Statistics (semester) & Trigonometry (semester)

Transcription

1 RIVER DELL REGIONAL SCHOOL DISTRICT MATHEMATICS CURRICULUM Math Connections Advanced Pre-Algebra Pre-Algebra Advanced Algebra I Algebra I Sequential Math I Honors Geometry Geometry Sequential Math II Sequential Math III HSPA Math 9, 10, 11, or 12 Honors Algebra 2 Algebra 2 Intermediate Algebra AP Statistics Honors Pre- Calculus BC Honors Pre- Calculus AB CP Pre- Calculus Statistics (semester) & Trigonometry (semester) AP Calculus BC AP Calculus AB Honors Calculus

2 River Dell Regional School District MATHEMATICAL CONNECTIONS Year Course/5 Credits Grade: 7 I Rationale The seventh grade Math Connections course is designed to establish a ground work for future work in pre-algebra and algebra. For each topic, students will work on mastering the skills and procedures necessary to solve the problem, understanding the principles behind the mathematics, applying mathematics in real-life situations, and representing the concepts with visual models. Topics will include introduction of the use of variables, algebraic reasoning, integers and rational numbers, patterns and functions, ratios and proportions, percents, data displays and analysis, spatial concepts, measurements, and simple probability. Students of the course will receive a more hands-on and visual experience with mathematics through the use of various tools such as Promethean Board, RM Framework, and other resources. II Goals Goals for this course include development of mathematical thinking, development of modeling skills, communication of mathematical concepts, use of appropriate technology in analyzing and interpreting mathematical data and integrating mathematical skills while problem solving. III Objectives/Proficiencies At the end of this course, students should be able to: 1. Represent and use numbers in a variety of equivalent forms (integers, fractions, decimals, percent, square root, exponential/scientific notation, calculator display) A Understand and apply the properties of the real numbers, including operations with signed numbers B.1 3. Apply concepts such as primes, factors, and multiples in problem-solving and recognizing patterns A.1 4. Understand the concept of a variable and use of variables C.1, E.1-3, B.4

3 5. Represent situations and number of patterns with tables, graphs, verbal rules, and equations and understand the interrelationships of these representations B.1, C.2, A.1-3, E.1 6. Analyze tables and graphs to identify properties and relationships C.2 7. To find the prime factorization of a number, find common factors of two numbers, and least common multiples of two numbers A Use ratio, proportions and percents in problem solving A.3 9. Classify geometric figures in terms of congruence and similarity A Estimate and find the perimeter and area of regular and irregular polygons and find the circumference and area of a circle E Visualize and represent two- and three-dimensional geometric figures A Use the appropriate tools and units to estimate and measure distance, areas, volume, mass, and angles E Select and use geometric models to represent and solve problems including the coordinate plane A.1, A Understand measurement, the structure of systems of measurement and the use of various systems of measurement D Find the probability and odds of a simple event by relative frequency or experimental methods To recognize displays and interpretations to possible misuse of statistics D Apply and interpret statistical data through different types of graphing and use of central tendencies A Solve basic one step linear equations D.3 IV Methods of Evaluation a. Teacher constructed and/or standardized examinations, tests, and quizzes b. Unit Test c. Classwork and class participation d. Homework assignments

4 e. Attendance in conformance with River Dell Board of Education policy V Suggested Resources / Materials a. Textbook: Mathematics: Course 2 (Holt) b. Calculators c. Computer Software VI Proficiencies At the end of this course, students should be able to: 1. Represent and use numbers in a variety of equivalent forms (integers, fractions, decimals, percent, square root, exponential/scientific notation, calculator display). convert percents, decimals and fractions and vice versa convert scientific notation and exponential form to decimal form and vice versa compute square roots and exponents use the calculator as a tool in assisting to solve related problems 2. Understand and apply the properties of the real numbers, including operations with signed numbers. identify and perform operations with integers, decimals, and fractions recognize and apply operations when appropriate using the distributive property, commutative property, associative property, identity property, symmetric property, and transitive property 3. Apply concepts such as primes, factors, and multiples in problem-solving and recognizing patterns. Identify prime and composite numbers, factors and multiples 4. Understand the concept of a variable and use of variables. Understand the use of a variable and identify what an individual variable represents To evaluate expressions involving variables 5. Represent situations and number of patterns with tables, graphs, verbal rules, and equations and understand the interrelationships of these representations. Complete tables and graphs given the verbal rule or equation To identify and complete the pattern 6. Analyze tables and graphs to identify properties and relationships.

