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Montclair Public Schools 2016 Algebra A Curriculum Guide 7th grade Math 0 Office of Curriculum & Instruction

Algebra A - Montclair Public Schools · PDF file · 2016-11-02Algebra A . Curriculum Guide . ... (integers, positive and negative fractions) 12. Multiplying & Dividing Rational Numbers

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Page 1: Algebra A - Montclair Public Schools · PDF file · 2016-11-02Algebra A . Curriculum Guide . ... (integers, positive and negative fractions) 12. Multiplying & Dividing Rational Numbers

Montclair Public Schools

2016

Algebra A Curriculum Guide 7th grade Math

0 Office of Curriculum & Instruction

Page 2: Algebra A - Montclair Public Schools · PDF file · 2016-11-02Algebra A . Curriculum Guide . ... (integers, positive and negative fractions) 12. Multiplying & Dividing Rational Numbers

Algebra A/7th Grade: Scope and Sequence Unit 1 – Operations with Fractions, The Number System, Algebra: Chapter 1

1. Adding and subtracting fractions & mixed numbers 2. Multiplying and dividing fractions and mixed numbers 3. Simplifying fractions 4. Comparing & Ordering Rational Numbers 5. Converting Decimals to Fractions (terminating & repeating decimals) 6. Variables & Expressions 7. Order of Operations and Evaluating Expressions 8. Real Number System & Square Roots 9. Properties 10. Simplifying expressions (including exponents) 11. Adding & Subtracting Rational Numbers (integers, positive and negative fractions) 12. Multiplying & Dividing Rational Numbers (integers, positive and negative fractions) 13. Distributive Property & Simplifying expressions (Combining like terms) 14. Graphing in a Coordinate Plane, Quadrants 15. Introduction to Equations 16. Patterns, Equations, Graphs

Unit 2 – Algebra: Chapter 2, Ratios/Proportional Relationships, & Percents

1. One-Step Equations (includes integers, fractional coefficients) 2. Two-step equations 3. Creating Two-Step Equations to solve word problems 4. Multi-step equations 5. Equations with variables on both sides of the equal sign 6. Literal equations 7. Ratios, rates, and unit rates 8. Unit rates with complex fractions 9. Unit Rates, Converting Units & Dimensional Analysis 10. Graphing & Recognizing Proportional Relationships 11. Solving Proportions 12. Proportions, Similar Figures, Word Problems 13. Percent of A Number & Percent of Change 14. Sales Tax, Tip & Markup 15. Discount & Simple Interest Formula

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Unit 3 – Algebra Chapters 3, 4 & Intro to Geometry 1. Inequalities & Graphs & Solving One-Step Inequalities (+ and -) 2. Solving One-Step Inequalities (× and ÷) 3. Solving Two-Step Inequalities 4. Multi-Step Inequalities 5. Compound Inequalities 6. Absolute Value Equations 7. Absolute value inequalities 8. Graphs (Independent & Dependent Variables) 9. Graphing Proportional Relationships 10. Functions 11. Patterns, Linear, & Nonlinear Functions 12. Constant Rate of Change 13. Graphing Functions (Relations) 14. Writing Function (Equations) Rules 15. Classifying Angles, Complementary & Supplementary angles

Unit 4 – Geometry, Algebra: Chapter 5, & Intro to Chapter 6

1. Triangles & Solving for missing angles and side lengths 2. Scale Drawings 3. 3-Dimensional figures & Cross-Sections 4. Area & circumference of circles 5. Area of composite figures 6. Volume of prisms & Pyramids 7. Surface area of prisms & pyramids 8. Volume & Surface area of composite figures 9. Rate of Change & Slope 10. Direct Variation 11. Slope-Intercept Form (Creating & Graphing) 12. Point-Slope Form 13. Standard Form 14. Parallel and Perpendicular Lines 15. Solving Systems of Equations by Graphing 16. Solving Systems of Equations by Substitution

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Montclair Public Schools Instructional Unit

Content: Mathematics : Algebra A Grade: 7th Grade

Marking Period:

1 Unit 1 Operations with Fractions, The Number System & Foundations of Algebra

Pacing: Marking Period 1 (9 weeks)

CRITICAL AREAS OF FOCUS FOR UNIT I In this unit, students will begin with fractions by converting fractions to decimals, comparing and ordering fractions, and completing operations involving fractions. Students will then learn how to classify fractions, rational numbers, square roots, and integers under the real number system. They will then complete order of operations, evaluating expressions, simplifying expressions, and operations involving rational numbers and exponents. Finally, the unit will end with an introduction to equations.

