Grade: MS: Subject: 9/24/2009 Unit 1 Algebra and Integers Chapter 1 The Tools of Algebra Time frame for Completion: 11-15 days Enduring Understandings / Big Ideas: Build a foundation of basic understandings of numbers, operations, algebraic thinking. Use these understandings to solve linear equations. Select and use appropriate operations to solve problems and justify solutions. Use graphs, tables, and algebraic representations to make predictions and solve problems. Essential Questions: In what type of situations is it acceptable to solve a problem with estimation? What operation does the phrase decreased by mean? What is the purpose of a variable? How are the Commutative and Associative Properties different? What is the difference between an expression and an open sentence? How can a graph be used to analyze data? What are the different patterns seen in scatter plots? Learning Competencies - What the students will know and be able to do upon completion of the unit Students will learn about the basic tools of algebra, including variables, integers, and equations. Students will use the UMASD designed template to solve problems, translate verbal phrases and expressions into algebraic expressions, and use mathematical properties and the order of operations. Students will compare and order integers and perform operations with integers. Students will evaluate and simplify algebraic Page 1 Supportive Teaching/Learning Activities Use UMASD designed template to solve problems. Choose an appropriate method of computation. Use the order of operations to evaluate expressions. Translate verbal phrases into numerical expressions. Evaluate expressions containing variables. Translate verbal phrases into algebraic expressions. *Extend Expressions and Spreadsheets use a spreadsheet to investigate patterns in data. Assessments Resources PDE Academic Standards Formative (suggestions): Anticipation Guide p. 3 Ticket out the door p. 30 (TWE) Crystal Ball p. 59 (TWE) Name the Math p. 36, 46, 53 (TWE) Yesterday s News p. 41, 66 (TWE) 4Sight Benchmark Assessment Summative (suggestions): Mid Chapter Quiz p. 48 (SE) Study Guide and Review. P. 69-72 (SE) Resource Glencoe McGraw-Hill Pre- Algebra Teacher Wraparound Edition, 2008 pages 22 75 D UMASD problem solving template ESL staff Bilingual dictionaries Student data from 4Sight Benchmark Assessment Supplemental Resources: Technology p. 24C 24D TeacherWorks All inone Planner and Resource Center Graphing Calculator Easy Files 2.1 Numbers, Number Systems and Number Relationships 2.2 Computation and Estimation 2.4 - Mathematical Reasoning and Connections 2.5 - Mathematical Problem Solving and Communication 2.8 Algebra and Functions Every Teacher Teaches ESL ELP Standard 1: English Language Learners communicate in English for social and instructional purposes within the school setting.
Grade: MS: Subject: 9/24/2009 Unit 1 Algebra and Integers Chapter 1 The Tools of Algebra Time frame for Completion: 11-15 days Learning Competencies - What the students will know and be able to do upon completion of the unit expressions and write and solve two-step equations. Students will use a coordinate plane to locate and graph ordered pairs and represent algebraic relationships. Differentiation Options: Chapter 1 pgs 24G 24H Supportive Teaching/Learning Activities Identify and use properties of addition and multiplication. Use properties of addition and multiplication to simplify algebraic expressions. Identify and solve open sentences. Translate verbal sentences into equations. Use ordered pairs to locate points. Use tables and graphs to represent relations. *Explore scatter plots use real world data to draw and analyze a scatter plot. Construct scatter plots. Analyze trends in scatter plots. *Extend graphing calculator scatter plots use a graphing calculator to create scatter plots. * -Optional [All activities are structured to work within each student s zone of proximal development* in English Language Acquisition] Assessments Resources PDE Academic Standards Standardized Test Practice p. 74-75 (SE) and 68-70 Quizzes. P. 51-52 Chapter practice test -. 73 (SE) Unit 1 Test p. 77-78 of the Chapter 3 Resource Masters Mid-chapter test p. 53 Vocabulary test p. 54 Extended response test p. 67 Leveled chapter tests. P. 55 66 ExamView Assessment Suite (CD) AssignmentWorks Interactive Classroom ExamView Assessment Suite StudentWorks Plus Math online prealgebra.com Manipulatives Computer with spreadsheet software. Centimeter ruler, graph paper Graphing calculator ELL: http://www.cal.org/siop: Fifty Strategies for Teaching; English Language Learners, 2 nd edition; Adrienne Herrell, Michael Jordan; (Merrill/Prentice Hall, 2003) ELP Standard 2: English Language Learners communicate information, ideas, and concepts necessary for academic success in the content area of Language Arts. Page 2
Grade: MS: Subject: 9/24/2009 Unit 1 Algebra and Integers Chapter 2 Integers Time frame for Completion: 11 days Enduring Understandings / Big Ideas: Build a foundation of basic understandings of numbers, operations, algebraic thinking. Use these understandings to solve linear equations. Understand that different forms of numbers are appropriate for different situations. Use graphs, tables, and algebraic representations to make predictions and solve problems. Essential Questions: Can the absolute value of a number be less than zero? Why or why not? How do you add integers with opposite signs? Why do you add the additive inverse of an integer to subtract an integer? What is the value of a, if -5a = 30? How do you know if the quotient is positive or negative? How does this compare with the products of multiplication? If an ordered pair is in quadrant II, what are the signs of the coordinates? Learning Competencies - What the students will know and be able to do upon completion of the unit Students will learn about the basic tools of algebra, including variables, integers, and equations. Students will use a fourstep plan to solve problems, translate verbal phrases and expressions into algebraic expressions, and use mathematical properties and the order of operations. Students will compare and order integers and perform operations with integers. Students will evaluate and simplify algebraic expressions and write and Supportive Teaching/Learning Activities Compare and order integers. Find the absolute value of an expression. Explore - Use algebra tiles to model addition with integers. Add two integers. Add more than two integers. Explore use algebra tiles to model subtraction of integers. Subtract integers. Evaluate expressions containing variables. Explore use algebra tiles to model multiplication of integers. Multiply integers. Assessments Resources PDE Academic Standards Formative (suggestions): Anticipation Guide p. 3 Ticket out the door p. 97, 110 (TWE) Crystal Ball p. 83, 104 (TWE) Name the Math p. 90, 115 (TWE) Yesterday s News none for this chapter (TWE) Summative (suggestions): Mid Chapter Quiz p. 98 (SE) Study Guide and Review. P. 116-118 (SE) Standardized Test Resource Glencoe McGraw-Hill Pre- Algebra Teacher Wraparound Edition, 2008 pages 76A 121 D ESL staff Bilingual dictionaries Supplemental Resources: Technology p. 76C 76D TeacherWorks All inone Planner and Resource Center Graphing Calculator Easy Files AssignmentWorks Interactive Classroom ExamView Assessment Suite 2.1 Numbers, Number Systems and Number Relationships 2.2 Computation and Estimation 2.4 - Mathematical Reasoning and Connections 2.5 - Mathematical Problem Solving and Communication 2.6 - Statistics and Data Analysis 2.8 Algebra and Functions Every Teacher Teaches ESL ELP Standard 1: English Language Learners communicate in English for social and instructional Page 3
Grade: MS: Subject: 9/24/2009 Unit 1 Algebra and Integers Chapter 2 Integers Time frame for Completion: 11 days Learning Competencies - What the students will know and be able to do upon completion of the unit solve two-step equations. Students will use a coordinate plane to locate and graph ordered pairs and represent algebraic relationships. Differentiation Options: Chapter 2 pgs 76G 76 H Supportive Teaching/Learning Activities Simplify algebraic expressions. Explore use algebra tiles to model division of integers. Divide integers. Find the average of a set of data. Graph points on a coordinate plane. Graph algebraic relationships. [All activities are structured to work within each student s zone of proximal development* in English Language Acquisition] Assessments Resources PDE Academic Standards Practice p. 120-121 (SE) and 62-64 Quizzes. P. 45-46 Chapter practice test -. P. 119 (SE) Unit 1 Test p. 77-78 of the Chapter 3 Resource Masters Mid-chapter test p. 47 Vocabulary test p. 48 Extended response test p. 61 Leveled chapter tests. P. 49 60 ExamView Assessment Suite (CD) StudentWorks Plus Math online prealgebra.com Manipulatives Computer with spreadsheet software. Centimeter ruler, graph paper Graphing calculator ELL: http://www.cal.org/siop: Fifty Strategies for Teaching; English Language Learners, 2 nd edition; Adrienne Herrell, Michael Jordan; (Merrill/Prentice Hall, 2003) purposes within the school setting. ELP Standard 2: English Language Learners communicate information, ideas, and concepts necessary for academic success in the content area of Language Arts. Page 4
Grade: MS: Subject: 9/24/2009 Unit 1 Algebra and Integers Chapter 3 Equations Time frame for Completion: 12-17 days Enduring Understandings / Big Ideas: Build a foundation of basic understandings of numbers, operations, algebraic thinking. Use these understandings to solve linear equations. Select and use appropriate operations to solve problems and justify solutions. Use graphs, tables, and algebraic representations to make predictions and solve problems. Essential Questions: Using the distributive property, why do you multiply the value outside the parentheses before you perform the operation inside the parentheses? Can you add 8x + 3x y? Why not? How do you find the value of the variable? How do you check your solution once you have found the value of the variable? When you solve a 2 step equation, what operations are performed 1 st? What is present in an equation that is not in an expression? Is the common difference positive, negative or both? What are the formulas for the perimeter and area of a rectangle? Learning Competencies - What the students will know and be able to do upon completion of the unit Students will learn about the basic tools of algebra, including variables, integers, and equations. Students will use UMASD problem solving template to solve problems, translate verbal phrases and expressions into algebraic expressions, and use mathematical properties and the order of operations. Students will compare and order integers and perform operations with integers. Students will evaluate and simplify algebraic Supportive Teaching/Learning Activities Use the distributive property to write equivalent numerical expressions Use the distributive property to write equivalent algebraic expressions Use the distributive property to simplify algebraic expressions *Explore - Model and solve equations with variables using manipulatives Solve equations by using the Subtraction Property of Equality Solve equations by using Assessments Resources PDE Academic Standards Formative (suggestions): Anticipation Guide p. 3 Ticket out the door p. 151, 157, 167 (TWE) Crystal Ball p. 133, 160 (TWE) Name the Math p. 128, 140 (TWE) Yesterday s News p. 145 (TWE) 4Sight Benchmark Assessment Summative (suggestions): Mid Chapter Quiz p. 146 Resource Glencoe McGraw-Hill Pre- Algebra Teacher Wraparound Edition, 2008 pages 122-175 UMASD problem solving template ESL staff Bilingual dictionaries Student data from 4Sight Benchmark Assessment Supplemental Resources: Technology p.122c 122D TeacherWorks All inone Planner and 2.1 Numbers, Number Systems and Number Relationships 2.4 - Mathematical Reasoning and Connections 2.5 - Mathematical Problem Solving and Communication 2.8 Algebra and Functions Every Teacher Teaches ESL ELP Standard 1: English Language Learners communicate in English for social and instructional purposes within the school setting. ELP Standard 2: English Page 5
