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Roselle Park School District Mathematics Department Course of Study Math Grade 7 1 MATH GRADE 7 The purpose of this guide is to provide the instructor with a scope and sequence and the course objectives. 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. This guide applies to all students and meets the Affirmative Action guidelines. Written by: Jessica Clausi Revised Summer 2007 Updated 2009 2 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. 3 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. 4 MATHEMATICS DEPARTMENT COURSE PROFICIENCIES Math7 I. Descriptions: The objective of the eighth grade math is to aid students in making the transition from elementary mathematics to more advanced high school math courses. The curriculum lays the foundations for the studies of algebra, geometry, and statistics. 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 basic trigonometry. Students will develop fluency with operations involving integers. A basic goal is to improve problemsolving 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: Variables and Equations Integer Operations Solving Equations Solving Inequalities Factors, Fractions, and Exponents Rational Number Operations Ratio, Proportion, and Percent Probability Polygons and Transformations Real Numbers and Right Triangles Measurement, Area, and Volume Data Analysis and Probability Multi-Step Equations and Inequalities Linear Equations and Graphs Polynomials and Functions NJ ASK Skills 5 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: Extend understanding of the number system by constructing meaning for rational numbers, percents, exponents, roots, absolute value, and numbers represented in scientific notation Recognize that repeating decimals correspond to fractions and determine their fractional equivalent Construct meaning for non-terminating and non-repeating decimals Determine the absolute value of a number given in a variety of forms Understand the relationship between different number systems Order and compare all different types of numbers Find whole number powers of numbers Understand the relationship between powers and roots. Grade Eight Proficiency Assessment Make appropriate estimations and approximations Understand numbers, our numeration system, and their applications in realworld situations Use ratios, proportions, and percents in a variety of situations 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 and compare the properties of a three dimensional figure Identify the different views of a three dimension figure including but not limited too nets and cross sections Find the volume of a rectangular prism and a cylinder Use a given formula to find the volume of a cone and pyramid Calculate the surface area of a rectangular prism by finding the area of each surface and then adding them together Find the surface area of a figure given the formula Determine the relationship between the quantitative change in the numbers of sides as related to the change in the area and volume Identify by name the relationship between the angles created when two parallel lines are cut by a transversal 6 Find the value of the angles created when two parallel lines are cut by a transversal Use the Pythagorean to solve problems Determine the formula for finding the sum of the interior angles of a polygon and use said formula given a figure with a specific number of sides Combine various geometric figures to create new figures and find the area of the new figure, include the use of the circle and the semi-circle Utilize the reference sheet provide by the state of New Jersey to solve problems Grade Eight Proficiency Assessment Recognize, identify, and represent spatial relationships and geometric properties Apply principles of congruence, similarity, symmetry, geometric transformations, and coordinate geometry Apply principles of measurement and geometry to solve problems involving direct and indirect measurement Patterns and Algebra All students will represent and analyze relationships among variable quantities and solve problems involving functions, and algebraic concepts and processes. Recognize, describe, extend and create patterns involving whole numbers, rational numbers and integers. Describe the relationships using tables, verbal and symbolic rules, graphs and simple equations. The relationships explored should include finite and infinite sequences, arithmetic and geometric sequences as well as recursive patterns such as the Fibonacci Sequence and Pascal’s Triangle Describe the behavior of all patterns including exponential growth and decay using a verbal rule and a formula Graph a function in two variable Discovery, describe and calculate the rate of change given a function Recognize and describe the difference between linear and exponential growth Use symbolic algebra to model