5 to recognize patterns and identify the function rule 7. To find the prime factorization of a number, find common factors of two numbers, and least common multiples of two numbers. Use the prime factorization of a set of numbers to calculate the least common multiple and greatest common factor 8. Use ratio, proportions and percents in problem solving. 9. Classify geometric figures in terms of congruence and similarity. Set up proportions to prove a set of geometric figures are congruent or similar Set up proportions to solve for the missing length of side(s) given a set of similar figures 10. Estimate and find the perimeter and area of regular and irregular polygons and circumference and area of a circle. Identify the figure and use the appropriate formula to calculate the perimeter or area of a given figure Calculate the area of an irregular polygon by recognizing how to break down the irregular polygon into basic figures 11. Visualize and represent two- and three-dimensional geometric figures. 12. Use the appropriate tools and units to estimate and measure distance, area, volume, mass, and angles. Apply the appropriate unit of measurement to estimate and calculate distance and mass Apply the appropriate unit of measurement and appropriate formula to calculate area and volume Given a protractor, be able to measure a given angle and create a given angle measurement Identify the classifications of angles and compute the complement and/or supplement of given angles 13. Select and use geometric models to represent and solve problems including the coordinate plane. 14. Understand measurement, the structure of systems of measurement and the use of various systems of measurement. Convert measurements using the metric system Convert measurements using the customary system 15. Find the probability and odds of a simple event by relative frequency or experimental methods. Understand the difference between probability and odds Find the probability and/or odds given a simple event Create and interpret tree diagrams

6 Recognize the correlation between tree diagrams and the counting principle Find probability by applying the counting principle 16. To recognize displays and interpretations to possible misuse of statistics. Identify when a graph is misleading identify how to alter the graph to not misguide the audience identify the appropriate measure of central tendency and be able to recognize when the selected measure of central tendency is not in proper use 17. Apply and interpret statistical data through different types of graphing and use of central tendencies. Create, read, and interpret bar graphs, line graphs, frequency tables, stem and leaf plots, circle graphs Calculate the measures of central tendencies from reading a frequency table or a stem and leaf plot 18. Solve basic one step linear equations. Apply the appropriate operations in order to solve one step linear equations with one variable Apply previous applications such as operations with integers, fractions and decimals VII Methods of Evaluation a. Teacher constructed and/or standardized examinations, tests, and quizzes b. Unit Test c. Class work and class participation d. Homework assignments e. Attendance in conformance with River Dell Board of Education policy

7 River Dell Regional School District PRE-ALGEBRA Year Course/5 Credits Grade: 7 I Rationale The seventh grade Pre Algebra course is designed to prepare students for future studies of Algebra and Geometry. Previously studied mathematical topics will be refined and enhanced. Students will focus on process-oriented goals, which include problem solving, communications of mathematical concepts, mathematical reasoning, and connections with different strands of math and real-life problems. One of the main objectives of the Pre Algebra course is for students to master solving multi-step equations and inequalities. Students will be exposed to linear systems. Other topics of study will include real numbers, number theory, data analysis/statistics, geometry, probability, discrete math, and functions in compliance with the standards set forth by New Jersey s Core Curriculum Standards and National Council of Teachers of Mathematics. II Goals Goals for this course include development of mathematical thinking, development of modeling skills, communication of mathematical concepts, use of appropriate technology in analyzing and interpreting mathematical data and integrating mathematical skills while problem solving. III Objectives/Proficiencies At the end of this course, students should be able to: 1. To evaluate algebraic expressions, including expressions with whole numbers, fractions, decimals, and integers A.1-6; A.1 2. To use the order of operations to compute and evaluate expressions d To simplify numerical and algebraic expressions involving the distributive property D To understand the concept of a power and to apply the rules of exponents in order to simplify an expression A.2; B.2; C.1 5. To recognize, describe, extend, and create patterns involving whole numbers, rational numbers, and integers A.1; C.2

8 6. To perform arithmetic operations on signed numbers, including addition, subtraction, multiplication, and division A.1; B.1 7. To use symbolic algebraic expressions and equations to represent real world situations C.1-2; 4.5.C.1 8. To understand and apply the properties of operations, numbers, linear equations, and linear inequalities C.1; A.2; D.4 9. To solve simple equations involving one variable D To understand and apply the properties of polygons, including triangles, quadrilaterals, and regular polygons A.1-2; 4.5.C To select and interpret appropriate representations for sets of data, including but not limited to pictographs, bar graphs, line graphs, frequency tables, histograms, stem-and-leaf plots, box-and-whisker plots, scatter plots, and circle graphs A.1-2; 4.5.C To find the mean, median, mode, and range of a set of data and interpret their meaning A.1-2; 4.5.C To identify basic geometric figures, including points, lines, rays, angles, and polygons A To understand and apply transformations, including translations, reflections, rotations, and dilations B.1; C Understand and use the coordinate plane C Understand and use ratios, proportions, and percents, including percents greater than 100 and less than 1, in a variety of situations A.3; A To understand and apply the concept of area, perimeter, and circumference E.1; 4.5.C To find the probability and the odds of a simple event or of a compound event B To use the counting principle or apply techniques of systematic listing, counting, and reasoning in a variety of different contexts C.1-3; 4.5.C To solve simple linear equations and inequalities written with one variable algebraically and graphically D.2; 4.5.C To develop strategies to find the surface area and volume of three dimensional figures E.2; 4.5.C.1-3