Grade: MS: Subject: 9/24/2009 Unit 1 Algebra and Integers Chapter 3 Equations Time frame for Completion: 12-17 days Learning Competencies - What the students will know and be able to do upon completion of the unit expressions and write and solve two-step equations. Students will use a coordinate plane to locate and graph ordered pairs and represent algebraic relationships. Differentiation Options: Chapter 3 pgs 122G 122H Supportive Teaching/Learning Activities the Addition Property of Equality Solve equations by using the Division Property of Equality Solve equations by using the Multiplication Property of Equality Solve 2 step equations Write verbal sentences as 2 step equations Solve verbal problems by writing and solving 2 step equations Describe sequences using words and symbols Find terms of arithmetic sequences Solve problems by using formulas Solve problems involving the perimeters and areas of rectangles *Extend- Use a spreadsheet and change formulas to investigate problems. * Optional Assessments Resources PDE Academic Standards (SE) Study Guide and Review. P. 169-172 (SE) Standardized Test Practice p. 174-175 (SE) and 74-76 Quizzes. P. 57, 58 Chapter practice test -. 173 (SE) Unit 1 Test p. 77-78 of the Chapter 3 Resource Masters Mid-chapter test p. 59 Vocabulary test p. 60 Extended response test p. 73 Leveled chapter tests. P. 61-72 ExamView Assessment Suite (CD) Resource Center Graphing Calculator Easy Files AssignmentWorks Interactive Classroom ExamView Assessment Suite StudentWorks Plus Math online prealgebra.com Manipulatives Algebra tiles and equation mat Computer with spreadsheet software ELL: http://www.cal.org/siop: Fifty Strategies for Teaching; English Language Learners, 2 nd edition; Adrienne Herrell, Michael Jordan; (Merrill/Prentice Hall, 2003) Language Learners communicate information, ideas, and concepts necessary for academic success in the content area of Language Arts. [All activities are structured to work within each student s zone of proximal development* in English Language Acquisition] Page 6
Grade: MS: Subject: 9/24/2009 Unit 2 Algebra and Rational Numbers Chapter 4 Factors and Fractions Time frame for Completion: 10-13 days Enduring Understandings / Big Ideas: Understand rational numbers, ways of representing numbers, relationships amount numbers, and number systems. Find measures of central tendency in data sets. Understand that different forms of numbers are appropriate for different situations. Select and use appropriate operations to solve problems and justify solutions. Essential Questions: What does an exponent tell you? What is a prime number? How do you find the GCF for a set of numbers? How do you know when a fraction is in simplest form? What is the Quotient of Powers Rule? How do negative exponents represent repeated division? (Optional) Why would you write a number in scientific notation? Learning Competencies - What the students will know and be able to do upon completion of the unit Students will explore rational numbers Students will use prime factorization and greatest common factor to solve real-world problems and simplify algebraic equations Students will examine exponents, multiply and divide monomials, and use scientific notation. Students will compute and solve equations with rational numbers Students will use rational numbers to describe data. Differentiation Options: Supportive Teaching/Learning Activities Write expressions using exponents Evaluate expressions containing exponents *Extend Algebra Lab: Base 2: Use a binary language with a base 2 system of numbers *Write the prime factorizations of composite numbers Factor monomials Find the greatest common factor of two or more numbers or monomials Use the Distributive Property to factor algebraic expressions Simplify fractions using Assessments Resources PDE Academic Standards Formative (suggestions): Anticipation Guide p. 3 Ticket out the door p. 200, 213 (TWE) Crystal Ball p. 190 (TWE) Name the Math p. 184,195, 207 (TWE) Yesterday s News p. 218 (TWE) Summative (suggestions): Mid Chapter Quiz p. 53 (SE) Study Guide and Review. P. 219-222 (SE) Standardized Test Resource Glencoe McGraw-Hill Pre- Algebra Teacher Wraparound Edition, 2008 pages 176-225B UMASD problem solving template ESL staff Bilingual dictionaries Supplemental Resources: Technology p. 178C 178D TeacherWorks All inone Planner and Resource Center Graphing Calculator Easy Files 2.1 Numbers, Number Systems and Number Relationships 2.4 - Mathematical Reasoning and Connections 2.5 - Mathematical Problem Solving and Communication 2.8 Algebra and Functions Every Teacher Teaches ESL ELP Standard 1: English Language Learners communicate in English for social and instructional purposes within the school setting. ELP Standard 2: English Page 7
Grade: MS: Subject: 9/24/2009 Unit 2 Algebra and Rational Numbers Chapter 4 Factors and Fractions Time frame for Completion: 10-13 days Learning Competencies - What the students will know and be able to do upon completion of the unit Chapter 4 pgs 178G 178H Supportive Teaching/Learning Activities the GCF Simplify algebraic fractions Multiply monomials Divide Monomials *Extend Algebra Lab: A half-life Simulation: Use a simulation of half-lives to practice exponents *Write expressions using negative exponents *Evaluate numerical expressions containing negative exponents Express numbers in standard form and in scientific notation Compare and order numbers written in scientific notations * Optional Assessments Resources PDE Academic Standards Practice p. 224-225 (SE) and 68-70 Quizzes. P. 51-52 Chapter practice test -. 223 (SE) Unit 2 Test p. 83-84 of the Chapter 5 Resource Masters Mid-chapter test p. 53 Vocabulary test p. 54 Extended response test p. 67 Leveled chapter tests. P. 55 64 ExamView Assessment Suite (CD) AssignmentWorks Interactive Classroom ExamView Assessment Suite StudentWorks Plus Math online prealgebra.com Manipulatives Grid Paper Pennies, shoebox and grid paper ELL: http://www.cal.org/siop: Fifty Strategies for Teaching; English Language Learners, 2 nd edition; Adrienne Herrell, Michael Jordan; (Merrill/Prentice Hall, 2003) Language Learners communicate information, ideas, and concepts necessary for academic success in the content area of Language Arts. [All activities are structured to work within each student s zone of proximal development* in English Language Acquisition] Page 8
Grade: MS: Subject: 9/24/2009 Unit 2 Algebra and Rational Numbers Chapter 5 Rational Numbers Time frame for Completion: 13-18 days Enduring Understandings / Big Ideas: Understand rational numbers, ways of representing numbers, relationships amount numbers, and number systems. Find measures of central tendency in data sets. Understand that different forms of numbers are appropriate for different situations. Use statistical procedures to describe data sets. Evaluate predictions and conclusions based on statistical data. Essential Questions: What is the difference between a terminating and repeating decimal? How do you write a repeating decimal as a fraction? Why would you want to simplify a fraction before multiplying instead of after? What is dimensional analysis? How would you demonstrate adding like fractions using algebra tiles? How would you model subtraction of like fractions? Under what circumstances would you want to find the least common multiple? Why would you write a mixed number as an improper fraction before addition or subtraction? How is solving an equation with rational numbers similar to solving equations with integers? Is the mean, median, or mode most influenced by an outlier, or extreme value? Learning Competencies - What the students will know and be able to do upon completion of the unit Students will explore rational numbers Students will use prime factorization and greatest common factor to solve real-world problems and simplify algebraic equations Students will examine exponents, multiply and divide monomials, and use scientific notation. Students will compute and solve equations with rational numbers Supportive Teaching/Learning Activities Write fractions as terminating or repeating decimals. Compare fractions and decimals. Write rational numbers as fractions Identify and classify rational numbers Multiply positive and negative fractions Use dimensional analysis to solve problems. Divide positive and Assessments Resources PDE Academic Standards Formative (suggestions): Anticipation Guide p. 3 Ticket out the door p. 249, 254, 279 (TWE) Crystal Ball p. 233, 244, 261 (TWE) Name the Math p. 238, 267 (TWE) Yesterday s News p. 272 (TWE) Resource Glencoe McGraw-Hill Pre- Algebra Teacher Wraparound Edition, 2008 pages 226A-287B UMASD problem solving template ESL staff Bilingual dictionaries Supplemental Resources: Technology p. 226C 226D TeacherWorks All in- 2.1 Numbers, Number Systems and Number Relationships 2.2 Computation and Estimation 2.3 Measurement and Estimation 2.4 - Mathematical Reasoning and Connections 2.5 - Mathematical Problem Solving and Communication 2.8 Algebra and Functions Page 9
Grade: MS: Subject: 9/24/2009 Unit 2 Algebra and Rational Numbers Chapter 5 Rational Numbers Time frame for Completion: 13-18 days Learning Competencies - Wh at the students will know and be able to do upon completion of the unit Students will use rational numbers to describe data. Differentiation Options: Chapter 5 pgs 226G 226H Supportive Teaching/Learning Activities negative fractions using multiplicative inverses. Use dimensional analysis to solve problems Add and subtract like fractions Find the least common multiple of two or more numbers. Find the least common denominator of two or more fractions *Extend- Algebra Lab: Juniper Green Add and subtract unlike fractions Solve equations containing rational numbers Use the mean, median, and mode as measures of central tendency Choose an appropriate measures of central tendency and recognize measures of statistics *Extend- Graphing Calculator Lab: Mean and Median * Optional Assessments Resources PDE Academic Standards Summative (suggestions): Mid Chapter Quiz p. 65 (SE) Study Guide and Review. P. 281-284 (SE) Standardized Test Practice p. 286-287 (SE) and 80-82 Quizzes. P. 63-64 Chapter practice test -. 285 (SE) Unit 2 Test p. 83-84 of the Chapter 5 Resource Masters Mid-chapter test p. 65 Vocabulary test p. 66 Extended response test p. 79 Leveled chapter tests. P. 67-78 ExamView Assessment Suite (CD) one Planner and Resource Center Graphing Calculator Easy Files AssignmentWorks Interactive Classroom ExamView Assessment Suite StudentWorks Plus Math online prealgebra.com Manipulatives Hundreds chart and colored markers Graping calculator ELL: http://www.cal.org/siop: Fifty Strategies for Teaching; English Language Learners, 2 nd edition; Adrienne Herrell, Michael Jordan; (Merrill/Prentice Hall, 2003) 2.10 Trigonometry Every Teacher Teaches ESL ELP Standard 1: English Language Learners communicate in English for social and instructional purposes within the school setting. ELP Standard 2: English Language Learners communicate information, ideas, and concepts necessary for academic success in the content area of Language Arts. [All activities are structured to work within each student s zone of proximal development* in English Page 10
Grade: MS: Subject: 9/24/2009 Unit 2 Algebra and Rational Numbers Chapter 5 Rational Numbers Time frame for Completion: 13-18 days Learning Competencies - What the students will know and be able to do upon completion of the unit Supportive Teaching/Learning Activities Language Acquisition] Assessments Resources PDE Academic Standards Page 11