ESSENTIAL QUESTIONS • How are fractions related to rational numbers? • How are quantities related to variables? • How can you represent quantities, patterns, relationships, and expressions in different forms?

TARGET STANDARDS

Math NJSLS

Standard Emphasis Mathematical

Practice Standard

Benchmark Assessment (Place an X or N/A)

7.NS.A.1 Apply and extend previous understandings of addition and subtraction to add and subtract rational numbers; represent addition and subtraction on a horizontal or vertical number line.

Major Content

#1, 3-6 X

7.NS.A.2 Apply and extend previous understandings of multiplication and division and of fractions to multiply and divide rational numbers.

Major Content

#1-3, 6-8 X

7.NS.A.3 Solve real-world and mathematical problems involving the four operations with rational numbers.

Major Content

#1-8 X

7.EE.A.1 Apply properties of operations as strategies to add, subtract, factor, and expand linear expressions with rational coefficients.

Major Content

#1-8 X

7.EE.A.2 Understand that rewriting an expression in different forms in a problem context can shed light on the problem and how the quantities in it are related.

Major Content

#1, 3, 6-8 X

7.EE.B.3 Solve multi-step real-life and mathematical problems posed with positive and negative rational numbers in any form (whole numbers, fractions, and decimals), using tools strategically. Apply properties of operations to

Major Content

#1-8 X

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calculate with numbers in any form; convert between forms as appropriate; and assess the reasonableness of answers using mental computation and estimation strategies

A.SSE.A.1 Interpret expressions that represent a quantity in terms of its context.

Major Content

#1-3, 6-8 X

MATHEMATICAL PRACTICE STANDARDS

Standard # Standards for Mathematical Practice

1 Make sense of problems and preserve in solving them.

• Explain how two equivalent expressions are the same, but in different forms. • Use the area model to illustrate the Distributive Property.

2 Reason abstractly and quantitatively. • Use Algebra tiles to introduce the concept of balancing equations.

3 Construct viable arguments and critique the reasoning of others.

• Students will use the “Find the Error” problems to identify errors within student work, rationalize the reason why the error was made, and then correct the error by properly solving the problem.

4 Model with mathematics.

• Model solving equations using Algebra tiles. • Use chips and number lines to represent adding and subtracting integers.

5 Use appropriate tools strategically.

• Students can use graphing calculators to graph a set of given points. • Students can use number lines and chips to represent adding and subtracting integers.

6 Attend to precision. • Students will approximate the values of non-perfect square roots to the nearest tenth.

7 Look for and make use of structure. • Students will interpret verbal expressions and then create algebraic expressions using the given information.

8 Look for and express regularity in repeated reasoning. • Students will justify reasoning and methodology when solving short-answer questions.

INTERDISCIPLINARY CONNECTIONS NJ CCCS Standard 8.1.8.A.1 Demonstrate knowledge of a real world problem using digital tools. 8.2.8.C.8 Develop a proposal for a chosen solution that include models (physical, graphical or mathematical) to communicate the

solution to peers.

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CRP1. Act as a responsible and contributing citizen and employee. CRP2. Apply appropriate academic and technical skills. CRP4. Communicate clearly and effectively and with reason. CRP8. Utilize critical thinking to make sense of problems and persevere in solving them. CRP11. Use technology to enhance productivity. 9.1.8.B.7 Construct a budget to save for long-term, short-term, and charitable goals. 9.1.8.C.4 Demonstrate an understanding of the terminology associated with different types of credit (e.g., credit cards, installment loans,

mortgages) and compare the interest rates associated with each. 9.1.8.D.4 Distinguish between income and investment growth. 9.1.8.D.5 Explain the economic principle of supply and demand. 9.1.8.E.1 Explain what it means to be a responsible consumer and the factors to consider when making consumer decisions. 9.1.8.E.3 Compare and contrast product facts versus advertising claims. 9.1.8.E.5 Analyze interest rates and fees associated with financial services, credit cards, debit cards, and gift cards. 9.1.8.E.6 Compare the value of goods or services from different sellers when purchasing large quantities and small quantities. 9.1.8.B.3 Evaluate communication, collaboration, and leadership skills that can be developed through school, home, work, and

extracurricular activities for use in a career. INSTRUCTIONAL PROGRESSION

Weekly Plan Concept

CMP2 Connection Vocabulary

Evidence of Learning

Week 1 • Pre-Assessment • Review adding, subtracting, multiplying, and

dividing fractions & mixed numbers (6th grade) • Simplifying and comparing fractions • Compare and order rational numbers