functions Solve multi-step equations with variables on both sides Solve both single and multi-step inequalities Simplify algebraic expression using the distributive property Grade Eight Proficiency Assessment Recognize, create, and extend a variety of patterns and use inductive reasoning to understand and represent mathematical and other real-world phenomena Use algebraic concepts and processes to concisely express, analyze, and model real-world situations 7 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. Create a box and whisker plot and identify the upper and lower quartiles Calculate the effect on the central tendencies if the data is changed Estimate the line of best of a scatter plot Determine the probability of a compound event Interpret probabilities as rates, percents and decimals Estimate the probability of an event occurring using theoretical data Apply the multiplication principle using permutations for ordered situations with and without replacement, using factorial notation. Understand the concept of combinations (choosing four officers from a class of twenty) Apply techniques of systematic listing, counting, and reasoning in a variety of contexts Use vertex edge graphs to represent a variety of situations such as the shortest network connecting different sites, the shortest route from one street to another, the shortest distance from one point on a map to another, the shortest circuit on a map that makes a tour of specific locations Grade Eight Proficiency Assessment Predict, determine, interpret, and use probabilities Collect, organize, represent, analyze, and evaluate data Apply the concepts and methods of discrete mathematics to model and explore a variety of practical situations Use iterative patterns and processes to describe real-world situations and solve problems 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. 8 IV Types of Evaluations: 1. 2. 3. 4. 5. 6. 7. V Standards of Evaluation: 1. 2. 3. 4. 5. 6. 7. VII Tests Quizzes Class work/Notebooks Class participation Homework Open ended questions Rubric based assessment Tests Quizzes Class notes/Notebooks Class participation Homework Open ended questions Rubric based assessment Expectations: 1. Students will be responsible for textbooks and other supplies necessary to complete 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. 9 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 Exponents Roots Absolute values Numbers represented in scientific notation 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. 10 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. 5/7 = 0. 714285714285… = 0.714285 7. Construct meanings for common irrational numbers, such as π(pi) and the square root of 2. B. Numerical Operations 1. 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 Calculator 2. Use exponentiation to find whole number powers of numbers. 3. Find square and cube roots of numbers and understand the inverse nature of powers and roots. 4. Solve problems involving proportions and percents. 5. Understand and apply the standard algebraic order of operations, including appropriate use of parentheses. C. Estimation 1. Estimate square and cube roots of numbers. 2. Use equivalent representations of numbers such as fractions, decimals, and percents to facilitate estimation. 11 3. Recognize the limitations of estimation and assess the amount of error resulting from estimation. 12 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 concepts involving lines, angles, and planes. Complementary and supplementary angles Vertical angles Bisectors and perpendicular bisectors Parallel, perpendicular, and intersecting planes Intersection of plane with cube, cylinder, cone, and sphere 2. Understand and apply the Pythagorean theorem. 3. Understand and apply properties of polygons. 4. Quadrilaterals, including squares, rectangles, parallelograms, trapezoids, rhombi Regular polygons Sum of measures of interior angles of a polygon Which polygons can be used alone to generate a tessellation and why 5. Understand and apply the concept of similarity. Using proportions to find missing measures Scale drawings Models of 3D objects 6. Use logic and reasoning to make and support conjectures about geometric objects. 13 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 2. Use iterative procedures to generate geometric patterns. Fractals (e.g., the Koch Snowflake) Self-similarity Construction of initial stages Patterns in successive stages (e.g., number of triangles in each stage of Sierpinski's Triangle) C. Coordinate Geometry 1. Use coordinates in four quadrants to represent geometric concepts. 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. Use approximate equivalents between standard and metric systems to estimate measurements (e.g., 5 kilometers is about 3 miles). 3. 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. 