9 22. To understand and to apply the process of simplifying polynomials through addition, subtraction, and/or multiplication by a monomial D To analyze linear equations with two variables through the coordinate plane B.1 IV Methods of Evaluation f. Teacher constructed and/or standardized examinations, tests, and quizzes g. Real World Applications h. Classwork and class participation i. Homework assignments j. Attendance in conformance with River Dell Board of Education policy V Suggested Resources / Materials d. Textbook: Pre Algebra (Holt) e. Calculators f. Computer Software VI Proficiencies At the end of this course, students should be able to: 1. To evaluate algebraic expressions, including expressions with whole numbers, fractions, decimals, and integers. To evaluate algebraic expressions by substituting integers, fractions, and decimals as values of the variables. 2. To use the order of operations to compute and evaluate expressions. To recognize the appropriate procedure in order to solve a multi-step expression or equation 3. To simplify numerical and algebraic expressions involving the distributive property.

10 4. To understand the concept of a power and to apply the rules of exponents in order to simplify an expression. 5. To recognize, describe, extend, and create patterns involving whole numbers, rational numbers, and integers. 6. To perform arithmetic operations on signed numbers, including addition, subtraction, multiplication, and division. 7. To use symbolic algebraic expressions and equations to represent real world situations. To translate verbal phrases and real-life situations into algebraic expressions and equations. 8. To understand and apply the properties of operations, numbers, linear equations, and linear inequalities. 9. To solve simple equations involving one variable. To solve multi-step equations involving integers, decimals, and fractions. To solve multi-step equations involving simplifying by combining like terms, distributive property. To solve multi-step equations with non-integer coefficients To solve one step / multi-step equations with non-integer solutions 10. To understand and apply the properties of polygons, including triangles, quadrilaterals, and regular polygons. Identify the classifications of polygons Identify the classifications of triangles by sides and by angles. Identify the classifications of quadrilaterals and their properties and apply that knowledge to compute the missing angles and sides of quadrilaterals. Understand and compute the sum of the angles of any polygon and apply that knowledge to find the missing angle of any given polygon. Identify the diagonals and compute the number of diagonals of any polygon. 11. To select and interpret appropriate representations for sets of data, including but not limited to pictographs, bar graphs, line graphs, frequency tables, histograms, stem-and-leaf plots, scatter plots, and circle graphs. To interpret the information/data on bar graphs, line graphs, frequency tables, histograms, stem-and-leaf plots, box, scatter plots, and circle graphs. To construct any of the graphs listed above given a set of data. To choose the most appropriate graph given a situation. To analyze the data and present a convincing argument whether or not the information is misleading. 12. To find the mean, median, mode, and range of a set of data and interpret their meaning.

11 To calculate the mean, median, mode, and range of a set of data involving integers and decimals. To calculate the mean, median, mode, and range of a set of data from stem-and-leaf plots and frequency tables To recognize the most appropriate measure of central tendency given a set of data. 13. To identify basic geometric figures, including points, lines, rays, angles, and polygons. To identify the basic geometric figures. To identify the classifications of angles, compute the complement and/or supplement of a given angle, draw, and measure angles. Identify parallel and perpendicular lines and use their properties to compute missing angles and sides of polygons. 14. To understand and apply transformations, including translations, reflections, rotations, and dilations. To recognize the different types of transformations. Given a figure, perform the various types of transformations. 15. Understand and use the coordinate plane. To plot given ordered pairs on the coordinate plane. To identify the four quadrants of the coordinate plane. 16. Understand and use ratios, proportions, and percents, including percents greater than 100 and less than 1, in a variety of situations. To represent rates and ratios given a situation. To simplify rates and ratios. To use proportions to solve word problems. To solve percent problems using both the equation method and the proportion method. To find the percent of increase and percent of decrease. 17. To understand and apply the concept of area, perimeter, and circumference. To compute the perimeter of regular and irregular polygons. To compute the area of triangles, quadrilaterals, circles, and irregular polygons and understand the basis of the formulas. To compute the circumference of a circle given the radius or diameter and vice versa. Given a figure, calculate the perimeter/area of its congruent and similar figure. Find the area of the shaded region of a figure containing a polygon and a circle and one of them is shaded. 18. To find the probability and the odds of a simple event or of a compound event. To understand the difference between probability and odds. To find the probability of the odds in favor of a simple event.