Grade: MS: Subject: 9/24/2009 Unit 3 Linear Equations, Inequalities, and Functions Chapter 6 Ratio, Proportion, and Percen t Time frame for Completion: 15-20 days Enduring Understandings / Big Ideas: Use basic principles of algebra and proportionality to analyze and represent linear functions. Identify proportional or nonproportional linear relationships in problem situations and solve problems. Use different forms of numbers appropriate for different situations. Essential Questions: When would it be useful to have a unit rate? How can you tell if 2 quantities are proportional? What is an example of when you might use a proportion in your life? If you want to make a scale drawing of a building, what are the steps that you would take to find the scale? What are the ways that a percent can be represented? In a percent proportion, what does the numerator represent? The denominator? What are 3 ways to estimate the percent of a value mentally? What is the simple interest formula? What does each variable stand for? How can you tell whether a value represents a percent of increase or a percent of decrease? (Optional) What are some examples when a biased sample might be desirable? (Optional) Learning Competencies - What the students will know and be able to do upon completion of the unit Students will learn about ratios, proportions, linear equations, inequalities, functions, and graphing. *Students will analyze data to discover whether a linear relationship exists. Students will learn that inequalities can help describe relationships between mathematical expressions Students will apply ratios and proportions to problems involving fractions, decimals, and percents Students will analyze how Page 12 Supportive Teaching/Learning Activities Write ratios as fractions in simplest form Determine unit rates Identify proportional and nonproportional relationships Describe a proportional relationship using an equation Solve proportions Use proportions to solve real world problems *Extend Algebra Lab: Capture - Recapture Use and construct scale drawings Express percents as fractions and vice versa Assessments Resources PDE Academic Standards Formative (suggestions): Anticipation Guide p. 3 Ticket out the door p. 296, 318, 331, 342 (TWE) Crystal Ball p. 306, 336 (TWE) Name the Math p. 326, 347 (TWE) Yesterday s News p. 299, 312 (TWE) 4Sight Benchmark Assessment Summative (suggestions): Mid Chapter Quiz p. 319 Resource Glencoe McGraw-Hill Pre- Algebra Teacher Wraparound Edition, 2008 pages 290-355 UMASD problem solving template ESL staff Bilingual dictionaries Student data from 4Sight Benchmark Assessment Supplemental Resources: Technology p.290c 290D TeacherWorks All in- 2.1 Numbers, Number Systems and Number Relationships 2.2 Computation and Estimation 2.3 Measurement and Estimation 2.4 - Mathematical Reasoning and Connections 2.5 - Mathematical Problem Solving and Communication 2.8 Algebra and Functions Every Teacher Teaches ESL ELP Standard 1: English Language Learners
Grade: MS: Subject: 9/24/2009 Unit 3 Linear Equations, Inequalities, and Functions Chapter 6 Ratio, Proportion, and Percen t Time frame for Completion: 15-20 days Learning Competencies - What the students will know and be able to do upon completion of the unit equations and graphs are used to describe mathematical relationships Students will expand their knowledge in the use of x- and y-intercepts, slope, and rate of change. Differentiation Options: Chapter 6 pgs 290G 290H Supportive Teaching/Learning Activities Express percents as decimals and vice versa *Explore Algebra Lab: Using a Percent Model Use the percent proportion to solve problems Compute mentally and estimate with percents Solve percent problems using percent equations Solve real life problems involving discount and interest *Extend Spreadsheet Lab: Compound Interest *Find percent of increase and percent of decrease *Identify various sampling techniques *Determine the validity of a sample and predict the actions of a larger group. * Optional [All activities are structured to work within each student s zone of proximal development* in English Language Acquisition] Assessments Resources PDE Academic Standards (SE) Study Guide and Review. P. 348-352 (SE) Standardized Test Practice p. 354-355 (SE) and 86-88 Quizzes. P. 69, 70 Chapter practice test -. 353 (SE) Unit 3 Test p. not listed of the Chapter 3 Resource Masters Mid-chapter test p. 71 Vocabulary test p. 72 Extended response test p. 85 Leveled chapter tests. P. 73-84 ExamView Assessment Suite (CD) one Planner and Resource Center Graphing Calculator Easy Files AssignmentWorks Interactive Classroom ExamView Assessment Suite StudentWorks Plus Math online prealgebra.com Manipulatives Algebra tiles and equation mat Computer with spreadsheet software ELL: http://www.cal.org/siop: Fifty Strategies for Teaching; English Language Learners, 2 nd edition; Adrienne Herrell, Michael Jordan; (Merrill/Prentice Hall, 2003) communicate in English for social and instructional purposes within the school setting. ELP Standard 2: English Language Learners communicate information, ideas, and concepts necessary for academic success in the content area of Language Arts. Page 13
Grade: MS: Subject: 9/24/2009 Unit 3 Linear Equations, Inequalities, and Functions Chapter 7 Functions and Graphing Time frame for Completion: 7-9 days Enduring Understandings / Big Ideas: Use basic principles of algebra and proportionality to analyze and represent linear functions. Connect various representations of a numerical relationship. Use graphs, tables, and algebraic representations to make predictions and solve problems. Essential Questions: Can a value in the domain have more than one value? What about a value in the range? (Optional) How do you find solutions of a linear equation? How do you find rates of change? How can you tell if a rate of change is positive or negative from a graph? (Optional) What does a linear graph that is a straight line tell you about the rate of change? (Optional) How are the slope of a line and the rate of change related? (Optional) How do you find the slope and y- intercept of a line? (Optional) What do you need to write a linear equation? (Optional) Why do you use points on a line of fit to write a line equation? (Optional) Learning Competencies - What the students will know and be able to do upon completion of the unit Students will learn about ratios, proportions, linear equations, inequalities, functions, and graphing. *Students will analyze data to discover whether a linear relationship exists. Students will learn that inequalities can help describe relationships between mathematical expressions Students will apply ratios and proportions to problems involving fractions, decimals, and percents Students will analyze how equations and graphs are used to describe Supportive Teaching/Learning Activities *Determine whether relations are functions. *Use functions to describe relationships between 2 quantities *Extend Graphing Calculator Lab: Function Table Solve linear equations with 2 variables Graph linear equations using ordered pairs *Find rates of change *Solve problems involving rates of change *Identify proportional and nonproportional relationships by finding a constant rate of change *Solve problems involving Assessments Resources PDE Academic Standards Formative (suggestions): Anticipation Guide p. 3 Ticket out the door p. 363, 375, 381, 393 (TWE) Crystal Ball none given (TWE) Name the Math p. 389, 407 (TWE) Yesterday s News p. 369, 402 (TWE) Summative (suggestions): Mid Chapter Quiz p. 382 (SE) Study Guide and Review. P. 408-412 (SE) Standardized Test Resource Glencoe McGraw-Hill Pre- Algebra Teacher Wraparound Edition, 2008 pages 356-415 UMASD problem solving template ESL staff Bilingual dictionaries Supplemental Resources: Technology p.356c 356D TeacherWorks All inone Planner and Resource Center Graphing Calculator Easy Files AssignmentWorks Interactive Classroom 2.1 Numbers, Number Systems and Number Relationships 2.2 Computation and Estimation 2.3 Measurement and Estimation 2.4 - Mathematical Reasoning and Connections 2.5 - Mathematical Problem Solving and Communication 2.6 - Statistics and Data Analysis 2.8 Algebra and Functions Every Teacher Teaches ESL ELP Standard 1: English Language Learners Page 14
Grade: MS: Subject: 9/24/2009 Unit 3 Linear Equations, Inequalities, and Functions Chapter 7 Functions and Graphing Time frame for Completion: 7-9 days Learning Competencies - What the students will know and be able to do upon completion of the unit mathematical relationships *Students will expand their knowledge in the use of x- and y-intercepts, slope, and rate of change. Differentiation Options: Chapter 7 pgs 356G 356H Supportive Teaching/Learning Activities direct variation *Explore Algebra Lab: It s All Downhill *Find the slope of a line *Extend Graphing Calculators Lab: The Family of Linear Graphs *Determine slopes and y- intercepts of lines *Graph linear equations using slope and y- intercept *Write equations given the slope and y- intercept, a graph, a table, or 2 points Draw lines of fit *or sets of data Use lines of fit to make predictions about data * Optional [All activities are structured to work within each student s zone of proximal development* in English Language Acquisition] Assessments Resources PDE Academic Standards Practice p. 414-415 (SE) and 74-76 Quizzes. P. 56, 57 Chapter practice test -. 413 (SE) Unit 3 Test p. not listed of the Chapter 3 Resource Masters Mid-chapter test p. 59 Vocabulary test p. 60 Extended response test p. 73 Leveled chapter tests. P. 61-72 ExamView Assessment Suite (CD) ExamView Assessment Suite StudentWorks Plus Math online prealgebra.com Manipulatives Index cards Graphing calculator Grid paper, water, beaker, metric ruler, tablespoon, 1/8 cup measuring cup ELL: http://www.cal.org/siop: Fifty Strategies for Teaching; English Language Learners, 2 nd edition; Adrienne Herrell, Michael Jordan; (Merrill/Prentice Hall, 2003) communicate in English for social and instructional purposes within the school setting. ELP Standard 2: English Language Learners communicate information, ideas, and concepts necessary for academic success in the content area of Language Arts. Page 15
Grade: MS: Subject: 9/24/2009 Unit 3 Linear Equations, Inequalities, and Functions Chapter 8 Equations and Inequalities Time frame for Completion: 9-12 days Enduring Understandings / Big Ideas: Use basic principles of algebra and proportionality to analyze and represent linear functions. Select and use appropriate operations to solve problems and justify solutions. Essential Questions: How is solving an equation with variables on both sides like solving an equation with variables on one side? (Optional) What is it called when there is no value for the variable that will make the inequality true? (Optional) What does it mean when an inequality is graphed on a number line with an open circle? How many solutions does an inequality have? Why do you reverse the inequality sign when multiplying both sides by a negative number? What is an inverse operation? Learning Competencies - What the students will know and be able to do upon completion of the unit Students will learn about ratios, proportions, linear equations, inequalities, functions, and graphing. *Students will analyze data to discover whether a linear relationship exists. Students will learn that inequalities can help describe relationships between mathematical expressions Students will apply ratios and proportions to problems involving fractions, decimals, and percents Students will analyze how equations and graphs are used to describe mathematical relationships Students will expand their knowledge in the use of x- Page 16 Supportive Teaching/Learning Activities *Explore Algebra Lab: Equations with Variables on Each Side: Use algebra tiles and an equation mat to solve equations with variables on both sides *Solve equations with variables on each side *Solve equations that involve grouping symbols *Identify equations that have no solution or infinite number of solutions Write inequalities Graph inequalities Solve inequalities by using the Addition and Subtraction Property of Inequality Solve inequalities by multiplying or dividing by a positive number Solve inequalities by Assessments Resources PDE Academic Standards Formative (suggestions): Anticipation Guide p. 3 Ticket out the door p. 428, 433, 444 (TWE) Crystal Ball none given (TWE) Name the Math p. 422 (TWE) Yesterday s News p. 439, 450 (TWE) Summative (suggestions): Mid Chapter Quiz p. 440 (SE) Study Guide and Review. P. 451-454 (SE) Standardized Test Practice p. 456-457 (SE) and 62-64 Quizzes. P. 45, 46 Chapter practice test -. Resource Glencoe McGraw-Hill Pre- Algebra Teacher Wraparound Edition, 2008 pages 416-457 UMASD problem solving template ESL staff Bilingual dictionaries Supplemental Resources: Technology p.416c 416D TeacherWorks All inone Planner and Resource Center Graphing Calculator Easy Files AssignmentWorks Interactive Classroom ExamView Assessment Suite StudentWorks Plus Math online pre- 2.1 Numbers, Number Systems and Number Relationships 2.4 - Mathematical Reasoning and Connections 2.5 - Mathematical Problem Solving and Communication 2.8 Algebra and Functions Every Teacher Teaches ESL ELP Standard 1: English Language Learners communicate in English for social and instructional purposes within the school setting. ELP Standard 2: English Language Learners communicate information, ideas, and concepts necessary for academic success in the content area of Language Arts.
