving, inquiry, and discovery. 2. Solve problems that arise in mathematics and in other contexts (cf. workplace readiness standard 8.3). Open-ended problems Non-routine problems Problems with multiple solutions Problems that can be solved in several ways 3. Select and apply a variety of appropriate problem-solving strategies (e.g., "try a simpler problem" or "make a diagram") to solve problems. 4. Pose problems of various types and levels of difficulty. 5. Monitor their progress and reflect on the process of their problem solving activity. B. Communication 1. Use communication to organize and clarify their mathematical thinking. Reading and writing Discussion, listening, and questioning 2. Communicate their mathematical thinking coherently and clearly to peers, teachers, and others, both orally and in writing. 3. Analyze and evaluate the mathematical thinking and strategies of others. 4. Use the language of mathematics to express mathematical ideas precisely. 17 C. Connections 1. Recognize recurring themes across mathematical domains (e.g., patterns in number, algebra, and geometry). 2. Use connections among mathematical ideas to explain concepts (e.g., two linear equations have a unique solution because the lines they represent intersect at a single point). 3. Recognize that mathematics is used in a variety of contexts outside of mathematics. 4. Apply mathematics in practical situations and in other disciplines. 5. Trace the development of mathematical concepts over time and across cultures (cf. world languages and social studies standards). 6. Understand how mathematical ideas interconnect and build on one another to produce a coherent whole. D. Reasoning 1. Recognize that mathematical facts, procedures, and claims must be justified. 2. Use reasoning to support their mathematical conclusions and problem solutions. 3. Select and use various types of reasoning and methods of proof. 4. Rely on reasoning, rather than answer keys, teachers, or peers, to check the correctness of their problem solutions. 5. Make and investigate mathematical conjectures. Counterexamples as a means of disproving conjectures Verifying conjectures using informal reasoning or proofs. 6. Evaluate examples of mathematical reasoning and determine whether they are valid. E. Representations 1. Create and use representations to organize, record, and communicate mathematical ideas. Concrete representations (e.g., base-ten blocks or algebra tiles) Pictorial representations (e.g., diagrams, charts, or tables) Symbolic representations (e.g., a formula) 18 Graphical representations (e.g., a line graph) 2. Select, apply, and translate among mathematical representations to solve problems. 3. Use representations to model and interpret physical, social, and mathematical phenomena. F. Technology 1. Use technology to gather, analyze, and communicate mathematical information. 2. Use computer spreadsheets, software, and graphing utilities to organize and display quantitative information. 3. Use graphing calculators and computer software to investigate properties of functions and their graphs. 4. Use calculators as problem-solving tools (e.g., to explore patterns, to validate solutions). 5. Use computer software to make and verify conjectures about geometric objects. 6. Use computer-based laboratory technology for mathematical applications in the sciences. 19 Scope and Sequence September Pretest Test Taking Strategies Calculator Instruction October Number Sense, Patterns, and Algebraic Thinking Decimal Operations November Data and Statistics December Number Patterns and Fractions Fraction Operations January Integers Equations, Inequalities, and Functions February Equations, Inequalities, and Functions Ratios and Proportions March Percents Probability Geometric Figures April Measurement and Area Surface Area and Volume May Integer Operations June Variables Equations 20 UNIT I A. TEST TAKING STRATEGIES Duration: September Major Objectives: 1. 2. 3. 4. 