12 To find the probability of a compound event, independent and dependent. 19. To use the counting principle or apply techniques of systematic listing, counting, and reasoning in a variety of different contexts. Create and interpret tree diagrams. Recognize the correlation between tree diagrams and the Counting Principle. Use the Counting Principle to compute the sample space and the probability of compound events. 20. To solve simple linear equations and inequalities written with one variable algebraically and graphically. 21. To develop strategies to find the surface area and volume of three dimensional figures. To identify types of three dimensional figures. To understand and to apply the appropriate formula for a given figure to calculate surface area and volume of prisms and cylinders. 22. To understand and to apply the process of simplifying polynomials through addition, subtraction, and/or multiplication by a monomial. To simplify polynomials by adding and/or subtracting like terms To write polynomials in standard form. To multiply a monomial with a polynomial. To understand and to apply the Product of Powers Rule and Quotient of Powers Rule. 23. To analyze linear equations with two variables through the coordinate plane. To understand and identify the slope, y-intercept, and x-intercept of a line. To graph a linear equation. VII Methods of Evaluation a. Teacher constructed and/or standardized examinations, tests, and quizzes Examples of Evaluate -5⅔ t for t = ⅝ Mrs. Smith wants to put a fence around 3 sides of a square garden that has an area of 225 sq. feet. How much fencing does she need? A cylinder has a volume of cubic inches and a height of 24 inches. Find the radius. b. Real World Applications, Examples of

13 Teresa has taken three tests worth 100 points each. Her scores are 85, 93, and 88. She has one test left to take. What score does she need on the fourth test to get an average of 90? The world s tallest Ferris wheel is in Osaka, Japan, and stands 369 feet tall. Its circumference is feet. How high does this Ferris Wheel stand? Contestants in a festival game have a 2% chance of winning $5, a 7% chance of winning $1, a 15% chance of winning $0.50, and 20% chance of winning $0.25. What is the probability of not winning anything? c. Class work and class participation Utilize the Guided Practice exercises in the textbook to assess student proficiency after the initial instruction has been provided. Utilize exploration worksheets as a lead into the development of a new skill or understanding of a new concept. Utilize a problem of the day for introduction, reinforcement, or extension. Journal writing to communicate knowledge of concepts, skills, or procedures. This writing is also an opportunity to comment on area of concern. d. Homework assignments Assign problems from textbook Writing samples as a form of communicating the solution to a problem. Worksheets Online assignments such as lessons from RM Framework Correcting assessments once they have been scored and returned to students. e. Attendance in conformance with River Dell Board of Education policy

14 River Dell Regional School District ADVANCED PRE-ALGEBRA Year Course/5 Credits Grade: 7 I Rationale The seventh grade Advanced Pre Algebra course is designed to provide students with a strong understanding of Pre Algebra as well as other strands of mathematics. The basic algebraic structure of the real number system will be refined and built upon. The properties of this algebraic structure will be enhanced by the study of linear systems and polynomials. The course includes a heavy concentration on multi-step equations, operations with polynomials, linear equations and inequalities, and systems of equations, solved algebraically and graphically. The course will also present topics in data analysis/statistics, geometry, probability, and discrete math in compliance with the standards set forth by New Jersey s Core Curriculum Standards and National Council of Teachers of Mathematics. II Goals Goals for this course include development of mathematical thinking, development of modeling skills, communication of mathematical concepts, use of appropriate technology in analyzing and interpreting mathematical data and integrating mathematical skills while problem solving. III Objectives/Proficiencies At the end of this course, students should be able to: 24. To evaluate algebraic expressions, including expressions involving real numbers A.1-6; A To use the order of operations to compute and evaluate expressions d To simplify numerical and algebraic expressions involving the distributive property D To understand the concept of a power and to apply the rules of exponents in order to simplify an expression A.2; B.2; C To recognize, describe, extend, and create patterns involving rational numbers A.1; C.2

15 29. To use symbolic algebraic expressions and equations to represent real world situations C.1-2; 4.5.C To understand and apply the properties of operations, numbers, equations, and inequalities C.1; A.2; D To solve linear equations involving one variable D To understand and apply the properties of polygons, including triangles, quadrilaterals, and regular polygons A.1-2; 4.5.C To select and interpret appropriate representations for sets of data, including but not limited to pictographs, bar graphs, line graphs, frequency tables, histograms, stem-and-leaf plots, box-and-whisker plots, scatter plots, and circle graphs A.1-2; 4.5.C To find the mean, median, mode, and range of a set of data and interpret their meaning A.1-2; 4.5.C To identify basic geometric figures, including points, lines, rays, angles, and polygons A To understand and apply transformations, including translations, reflections, rotations, and dilations B.1; C Understand and use the coordinate plane C Understand and use ratios, proportions, and percents, including percents greater than 100 and less than 1, in a variety of situations A.3; A To understand and apply the concept of area, perimeter, and circumference E.1; 4.5.C To find the probability and the odds of a simple event or of a compound event B To understand and compute combinations and permutations in various situations C.1-3; 4.5.A To use the counting principle or apply techniques of systematic listing, counting, and reasoning in a variety of different contexts C.1-3; 4.5.C To solve linear equations and inequalities written with one variable algebraically and graphically D.2; 4.5.C To develop strategies to find the surface area and volume of three dimensional figures E.2; 4.5.C.1-3