Grade: MS: Subject: 9/24/2009 Unit 3 Linear Equations, Inequalities, and Functions Chapter 8 Equations and Inequalities Time frame for Completion: 9-12 days Learning Competencies - What the students will know and be able to do upon completion of the unit and y-intercepts, slope, and rate of change. Differentiation Options: Chapter 8 pgs 416G 416H Supportive Teaching/Learning Activities multiplying or dividing by a negative number Solve inequalities that involve more than one operation * Optional [All activities are structured to work within each student s zone of proximal development* in English Language Acquisition] Assessments Resources PDE Academic Standards 455 (SE) Unit 3 Test p. not listed of the Chapter 3 Resource Masters Mid-chapter test p. 47 Vocabulary test p. 48 Extended response test p. 61 Leveled chapter tests. P. 49-60 ExamView Assessment Suite (CD) algebra.com Manipulatives Algebra tiles and equation mat ELL: http://www.cal.org/siop: Fifty Strategies for Teaching; English Language Learners, 2 nd edition; Adrienne Herrell, Michael Jordan; (Merrill/Prentice Hall, 2003) Page 17
Grade: MS: Subject: 9/24/2009 Unit 4 Applying Algebra to Geometry Chapter 9 Real Numbers and Right Tr iangles Time frame for Completion: 12-15 days Enduring Understandings / Big Ideas: Analyze figures in two- and three-dimensional space. Find areas of two-dimensional figures and volumes and surface areas of three-dimensional figures. Use different forms of numbers appropriate for different situations. Use indirect measurement to solve problems. Essential Questions: Is there such a thing as a negative square root? What do rational and irrational numbers have in common? What are their differences (rational and irrational)? What are the two ways of classifying triangles? How are some ways of knowing whether a triangle is a right triangle? How can you verify the Pythagorean Theorem? (Optional) What does it mean when two figures are similar? Learning Competencies - What the students will know and be able to do upon completion of the unit Students will examine square roots, and the real number system. Students will classify angles and triangles, and explore the Pythagorean Theorem, the distance formula and the properties of similar figures Students will classify, find the angle measures and find the area of various polygons. Students will examine circumference and area of circles. Students will find the volume and surface area of three-dimensional Supportive Teaching/Learning Activities *Explore- Algebra Lab: Squares and Squares Roots: Use Algebra tiles to express squares and square roots Find squares and square roots Estimate square roots Identify and compare numbers in the real number system Solve equations by finding square roots Find the missing angle measure of a triangle Classify triangles by properties and attributes. *Explore- Algebra Lab: The Pythagorean Assessments Resources PDE Academic Standards Formative (suggestions): Anticipation Guide p. 3 Ticket out the door p. 481, 496 (TWE) Crystal Ball none given (TWE) Name the Math p. 474, 490 (TWE) Yesterday s News p. 468, 502 (TWE) Summative (suggestions): Mid Chapter Quiz p. 482 (SE) Study Guide and Review. P. 503-506 (SE) Resource Glencoe McGraw-Hill Pre- Algebra Teacher Wraparound Edition, 2008 pages 458-509D UMASD problem solving template ESL staff Bilingual dictionaries Supplemental Resources: Technology p. 460C 460D TeacherWorks All inone Planner and Resource Center Graphing Calculator Easy Files 2.1 Numbers, Number Systems and Number Relationships 2.2 Computation and Estimation 2.3 Measurement and Estimation 2.4 - Mathematical Reasoning and Connections 2.5 - Mathematical Problem Solving and Communication 2.8 Algebra and Functions 2.9 Geometry 2.10 Trigonometry Every Teacher Teaches ESL ELP Standard 1: English Page 18
Grade: MS: Subject: 9/24/2009 Unit 4 Applying Algebra to Geometry Chapter 9 Real Numbers and Right Tr iangles Time frame for Completion: 12-15 days Learning Competencies - What the students will know and be able to do upon completion of the unit objects Differentiation Options: Chapter 9 pgs 460G 460H Supportive Teaching/Learning Activities Theorem Find the area of figures using rectangular dot paper Use the Pythagorean Theorem to find the length of a side of a right triangle. Use the converse of the Pythagorean Theorem to determine whether a triangle is a right triangle. *Extend- Algebra Lab: Graphing Irrational numbers Graph irrational numbers on a number line *Use the Distance Formula to determine lenths on a coordinate plane. Identify corresponding parts and find missing measures of similar polygons Solve problems involving indirect measurement using similar triangles *Optional [All activities are structured to work within each student s zone of proximal development* in English Language Acquisition] Assessments Resources PDE Academic Standards Standardized Test Practice p. 508-509 (SE) and 62-64 Quizzes. P. 45-46 Chapter practice test -. 507 (SE) Unit 4 Test p. 65-66 of the Chapter 11 Resource Masters Mid-chapter test p. 47 Vocabulary test p. 48 Extended response test p. 61 Leveled chapter tests. P. 49-60 ExamView Assessment Suite (CD) AssignmentWorks Interactive Classroom ExamView Assessment Suite StudentWorks Plus Math online prealgebra.com Manipulatives Algebra tiles Regular dot paper Compass and grid paper ELL: http://www.cal.org/siop: Fifty Strategies for Teaching; English Language Learners, 2 nd edition; Adrienne Herrell, Michael Jordan; (Merrill/Prentice Hall, 2003) Language Learners communicate in English for social and instructional purposes within the school setting. ELP Standard 2: English Language Learners communicate information, ideas, and concepts necessary for academic success in the content area of Language Arts. Page 19
Grade: MS: Subject: 9/24/2009 Unit 4 Applying Algebra to Geometry Chapter 10 Two-Dimensional Figures Time frame for Completion: 13-17 days Enduring Understandings / Big Ideas: Analyze figures in two- and three-dimensional space. Find areas of two-dimensional figures and volumes and surface areas of three-dimensional figures. Use transformational geometry to develop special sense. Use geometry to model and describe the physical world. Essential Questions: Describe the angle relationships formed when lines intersect What is the difference between similar figures and congruent figures? Are figures congruent or similar when translated? Reflected? Dilated? How do you find the missing angle measures in a quadrilateral? Why does the interior angles formula work to find the measures of the interior angles of a polygon? What is area? What unit is area in? To what degree is the unit for circumference? Why? To what degree is the unit for volume? Why? How do you find the area of a composite figure? Learning Competencies - What the students will know and be able to do upon completion of the unit Students will examine square roots, and the real number system. Students will classify angles and triangles, and explore the Pythagorean Theorem, the distance formula and the properties of similar figures Students will classify, find the angle measures and find the area of various polygons. Students will examine circumference and area of circles. Supportive Teaching/Learning Activities Identify the relationships of angles formed by two parallel lines and a transversal. Identify the relationships of vertical, adjacent, complementary and supplementary angles Identify congruent triangles and corresponding parts of congruent triangles Draw translations, reflections and *dilations on a coordinate plane. *Extend- Geometry Lab: Assessments Resources PDE Academic Standards Formative (suggestions): Anticipation Guide p. 3 Ticket out the door p. 517, 536, 543 (TWE) Crystal Ball none given (TWE) Name the Math p. 530, 556 (TWE) Yesterday s News p. 523, 550, 562 (TWE) Summative (suggestions): Mid Chapter Quiz p. 537 Resource Glencoe McGraw-Hill Pre- Algebra Teacher Wraparound Edition, 2008 pages 510A-571F UMASD problem solving template ESL staff Bilingual dictionaries Supplemental Resources: Technology p. 510C- 510D TeacherWorks All inone Planner and Resource Center 2.1 Numbers, Number Systems and Number Relationships 2.3 Measurement and Estimation 2.4 - Mathematical Reasoning and Connections 2.5 - Mathematical Problem Solving and Communication 2.8 Algebra and Functions 2.9 Geometry 2.10 Trigonometry Every Teacher Teaches ESL Page 20
Grade: MS: Subject: 9/24/2009 Unit 4 Applying Algebra to Geometry Chapter 10 Two-Dimensional Figures Time frame for Completion: 13-17 days Learning Competencies - What the students will know and be able to do upon completion of the unit Students will find the volume and surface area of three-dimensional objects Differentiation Options: Chapter 10 pgs 510G 510H Supportive Teaching/Learning Activities Roations Find the missing angle measures of a quadrilateral Classify quadrilaterals Classify polygons Determine the sum of the measures of the interior and exterior angles of a polygon *Extend- Geometry Lab: Tessellations Find areas of parallelograms Find the areas of triangles and trapezoids Find circumference of circles Find area of circles *Extend- Spreadsheet Lab: Circle graphs and Spreadsheets Find area of composite figures (Quads and Triangles only) *Extend- Spreadsheet Lab: Dilations and Perimeter and Area [All activities are structured to work within each student s zone of proximal development* in English Language Acquisition] Assessments Resources PDE Academic Standards (SE) Study Guide and Review. P. 564-568 (SE) Standardized Test Practice p. 570-571 (SE) and 74-76 Quizzes. P. 57-58 Chapter practice test -. 569 (SE) Unit 4 Test p. 65-66 of the Chapter 11 Resource Masters Mid-chapter test p. 59 Vocabulary test p. 60 Extended response test p. 73 Leveled chapter tests. P. 61-72 ExamView Assessment Suite (CD) Graphing Calculator Easy Files AssignmentWorks Interactive Classroom ExamView Assessment Suite StudentWorks Plus Math online prealgebra.com Manipulatives Computer with spreadsheet program ELL: http://www.cal.org/siop: Fifty Strategies for Teaching; English Language Learners, 2 nd edition; Adrienne Herrell, Michael Jordan; (Merrill/Prentice Hall, 2003) ELP Standard 1: English Language Learners communicate in English for social and instructional purposes within the school setting. ELP Standard 2: English Language Learners communicate information, ideas, and concepts necessary for academic success in the content area of Language Arts. Page 21