5. B. Sequence of Topics: 1. 2. 3. 4. 5. 6. 7. C. To learn and utilize the skills necessary to answer multiple choice questions. To learn and utilize the skills necessary to answer extended response questions. To learn and utilize the skills necessary to answer short response questions. To review basic mathematical facts, including decimal operations. To explore basic calculator skills. Answering the question asked (4.5) (p. 2) Eliminating answers (4.5) (p. 6) Writing a short answer response (4.5) (p. 3) Writing extended responses (4.5) (p. 4) Working backwards (4.5) (p. 7) Review operations with decimals (4.1) (p. 22, 35, 38) Explore basic calculator skills. Core Material: Test-Taking Strategies Pearson Prentice Hall 2007 Measuring Up 7 Brooks, Carlin, McLaughlin, Perry, Vogt People’s Education 2006 D. Supplemental Materials: 1. 2. 3. 4. 5. 6. 7. 8. Teacher made transparencies Teacher made worksheets Power Point Presentations Study Island Success Maker Calculators Internet NJASK Coach WriteMath 21 E. Suggested Assignments, Projects, Field Trips, Speakers: 1. 2. 3. 4. 5. F. Complete exercises in book for each lesson Complete practice worksheets Use calculator/computer to complete classroom and homework problems Complete/review chapter prior to test/quizzes using text and teacher made materials. NJASK Do Now Suggested Assessments: 1. 2. 3. 4. 5. 6. Test Quizzes Class Participation Notebook/Classwork Homework Benchmark Tests 22 UNIT II A. NUMBER SENSE, PATTERNS, AND ALGEBRAIC THINKING Duration: October Major Objectives: 1. 2. To describe patterns and use them to solve problems. To apply the order of operations to evaluate variable expressions involving powers and exponents and to solve equations. B. Sequence of Topics: 1. Describe patterns using whole number operations. (4.3) 2. Evaluate variable expressions. (4.3) 3. Write repeated multiplication using exponents. (4.1) 4. Use the order of operations to evaluate expressions involving two or more operations. (4.1) 5. Use mental math to solve equations. (4.3) 6. Use formulas to find perimeter and area. (4.2) 7. Use a 4-step plan to solve problems. (4.5) C. Core Material: New Jersey ASK Coach Kaplan Triumph Learning 2005 Measuring Up Peoples Education 2006 D. Supplemental Materials: 1. 2. 3. 4. 5. 6. 7. E. Educational Design- Pre GEPA Instructivision Inc.– Pre GEPA Success Peoples Publishing- Measuring Up on the NJ GEPA Teacher made transparencies Teacher made worksheets Study Island Success Maker Suggested Assignments, Projects, Field Trips, Speakers: 1. 2. 3. Complete exercises in NJASK Coach / Measuring Up for each lesson Complete sample test questions at the end of each unit Use calculator/computer to complete classroom and homework problems 23 4. 5. F. Complete/review chapter prior to test/quizzes using text and teacher made materials NJASK Do Now Suggested Assessments: 1. 2. 3. 4. 5. 6. 7. Test Quizzes Class participation Notebook/classwork Homework Study Island Success Maker 24 UNIT III A. DECIMAL OPERATIONS Duration: October Major Objectives: 1. 2. B. Sequence of Topics: 1. 2. 3. 4. 5. 6. 7. C. To perform operations with decimals, including comparing and rounding decimals. To solve real-world problems involving scientific notation and metric measurements. Compare, order, and round decimals. (4.1) Add and subtract decimals. (4.1) Multiply decimals. (4.1) Divide decimals. (4.1) Read and write numbers using scientific notation. (4.1) Measure and estimate using metric units. (4.2) Convert between metric units. (4.2) Core Material: New Jersey ASK Coach Kaplan Triumph Learning 2005 Measuring Up Peoples Education 2006 D. Supplemental Materials: 1. 2. 3. 4. 5. 6. 7. E. Educational Design- Pre GEPA Instructivision Inc.– Pre GEPA Success Peoples Publishing- Measuring Up on the NJ GEPA Teacher made transparencies Teacher made worksheets Study Island Success Maker Suggested Assignments, Projects, Field Trips, Speakers: 1. Complete exercises in NJASK Coach / Measuring Up for each lesson 25 2. 