Bits & Pieces II

• Reciprocal • Multiplicative inverse

Pre-assessment Fractions Review Packet

Week 2 • Convert fractions to decimals using long division

• Explain whether a fraction turned to decimal is terminating or repeating

• Fractions Assessment

Glencoe: Course 2: Vol 1 - Pg. 263-270

• Terminating decimal • Repeating decimal • Bar notation

Fractions Assessment

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Week 3 • Chap 1.1 o Create algebraic expressions o Create verbal expressions o Write a rule (using a given

relationship) in both verbal and algebraic form

• Chap 1.2 o Simplify expressions involving

exponents o Use order of operations to evaluate

expressions

NJSLS: Investigation 2

• Quantity • Variable • Algebraic expression • Numerical expression • Exponent • Power • Base • Simplify • Evaluate

Lesson Check Pg. 7-9 #9=30 Pg. 13-14 #9-42 Practice WS 1.1 and 1.2 Form G

Week 4 • Quiz • Chap 1.3

o Simplify square root expressions o Perfect square numbers o Identify rational v. irrational numbers o Compare & order rational numbers o Estimate Square numbers

• Chap 1.4 o Identify and use properties of real

numbers o Creating equivalent expressions by

simplifying

Say It With Symbols: Investigation 1

• Square root • Radicand • Radical • Perfect square number • Rational number • Natural number • Whole number • Integer • Irrational number • Inequality • Equivalent expressions • Commutative Property • Associative Property • Identity Properties • Zero Property of

Multiplication

Quiz Lesson Check Pg. 20-21 #9-50 Practice WS 1.3 Form G

Week 5 • Quiz • Chap 1.5

o Adding and subtracting real numbers o Absolute value expressions o Additive inverse and opposite numbers o Addition & Subtraction using number

lines • Chap 1.6

o Multiply and divide real numbers

Accentuate the Negative: Invest 1-3

• Absolute value • Opposite numbers • Additive inverse • Inverse Property of Addition

Lesson Check Practice WS 1.5 and 1.6 Pg. 34-35 #10-51

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o Simplify square root expressions

Pg. 42 – 43 #8-47

Week 6 • Quiz on Operations with Rational Numbers • Chap 1.7

o Use the Distributive Property to simplify expressions

o Equivalent expressions (factored and expanded form)

o Distributing a negative 1 to a set of parentheses

o Identify and combine like terms

NJSLS: Investigation 2 Accentuate the Negative: Invest 4

• Distributive Property • Term • Constant • Coefficient

Lesson Check Practice WS 1.7 Pg. 50-51 #9-40, #53-64

Week 7 • Factor linear expressions (supplement) • Chap 1.8

o Classify equations as true, false, or open

o Identify solutions of an equation o Create a table to find a solution

NJSLS: Investigation 2

Lesson Check Practice WS 1.8 Pg. 56-57 #7-45

Week 8 • Graphing in the Coordinate Plane • Chap 1.9

o Identify solutions of a two-variable equation

o Create a table, graph, and an equation to represent a relationship

o Independent and dependent variables

Variables and Patterns: Invest 1

• Coordinate plane • X-axis • Y-axis • Quadrants • Ordered pair • coordinates

Variables & Patterns Text Pg. 60 Lesson Check Pg. 64 #8-24

Week 9 • Chapter 1 Review • Chapter 1 Assessment

Textbook Pg. 68-73

Resources/Technology Infusion Course Textbook: Pearson Common Core Edition 2012 Course Workbooks: Pearson Common Core Practice Workbook (Forms G and K), Student Companion (Pearson Online Access) Online Resources: Pearson Student Access: www.pearsonsuccessnet.com