16 45. To understand and to apply the process of simplifying polynomials through addition, subtraction, multiplication by a monomial and binomial, and division by a monomial D To analyze linear equations with two variables through the coordinate plane B To transform algebraic formulas for a given variable E.2 IV Methods of Evaluation k. Teacher constructed and/or standardized examinations, tests, and quizzes l. Real World Applications m. Classwork and class participation n. Homework assignments o. Attendance in conformance with River Dell Board of Education policy V Suggested Resources / Materials g. Textbook: Pre Algebra (Holt) h. Calculators i. Computer Software VI Proficiencies At the end of this course, students should be able: 24. To evaluate algebraic expressions, including expressions involving real numbers. To evaluate algebraic expressions by substituting integers, fractions, and decimals as values of the variables. 25. To use the order of operations to compute and evaluate numerical and algebraic expressions and equations. To recognize the appropriate procedure in order to solve a multi-step expression or equation 26. To simplify numerical and algebraic expressions involving the distributive property.

17 27. To understand the concept of a power and to apply the rules of exponents in order to simplify an expression. 28. To recognize, describe, extend, and create patterns involving rational numbers. 29. To use symbolic algebraic expressions and equations to represent real world situations. To translate verbal phrases and real-life situations into algebraic expressions and equations. To explore and create various word problems representing a given expression or an equation. 30. To understand and apply the properties of operations, numbers, equations, and inequalities. 31. To solve linear equations involving one variable. To solve multi-step equations involving integers, decimals, and fractions. To solve multi-step equations involving simplifying by combining like terms, distributive property. To solve multi-step equations with variables on both sides of the equation. To solve multi-step equations with non-integer coefficients To solve one step / multi-step equations with non-integer solutions 32. To understand and apply the properties of polygons, including triangles, quadrilaterals, and regular polygons. Identify the classifications of polygons Identify the classifications of triangles by sides and by angles. Identify the classifications of quadrilaterals and their properties and apply that knowledge to compute the missing angles and sides of quadrilaterals. Understand and compute the sum of the angles of any polygon and apply that knowledge to find the missing angle of any given polygon. Understand and compute the number of diagonals of any polygon. 33. To select and interpret appropriate representations for sets of data, including but not limited to pictographs, bar graphs, line graphs, frequency tables, histograms, stem-and-leaf plots, box-and-whisker plots, scatter plots, and circle graphs. To interpret the information/data on bar graphs, line graphs, frequency tables, histograms, stem-and-leaf plots, box-and-whisker plots, scatter plots, and circle graphs. To construct any of the graphs listed above given a set of data. To choose the most appropriate graph given a situation. To analyze the data and present a convincing argument whether or not the information is misleading. 34. To find the mean, median, mode, 1 st and 3 rd quartile, and range of a set of data and interpret their meaning. To calculate the mean, median, mode, and range of a set of data involving integers, fractions, and decimals.

18 To calculate the mean, median, mode, and range of a set of data from stem-and-leaf plots, frequency tables, histograms, and scatter plots. To recognize the most appropriate measure of central tendency given a set of data. 35. To identify basic geometric figures, including points, lines, rays, angles, and polygons. To identify the basic geometric figures. To identify the classifications of angles, compute the complement and/or supplement of a given angle, draw, and measure angles. Identify parallel and perpendicular lines and use their properties to compute missing angles and sides of polygons. 36. To understand and apply transformations, including translations, reflections, rotations, and dilations. To recognize the different types of transformations. Given a figure, perform the various types of transformations. 37. Understand and use the coordinate plane. To plot given ordered pairs on the coordinate plane. To identify the four quadrants of the coordinate plane. 38. Understand and use rates, ratios, proportions, and percents, including percents greater than 100 and less than 1, in a variety of situations. To represent rates and ratios given a situation. To simplify rates and ratios. To use proportions to solve word problems. To solve percent problems using both the equation method and the proportion method. To find the percent of increase and percent of decrease. 39. To understand and apply the concept of area, perimeter, and circumference. To compute the perimeter of regular and irregular polygons. To compute the area of triangles, quadrilaterals, circles, and irregular polygons and understand the basis of the formulas. To compute the circumference of a circle given the radius or diameter and vice versa. Given a figure, calculate the perimeter/area of its congruent and similar figure. Find the area of the shaded region of a figure containing a polygon and a circle and one of them is shaded. 40. To find the probability and the odds in favor of a simple event or of a compound event. To understand the difference between probability and odds. To find the probability of the odds in favor of a simple event. To find the probability of a compound event, independent and dependent.