3. 4. 5. F. Complete sample test questions at the end of each unit Use calculator/computer to complete classroom and homework problems Complete/review chapter prior to test/quizzes using text and teacher made materials NJASK Do Now Suggested Assessments: 1. 2. 3. 4. 5. 6. 7. Test Quizzes Class participation Notebook/classwork Homework Study Island Success Maker 26 UNIT IV A. DATA AND STATISTICS Duration: November Major Objectives: 1. 2. B. Sequence of Topics: 1. 2. 3. 4. 5. 6. 7. C. To study the mean, median, and mode of a data set. Use bar graphs, line graphs, stem-and-leaf plots, box-and-whisker plots, and histograms to display and analyze the distribution of the values in a data set. Describe data using mean, median, and mode. (4.4) Make and interpret bar graphs and line graphs. (4.4) Display data using stem-and-leaf plots. (4.4) Display data using box-and-whisker plots (4.4) Make and interpret histograms (4.4) Choose an appropriate display for a data set. (4.4) NJASK Preparation, Coach book. (4.1) Core Material: New Jersey ASK Coach Kaplan Triumph Learning 2005 Measuring Up Peoples Education 2006 D. Supplemental Materials: 1. 2. 3. 4. 5. 6. 7. Educational Design- Pre GEPA Instructivision Inc.– Pre GEPA Success Peoples Publishing- Measuring Up on the NJ GEPA Teacher made transparencies Teacher made worksheets Study Island Success Maker 27 E. Suggested Assignments, Projects, Field Trips, Speakers: 1. 2. 3. 4. 5. F. Complete exercises in NJASK Coach / Measuring Up for each lesson Complete sample test questions at the end of each unit Use calculator/computer to complete classroom and homework problems Complete/review chapter prior to test/quizzes using text and teacher made materials NJASK Do Now Suggested Assessments: 1. 2. 3. 4. 5. 6. 7. Test Quizzes Class participation Notebook/classwork Homework Study Island Success Maker 28 UNIT V A. NUMBER PATTERNS AND FRACTIONS Duration: December Major Objectives: 1. 2. B. Sequence of Topics: 1. 2. 3. 4. 5. 6. 7. 8. C. To find the greatest common factor and least common multiple of two or more numbers. To compare fractions and mixed numbers, and to write fractions as decimals and vice versa. Write a number as a product of primes. (4.1) (pp. 165-169) Find the greatest common factor of two or more numbers. (4.1) (pp. 170-174) Write equivalent fractions. (4.1) (pp. 176-180) Find the least common multiple of two or more numbers. (4.1) (pp. 182-186) Compare and order fractions. (4.1) (pp. 189-192) Compare and order fractions and mixed numbers. (4.1) (pp. 194-198) Write fractions as decimals and decimals as fractions. (4.1) (pp. 199-204) NJASK Preparation, Coach book. (4.2) (pp. 82-111) Core Material: New Jersey ASK Coach Kaplan Triumph Learning 2005 Measuring Up Peoples Education 2006 D. Supplemental Materials: 1. 2. 3. 4. 5. 6. 7. Educational Design- Pre GEPA Instructivision Inc.– Pre GEPA Success Peoples Publishing- Measuring Up on the NJ GEPA Teacher made transparencies Teacher made worksheets Study Island Success Make 29 E. Suggested Assignments, Projects, Field Trips, Speakers: 1. 2. 3. 4. 5. F. Complete exercises in NJASK Coach / Measuring Up for each lesson Complete sample test questions at the end of each unit Use calculator/computer to complete classroom and homework problems Complete/review chapter prior to test/quizzes using text and teacher made materials NJASK Do Now Suggested Assessments: 1. 2. 3. 4. 5. 6. 7. Test Quizzes Class participation Notebook/classwork Homework Study Island Success Maker 30 UNIT VI A. FRACTION OPERATIONS Duration: December Major Objectives: 1. 2. B. Sequence of Topics: 1. 2. 3. 4. 5. 6. C. To add and subtract fractions and mixed numbers. To multiply and divide fractions and mixed numbers, and to learn about customary units. Add and subtract fractions. (4.1) Add and subtract mixed numbers. (4.1) Multiply fractions and mixed numbers. (4.1) Divide fractions and mixed numbers. (4.1) Measure and estimate using customary units. (4.1) Convert between customary units. (4.1) Core Material: New Jersey ASK Coach Kaplan Triumph Learning 2005 Measuring Up Peoples Education 2006 D. Supplemental Materials: 1. 