14 4. Select and use appropriate units and tools to measure quantities to the degree of precision needed in a particular problem-solving situation. 5. Recognize that all measurements of continuous quantities are approximations. 6. 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). 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 Impact of a dilation on the perimeter and area of a 2-dimensional figure 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). 3. Develop and apply strategies and formulas for finding the surface area and volume of a three-dimensional figure. Volume - prism, cone, pyramid Surface area - prism (triangular or rectangular base), pyramid (triangular or rectangular base) Impact of a dilation on the surface area and volume of a three-dimensional figure 4. Use formulas to find the volume and surface area of a sphere. 15 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 Arithmetic sequences (i.e., sequences generated by repeated addition of a fixed number, positive or negative) Geometric sequences (i.e., sequences generated by repeated multiplication by a fixed positive ratio, greater than 1 or less than 1) 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 Rates of change (informal notion of slope) 16 2. Recognize and describe the difference between linear and exponential growth, using tables, graphs, and equations. 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 concrete materials (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) 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, graphically, and using formal algebraic methods. Multi-step, integer coefficients only (although answers may not be integers) Using paper-and-pencil, calculators, graphing calculators, spreadsheets, and other technology 3. Solve simple linear inequalities. 4. Create, evaluate, and simplify algebraic expressions involving variables. 17 Order of operations, including appropriate use of parentheses Distributive property Substitution of a number for a variable Translation of a verbal phrase or sentence into an algebraic expression, equation, or inequality, and vice versa 5. Understand and apply the properties of operations, numbers, equations, and inequalities. Additive inverse Multiplicative inverse Addition and multiplication properties of equality Addition and multiplication properties of inequalities 18 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 Finding the median and mean (weighted average) using frequency data. Effect of additional data on measures of central tendency 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. B. Probability 1. Interpret probabilities as ratios, percents, and decimals. 19 2. Determine probabilities of compound events. 3. 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). 4. Model situations involving probability with simulations (using spinners, dice, calculators and computers) and theoretical models. Frequency, relative frequency 5. Estimate probabilities and make predictions based on experimental and theoretical probabilities. 6. Play and analyze probability-based games, and discuss the concepts of fairness and expected value. 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) Factorial notation Concept of combinations (e.g., number of possible delegations of 3 out of 23 students) 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. 20 D. Discrete Mathematics—Vertex-Edge Graphs and Algorithms 1. Use vertex-edge graphs and algorithmic thinking to represent and find solutions to practical problems. Finding the shortest network connecting specified sites Finding a minimal route that includes every street (e.g., for trash pick-up) 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 Limitations of computers (e.g., the number of routes for a delivery truck visiting n sites is n!, so finding the shortest circuit by examining all circuits would overwhelm the capacity of any computer, now or in the future, even if n is less than 100) 21 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. 22 4. Use the language of mathematics to express mathematical ideas precisely. 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) 23 Pictorial representations (e.g., diagrams, charts, or tables) Symbolic representations (e.g., a formula) 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. 24 SCOPE AND SEQUENCE MONTH UNITS COVERED September 1: Variables and Equations Begin 2: Integer Operations October Complete 2: Integer Operations 3: Solving Equations & Inequalities November 4: Factors, Fractions, & Exponents December 5: Rational Number Operations Begin 6: Ratio, Proportion, & Percent Complete 6: Ratio, Proportion, & Percent 7: Polygons & Transformations January February 8: Real Numbers & Right Triangles 9: Measurement, Area, & Volume March 10: Data Analysis & Probability April 11: Multi-Step Equations & Inequalities May 12: Linear Equations & Graphs June 13: Polynomials & Functions 25 UNIT 1 A. VARIABLES AND EQUATIONS Major Objectives: 1. 