Grade: MS: Subject: 9/24/2009 Unit 4 Applying Algebra to Geometry Chapter 11 Three Dimensional Figur es Time frame for Completion: 12-15 days Enduring Understandings / Big Ideas: Analyze figures in two- and three-dimensional space. Find areas of two-dimensional figures and volumes and surface areas of three-dimensional figures. Determine measures of three-dimensional figures Describe how changes in dimensions affect area and volume measures Essential Questions: How is a circle different from a cone? Is the formula to find the volume of a rectangular cube different from the formula to find the volume of a triangular prism? If so, in what way? How can you verify that the volume of a cone is one-third the volume of a cube with the same base and height? (Optional) Why are the sums of the lateral area and the surface area calculated separately and then added? What is the difference between the formulas for the surface area of a pyramid and the surface area of a cone? (Optional) What are the ratios needed to prove that two solids are similar? (Optional) Learning Competencies - What the students will know and be able to do upon completion of the unit Students will examine square roots, and the real number system. Students will classify angles and triangles, and explore the Pythagorean Theorem, the distance formula and the properties of similar figures Students will classify, find the angle measures and find the area of various polygons. Students will examine circumference and area of circles. Students will find the volume and surface area of three-dimensional objects Supportive Teaching/Learning Activities *Explore- Geometry Lab: Building Three- Dimensional Figures: Draw three-dimensional figures using different perspectives Identify three-dimensional figures *Draw various views of three-dimensional figures *Explore Geometry Lab: Volume: Investigate volume by creating and comparing containers of various shapes Find volumes of prisms Find volumes of circular cylinders Find volumes of pyramids *Find volumes of cones Assessments Resources PDE Academic Standards Formative (suggestions): Anticipation Guide p. 3 Ticket out the door p. 594, 606, 613 (TWE) Crystal Ball none given (TWE) Name the Math p. 581, 601 (TWE) Yesterday s News p. 588 (TWE) Summative (suggestions): Mid Chapter Quiz p. 595 (SE) Study Guide and Review. P. 615-618 (SE) Standardized Test Resource Glencoe McGraw-Hill Pre- Algebra Teacher Wraparound Edition, 2008 pages 572A- 621B UMASD problem solving template ESL staff Bilingual dictionaries Supplemental Resources: Technology p. 572C- 572D TeacherWorks All inone Planner and Resource Center Graphing Calculator Easy Files AssignmentWorks Interactive Classroom 2.3 Measurement and Estimation 2.4 - Mathematical Reasoning and Connections 2.5 - Mathematical Problem Solving and Communication 2.8 Algebra and Functions 2.9 Geometry Every Teacher Teaches ESL ELP Standard 1: English Language Learners communicate in English for social and instructional purposes within the school setting. ELP Standard 2: English Language Learners Page 22
Grade: MS: Subject: 9/24/2009 Unit 5 Extending Algebra to Statistics and Polynomials Chapter 12 More Statistics and Probab ility Time frame for Completion: 12-15 days Learning Competencies - What the students will know and be able to do upon completion of the unit Differentiation Options: Chapter 11 pgs 572G-572H Supportive Teaching/Learning Activities and spheres *Explore- Geometry Lab: Exploring Lateral Area and Surface Area Find the lateral and surface areas of prisms and cylinders Find lateral areas and surface area of prisms Find lateral areas and surface areas of cylinders *Find surface areas of pyramids *Find surface areas of cones *Explore- Geometry Lab: Similar Solids: Investigate similar solids using sugar cubes or centimeter cubes *Identify similar solids *Solve problems involving similar solids *Optional [All activities are structured to work within each student s zone of proximal development* in English Language Acquisition] Assessments Resources PDE Academic Standards Practice p. 620-621 (SE) and 62-64 Quizzes. P. 45-46 Chapter practice test -. 619 (SE) Unit 4 Test p. 65-66 of the Chapter 11 Resource Masters Mid-chapter test p. 47 Vocabulary test p. 48 Extended response test p. 61 Leveled chapter tests. P. 49-60 ExamView Assessment Suite (CD) ExamView Assessment Suite StudentWorks Plus Math online prealgebra.com Manipulatives Isometric dot paper, centimeter cubes, scissors and tape Index cards, tape and rice Rectangular prism, cylinder and measuring tape Sugar on centimeter cubes ELL: http://www.cal.org/siop: Fifty Strategies for Teaching; English Language Learners, 2 nd edition; Adrienne Herrell, Michael Jordan; (Merrill/Prentice Hall, 2003) communicate information, ideas, and concepts necessary for academic success in the content area of Language Arts. Page 23
Grade: MS: Subject: 9/24/2009 Unit 5 Extending Algebra to Statistics and Polynomials Chapter 12 More Statistics and Probab ility Time frame for Completion: 12-15 days Enduring Understandings / Big Ideas: Using statistical procedures to describe data sets and make predictions. Use basic principles of algebra to analyze and represent proportional and nonproportional linear relationships. Use statistical procedures to describe data Evaluate predictions and conclusions based on statistical data Apply concepts of theoretical and experimental probability to make predictions Essential Questions: What method can you use to ensure the data is entered correctly into the plot? Which is more affected by extreme values, the range or the interquartile range of data? If a line runs through the middle of the box in a box and whisker plot, what does it mean? If a histogram has a rectangle that is taller than the rest, how would this be interpreted? If you had 2 sets of data which to compare, what type of graph would you select and why? What are ways that a graph can be misleading? What is the difference between theoretical and experimental probability? How do you write the probability of the outcome of an event? What is the difference between a permutation and combination? Which is greater, the probability of a dependent or independent composite event and why? Learning Competencies - What the students will know and be able to do upon completion of the unit Students will display and interpret data in various plots and graphs and use measures of variation to compare data Students will count outcomes and use permutations and combinations Students will determine probability using simulations, finding experimental probability, and finding the probability of multiple events Page 24 Supportive Teaching/Learning Activities Display and interpret data in stem ad leaf plots *Extend Graphing Calculator Lab: Stem-and- Leaf Plots and Line Plots Find measures of variation Use measures of variation to interpret and compare data Display and interpret data in a box and whisker plot *Extend Graphing Calculator Lab: Box-and Assessments Resources PDE Academic Standards Formative (suggestions): Anticipation Guide p. 3 Ticket out the door p. 656, 663, 680 (TWE) Crystal Ball p. 637, 649, 669 (TWE) Name the Math p. 631, 642, 674 (TWE) Yesterday s News p. 687 (TWE) Summative (suggestions): Resource Glencoe McGraw-Hill Pre- Algebra Teacher Wraparound Edition, 2008 pages 624-697 UMASD Problem solving template ESL staff Bilingual dictionaries Supplemental Resources: Technology p.624c 624D TeacherWorks All inone Planner and 2.4 - Mathematical Reasoning and Connections 2.5 - Mathematical Problem Solving and Communication 2.6 - Statistics and Data Analysis 2.7 Probability and Predictions 2.8 Algebra and Functions Every Teacher Teaches ESL ELP Standard 1: English Language Learners