2. 3. 4. 5. 6. 7. E. Educational Design- Pre GEPA Instructivision Inc.– Pre GEPA Success Peoples Publishing- Measuring Up on the NJ GEPA Teacher made transparencies Teacher made worksheets Study Island Success Maker Suggested Assignments, Projects, Field Trips, Speakers: 1. 2. 3. Complete exercises in NJASK Coach / Measuring Up for each lesson Complete sample test questions at the end of each unit Use calculator/computer to complete classroom and homework problems 31 4. 5. F. Complete/review chapter prior to test/quizzes using text and teacher made materials NJASK Do Now Suggested Assessments: 1. 2. 3. 4. 5. 6. 7. Test Quizzes Class participation Notebook/classwork Homework Study Island Success Maker 32 UNIT VII A. INTEGERS Duration: January Major Objectives: 1. 2. B. Sequence of Topics: 1. 2. 3. 4. 5. 6. 7. 8. 7. C. To compare and order integers and perform integer addition, subtractions, multiplication, and division. To define rational numbers and graph points in the coordinate plane. Compare and order integers. (4.1) Add integers. (4.1) Subtract integers. (4.1) Multiply integers. (4.1) Divide integers (4.1) Perform operations on rational numbers. (4.1) Evaluate expression using the distributive property. (4.3) Identify and plot points in a coordinate plane. (4.2) NJASK Preparation, Coach book. (4.3) Core Material: New Jersey ASK Coach Kaplan Triumph Learning 2005 Measuring Up Peoples Education 2006 D. Supplemental Materials: 1. 2. 3. 4. 5. 6. 7. E. Educational Design- Pre GEPA Instructivision Inc.– Pre GEPA Success Peoples Publishing- Measuring Up on the NJ GEPA Teacher made transparencies Teacher made worksheets Study Island Success Maker Suggested Assignments, Projects, Field Trips, Speakers: 33 1. 2. 3. 4. 5. F. Complete exercises in NJASK Coach / Measuring Up for each lesson Complete sample test questions at the end of each unit Use calculator/computer to complete classroom and homework problems Complete/review chapter prior to test/quizzes using text and teacher made materials NJASK Do Now Suggested Assessments: 1. 2. 3. 4. 5. 6. 7. Test Quizzes Class participation Notebook/classwork Homework Study Island Success Maker 34 UNIT VIII A. EQUATIONS, INEQUALITIES, AND FUNCTIONS Duration: January / February Major Objectives: 1. 2. B. Sequence of Topics: 1. 2. 3. 4. 5. 6. 7. 8. C. To write and simplify expressions, and solve equations and inequalities. To use equations, table, and graphs to represent functions. Write variable expressions and equations. (4.3) Simplify variable expressions. (4.3) Solve addition and subtraction equations. (4.3) Solve multiplication and division equations. (4.3)) Solve two-step equations. (4.3) Write and solve inequalities. (4.3) Write and evaluate function rules. (4.3) Graph functions in a coordinate plane. (4.3) Core Material: New Jersey ASK Coach Kaplan Triumph Learning 2005 Measuring Up Peoples Education 2006 D. Supplemental Materials: 1. 2. 3. 4. 5. 6. 7. E. Educational Design- Pre GEPA Instructivision Inc.– Pre GEPA Success Peoples Publishing- Measuring Up on the NJ GEPA Teacher made transparencies Teacher made worksheets Study Island Success Maker Suggested Assignments, Projects, Field Trips, Speakers: 1. Complete exercises in NJASK Coach / Measuring Up for each lesson 35 2. 3. F. Complete sample test questions at the end of each unit Use calculator/computer to complete classroom and homework problems 4. Complete/review chapter prior to test/quizzes using text and teacher made materials 5. NJASK Do Now Suggested Assessments: 1. 2. 3. 4. 5. 6. 7. Test Quizzes Class participation Notebook/classwork Homework Study Island Success Maker 36 UNIT IX A. RATIOS AND PROPORTIONS Duration: February Major Objectives: 1. 2. B. Sequence of Topics: 1. 2. 3. 4. 5. 