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Glencoe Student Intervention Workbook: http://glencoe.mheducation.com/sites/0078884802/student_view0/student_workbooks.html Kutasoftware: www.kutasoftware.com Interactive Lessons: https://illuminations.nctm.org Virtual Manipulatives: http://nlvm.usu.edu/en/nav/vlibrary.html Additional Online Resources: Seventh Grade Resources: Khan Academy – The Number System: https://www.khanacademy.org/commoncore/grade-7-NS Number System and Properties Resources: https://www.opened.com/search?offset=0&standard=7.NS.1.d 7th Grade Worksheets (issued by standard): http://www.mathworksheetsland.com/7/ Khan Academy – Expressions & Equations: https://www.khanacademy.org/commoncore/grade-7-EE Algebra Resources: Algebra Worksheets (issued by standard): http://www.mathworksheetsland.com/algebra/ A.SSE Online Resources: https://www.opened.com/search?standard=A.SSE.1.a Performance Based Tasks: Textbook - Page. 67 Resource Links Listed by Standard: 7.NS.A.1 Comparing Freezing Points

7.NS.A.1b-c Differences of Integers

7.NS.A.2 Why is a Negative Times a Negative Always Positive

7.NS.A.2d Equivalent fractions approach to non-repeating decimals

7.NS.A.2d Repeating decimal as approximation

7.EE.A.1 Writing Expressions

7.EE.A.2 Ticket to Ride

A.CED.A.1 Planes and wheat

A-CED.A.1 Paying the rent

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A.REI.A.1 Zero Product Property 1

Modifications for all learners 1. Providing manipulatives (Virtual Manipulatives) 2. Providing notes (Student Companion) 3. Use of graphic organizers (Student Companion) 4. Use of interactive math journals (Reflections) – “Do you Know How?” and “Do you Understand?” questions 5. Identify opportunities for individual and small group review and practice 6. Test modifications as dictated by IEP/504 plan

ALIGNMENT TO 21st CENTURY THEMES AND SKILLS 21st Century/ Interdisciplinary Themes: Bold all that apply 21st Century Skills: Bold all that apply 1. Global Awareness 2. Financial, Economic, Business and Entrepreneurial Literacy 3. Civic Literacy 4. Health Literacy 5. Environmental Literacy

1. Creativity & Innovation 2. Critical Thinking & Problem Solving 3. Communication & Collaboration 4. Media Literacy 5. Information Literacy 6. Information, Communication &Technology 7. Life & Career Skills

Special Notes:

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Montclair Public Schools Instructional Unit Content: Mathematics : Algebra A Grade: 7th Grade

Marking Period: 2 Unit 2 Equations, Proportions, & Percents Pacing: Marking Period 2 (9

weeks)

CRITICAL AREAS OF FOCUS FOR UNIT 2 In this unit, students will work on solving equations; one-step equations, two-step equations, multi-step equations, equations with variables on both sides, and literal equations. Moreover, students will work on creating equations to solve word problems involving real-life situations. After working with equations, students will then work on ratios, rates, unit rates, proportions, and proportional relationships. Finally, students will solve percent problems involving percent of change, sales tax, discount, and the simple interest formula.

ESSENTIAL QUESTIONS • How can you solve equations? • Can equations have more than one solution? • How are equations useful when solving real-life situations? • What kinds of relationships can proportions represent? • What does it mean when two variables represent a proportional relationship?

TARGET STANDARDS

Math NJSLS Standard Emphasis

Mathematical Practice Standard

Benchmark Assessment (Place an X or N/A)

A.REI.B.3 Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters.

Major Content

#1-8 X

A.REI.A.1 Explain each step in solving a simple equation as following from the equality of numbers asserted at the previous step, starting from the assumption that the original equation has a solution. Construct a viable argument to justify a solution method

Major Content

#1-8 X

A.CED.A.4 Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations. For example, rearrange Ohm's law V = IR to highlight resistance R.

Major Content

#1-8 X

A.CED.A.1 Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear functions and quadratic functions, and simple rational and exponential

Major Content

#1-8 X

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A.REI.A.1 Explain each step in solving a simple equation as following from the equality of numbers asserted at the previous step, starting from the assumption that the original equation has a solution. Construct a viable argument to justify a solution method.

Major Content

#1-3, 6-8 X

7.EE.B.3 Solve multi-step real-life and mathematical problems posed with positive and negative rational numbers in any form (whole numbers, fractions, and decimals), using tools strategically. Apply properties of operations to calculate with numbers in any form; convert between forms as appropriate; and assess the reasonableness of answers using mental computation and estimation strategies.

Major Content

#1-8 X

7.EE.B.4 Use variables to represent quantities in a real-world or mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities .

Major Content

#1-3, 6-8 X

7.RP.A.1 Compute unit rates associated with ratios of fractions, including ratios of lengths, areas and other quantities measured in like or different units

Major Content

#1-3, 6-8 X

7.RP.A.2 Recognize and represent proportional relationships between quantities X 7.RP.A.3 Use proportional relationships to solve multistep ratio and percent problems Major

Content #1-3, 6-8 X

MATHEMATICAL PRACTICE STANDARDS

Standard # Standards for Mathematical Practice

1 Make sense of problems and preserve in solving them.

2 Reason abstractly and quantitatively. • Use Algebra tiles to balance equations.

3 Construct viable arguments and critique the reasoning of others.

• Students will use the “Find the Error” problems to identify errors within student work, rationalize the reason why the error was made, and then correct the error by properly solving the problem.

4 Model with mathematics. • Model solving equations using Algebra tiles and the bags and coins method (CMP2).

5 Use appropriate tools strategically.

6 Attend to precision. • Students will approximate the values of unit rates involving whole units and decimals.

7 Look for and make use of structure. • Students will understand that proportions represent two equivalent ratios.

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8

Look for and express regularity in repeated reasoning. • Students will justify reasoning and methodology when solving short-answer questions. • Students will interpret word problems to create proportions and equations.

INTERDISCIPLINARY CONNECTIONS

NJ CCCS Standard 8.1.8.A.1 Demonstrate knowledge of a real world problem using digital tools. 8.2.8.C.8 Develop a proposal for a chosen solution that include models (physical, graphical or mathematical) to communicate the

solution to peers. CRP1. Act as a responsible and contributing citizen and employee. CRP2. Apply appropriate academic and technical skills. CRP4. Communicate clearly and effectively and with reason. CRP8. Utilize critical thinking to make sense of problems and persevere in solving them. CRP11. Use technology to enhance productivity. 9.1.8.B.3 Evaluate communication, collaboration, and leadership skills that can be developed through school, home, work, and

extracurricular activities for use in a career.

INSTRUCTIONAL PROGRESSION Weekly

Plan Concept CMP2 Connection Vocabulary Evidence of

Learning Week 1 • Chapter 2.1

o One-step equations (with rational coefficients)

o Addition, Subtraction, Multiplication, and Division Properties of Equality

o One-step equation word problems • Chapter 2.2

o Two-step equations o Creating equations from a word

problem o Justifying reasoning for solving

equations

Moving Straight Ahead: Invest 3

• Inverse operation • Isolate

Lesson Check Practice WS 2.1 Pg. 85-86 #10-69 Lesson Check Practice WS 2.2 Pg. 91-92 #11-55

Week 2 • Quiz • Chapter 2.3

o Multi-step equations o Combining like terms o Equations with Distributive Property

Lesson Check Practice WS 2.3 Pg. 98-99 #10-53, #61-63

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o Equations containing fractions and decimals

Week 3 • Chapter 2.4 o Equations with variables on both sides o Special type solutions (no solution,

identity) • Chapter 2.5

o Solving literal equations o Rewriting literal equations that contain

only variables

Moving Straight Ahead: Investigations 3 and 4

• Identity • No solution • Literal equation • Formula

Lesson Check Practice WS 2.4 Pg. 105-106 #10-40 Lesson Check Practice WS 2.5 Pg. 112-113 #11-41

Week 4 • Quiz • Chapter 2.6

o Ratios, rates, and unit rates o Converting units o Dimensional analysis o Unit Rates with Complex Fractions

(supplement)

Comparing and Scaling: Investigations 1-2

• Ratio • Rate • Unit rate • Conversion factor • Dimensional analysis

Lesson Check Practice WS 2.6 Pg.119-120 #9-30

Week 5 • Graphing and Recognizing Proportional relationships (supplement)

• Chapter 2.7 o Solving proportions o Solving mult-step proportions

Pearson CC Additional Invest: 1

• Proportion • Cross products

Lesson Check Practice WS 2.7 Pg. 127-128 #10-52

Week 6 • Chapter 2.7 Part II o Creating proportions to solve word

problems • Chapter 2.8

o Proportions involving similar figures o Corresponding sides and angles

Comparing and Scaling: Investigations3-4

• Scale drawing Lesson Check Practice WS 2.8 Pg. 133-134 #6-18

Week 7 • Quiz • Chapter 2.9 Part I

o Finding percent of a number using proportion and equation methods

o Finding what percent of a number a value is

• Part • Base

Lesson Check Practice WS 2.9 Pg. 141-142 #9-44 Lesson Check Practice WS 2.10 Pg. 148-149 #7-33