2. B. Duration: September To provide students with a review of important foundational skills in calculation, data analysis, algebra, and problem solving that will be applied and further developed throughout the course. To evaluate and use variable expressions in order to solve realworld problems. Sequence of Topics: 1. 2. 3. 4. 5. 6. 7. 8. Use graphs to analyze data. (4.4) (pp.3–7) Use the order of operations to evaluate numerical expressions. (4.3) (pp.8-12) Write and evaluate variable expressions. (4.3) (pp.13-18) Evaluate expressions with powers. (4.1) (pp.19-24) Write and solve equations using mental math. (4.1) (pp.26-30) Use formulas to find unknown values. (4.3) (pp.32-36) Use a problem solving plan to solve problems. (4.5) (pp.37-42) NJ ASK Preparation, Coach book (4.5) (pp.1-19) C. Core Material: Math: Course 3 Larson, Boswell, Kanold, and Stiff McDougal Littell 2007 D. Supplemental Materials: 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. McDougall – Practice Book McDougall – Remediation Book McDougall – Benchmark Tests McDougall – Assessment Book McDougall – Notetaking Guide McDougall – Daily WarmUps McDougall – Worked Out Solution Key NJ ASK Mathematics Coach Teacher made transparencies Teacher made worksheets 26 E. Suggested Assignments, Projects, Field Trips, Speakers; 1. 2. 3. 4. 5. F. Complete exercises in textbook for each lesson. Complete practice worksheets Use calculator/computer to complete classroom and computer problems when necessary. Complete and review chapter prior to test/quizzes using text and teacher made materials. NJ ASK Do Now Suggested Assessments: 1. 2. 3. 4. 5. Test Quizzes Class participation Notebook/classwork Homework 27 UNIT 2 A. INTEGER OPERATIONS Major Objectives: 1. 2. B. Duration: September/October To use a number line to explore integers and absolute value, as they add, subtract, multiply, and divide integers. Students use the commutative, associative, and distributive properties to evaluate expressions. Sequence of Topics: 1. 2. 3. 4. 5. 6. 7. 8. 9. Integers and absolute value (4.1) (pp.57-61) Adding integers (4.1) (pp.62-67) Subtracting integers (4.1) (pp.68-72) Multiplying integers (4.1) (pp.73-76) Dividing integers (4.1) (pp.77-81) Using properties to evaluate expressions (4.1) (pp.83-87) The distributive property (4.3) (pp.88-92) Identify and plot points on the coordinate plane (4.2) (pp.94-99) NJ ASK preparation, Coach book (4.5) (pp.20-47) C. Core Material: Math: Course 3 Larson, Boswell, Kanold, and Stiff McDougal Littell 2007 D. Supplemental Materials: 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. E. McDougall – Practice Book McDougall – Remediation Book McDougall – Benchmark Tests McDougall – Assessment Book McDougall – Notetaking Guide McDougall – Daily WarmUps McDougall – Worked Out Solution Key NJ NJ ASK Mathematics Coach Teacher made transparencies Teacher made worksheets Suggested Assignments, Projects, Field Trips, Speakers; 1. 2. 3. Complete exercises in textbook for each lesson. Complete practice worksheets Use calculator/computer to complete classroom and computer problems when necessary. 28 4. 5. F. Complete and review chapter prior to test/quizzes using text and teacher made materials. NJ ASK Do Now Suggested Assessments: 1. 2. 3. 4. 5. Test Quizzes Class participation Notebook/classwork Homework 29 UNIT 3 A. SOLVING EQUATIONS AND INEQUALITIES Duration: October Major Objectives: 1. 2. B. To solve one- and two- step equations and inequalities. To write and solve each type of equation and inequality to solve real-world problems. Sequence of Topics: 1. 2. 3. 4. 5. 6. 7. 8. Solving equations using addition or subtraction. (4.3)(pp.117-121) Solving equations using multiplication or division. (4.3) (pp.122-126) Solving two-step equations. (4.3) (pp.129-133) Writing two-step equations. (4.3) (pp.134-139) Using formulas for perimeter and area. (4.2) (pp.142-147) Solving inequalities using addition or subtraction. (4.3) (pp.148-153) Solving inequalities using multiplication or division. (4.3) (pp.153-159) NJ ASK preparation, Coach book (4.5) (pp.55-76) C. Core Material: Math: Course 3 Larson, Boswell, Kanold, and Stiff McDougal Littell 2007 D. Supplemental Materials: 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. E. McDougall – Practice Book McDougall – Remediation Book McDougall – Benchmark Tests McDougall – Assessment Book McDougall – Notetaking Guide McDougall – Daily WarmUps McDougall – Worked Out Solution Key NJ NJ ASK Mathematics Coach Teacher made transparencies Teacher made worksheets Suggested Assignments, Projects, Field Trips, Speakers; 1. 2. Complete exercises in textbook for each lesson. Complete practice worksheets 30 3. 4. 