19 41. To understand and compute combinations and permutations in various situations. To recognize the different between combinations and permutations. To choose the appropriate procedure to use given a situation. To compute combinations and permutations through the use of a calculator and the formula. 42. To use the counting principle or apply techniques of systematic listing, counting, and reasoning in a variety of different contexts. Create and interpret tree diagrams. Recognize the correlation between tree diagrams and the Counting Principle. Use the Counting Principle to compute the sample space and the probability of compound events. 43. To solve linear equations and inequalities written with one variable algebraically and graphically. 44. To develop strategies to find the surface area and volume of three dimensional figures. To identify types of three dimensional figures. To understand and to apply the appropriate formula for a given figure to calculate surface area and volume of prisms, pyramids, cones, and cylinders. To manipulate the surface area and volume formulas to calculate any variable. 45. To understand and to apply the process of simplifying polynomials through addition, subtraction, multiplication by a monomial and binomial, and division by a monomial. To simplify polynomials by adding and/or subtracting like terms To write polynomials in standard form. To multiply a monomial with a polynomial. To multiply a binomial with a binomial using the F-O-I-L method. To understand and to apply the Product of Powers Rule and Quotient of Powers Rule. To divide a polynomial by a monomial. 46. To analyze linear equations and inequalities with two variables through the coordinate plane. To understand and identify the slope, y-intercept, and x-intercept of a line. To graph a linear equation. To write a linear equation given a graph of a line.

20 To solve the system of equations by graphing, substitution, and elimination methods. To identify the standard form, slope-intercept form, and point-slope form of an equation and to choose the most appropriate form to use given a situation. To graph inequalities with two variables. 47. To transform algebraic formulas for a given variable. To manipulate algebraic equations for a given variable to solve a problem. VII Methods of Evaluation f. Teacher constructed and/or standardized examinations, tests, and quizzes, Examples of: Solve: x + 6 4x = 19 3x Graph the inequality: 3y < x 6 Marge made a down payment of $200 for a computer and is making weekly payments of $25. Write an algebraic equation to represent the amount paid after x weeks. g. Real World Applications, Examples of A cement truck is pouring cement for a new 4 in. thick driveway. The driveway is 90 feet long and 20 feet wide. How long will it take the truck to pour the cement if it releases 10 cubic feet of cement per minute? Our school s cross country team has 15 members. A team of 7 runners will be chosen to run at the first invitational as the varsity team. How many different teams are possible? If the tuition for University of Connecticut is $13,445 per semester and increases 5% each year, what will the tuition be in 4 years? h. Class work and class participation Utilize the Guided Practice exercises in the textbook to assess student proficiency after the initial instruction has been provided. Utilize exploration worksheets as a lead into the development of a new skill or understanding of a new concept. Utilize a problem of the day for introduction, reinforcement, or extension. Journal writing to communicate knowledge of concepts, skills, or procedures. This writing is also an opportunity to comment on area of concern. i. Homework assignments Assign problems from textbook Writing samples as a form of communicating the solution to a problem. Worksheets

21 Online assignments such as lessons from RM Framework Correcting assessments once they have been scored and returned to students. j. Attendance in conformance with River Dell Board of Education policy

22 River Dell Regional School District PRE-ALGEBRA Year Course/5 Credits Grade: 8 I Rationale The eighth grade Pre Algebra course is designed to prepare students for future studies of Algebra and Geometry. Previously studied mathematical topics will be refined and enhanced. Students will focus on process-oriented goals, which include problem solving, communications of mathematical concepts, mathematical reasoning, and connections with different strands of math and real-life problems. One of the main objectives of the Pre Algebra course is for students to master solving multi-step equations and inequalities. Students will be exposed to linear systems. Other topics of study will include real numbers, number theory, data analysis/statistics, geometry, probability, discrete math, and functions in compliance with the standards set forth by New Jersey s Core Curriculum Standards and National Council of Teachers of Mathematics. II Goals Goals for this course include development of mathematical thinking, development of modeling skills, communication of mathematical concepts, use of appropriate technology in analyzing and interpreting mathematical data and integrating mathematical skills while problem solving. III Objectives/Proficiencies At the end of this course, students should be able to: 48. To evaluate algebraic expressions, including expressions with whole numbers, fractions, decimals, and integers A.1-6; A To use the order of operations to compute and evaluate expressions d To simplify numerical and algebraic expressions involving the distributive property D To understand the concept of a power and to apply the rules of exponents in order to simplify an expression A.2; B.2; C To recognize, describe, extend, and create patterns involving whole numbers, rational numbers, and integers A.1; C.2

23 53. To perform arithmetic operations on signed numbers, including addition, subtraction, multiplication, and division A.1; B To use symbolic algebraic expressions and equations to represent real world situations C.1-2; 4.5.C To understand and apply the properties of operations, numbers, linear equations, and linear inequalities C.1; A.2; D To solve simple equations involving one variable D To understand and apply the properties of polygons, including triangles, quadrilaterals, and regular polygons A.1-2; 4.5.C To select and interpret appropriate representations for sets of data, including but not limited to pictographs, bar graphs, line graphs, frequency tables, histograms, stem-and-leaf plots, box-and-whisker plots, scatter plots, and circle graphs A.1-2; 4.5.C To find the mean, median, mode, and range of a set of data and interpret their meaning A.1-2; 4.5.C To identify basic geometric figures, including points, lines, rays, angles, and polygons A To understand and apply transformations, including translations, reflections, rotations, and dilations B.1; C Understand and use the coordinate plane C Understand and use ratios, proportions, and percents, including percents greater than 100 and less than 1, in a variety of situations A.3; A To understand and apply the concept of area, perimeter, and circumference E.1; 4.5.C To find the probability and the odds of a simple event or of a compound event B To use the counting principle or apply techniques of systematic listing, counting, and reasoning in a variety of different contexts C.1-3; 4.5.C To solve simple linear equations and inequalities written with one variable algebraically and graphically D.2; 4.5.C To develop strategies to find the surface area and volume of three dimensional figures E.2; 4.5.C.1-3