Week 8 • Chapter 2.9 Part II o Percent Problems: Sales tax, tip,

markup, discount

• Discount • Tax

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• Chapter 2.10 o Percent of change formula o Percent error

• Markup

Week 9 • Chapter 2 Review • Chapter 2 Assessment

Textbook Pg. 152-157 Chapter 2 Exam

Resources/Technology Infusion Course Textbook: Pearson Common Core Edition 2012 Pearson Resources: Pearson Common Core Practice Workbook (Forms G and K), Student Companion (Pearson Online Access), Re-teaching worksheets (RTI), Additional Vocabulary Support (RTI), Find the error worksheets, Cumulative Review worksheets, Performance based tasks Online Resources: Pearson Student Access: www.pearsonsuccessnet.com Glencoe Student Intervention Workbook: http://glencoe.mheducation.com/sites/0078884802/student_view0/student_workbooks.html Kutasoftware: www.kutasoftware.com Interactive Lessons: https://illuminations.nctm.org Virtual Manipulatives: http://nlvm.usu.edu/en/nav/vlibrary.html Additional Worksheets: www.math-aids.com Additional Performance Based Tasks: Textbook - Page. 151 7.RP.A.1 Cooking with the Whole Cup

7.RP.A.2 Sore Throats, Variation 1

7.RP.A.2 Buying Coffee

7.RP.A.2c Gym Membership Plans

A.CED.A.4 Equations and Formulas

Modifications for all learners 7. Providing manipulatives (Virtual Manipulatives) 8. Providing notes (Student Companion)

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9. Use of graphic organizers (Student Companion) 10. Use of interactive math journals (Reflections) – “Do you Know How?” and “Do you Understand?” questions 11. Identify opportunities for individual and small group review and practice (Chapter reviews) 12. Test modifications as dictated by IEP/504 plan

ALIGNMENT TO 21st CENTURY THEMES AND SKILLS 21st Century/ Interdisciplinary Themes: Bold all that apply 21st Century Skills: Bold all that apply 6. Global Awareness 7. Financial, Economic, Business and Entrepreneurial Literacy 8. Civic Literacy 9. Health Literacy 10. Environmental Literacy

8. Creativity & Innovation 9. Critical Thinking & Problem Solving 10. Communication & Collaboration 11. Media Literacy 12. Information Literacy 13. Information, Communication &Technology 14. Life & Career Skills

Special Notes:

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Montclair Public Schools Instructional Unit Content: Mathematics : Algebra A Grade: 7th Grade

Marking Period: 3 Unit 3 Inequalities, Functions & Geometry Pacing: 11 weeks

CRITICAL AREAS OF FOCUS FOR UNIT 3 In this unit, students will work on solving graphing and solving inequalities: one-step inequalities, two-step inequalities, multi-step inequalities, and compound inequalities. Students will also solve absolute value equations and inequalities. After completing inequalities, students will transition to functions. Follow the functions section, students will transition to Geometry, where they will focus on two-dimensional and three-dimensional figures, as well as composite figures.

ESSENTIAL QUESTIONS • How do you represent relationships between quantities that are not equal? • Can inequalities that appear to be different be equivalent? • How do you solve inequalities? • Can functions describe real-world situations? • How can you use formulas to find the area, perimeter, circumference, volume, and surface area of geometric figures?

TARGET STANDARDS

Math NJSLS Standard Emphasis

Mathematical Practice Standard

Benchmark Assessment (Place an X or N/A)

A.REI.B.3 Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters.

Major Content

#1, 4, 6-8 X

7.EE.B.4 Use variables to represent quantities in a real-world or mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities

Major Content

#1-8 X

A.CED.A.1 Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear functions and quadratic functions, and simple rational and exponential

Major Content

#1-8 X

A.REI.B.3 Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters.

Major Content

#1-3, 6-8 X

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7.EE.B.4 Use variables to represent quantities in a real-world or mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities.

Major Content

#1-8 X

F.IF.B.4 For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship

Major Content

#1, 7-8 X

7.RP.A.2 Recognize and represent proportional relationships between quantities Major Content

#1-8 X

A.REI.D.10 Understand that the graph of an equation in two variables is the set of all its solutions plotted in the coordinate plane, often forming a curve (which could be a line).