6. C. Apply ratios, rates, and unit rates to solve proportions and to scale drawings. To explore the relationship between rate and the slope of a line Write and compare ratios. (4.1) Use rates to compare two quantities with different units. (4.1) Find the slope of a line. (4.3) Solve proportions using equivalent ratios and algebra (4.3) Solve proportions using cross products. (4.3) Use proportions with models. (4.5) Core Material: New Jersey ASK Coach Kaplan Triumph Learning 2005 Measuring Up Peoples Education 2006 D. Supplemental Materials: 1. 2. 3. 4. 5. 6. 7. E. Educational Design- Pre GEPA Instructivision Inc.– Pre GEPA Success Peoples Publishing- Measuring Up on the NJ GEPA Teacher made transparencies Teacher made worksheets Study Island Success Maker Suggested Assignments, Projects, Field Trips, Speakers: 1. 2. 3. Complete exercises in NJASK Coach / Measuring Up for each lesson Complete sample test questions at the end of each unit Use calculator/computer to complete classroom and homework problems 37 4. 5. F. Complete/review chapter prior to test/quizzes using text and teacher made materials NJASK Do Now Suggested Assessments: 1. 2. 3. 4. 5. 6. 7. Test Quizzes Class participation Notebook/classwork Homework Study Island Success Maker 38 UNIT X A. PERCENTS Duration: March Major Objectives: 1. 2. B. C. Examine the relationships among fractions, decimals, and percents when writing fractions and decimals as percents. Solve percent problems, including discounts, markups, sales tax, tips, and simple interest. Sequence of Topics: 1. 2. Use a fraction to find the percent of a number. (4.1) Use proportions to solve percent problems. (4.1 3. 4. 5. 6. 7. 8. 9. 10. Write percents as decimals and decimals as percents. (4.1) Solve proportions using equivalent ratios and algebra. (4.3) Use equations to solve percent problems. (4.3) Use percents to interpret and make circle graphs. (4.4) Find a percent of change in a quantity. (4.5) Find discounts, markups, sales tax, and tips. (4.5) Calculate simple interest. (4.5) NJASK Preparation, Coach book. (4.4) Core Material: New Jersey ASK Coach Kaplan Triumph Learning 2005 Measuring Up Peoples Education 2006 D. Supplemental Materials: 1. 2. 3. 4. 5. 6. 7. Educational Design- Pre GEPA Instructivision Inc.– Pre GEPA Success Peoples Publishing- Measuring Up on the NJ GEPA Teacher made transparencies Teacher made worksheets Study Island Success Maker 39 E. Suggested Assignments, Projects, Field Trips, Speakers: 1. 2. 3. 4. 5. F. Complete exercises in NJASK Coach / Measuring Up for each lesson Complete sample test questions at the end of each unit Use calculator/computer to complete classroom and homework problems Complete/review chapter prior to test/quizzes using text and teacher made materials NJASK Do Now Suggested Assessments: 1. 2. 3. 4. 5. 6. 7. Test Quizzes Class participation Notebook/classwork Homework Study Island Success Maker 40 UNIT XI A. PROBABILITY Duration: March Major Objectives: 1. 2. B. Sequence of Topics: 1. 2. 3. 4. 5. 6. 7. C. To count the possible outcomes of an experiment using tree diagrams and the counting principle, and study permutations and combinations. Examine methods for calculating the probability of events, including dependent and independent events. Find probabilities. (4.4) Use a tree diagram to find all possible outcomes. (4.4) Use the counting principle to count outcomes. (4.4) Use permutations and combinations (4.4) Find the probability that either of two events occurs. (4.4) Find the probability of compound events. (4.4) NJASK Preparation, Coach book. (4.5) Core Material: New Jersey ASK Coach Kaplan Triumph Learning 2005 Measuring Up Peoples Education 2006 D. Supplemental Materials: 1. 2. 3. 4. 5. 6. 7. E. Educational Design- Pre GEPA Instructivision Inc.– Pre GEPA Success Peoples Publishing- Measuring Up on the NJ GEPA Teacher made transparencies Teacher made worksheets Study Island Success Maker Suggested Assignments, Projects, Field Trips, Speakers: 1. Complete exercises in NJASK Coach / Measuring Up for each lesson 41 2. 