5. F. Use calculator/computer to complete classroom and computer problems when necessary. Complete and review chapter prior to test/quizzes using text and teacher made materials. NJ ASK Do Now Suggested Assessments: 1. 2. 3. 4. 5. Test Quizzes Class participation Notebook/classwork Homework 31 UNIT 4 A. FACTORS, FRACTIONS, AND EXPONENTS Duration: November Major Objectives: 1. 2. B. Use factorization trees to find prime factorization, the greatest common factor, and least common multiple of numbers and monomials. Multiply and divide expressions with exponents and use scientific notation. Sequence of Topics: 1. 2. 3. 4. 5. 6. 7. 8. 9. Write the prime factorization of numbers. (4.1) (pp.176-180) Find the greatest common factor of two or more numbers. (4.1) (pp.181-185) Simplify fractions. (4.1) (pp.187-191) Find the least common multiple of two numbers. (4.1) (pp.192-196) Compare and order fractions and mixed numbers. (4.1) (pp.198-201) Multiply and divide expressions with exponents. (4.1) (pp.202-207) Simplify expressions with negative exponents. (4.1) (pp.208-211) Read and write numbers using scientific notation. (4.1) (pp.212-217) NJ ASK preparation, Coach book (4.5) (pp.77-106) C. Core Material: Math: Course 3 Larson, Boswell, Kanold, and Stiff McDougal Littell 2007 D. Supplemental Materials: 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. McDougall – Practice Book McDougall – Remediation Book McDougall – Benchmark Tests McDougall – Assessment Book McDougall – Notetaking Guide McDougall – Daily WarmUps McDougall – Worked Out Solution Key NJ NJ ASK Mathematics Coach Teacher made transparencies Teacher made worksheets 32 E. Suggested Assignments, Projects, Field Trips, Speakers; 1. 2. 3. 4. 5. F. Complete exercises in textbook for each lesson. Complete practice worksheets Use calculator/computer to complete classroom and computer problems when necessary. Complete and review chapter prior to test/quizzes using text and teacher made materials. NJ ASK Do Now Suggested Assessments: 1. 2. 3. 4. 5. Test Quizzes Class participation Notebook/classwork Homework 33 UNIT 5 A. RATIONAL NUMBER OPERATIONS Major Objectives: 1. 2. 3. 4. B. Duration: December To add and subtract fractions and mixed numbers with like and unlike denominators, and multiply and divide fractions and mixed numbers. To write fractions and mixed numbers as decimals and vice versa. To add and subtract decimals, including using front-end estimation, and multiply and divide decimals. To find the mean, median, mode, and range of a data set. Sequence of Topics: 1. 2. 3. 4. 5. 6. 7. 8. 9. To add and subtract fractions with common denominators. (4.1) (pp.233-237) To add and subtract fractions with different denominators. (4.1) (pp.238-242) To multiply fractions and mixed numbers. (4.1) (pp.243-246) To divide fractions. (4.1) (pp. 247-252) To write fractions as decimals and decimals as fractions. (4.1) (pp. 255-259) To add and subtract decimals. (4.1) (pp.260-264) To multiply and divide decimals. (4.1) (pp.265-269) To describe data sets using mean, median, mode, and range. (4.4) (pp. 272-278) NJ ASK preparation, coach book (4.5) (pp.107-143) C. Core Material: Math: Course 3 Larson, Boswell, Kanold, and Stiff McDougal Littell 2007 D. Supplemental Materials: 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. McDougall – Practice Book McDougall – Remediation Book McDougall – Benchmark Tests McDougall – Assessment Book McDougall – Notetaking Guide McDougall – Daily WarmUps McDougall – Worked Out Solution Key NJ NJ ASK Mathematics Coach Teacher made transparencies Teacher made worksheets 34 E. Suggested Assignments, Projects, Field Trips, Speakers; 1. 2. 3. 4. 5. F. Complete exercises in textbook for each lesson. Complete practice worksheets Use calculator/computer to complete classroom and computer problems when necessary. Complete and review chapter prior to test/quizzes using text and teacher made materials. NJ ASK Do Now Suggested Assessments: 1. 2. 3. 4. 5. Test Quizzes Class participation Notebook/classwork Homework 35 UNIT 6 RATIO, PROPORTION, AND PERCENT Duration: December/January Note: Chapter 6 is being skipped and will be covered later in the year. This unit is from Chapter 7 in the book. Chapter 6 is covered in Unit 11. A. Major Objectives: 1. 2. 3. 4. B. To find ratio and unit rates, and write and then solve proportions, including by using cross products. To solve percent problems both by writing proportions and by using the percent equation. To translate among fractions, decimals, and percents including in the use of circle graphs. To apply percents to solving discount, markup, and other problems involving price. Sequence of Topics: 1. 2. 3. 4. 5. 6. 7. 8. 