Grade: MS: Subject: 9/24/2009 Unit 5 Extending Algebra to Statistics and Polynomials Chapter 12 More Statistics and Probab ility Time frame for Completion: 12-15 days Learning Competencies - What the students will know and be able to do upon completion of the unit *Students will identify and classify polynomials and find the degree of a polynomial *Students will learn to use operations involving monomials and polynomials *Students will examine linear and nonlinear functions, extending to the graphing of quadratic and cubic functions Differentiation Options: Chapter 12 pgs 624G 624H Supportive Teaching/Learning Activities Whisker Plots Display and interpret data in a histogram *Extend Graphing Calculator Lab: Histograms Select an appropriate display for a set of data *Extend Spreadsheet Lab: Bar Graphs and Line Graphs Recognize when graphs are misleading Evaluate predictions and conclusions based on data analysis Find the probability of simple events Use a sample to predict the actions of a larger group Use tree diagrams or the Fundamental Counting Principle to count outcomes and find the probability of events *Extend Algebra Lab: Probability and Pascal s Triangle Use permutations and combinations *Explore Graphing Calculator Lab: Probability Simulation Find the probability of independent and Assessments Resources PDE Academic Standards Mid Chapter Quiz p. 658 (SE) Study Guide and Review. P. 690-694 (SE) Standardized Test Practice p. 696-697 (SE) and 88-90 Quizzes. P. 71, 72 Chapter practice test -. 695 (SE) Unit 5 Test p. 65-66 of the Chapter 5 Resource Masters Mid-chapter test p. 73 Vocabulary test p. 74 Extended response test p. 87 Leveled chapter tests. P. 75-86 ExamView Assessment Suite (CD) Resource Center Graphing Calculator Easy Files AssignmentWorks Interactive Classroom ExamView Assessment Suite StudentWorks Plus Math online prealgebra.com Manipulatives Graphing calculator Computer with spreadsheet software Penny, nickel, dime, and quarter Coin, number cube, red and white counters, blue and red marbles ELL: http://www.cal.org/siop: Fifty Strategies for Teaching; English Language Learners, 2 nd edition; Adrienne Herrell, Michael Jordan; (Merrill/Prentice Hall, 2003) communicate in English for social and instructional purposes within the school setting. ELP Standard 2: English Language Learners communicate information, ideas, and concepts necessary for academic success in the content area of Language Arts. Page 25
Grade: MS: Subject: 9/24/2009 Unit 5 Extending Algebra to Statistics and Polynomials Chapter 12 More Statistics and Probab ility Time frame for Completion: 12-15 days Learning Competencies - What the students will know and be able to do upon completion of the unit Supportive Teaching/Learning Activities dependent events Find the probability of mutually exclusive events *Extend Algebra Lab: Simulations *Optional [All activities are structured to work within each student s zone of proximal development* in English Language Acquisition] Assessments Resources PDE Academic Standards Page 26
Grade: MS: Subject: 9/24/2009 Unit 5 Extending Algebra to Statistics and Polynomials Chapter 13 Polynomials and Nonlinear Functions Time frame for Completion: 0 days optional chapter (14 days if completed) Enduring Understandings / Big Ideas: Using statistical procedures to describe data sets and make predictions. Use basic principles of algebra to analyze and represent proportional and nonproportional linear relationships. Understand that a function can be described in a variety of ways Essential Questions: How do you determine the degree of a polynomial? (Optional) What does the Commutative Property of Multiplication have to do with determining whether monomials are like terms? (Optional) How can you model the subtraction of polynomials with algebra tiles? (Optional) What property do you use when multiplying polynomials? (Optional) What does the graph of a nonlinear function look like, as compared to a graph of a linear function? (Optional) Do all quadratic functions open up or down? What is an example? (Optional) Learning Competencies - What the students will know and be able to do upon completion of the unit Students will display and interpret data in various plots and graphs and use measures of variation to compare data Students will count outcomes and use permutations and combinations Students will determine probability using simulations, finding experimental probability, and finding the probability of multiple events *Students will identify and classify polynomials and find the degree of a polynomial *Students will learn to use operations involving monomials and polynomials Page 27 Supportive Teaching/Learning Activities *Identify and classify polynomials *Find the degree of a polynomial *Extend Algebra Lab: Modeling Polynomials with Algebra Tiles Model polynomials with algebra tiles *Add polynomials *Subtract polynomials *Explore- Algebra Lab: Modeling Multiplication: Model multiplication with algebra tiles *Multiply a polynomial by a monomial *Determine whether a function is a linear or nonlinear *Graph quadratic functions *Graph cubic functions Assessments Resources PDE Academic Standards Formative (suggestions): Anticipation Guide p. 3 Ticket out the door p. 712, 729 (TWE) Crystal Ball 703 (TWE) Name the Math p. 708, 725 (TWE) Yesterday s News p. 718 (TWE) Summative (suggestions): Mid Chapter Quiz p. 714 (SE) Study Guide and Review. P. 732-734 (SE) Standardized Test Practice p. 736-737 (SE) and 62-64 Quizzes. P. 45, 46 Chapter practice test -. Resource Glencoe McGraw-Hill Pre- Algebra Teacher Wraparound Edition, 2008 pages -698A- 737F UMASD problem solving template ESL staff Bilingual dictionaries Supplemental Resources: Technology p.698c 698D TeacherWorks All inone Planner and Resource Center Graphing Calculator Easy Files AssignmentWorks Interactive Classroom ExamView Assessment Suite StudentWorks Plus 2.1 Numbers, Number Systems and Number Relationships 2.2 Computation and Estimation 2.4 - Mathematical Reasoning and Connections 2.5 - Mathematical Problem Solving and Communication 2.6 - Statistics and Data Analysis 2.8 Algebra and Functions Every Teacher Teaches ESL ELP Standard 1: English Language Learners communicate in English for social and instructional purposes within the school setting. ELP Standard 2: English
Grade: MS: Subject: 9/24/2009 Unit 5 Extending Algebra to Statistics and Polynomials Chapter 13 Polynomials and Nonlinear Functions Time frame for Completion: 0 days optional chapter (14 days if completed) Learning Competencies - Supportive Assessments Resources PDE Academic Standards What the students will know Teaching/Learning and be able to do upon Activities completion of the unit *Students will examine linear and nonlinear functions, extending to the graphing of quadratic and cubic functions Differentiation Options: Chapter 13 pgs 698G 698H *Extend- Graphing Calculator Lab: The Family of Quadratic Functions Explore families of quadratic functions on a graphing calculator *Optional [All activities are structured to work within each student s zone of proximal development* in English Language Acquisition] 735 (SE) Unit 5 Test p. 65-66 of the Chapter 13 Resource Masters Mid-chapter test p. 47 Vocabulary test p. 48 Extended response test p. 61 Leveled chapter tests. P. 49-60 ExamView Assessment Suite (CD) Math online prealgebra.com Manipulatives Algebra tiles Product mat Graphing calculator ELL: http://www.cal.org/siop: Fifty Strategies for Teaching; English Language Learners, 2 nd edition; Adrienne Herrell, Michael Jordan; (Merrill/Prentice Hall, 2003) Language Learners communicate information, ideas, and concepts necessary for academic success in the content area of Language Arts. Page 28
English Language Proficiency Standard 1: English language learners communicate in English for SOCIAL AND INSTRUCTIONAL purposes within the school setting. Grade Level Cluster: 9-12 Level 1 Entering Level 2 Beginning Level 3 Developing Level 4 Expanding Level 5 Bridging Standard or Anchor Listening Follow instructions or requests from peers supported by gestures (such as: Meet me at my locker after 8 th period ). Process and respond to discourse from unfamiliar speakers with visual support (such as: at assemblies or on field trips). Process and respond to discourse from indirect sources (such as: cassettes or CDs) working with a partner. Follow, process and respond to announcements over the intercom with peer support. Analyze and interpret the appropriateness of oral messages or information from a variety of sources (such as: popular songs and voicemail messages) within a small group. Reading Speaking Preview visually supported text to glean basic facts. State preferences for types of music, games, TV programs or recreational activities using pictures. Connect information from visually supported text to self. Describe preferred movies, magazines, stories, or authors to a partner. Skim/scan material to confirm information or hypotheses working with a partner. Compare and contrast plays, films, books, songs, computer programs or magazine articles using realia. Summarize information from a variety of visually supported print resources. Recommend games, songs, books, films or computer programs with a peer. Evaluate hypotheses based on information from visually supported text. Critique and evaluate plays, films, books, songs, computer programs, or magazine articles within a small group. Level 6- Reaching Writing List common personal interests working with a partner. Create a graphic organizer about common personal interests working with a partner. Develop interview questions for a personal interest questionnaire within a small group. Write a summary of information from personal interest questionnaires within a small group. Make written conclusions and inferences about data collected from questionnaires working with a partner. Page 29