24 69. To understand and to apply the process of simplifying polynomials through addition, subtraction, and/or multiplication by a monomial D To analyze linear equations with two variables through the coordinate plane B.1 IV Methods of Evaluation p. Teacher constructed and/or standardized examinations, tests, and quizzes q. Real World Applications r. Class work and class participation s. Homework assignments t. Attendance in conformance with River Dell Board of Education policy V Suggested Resources / Materials j. Textbook: Pre Algebra (Holt) k. Calculators l. Computer Software VI Proficiencies At the end of this course, students should be able to: 48. To evaluate algebraic expressions, including expressions with whole numbers, fractions, decimals, and integers. To evaluate algebraic expressions by substituting integers, fractions, and decimals as values of the variables. 49. To use the order of operations to compute and evaluate expressions. To recognize the appropriate procedure in order to solve a multi-step expression or equation 50. To simplify numerical and algebraic expressions involving the distributive property.

25 51. To understand the concept of a power and to apply the rules of exponents in order to simplify an expression. 52. To recognize, describe, extend, and create patterns involving whole numbers, rational numbers, and integers. 53. To perform arithmetic operations on signed numbers, including addition, subtraction, multiplication, and division. 54. To use symbolic algebraic expressions and equations to represent real world situations. To translate verbal phrases and real-life situations into algebraic expressions and equations. 55. To understand and apply the properties of operations, numbers, linear equations, and linear inequalities. 56. To solve simple equations involving one variable. To solve multi-step equations involving integers, decimals, and fractions. To solve multi-step equations involving simplifying by combining like terms, distributive property. To solve multi-step equations with non-integer coefficients To solve one step / multi-step equations with non-integer solutions 57. To understand and apply the properties of polygons, including triangles, quadrilaterals, and regular polygons. Identify the classifications of polygons Identify the classifications of triangles by sides and by angles. Identify the classifications of quadrilaterals and their properties and apply that knowledge to compute the missing angles and sides of quadrilaterals. Understand and compute the sum of the angles of any polygon and apply that knowledge to find the missing angle of any given polygon. Identify the diagonals and compute the number of diagonals of any polygon. 58. To select and interpret appropriate representations for sets of data, including but not limited to pictographs, bar graphs, line graphs, frequency tables, histograms, stem-and-leaf plots, scatter plots, and circle graphs. To interpret the information/data on bar graphs, line graphs, frequency tables, histograms, stem-and-leaf plots, box, scatter plots, and circle graphs. To construct any of the graphs listed above given a set of data. To choose the most appropriate graph given a situation. To analyze the data and present a convincing argument whether or not the information is misleading. 59. To find the mean, median, mode, and range of a set of data and interpret their meaning.

26 To calculate the mean, median, mode, and range of a set of data involving integers and decimals. To calculate the mean, median, mode, and range of a set of data from stem-and-leaf plots and frequency tables To recognize the most appropriate measure of central tendency given a set of data. 60. To identify basic geometric figures, including points, lines, rays, angles, and polygons. To identify the basic geometric figures. To identify the classifications of angles, compute the complement and/or supplement of a given angle, draw, and measure angles. Identify parallel and perpendicular lines and use their properties to compute missing angles and sides of polygons. 61. To understand and apply transformations, including translations, reflections, rotations, and dilations. To recognize the different types of transformations. Given a figure, perform the various types of transformations. 62. Understand and use the coordinate plane. To plot given ordered pairs on the coordinate plane. To identify the four quadrants of the coordinate plane. 63. Understand and use ratios, proportions, and percents, including percents greater than 100 and less than 1, in a variety of situations. To represent rates and ratios given a situation. To simplify rates and ratios. To use proportions to solve word problems. To solve percent problems using both the equation method and the proportion method. To find the percent of increase and percent of decrease. 64. To understand and apply the concept of area, perimeter, and circumference. To compute the perimeter of regular and irregular polygons. To compute the area of triangles, quadrilaterals, circles, and irregular polygons and understand the basis of the formulas. To compute the circumference of a circle given the radius or diameter and vice versa. Given a figure, calculate the perimeter/area of its congruent and similar figure. Find the area of the shaded region of a figure containing a polygon and a circle and one of them is shaded. 65. To find the probability and the odds of a simple event or of a compound event. To understand the difference between probability and odds. To find the probability of the odds in favor of a simple event.