3. 4. 5. F. Complete sample test questions at the end of each unit Use calculator/computer to complete classroom and homework problems Complete/review chapter prior to test/quizzes using text and teacher made materials NJASK Do Now Suggested Assessments: 1. 2. 3. 4. 5. 6. 7. Test Quizzes Class participation Notebook/classwork Homework Study Island Success Maker 42 UNIT XII A. GEOMETRIC FIGURES Duration: March Major Objectives: 1. 2. B. Sequence of Topics: 1. 2. 3. 4. 5. 6. 7. 8. C. To explore angles, triangles, and polygons, and investigate congruent and similar polygons. To study three types of transformations: translations, reflections, and rotations. Classify angles by their measures. (4.2) Identify special pairs of angles and types of lines. (4.2) Classify triangles. (4.2) Classify quadrilaterals and other polygons. (4.2) Use properties of similar and congruent polygons. (4.2) Use similar triangles to find lengths. (4.2) Identify transformations and symmetry in figures. (4.2) Graph transformations in a coordinate plane. (4.2) Core Material: New Jersey ASK Coach Kaplan Triumph Learning 2005 Measuring Up Peoples Education 2006 D. Supplemental Materials: 1. 2. 3. 4. 5. 6. 7. E. Educational Design- Pre GEPA Instructivision Inc.– Pre GEPA Success Peoples Publishing- Measuring Up on the NJ GEPA Teacher made transparencies Teacher made worksheets Study Island Success Maker Suggested Assignments, Projects, Field Trips, Speakers: 1. 2. Complete exercises in NJASK Coach / Measuring Up for each lesson Complete sample test questions at the end of each unit 43 3. 4. 5. F. Use calculator/computer to complete classroom and homework problems Complete/review chapter prior to test/quizzes using text and teacher made materials NJASK Do Now Suggested Assessments: 1. 2. 3. 4. 5. 6. 7. Test Quizzes Class participation Notebook/classwork Homework Study Island Success Maker 44 UNIT XIII A. MEASUREMENT AND AREA Duration: April Major Objectives: 1. 2. B. Sequence of Topics: 1. 2. 3. 4. 5. 6. 7. C. To use the Pythagorean Theorem. To apply the area formulas for parallelograms, triangles, trapezoids, and circles to solve real-world problems. Evaluate expression involving square roots. (4.1) Approximate square roots of numbers. (4.1) Find the length of a side of a right triangle. (4.2) Find the area of parallelograms. (4.2) Find the areas of triangles and trapezoids. (4.2) Find the circumferences of circles. (4.2) Find the areas of circles. (4.2) Core Material: New Jersey ASK Coach Kaplan Triumph Learning 2005 Measuring Up Peoples Education 2006 D. Supplemental Materials: 1. 2. 3. 4. 5. 6. 7. E. Educational Design- Pre GEPA Instructivision Inc.– Pre GEPA Success Peoples Publishing- Measuring Up on the NJ GEPA Teacher made transparencies Teacher made worksheets Study Island Success Maker Suggested Assignments, Projects, Field Trips, Speakers: 1. 2. 3. Complete exercises in NJASK Coach / Measuring Up for each lesson Complete sample test questions at the end of each unit Use calculator/computer to complete classroom and homework problems 45 4. 5. F. Complete/review chapter prior to test/quizzes using text and teacher made materials NJASK Do Now Suggested Assessments: 1. 2. 3. 4. 5. 6. 7. Test Quizzes Class participation Notebook/classwork Homework Study Island Success Maker 46 UNIT XIV A. SURFACE AREA AND VOLUME Duration: April Major Objectives: 1. 2. B. Sequence of Topics: 1. 2. 3. 4. 5. 6. C. To classify and sketch prisms, pyramids, cylinders, and cones, and their nets. To explore and use the formulas for the surface area and volume of rectangular prisms and cylinders. Classify solids and identify their parts. (4.2) Sketch solids. (4.2) Find surface areas of rectangular prisms. (4.2) Find surface areas of cylinders. (4.2) Find volumes of rectangular prisms. (4.2) Find volumes of cylinders. (4.2) Core Material: New Jersey ASK Coach Kaplan Triumph Learning 2005 Measuring Up Peoples Education 2006 D. Supplemental Materials: 1. 