Level 1 Entering Level 2 Beginning Level 3 Developing Level 4 Expanding Level 5 Bridging Standard or Anchor Listening Identify properties of geometric figures (such as: parallels, diagonals and congruent sides) based on oral statements supported visually within a small group. Sort orally described geometric figures using manipulatives supported by a pictorial vocabulary chart. Generate 2-D and 3-D figures based on multistep oral directions working with a partner. Identify geometric figures based on orally presented deductive proofs working with a partner. Generate transformations of geometric shapes based on oral directions using computer software or paper and pencil working with a partner. M.11.C.1 Reading Speaking Match data with the correct graph (such as: a data table to a circle graph) working with a partner. Identify the order of operations using visual support. Locate key data on a graph working with a partner. Sequence steps in the order of operations in problem solving relying on mental math or think-aloud within a small group. Draw conclusions using comparative language based on data in a graph working with a partner. Discuss the solution to a problem involving the order of operations within a small group. Analyze conclusions drawn from data on a graph within a small group. Explain the solution to a problem involving the order of operations using visual supports. Predict the impact of changes in data displayed on a graph within a small group. Analyze the solution to a problem involving the order of operations working with a partner. M.11.E.1 M.11.A.3 Level 6- Reaching Writing Copy the process used to solve an algebraic equation, inequality or expression. Write and solve a simple algebraic equation, inequality or expression using a guided model. Write the steps used to solve an algebraic equation, inequality or expression using a word bank. Write a justification to the solution of an algebraic equation, inequality or expression using a word bank. Write a word problem that fits an algebraic equation, inequality or expression working with a partner. M.11.D.2 Page 30
*Zone of Proximal Development: That area between what the student is capable of at the moment and the point you want the student to reach next (Vygotsky, 1978) Stages of Second Language Acquisition: (Hill, J., Flynn, K., 2006) Stage Characteristics Approximate Time Frame Teacher Prompts Preproduction PDE: Entering The student Has minimal comprehension Does not verbalize Nods yes and no Draws and points 0-6 months Show me Circle the Where is? Who has? Early Production PDE: Beginning Speech Emergence PDE: Developing Intermediate Fluency PDE: Expanding Advanced Fluency: PDE: Bridging The student Has limited comprehension Produces one- or two-word responses Participates using key words and familiar phrases Uses present-tense verbs The student Has good comprehension Can produce simple sentences Makes grammar and pronunciation errors Frequently misunderstands jokes The Student Has excellent comprehension Makes few grammatical errors The student has a near native level of speech. 6 months to 1 year Yes/no questions Either/or questions One-or two-word answers Lists Labels 1-3 years Why? How? Explain Phrase or short-sentence answers 3-5 years What would happen if? Why do you think? 5-7 years Decide if Retell Page 31
PRE-ALGEBRA - CURRICULUM IPG GUIDE TIMELINE AND STANDARDS SECTION # OF DAYS STANDARDS CLASSROOM EXPECTATIONS; 4 2.2.8.B, 2.5.8.A, 2.5.8.B, 2.5.8.C, 2.5.8.D TEXTBOOK ORIENTATION; SUMMER PACKET REVIEW HIGHLIGHTING ADDING, SUBTRACTING, MULTIPLYING AND DIVIDING POSITIVE FRACTIONS AND DECIMALS; INTRODUCE UMASD PROBLEM SOLVING TEMPLATE (SP. ED. PROGRESS MONITORING) 1-6 and 2-6 ORDERED PAIRS AND 2 2.8.8.G,, 2.8.8.J RELATIONS AND COORDINATE SYSTEM Quadrants, axis, origin Algebraic Relationships Graphing and identifying points Points on horizontal or vertical lines Characteristics of points in each quadrant 2-1 INTEGER AND ABSOLUTE VALUE 1 2.1.8.A, 2.1.8.F Comparing and ordering integers Find absolute value Write integers for real world situations Solving expressions with absolute value Graph integers on number line 2-2 ADDING INTEGERS 2 2.1.8.F, 2.2.8.B, 2.4.8.D Add two or more integers Explain process of adding integers 2-3 SUBTRACTING INTEGERS 2 2.1.8.F, 2.2.8.B, 2.4.8.D Subtract two or more integers Explain process of subtracting integers 2-4 MULTIPLYING INTEGERS.5 2.2.8.B, 2.4.8.D Multiply two or more integers Explain process of subtracting integers 2-5 DIVIDING INTEGERS.5 2.2.8.B, 2.4.8.D, 2.6.8.A Divide integers Find average/mean of data set with integers Tie in mean/median/mode Estimate average of set of data (using difference of estimation compared to each score) 1-1 INCORPORATE UMASD PROBLEM 2.5.8.A, 2.5.8.B, 2.5.8.C, 2.5.8.D SOLVING TEMPLATE WITH PROBLEMS REVIEW 2 ASSESSMENT 1 TOTAL DAYS 15
SECTION 5-3 MULTIPLYING RATIONAL NUMBERS INCLUDING DECIMALS Multiply signed fractions Multiply signed decimals Explain process of multiplying fractions and decimals Estimate to justify answer Simplify fractions Use dimensional analysis to solve problems 5-4 DIVIDING RATIONAL NUMBERS INCLUDING DECIMALS Divide signed fractions Divide signed decimals Explain process of dividing fractions and decimals Estimate to justify your answer Simplify fractions Use dimensional analysis to solve problems ADDING AND SUBTRACTING SIGNED DECIMALS Add and subtract signed decimals Explain process of adding and subtracting decimals Estimate to justify your answer 5-5 ADDING AND SUBTRACTING LIKE FRACTIONS Add and subtract like signed fractions Estimate to justify your answer Explain process of adding and subtracting unlike fractions Simplify fractions 5-6 LEAST COMMON MULTIPLES (WARM-UPS) 5-6 ADDING AND SUBTRACTING UNLIKE FRACTIONS Add and subtract unlike signed fractions Find a common denominator Explain process of adding and subtracting unlike fractions Estimate to justify your answer Simplify fractions 1-1 INCORPORATE UMASD PROBLEM SOLVING TEMPLATE WITH PROBLEMS REVIEW 3 ASSESSMENT 1 TOTAL DAYS 11 NUMBER STANDARDS OF DAYS 1.5 2.2.8.B, 2.2.8.F, 2.4.8.D 1.5 2.2.8.B, 2.2.8.F, 2.4.8.D 1 2.2.8.B, 2.2.8.F, 2.4.8.D 1 2.2.8.B, 2.2.8.F, 2.4.8.D 2.1.8.A 2 2.2.8.B, 2.2.8.F, 2.4.8.D, 2.1.8.A 2.5.8.A, 2.5.8.B, 2.5.8.C, 2.5.8.D
SECTION # OF DAYS STANDARDS 1-2 NUMBERS AND EXPRESSIONS 2 2.1.8.B, 2.2.8.A Use order of operations to evaluate problems (signed rational numbers include absolute value) Translate verbal phrases into numerical expressions Highlight term EVALUATE (order of operations) 1-3 VARIABLES AND EXPRESSIONS 2 2.1.8.B, 2.2.8.A Evaluate expressions containing variables (signed rational numbers include absolute value) Translate verbal phrases into algebraic expressions Define a variable Highlight term EVALUATE (order of operations) 1-4 PROPERTIES 2 2.4.8.D Identify and use properties of multiplication and addition (Commutative, Associative, Identity, Zero) in words, symbols and examples If not a property explain why (Counterexample) Use properties to simplify algebraic expressions 1-5 VARIABLES AND EQUATIONS 1 2.1.8.G, 2.8.8.E Identify and solve algebraic equations (be sure to use signed rational numbers) Translate verbal sentences into equations Define a variable Highlight the term SOLVE (equations) Check solution by substitution 7-2 REPRESENTING LINEAR 2 2.8.8.G, 2.8.8.H, 2.8.8.J FUNCTIONS Solve linear equations with two variables to determine ordered pairs Create a table of solutions Graph linear equations using the ordered pairs Teacher demonstrate nonlinear equations using graphing calculator 1-1 INCORPORATE UMASD PROBLEM SOLVING TEMPLATE WITH PROBLEMS 2.5.8.A, 2.5.8.B, 2.5.8.C, 2.5.8.D REVIEW 3 ASSESSMENT 1 TOTAL DAYS 13
SECTION 3-1 DISTRIBUTIVE PROPERTY Identify and use the Distributive Property of multiplication over addition/subtraction (words, symbols and examples) Use Distributive Property to write equivalent numeric and algebraic expressions Distribute the negative 3-2 SIMPLIFYING ALGEBRAIC EXPRESSIONS Use the Distributive Property of Multiplication over addition/subtraction to simplify algebraic expressions Write expressions in simplest form Identify and combine like terms 3-3 SOLVING EQUATIONS BY ADDING AND SUBTRACTING Use inverse operations (Additive Inverse, Addition Property of Equality and Subtraction Property of Equality) to solve equations Demonstrate understanding of concept using words, symbols and examples Highlight Isolating the Variable 3-4 SOLVING EQUATIONS BY MULTIPLYING AND DIVIDING Use inverse operations (Multiplicative Inverse, Multiplication Property of Equality and Division Property of Equality) to solve equations Demonstrate understanding of concept using words, symbols and examples Highlight Isolating the Variable 5-8 SOLVING EQUATIONS WITH RATIONAL NUMBERS Solve equations using rational numbers Reiterate terms from 3-3 and 3-4 Could be completed after PSSA 3-5 SOLVING TWO-STEP EQUATIONS Reinforce checking solution and vocabulary 3-6 WRITING TWO-STEP EQUATIONS Write verbal sentences as two-step equations and solve 3-7 SEQUENCES AND EQUATIONS (EXTENDING PATTERNS - WARM-UP) Describe sequences using words and symbols Find given term in a sequence 3-8 USING FORMULAS Solve problems using formulas NUMBER OF DAYS 1 2.1.8.B, 2.1.8.E 2 2.1.8.B 1 2.1.8.G, 2.8.8.E 1 2.1.8.G, 2.8.8.E 2 2.1.8.G, 2.8.8.E 2 2.1.8.G, 2.8.8.E 1 2.8.8.C 2 2.8.8.A, 2.8.8.B 1 2.8.8.A STANDARDS
Incorporate formulas from PSSA formula sheet 1-1 INCORPORATE UMASD PROBLEM SOLVING TEMPLATE WITH PROBLEMS REVIEW 3 ASSESSMENT 1 2.5.8.A, 2.5.8.B, 2.5.8.C, 2.5.8.D TOTAL DAYS 17 SECTION # OF DAYS STANDARDS
8-3 INEQUALITIES Write inequalities Graph inequalities Determine truth of an inequality 8-4 SOLVING INEQUALITIES BY ADDING OR SUBTRACTING Use inverse operations (Additive Inverse, Addition Property of Inequality and Subtraction Property of Inequality) to solve inequalities Demonstrate understanding of concept using words, symbols and examples Highlight Isolating the Variable 8-5 SOLVING INEQUALITIES BY MULTIPLYING AND DIVIDING Use inverse operations (Multiplicative Inverse, Multiplication Property of Inequality and Division Property of Inequality) to solve inequalities Demonstrate understanding of concept using words, symbols and examples Highlight Isolating the Variable 8-6 SOLVING MULTISTEP INEQUALITIES Reinforce checking solution and vocabulary 1-1 INCORPORATE UMASD PROBLEM SOLVING TEMPLATE WITH PROBLEMS 1 2.8.8.C 1 2.1.8.G, 2.8.8.E 2 2.1.8.G, 2.8.8.E 1 2.1.8.G, 2.8.8.E 2.5.8.A, 2.5.8.B, 2.5.8.C, 2.5.8.D REVIEW 2 ASSESSMENT 1 TOTAL DAYS 8 SECTION # OF DAYS STANDARDS