9. Finding ratios and unit rates. (4.1) (pp.343-346) Write and solve proportions. (4.1) (pp.348-353) Solve percent problems using proportions. (4.1) (pp.354-358) Rewrite fractions, decimals, and percents. (4.1) (pp.359-364) Solve problems with percent of increase or decrease. (4.1) (pp.366-369) Solve percent application problems. (4.5) (pp.370-374) Solve percent problems using the percent equation. (4.5) (pp.375-379) Finding probabilities of events. (4.4) (pp.381-386) NJ ASK preparation, Coach book (4.5) (pp.196-215) C. Core Material: Math: Course 3 Larson, Boswell, Kanold, and Stiff McDougal Littell 2007 D. Supplemental Materials: 1. 2. 3. 4. 5. 6. 7. 8. 9. McDougall – Practice Book McDougall – Remediation Book McDougall – Benchmark Tests McDougall – Assessment Book McDougall – Notetaking Guide McDougall – Daily WarmUps McDougall – Worked Out Solution Key NJ NJ ASK Mathematics Coach Teacher made transparencies 36 10. E. Suggested Assignments, Projects, Field Trips, Speakers; 1. 2. 3. 4. 5. F. Teacher made worksheets Complete exercises in textbook for each lesson. Complete practice worksheets Use calculator/computer to complete classroom and computer problems when necessary. Complete and review chapter prior to test/quizzes using text and teacher made materials. NJ ASK Do Now Suggested Assessments: 1. 2. 3. 4. 5. Test Quizzes Class participation Notebook/classwork Homework 37 UNIT 7 A. POLYGONS AND TRANSFORMATIONS Duration: January Major Objectives: 1. 2. 3. 4. B. To solve equations to find angle measures involving supplementary and complementary angles and angles formed by a line intersecting parallel lines. To classify angles, triangles, and quadrilaterals, and find angle measures in polygons. To identify and name congruent polygons, and use the special rules for identifying congruent triangles. To identify reflected figures and their lines of symmetry and reflect, translate, rotate, and dilate figures in a coordinate plane. Sequence of Topics: 1. 2. 3. 4. 5. 6. 7. 8. 9. Solve equations to find angle measures. (4.2) (pp. 403-408) Classify angles and triangles. (4.2) (pp.411-415) Classify quadrilaterals. (4.2) (pp.416-419) Finding angle measures in polygons. (4.2) (pp.420-424) Identify and name congruent polygons. (4.2) (pp.427-432) Reflect figures and identify lines of symmetry. (4.2) (pp. 433-438) Translating and rotating figures in the coordinate plane. (4.2) (pp.439-444) Using similar figures to find missing measures. (4.2) (pp.447-454) NJ ASK preparation, Coach book (4.5) (pp.216-249) C. Core Material: Math: Course 3 Larson, Boswell, Kanold, and Stiff McDougal Littell 2007 D. Supplemental Materials: 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. McDougall – Practice Book McDougall – Remediation Book McDougall – Benchmark Tests McDougall – Assessment Book McDougall – Notetaking Guide McDougall – Daily WarmUps McDougall – Worked Out Solution Key NJ NJ ASK Mathematics Coach Teacher made transparencies Teacher made worksheets 38 E. Suggested Assignments, Projects, Field Trips, Speakers; 1. 2. 3. 4. 5. F. Complete exercises in textbook for each lesson. Complete practice worksheets Use calculator/computer to complete classroom and computer problems when necessary. Complete and review chapter prior to test/quizzes using text and teacher made materials. NJ ASK Do Now Suggested Assessments: 1. 2. 3. 4. 5. Test Quizzes Class participation Notebook/classwork Homework 39 UNIT 8 A. REAL NUMBERS AND RIGHT TRIANGLES Duration: February Major Objectives: 1. 2. B. To find and approximate square roots and classify real numbers as rational or irrational. To solve real-world problems involving square roots, including problems that use the Pythagorean Theorem. Sequence of Topics: 1. 2. 3. 4. 5. 6. 7. To find and approximate square roots of numbers. (4.1) (pp.469-474) To work with irrational numbers. (4.1) (pp.475-480) To use the Pythagorean Theorem to solve problems. (4.2) (pp.482-486) To solve real-world problems using the Pythagorean Theorem. (4.2) (pp.487-491) To use special right triangles to solve real-life problems. (4.2) (pp.493-497) Supplemental Using trigonometric ratios to find the side lengths of a triangle. (4.2) (pp.500-506) Supplemental NJ ASK preparation, Coach book (4.5) (pp.250-278) C. Core Material: Math: Course 3 Larson, Boswell, Kanold, and Stiff McDougal Littell 2007 D. Supplemental Materials: 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. McDougall – Practice Book McDougall – Remediation Book McDougall – Benchmark Tests McDougall – Assessment Book McDougall – Notetaking Guide McDougall – Daily WarmUps McDougall – Worked Out Solution Key NJ NJ ASK Mathematics Coach Teacher made transparencies Teacher made worksheets 40 E. Suggested Assignments, Projects, Field Trips, Speakers; 1. 2. 3. 4. 5. F. Complete exercises in textbook for each lesson. Complete practice worksheets Use calculator/computer to complete classroom and computer problems when necessary. Complete and review chapter prior to test/quizzes using text and teacher made materials. NJ ASK Do Now Suggested Assessments: 1. 2. 3. 4. 5. Test Quizzes Class participation Notebook/classwork Homework 41 UNIT 9 A. MEASUREMENT, AREA, AND VOLUME Duration: February Major Objectives: 1. 