2. 3. 4. 5. 6. 7. E. Educational Design- Pre GEPA Instructivision Inc.– Pre GEPA Success Peoples Publishing- Measuring Up on the NJ GEPA Teacher made transparencies Teacher made worksheets Study Island Success Maker Suggested Assignments, Projects, Field Trips, Speakers: 1. 2. 3. 4. Complete exercises in NJASK Coach / Measuring Up for each lesson Complete sample test questions at the end of each unit Use calculator/computer to complete classroom and homework problems Complete/review chapter prior to test/quizzes using text and teacher made materials 47 5. F. NJASK Do Now Suggested Assessments: 1. 2. 3. 4. 5. 6. 7. Test Quizzes Class participation Notebook/classwork Homework Study Island Success Maker 48 UNIT XV A. REVIEW INTEGER OPERATIONS (beginning 8th Grade Topic) Duration: May Major Objectives: 1. 2. 3. B. Sequence of Topics: 1. 2. 3. 4. 5. 6. 7. 8. 7. C. To compare and order integers and perform integer addition, subtractions, multiplication, and division. To define rational numbers and graph points in the coordinate plane. To expand on topics learned earlier in the year to ensure students are well prepared for the beginning of 8th grade. Compare and order integers. (4.1) Add integers. (4.1) Subtract integers. (4.1) Multiply integers. (4.1) Divide integers (4.1) Perform operations on rational numbers. (4.1) Evaluate expression using the distributive property. (4.3) Identify and plot points in a coordinate plane. (4.2) NJASK Preparation, Coach book. (4.3) Core Material: New Jersey ASK Coach Kaplan Triumph Learning 2005 Measuring Up Peoples Education 2006 D. Supplemental Materials: 1. 2. 3. 4. 5. 6. 7. E. Educational Design- Pre GEPA Instructivision Inc.– Pre GEPA Success Peoples Publishing- Measuring Up on the NJ GEPA Teacher made transparencies Teacher made worksheets Study Island Success Maker Suggested Assignments, Projects, Field Trips, Speakers: 49 1. 2. 3. 4. 5. F. Complete exercises in NJASK Coach / Measuring Up for each lesson Complete sample test questions at the end of each unit Use calculator/computer to complete classroom and homework problems Complete/review chapter prior to test/quizzes using text and teacher made materials NJASK Do Now Suggested Assessments: 1. 2. 3. 4. 5. 6. 7. Test Quizzes Class participation Notebook/classwork Homework Study Island Success Maker 50 UNIT XVI Topic) REVIEW VARIABLES AND EQUATIONS (beginning 8th Grade Duration: June A. Major Objectives: 1. 2. 3. B. Sequence of Topics: 1. 2. 3. 4. 5. 6. 7. 8. 9. C. To write and simplify expressions, and solve equations and inequalities. To use equations, table, and graphs to represent functions. To expand on topics learned earlier in the year to ensure students are well prepared for the beginning of 8th grade. Write variable expressions and equations. (4.3) Simplify variable expressions. (4.3) Solve addition and subtraction equations. (4.3) Solve multiplication and division equations. (4.3)) Solve two-step equations. (4.3) Write and solve inequalities. (4.3) Write and evaluate function rules. (4.3) Graph functions in a coordinate plane. (4.3) NJASK Preparation, Coach book. (4.3) Core Material: New Jersey ASK Coach Kaplan Triumph Learning 2005 Measuring Up Peoples Education 2006 D. Supplemental Materials: 1. 2. 3. 4. 5. 6. 7. E. Educational Design- Pre GEPA Instructivision Inc.– Pre GEPA Success Peoples Publishing- Measuring Up on the NJ GEPA Teacher made transparencies Teacher made worksheets Study Island Success Maker Suggested Assignments, Projects, Field Trips, Speakers: 1. Complete exercises in NJASK Coach / Measuring Up for each lesson 51 2. 3. 4. 5. F. Complete sample test questions at the end of each unit Use calculator/computer to complete classroom and homework problems Complete/review chapter prior to test/quizzes using text and teacher made materials NJASK Do Now Suggested Assessments: 1. 2. 3. 4. 5. 6. 7. Test Quizzes Class participation Notebook/classwork Homework Study Island Success Maker 52