4-1 POWERS AND EXPONENTS Write expressions using exponents Evaluate expressions containing exponents Clarify difference between x 2 and( x) 2 4-3 GREATEST COMMON FACTOR (WARM-UP) 4-4 SIMPLIFYING ALGEBRAIC FRACTIONS Simplify algebraic fractions 4-5 MULTIPLYING AND DIVIDING MONOMIALS Multiply and divide monomials Explain steps 4-7 SCIENTIFIC NOTATION Express numbers in standard and scientific form Compare and order numbers written in scientific notation 1-1 INCORPORATE UMASD PROBLEM SOLVING TEMPLATE WITH PROBLEMS 1 2.1.8.B???? 1 2.1.8.E 1 2.1.8.B, 2.1.8.E 2 2.1.8.A 2.5.8.A, 2.5.8.B, 2.5.8.C, 2.5.8.D REVIEW 2 ASSESSMENT 1 TOTAL DAYS 8
SECTION # OF DAYS STANDARDS 5-1 WRITING FRACTIONS AS.5 2.1.8.A, 2.1.8.C DECIMALS Write fractions as terminating or repeating decimals Compare fractions and decimals 5-2 RATIONAL NUMBERS.5 2.1.8.A, 2.1.8.C Write rational numbers as fractions Identify and classify rational numbers ADD, SUBTRACT OR CONVERT 2 2.3.8.A, 2.3.8.D MEASUREMENTS Add, subtract, or convert measurements using only the units below, with and without regrouping. Should be converted to largest whole unit. Conversion chart provided on the reference sheet (in, ft, yd; fl. oz, cup, pint, quart, gallon; oz, pd.; sec, min, hours, days; metrics including milli, centi, and kilo (m, g, or L) 6-1 RATIOS AND RATES 2 2.1.8.D, 2.11.8.B Write rations as fractions in simplest form Convert rates Unit rates; best buy 6-2 PROPORTIONAL AND 1 2.1.8.D NONPROPORTIONAL RELATIONSHIPS Identify proportional and nonproportional relationships in tables and graphs Describe proportional relationships using equations Constant of proportionality 6-3 USING PROPORTIONS 1 2.1.8.D, 2.2.3.D, 2.2.3.D Solve proportions Cross products Solve real world problems Use to convert measurement 9-6 SIMILAR FIGURES AND INDIRECT 2 2.1.8.D, 2.10.8.B MEASUREMENT Identify corresponding parts and find missing measures of similar figures using proportions Solve problems involving indirect measurement 6-4 SCALE DRAWINGS AND MODELS 2 2.2.3.F, 2.2.3.G Use scale drawings Construct scale drawings Determine scale Identify actual measurements 1-1 INCORPORATE UMASD PROBLEM 2.5.8.A, 2.5.8.B, 2.5.8.C, 2.5.8.D SOLVING TEMPLATE WITH PROBLEMS REVIEW 3
ASSESSMENT 1 TOTAL DAYS 15
SECTION # OF DAYS STANDARDS 6-5 FRACTIONS, DECIMALS AND 2 2.1.8.A, 2.1.8.C PERCENTS Express percents as fractions and vice versa Express percents as decimals and vice versa Compare fractions, decimals and percents 6-6 USING THE PERCENT 2 2.3.8.B PROPORTION Use percent proportion to solve problems Explain using words and symbols Find whole, part and percent 6-7 FINDING PERCENTS MENTALLY 1 2.2.8.D, 2.2.8.E, 2.2.8.F Compute mentally with percents Estimate to justify your solution 6-8 USING PERCENT EQUATIONS 3 2.2.8.B, 2.3.8.B Use percent equations to solve percent problems Find part, whole and percent Solve real life problems involving: tax, discount, tips, commission and I= PRT Estimate to justify your solution 1-1 INCORPORATE UMASD PROBLEM SOLVING TEMPLATE WITH PROBLEMS 2.5.8.A, 2.5.8.B, 2.5.8.C, 2.5.8.D REVIEW 2 ASSESSMENT 1 TOTAL DAYS 11
SECTION # OF DAYS STANDARDS 9-1 SQUARES AND SQUARE ROOTS 1 2.1.8.A, 2.1.8B Find squares and square roots Estimate square roots 9-2 THE REAL NUMBER SYSTEM 1 2.1.8.C, 2.1.8.B, 2.1.8.E, 2.2.8.C Identify and compare numbers in the real number system Solve equations by finding square roots 9-3 TRIANGLES 2 2.3.3.D, 2.9.8.C, 2.9.8.D, Find the missing angle measure of a triangle Sum of all angles = 180 Classify triangles by properties and attributes 9-4 THE PYTHAGOREAN THEOREM 2 2.10.8.A Use the Pythagorean Theorem to find the length of a side of a right triangle Use the converse of the Pythagorean Theorem to determine whether a triangle is a right triangle 1-1 INCORPORATE UMASD PROBLEM 2.5.8.A, 2.5.8.B, 2.5.8.C, 2.5.8.D SOLVING TEMPLATE WITH PROBLEMS REVIEW 2 ASSESSMENT 1 TOTAL DAYS 9
SECTION # OF DAYS STANDARDS 10-1 LINE AND ANGLE 2 RELATIONSHIPS Identify skew lines Identify relationships of angles formed by two parallel lines and a transversal (Alt. Interior, Alt. Exterior, Corresponding) Identify the relationships of vertical, adjacent, complementary and supplementary angles Find angle measures using the relationships 10-2 CONGRUENT TRIANGLES 1 Identify congruent triangles and corresponding parts Identify difference between similar and congruent IDENTIFY CONGRUENCE AND/OR 1 SIMILARITY IN POLYGONS Identify congruent polygons and corresponding parts Identify difference between similar and congruent 10-3 TRANSFORMATIONS ON THE 1 COORDINATE PLANE Identify and draw translations, reflections and rotations on a coordinate plane 10-4 QUADRILATERALS 1 Identify and classify quadrilaterals Find the missing angle measures 10-5 POLYGONS 2 Identify and classify polygons Determine the sum of the measures of the interior and exterior angles of a polygon (n-2)180 Interior Angle of a Regular polygons Determine number of sides when the sum is given 10-6 AREA: PARALLELOGRAM, 2 TRIANGLES AND TRAPEZOIDS Find perimeter and area of parallelogram, triangles and trapezoids For quadrilaterals be sure to use P=2l +2w or 2(l+w) Altitude 10-7 CIRCLES: CIRCUMFERENCE AND 2 AREA Identify chords Find circumference of circles Find area of circles Determine radius and diameter when area or circumference is given
10-8 AREA: COMPOSITE FIGURES 1 Find area of composite figures using triangles and quadrilaterals only 1-1 INCORPORATE UMASD PROBLEM SOLVING TEMPLATE WITH PROBLEMS REVIEW 3 ASSESSMENT 1 2.5.8.A, 2.5.8.B, 2.5.8.C, 2.5.8.D TOTAL DAYS 17
SECTION # OF DAYS STANDARDS 11-1 3-DIMENSIONAL FIGURES 1 Classify and Identify three- dimensional figures Identify nets 11-2 VOLUME: PRISMS AND 2 CYLINDERS Find volume of prisms (triangular and rectangular, cubes) Clarify difference between height of triangle and height of prism Find volume of circular cylinders Given volume and h or B, determine missing measure Use appropriate labels 11-3 VOLUME: PYRAMIDS, CONES, 2 CYLINDERS Find volume of rectangular pyramid Given volume or h or B, determine missing measure Use appropriate labels 11-4 SURFACE AREA: PRISMS AND 1 CYLINDERS Find lateral area and surface area of rectangular prisms Find lateral area and surface area of cylinders Use appropriate labels 1-1 INCORPORATE UMASD PROBLEM 2.5.8.A, 2.5.8.B, 2.5.8.C, 2.5.8.D SOLVING TEMPLATE WITH PROBLEMS REVIEW 3 ASSESSMENT 1 TOTAL DAYS 10
SECTION # OF DAYS STANDARDS 5-9 MEASURES OF CENTRAL 1 TENDENCY Find mean, median, and mode Given the mean and set of scores, find the missing score from the list 12-1 STEM-AND-LEAF PLOTS 1 Display data in stem and leaf plot Interpret data on Stem and Leaf Plot Double step-and-leaf plots 12-2/12-3 BOX-AND-WHISKER PLOTS/ 1 MEASURES OF VARIATION Find measures of variation (range, quartiles, interquartile range and outliers) Display data in box-and-whisker plot. Interpret data in a box-and-whisker plot Use football game analogy BAR GRAPHS/LINE GRAPHS/ CIRCLE 2 GRAPHS Read and interpret circle graphs Read/interpret/construct line graphs and bar graphs 12-4 HISTOGRAMS 1 Display data in a histogram Interpret data in a histogram Relate to sideways stem-and-leaf plot 1-7 SCATTERPLOTS/ 7-8PREDICTING 1 EQUATIONS 12-5/12-6 SELECTING AN 1 APPROPRIATE DISPLAY/ MISLEADING GRAPHS Identify best time to use bar, line, scatterplots, circle graphs, stem-and-leaf plots, histogram, box-and-whisker plots Recognize when graphs are misleading Evaluate predictions and make conclusions based on data analysis 1-1 INCORPORATE UMASD PROBLEM 2.5.8.A, 2.5.8.B, 2.5.8.C, 2.5.8.D SOLVING TEMPLATE WITH PROBLEMS REVIEW 3 ASSESSMENT 1 TOTAL DAYS 12
SECTION # OF DAYS STANDARDS 12-7 SIMPLE PROBABILITY 1 Find probability of simple events Use a sample to predict actions of groups 12-8 COUNTING OUTCOMES 2 Use tree diagrams Use Fundamental Counting Principal (FCP) Use FCP to find probability of event 12-9 PERMUTATIONS AND 3 COMBINATIONS Identify when order matters Use permutations Use combinations 12-10 PROBABILITY OF COMPOSITE 1 EVENTS Find probability of independent and dependent events 1-1 INCORPORATE UMASD PROBLEM SOLVING TEMPLATE WITH PROBLEMS 0 2.5.8.A, 2.5.8.B, 2.5.8.C, 2.5.8.D REVIEW 2 ASSESSMENT 1 TOTAL DAYS 10
Math Grade 8 Assessment Anchors and Eligible Content Pennsylvania Wisconsin Ohio 2008 STANDARDS PAGE REFERENCES M8.A Numbers and Operations ASSESSMENT ANCHOR M8.A.1 Demonstrate an understanding of numbers, ways of representing numbers, relationships among numbers and number systems. M8.A.1.1 Represent numbers in equivalent forms. Reference: 2.1.8.A, 2.1.8.B M8.A.1.1.1 Represent numbers using scientific notation and/or exponential forms. M8.A.1.1.2 Find the square or cube of a whole number (single digit) and/or the square root of a perfect square (without a calculator) and explain the relationship between the two (i.e. square and square root). 214-218, 222, 238 #62-#65, 296 #58-#61, 355 #8, #11, 363 #40 Practice Test 223 Standardized Test Practice 224 #2, #5, 225 #12, 287 #11 464-468, 471, 474 #62-#65, 481 #56-#59, 504, 781, 802 Algebra Lab 462-463 Mid-Chapter Quiz 482 #5-#8 Practice Test 507