2. 3. 4. B. To find the areas of parallelograms, trapezoids, and circles. To identify solids and sketch solids that include front, top, and side views, as well as isometric drawings. To draw nets of prisms, pyramids, cylinders, and cones and use them to find the surface area of these solids. To find the volume of these solids. Sequence of Topics: 1. 2. 3. 4. 5. 6. 7. 8. Finding the areas of parallelograms and trapezoids. (4.2) (521-526) Finding the areas of circles. (4.2) (pp.527-532) Classifying and sketching solids. (4.2) (pp.534-538) Finding the surface area of prisms and cylinders. (4.2) (pp.542-547) Finding the surface areas of pyramids and cones. (4.2) (pp.548-552) Finding the volumes of prisms and cylinders. (4.2) (pp.554-559) Finding the volumes of pyramids and cones. (4.2) (pp.561-566) NJ ASK preparation, Coach book (pp.279-295) C. Core Material: Math: Course 3 Larson, Boswell, Kanold, and Stiff McDougal Littell 2007 D. Supplemental Materials: 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. McDougall – Practice Book McDougall – Remediation Book McDougall – Benchmark Tests McDougall – Assessment Book McDougall – Notetaking Guide McDougall – Daily WarmUps McDougall – Worked Out Solution Key NJ NJ ASK Mathematics Coach Teacher made transparencies Teacher made worksheets 42 E. Suggested Assignments, Projects, Field Trips, Speakers; 1. 2. 3. 4. 5. F. Complete exercises in textbook for each lesson. Complete practice worksheets Use calculator/computer to complete classroom and computer problems when necessary. Complete and review chapter prior to test/quizzes using text and teacher made materials. NJ ASK Do Now Suggested Assessments: 1. 2. 3. 4. 5. Test Quizzes Class participation Notebook/classwork Homework 43 UNIT 10 A. DATA ANALYSIS AND PROBABILITY Major Objectives: 1. 2. 3. B. Duration: March To make and interpret stem-and-leaf plots, box-and-whisker plots, circle graphs, and line graphs and decide which graph or plot is most appropriate for a data set. Use tree diagrams, the counting principle, permutations, and combinations to count choices or possibilities. To apply these counting methods to find the probability and odds of simple events and to distinguish between independent and dependent events. Sequence of Topics: 1. 2. 3. 4. 5. 6. 7. 8. Making and interpreting stem-and-leaf plots. (4.4) (pp.649-653) Making and interpreting box-and-whisker plots. (4.4) (pp.654-658) Organizing data using circle graphs and line graphs. (4.4) (pp.659-664) Using counting methods to count the number of choices. (4.4) (pp.670-674) Using permutations to count possibilities. (4.4) (pp.675-679) Using combinations to count possibilities. (4.4) (pp.680-684) Finding the odds in favor of an event. (4.4) (pp.685-689) Studying independent and dependent events. (4.4) (pp.694-700) C. Core Material: Math: Course 3 Larson, Boswell, Kanold, and Stiff McDougal Littell 2007 D. Supplemental Materials: 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. McDougall – Practice Book McDougall – Remediation Book McDougall – Benchmark Tests McDougall – Assessment Book McDougall – Notetaking Guide McDougall – Daily WarmUps McDougall – Worked Out Solution Key NJ NJ ASK Mathematics Coach Teacher made transparencies Teacher made worksheets 44 E. Suggested Assignments, Projects, Field Trips, Speakers; 1. 2. 3. 4. 5. F. Complete exercises in textbook for each lesson. Complete practice worksheets Use calculator/computer to complete classroom and computer problems when necessary. Complete and review chapter prior to test/quizzes using text and teacher made materials. NJ ASK Do Now Suggested Assessments: 1. 2. 3. 4. 5. Test Quizzes Class participation Notebook/classwork Homework 45 UNIT 11 A. MULTI-STEP EQUATIONS AND INEQUALITIES Duration: April Major Objectives: 1. 2. 3. B. To solve multi-step equations by combining like terms and using the distributive property. To solve equations involving fractions and decimals, and apply them to solve equations involving the circumference of a circle and other real-world problems. To solve multi-step inequalities and use them to solve real-world problems. Sequence of Topics: 1. 2. 3. 4. 5. 6. 7. Solve equations by using two or more steps. (4.3) (pp.293-297) Solve equations that have variables on both sides. (4.3) (pp.298-302) Solve equations with fractions and decimals. (4.3) (pp.303-308) Solve equations involving the circumference of a circle. (4.2) (pp.312-317) Solve multi-step inequalities. (4.3) (pp.318-322) Writing and solving multi-step inequalities. (4.5) (pp.324-329) NJ ASK preparation, Coach book (4.5) (pp.144-184) C. Core Material: Math: Course 3 Larson, Boswell, Kanold, and Stiff McDougal Littell 2007 D. Supplemental Materials: 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. McDougall – Practice Book McDougall – Remediation Book McDougall – Benchmark Tests McDougall – Assessment Book McDougall – Notetaking Guide McDougall – Daily WarmUps McDougall – Worked Out Solution Key NJ NJ ASK Mathematics Coach Teacher made transparencies Teacher made worksheets 46 E. Suggested Assignments, Projects, Field Trips, Speakers; 1. 