27 To find the probability of a compound event, independent and dependent. 66. To use the counting principle or apply techniques of systematic listing, counting, and reasoning in a variety of different contexts. Create and interpret tree diagrams. Recognize the correlation between tree diagrams and the Counting Principle. Use the Counting Principle to compute the sample space and the probability of compound events. 67. To solve simple linear equations and inequalities written with one variable algebraically and graphically. 68. To develop strategies to find the surface area and volume of three dimensional figures. To identify types of three dimensional figures. To understand and to apply the appropriate formula for a given figure to calculate surface area and volume of prisms and cylinders. 69. To understand and to apply the process of simplifying polynomials through addition, subtraction, and/or multiplication by a monomial. To simplify polynomials by adding and/or subtracting like terms To write polynomials in standard form. To multiply a monomial with a polynomial. To understand and to apply the Product of Powers Rule and Quotient of Powers Rule. 70. To analyze linear equations with two variables through the coordinate plane. To understand and identify the slope, y-intercept, and x-intercept of a line. To graph a linear equation. VII Methods of Evaluation k. Teacher constructed and/or standardized examinations, tests, and quizzes Examples of Evaluate -5⅔ t for t = ⅝ Mrs. Smith wants to put a fence around 3 sides of a square garden that has an area of 225 sq. feet. How much fencing does she need? A cylinder has a volume of cubic inches and a height of 24 inches. Find the radius. l. Real World Applications, Examples of

28 Teresa has taken three tests worth 100 points each. Her scores are 85, 93, and 88. She has one test left to take. What score does she need on the fourth test to get an average of 90? The world s tallest Ferris wheel is in Osaka, Japan, and stands 369 feet tall. Its circumference is feet. How high does this Ferris Wheel stand? Contestants in a festival game have a 2% chance of winning $5, a 8% chance of winning $1, a 15% chance of winning $0.50, and 20% chance of winning $0.25. What is the probability of not winning anything? m. Class work and class participation Utilize the Guided Practice exercises in the textbook to assess student proficiency after the initial instruction has been provided. Utilize exploration worksheets as a lead into the development of a new skill or understanding of a new concept. Utilize a problem of the day for introduction, reinforcement, or extension. Journal writing to communicate knowledge of concepts, skills, or procedures. This writing is also an opportunity to comment on area of concern. n. Homework assignments Assign problems from textbook Writing samples as a form of communicating the solution to a problem. Worksheets Online assignments such as lessons from RM Framework Correcting assessments once they have been scored and returned to students. o. Attendance in conformance with River Dell Board of Education policy

29 River Dell Regional School District ALGEBRA Year Course/5 Credits Grade: 8 I Rationale This course is designed to provide students with a strong understanding of algebra, as well as other strands of mathematics. The algebraic structure of the real number system will be reviewed and extended. The basic properties of this algebraic structure will be applied to the study of equations, inequalities, and polynomials. Students will master graphing of equations and inequalities. Topics will include a study of factoring, operations with polynomials, linear systems, properties of exponents and radicals. II Goals Goals for this course include development of mathematical thinking, development of modeling skills, communication of mathematical concepts, use of appropriate technology in analyzing and interpreting mathematical data and integrating mathematical skills while problem solving. III Objectives/Proficiencies At the end of this course, students should be able to: 1. Represent and use numbers in a variety of equivalent forms (integers, fractions, decimals, percent, square root, exponential/scientific notation, calculator display) A.1-2, Understand and apply the properties of the real numbers, including operations with signed numbers A.1, B Understand the concept of variable and use of variables C.1, B.4, E Understand and use mathematical language, notation and structure to represent ideas, describe relationships, and model situations B.1-2, C Represent situations and number patterns with tables, graphs, verbal rules, and equations and understand the interrelationships of these representations B.1-2, C.2, A.1-3, E.1-3

30 6. Analyze tables and graphs to identify properties and relationships B.2, C.2, A Formulate, simplify and evaluate algebraic expressions D.1 8. Use algebraic expressions to represent mathematical situations C.1, C.4, E.2 9. Understand the process of solving linear equations and inequalities in one or two variables and, where appropriate, represent their solution graphically B.1-2, D Perform operations on and simplify polynomial expressions A.3, B.1-4, D Apply skill in factoring polynomial expressions D Apply the process of solving problems using equations and inequalities B.1-2, C.1-2, D Apply algebraic methods to solve a variety of real-world and mathematical problems C Represent and analyze linear relationships among a table of values, an algebraic formula, a written statement and a graph, including the concepts of slope and intercept B.2, C.1-2, F Understand the process of solving linear equations in two variables by elimination, substitution, or graphing B.2, C.2, F Construct, interpret and/or draw inferences from graphs, tables, and charts that reflect data from real-world situations C.1-2, A.2-4, C.3, E Represent and solve problems using geometric models A Apply algebraic techniques to geometric problems involving perimeter and area E.1-3, D Do basic probability and odds problems for simple events and compound events B Make predictions based on experimental or mathematical probabilities B Perform operations on and simplify rational expressions A.3, B.1-4, D.1