2. 3. 4. 5. F. Complete exercises in textbook for each lesson. Complete practice worksheets Use calculator/computer to complete classroom and computer problems when necessary. Complete and review chapter prior to test/quizzes using text and teacher made materials. NJ ASK Do Now Suggested Assessments: 1. 2. 3. 4. 5. Test Quizzes Class participation Notebook/classwork Homework 47 UNIT 12 LINEAR EQUATIONS AND GRAPHS Duration: May Note: Some sections in this chapter are supplemental. Teachers should use their judgment as to whether or not they can be completed. A. Major Objectives: 1. 2. 3. 4. B. To identify and write functions, represent them with tables, and evaluate them. To make and interpret scatter plots and use them to identify relationships between data sets. To find solutions of equations in two variables, identify linear equations and sketch their graphs using tables of values. To find and interpret slope, and write and graph linear equations. Sequence of Topics: 1. 2. 3. 4. 5. 6. 7. 8. Use tables to represent functions. (4.3) (pp.583-587) Making and interpreting scatter plots. (4.4) (pp.588-592) Finding solutions of equations in two variables. (4.3) (pp.593-597) Sketching the graph of a linear equation. (4.3) (pp.598-603) Finding x- and y- intercepts. (4.3) (pp.606-609) Supplemental Finding and interpreting slopes of lines. (4.3) (pp.612-617) Writing and graphing equations in slope-intercept form. (4.3) (pp.622-626) Supplemental Graphing linear inequalities. (4.3) (pp.629-633) Supplemental C. Core Material: Math: Course 3 Larson, Boswell, Kanold, and Stiff McDougal Littell 2007 D. Supplemental Materials: 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. McDougall – Practice Book McDougall – Remediation Book McDougall – Benchmark Tests McDougall – Assessment Book McDougall – Notetaking Guide McDougall – Daily WarmUps McDougall – Worked Out Solution Key NJ NJ ASK Mathematics Coach Teacher made transparencies Teacher made worksheets 48 E. Suggested Assignments, Projects, Field Trips, Speakers; 1. 2. 3. 4. 5. F. Complete exercises in textbook for each lesson. Complete practice worksheets Use calculator/computer to complete classroom and computer problems when necessary. Complete and review chapter prior to test/quizzes using text and teacher made materials. NJ ASK Do Now Suggested Assessments: 1. 2. 3. 4. 5. Test Quizzes Class participation Notebook/classwork Homework 49 UNIT 13 POLYNOMIALS AND FUNCTIONS Duration: June Note: Some sections in this chapter are supplemental. Teachers should use their judgment as to whether or not they can be completed. A. Major Objectives: 1. 2. 3. 4. 5. B. To identify polynomials by the number of terms, simplify them by combining like terms, and evaluate them. To add and subtract polynomials. To apply properties of exponents to monomials and multiply them. To multiply binomials by using the foil method. To use function notation, graph nonlinear functions, and apply the vertical line test. Sequence of Topics: 1. 2. 3. 4. 5. Simplifying polynomials by combining like terms. (4.3) (pp.717-720) Supplemental Adding and subtracting polynomials. (4.3) (pp.721-725) Supplemental Applying properties of exponents to monomials. (4.3) (pp.726-731) Supplemental Multiplying binomials. (4.3) (pp.734-738) Supplemental Using function notation and graphing nonlinear functions. (4.5) (pp.739-745) Supplemental C. Core Material: Math: Course 3 Larson, Boswell, Kanold, and Stiff McDougal Littell 2007 D. Supplemental Materials: 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. McDougall – Practice Book McDougall – Remediation Book McDougall – Benchmark Tests McDougall – Assessment Book McDougall – Notetaking Guide McDougall – Daily WarmUps McDougall – Worked Out Solution Key NJ NJ ASK Mathematics Coach Teacher made transparencies Teacher made worksheets 50 E. Suggested Assignments, Projects, Field Trips, Speakers; 1. 2. 3. 4. 5. F. Complete exercises in textbook for each lesson. Complete practice worksheets Use calculator/computer to complete classroom and computer problems when necessary. Complete and review chapter prior to test/quizzes using text and teacher made materials. NJ ASK Do Now Suggested Assessments: 1. 2. 3. 4. 5. Test Quizzes Class participation Notebook/classwork Homework 51 Bibliography Larson, Ron; Boswell, Laurie; Kanold, Timothy D.; Stiff, Lee. Math Course 3. Illinois: McDougal Littell, 2007. Edwards, Mervine. The New Jersey NJ ASK Mathematics Coach. New York: Educational Design, Inc., 2000. NJ Core Curriculum Standards: http://education.state.nj.us/cccs/?_standard_matrix;c=4 52