Major Content

#1-8 X

F.IF.B.5 Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes

Major Content

#1-8 X

F.IF.A.1 Understand that a function from one set (called the domain) to another set (called the range) assigns to each element of the domain exactly one element of the range. If f is a function and x is an element of its domain, then f(x) denotes the output of f corresponding to the input x. The graph of f is the graph of the equation y = f(x).

Major Content

#1-3, 6-8 X

7.G.B.4 Know the formulas for the area and circumference of a circle and use them to solve problems; give an informal derivation of the relationship between the circumference and area of a circle.

Additional Content

#1-8 X

7.G.B.5 Use facts about supplementary, complementary, vertical, and adjacent angles in a multi-step problem to write and solve simple equations for an unknown angle in a figure.

Additional Content

#4, 7-8 X

7.G.B.6 Solve real-world and mathematical problems involving area, volume and surface area of two- and three-dimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms.

Additional Content

#1-8 X

7.G.A.3 Describe the two-dimensional figures that result from slicing three-dimensional figures, as in plane sections of right rectangular prisms and right rectangular pyramids.

Additional Content

#1-8 X

MATHEMATICAL PRACTICE STANDARDS

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Standard # Standards for Mathematical Practice

1 Make sense of problems and preserve in solving them. • Solve multi-step inequalities that involve many different skills combined into one problem.

2 Reason abstractly and quantitatively.

• Explain the mathematical reasoning behind shaded and unshaded circles when graphing inequalities. • Explain how the dependent variable is changed or affected by the independent variable.

3

Construct viable arguments and critique the reasoning of others. • Students will use the “Find the Error” problems to identify errors within student work, rationalize the reason why the

error was made, and then correct the error by properly solving the problem. • Explain why the graphs of “and” and “or” compound inequalities fit the solution sets of a given problem.

4

Model with mathematics. • Create inequalities to represent real-world situations. • Graph absolute value inequalities. • Use diagrams and figures to help solve geometry problems.

5 Use appropriate tools strategically. • Students can use graphing calculators to graph functions.

6 Attend to precision

7 Look for and make use of structure. • Create a “story” to match the data represented in a given graph.

8 Look for and express regularity in repeated reasoning. • Identify and justify whether or not a relation is a function, and then determine if its linear or nonlinear.

INTERDISCIPLINARY CONNECTIONS NJ CCCS Standard 8.1.8.A.1 Demonstrate knowledge of a real world problem using digital tools. 8.2.8.C.8 Develop a proposal for a chosen solution that include models (physical, graphical or mathematical) to communicate the

solution to peers. CRP1. Act as a responsible and contributing citizen and employee. CRP2. Apply appropriate academic and technical skills. CRP4. Communicate clearly and effectively and with reason. CRP8. Utilize critical thinking to make sense of problems and persevere in solving them. CRP11. Use technology to enhance productivity. 9.1.8.B.3 Evaluate communication, collaboration, and leadership skills that can be developed through school, home, work, and

extracurricular activities for use in a career.

INSTRUCTIONAL PROGRESSION

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Weekly Plan Concept CMP2

Connection Vocabulary Evidence of Learning

Week 1 • Chapter 3.1 o Write inequalities from verbal

expressions o Identify solutions of an inequality o Graph inequalities o Create inequalities from graphs o Create inequalities from word

problems • Chapter 3.2

o Solve inequalities using addition or subtraction

• Chapter 3.3 o Solve inequalities using multiplication

or division

NJSLS: Invest 3

• Solution of an inequality • Equivalent inequalities

Lesson Check Practice WS 3.1 Pg. 168-169 #8-55 Lesson Check Practice WS 3.2 Pg. 174-175 #9-65 Lesson Check Practice WS 3.3 Pg. 181-182 #7-57

Week 2 • Quiz • Chapter 3.4

o Solve two-step inequalities o Solve multi-step inequalities o Create multi-step inequalities to solve

word problems o Inequalities with special solutions

NJSLS: Invest 3

• All real numbers

Lesson Check Practice WS 3.4 Pg. 190 #9-43

Week 3 • Quiz • Chapter 3.6

o Solve, graph, and create compound inequalities involving and or or

• Compound inequality Lesson Check Practice WS 3.6 Pg. 204-205 #9-41

Week 4 • Chapter 3.7 o Solve absolute value equations o Solve absolute value inequalities o Graph absolute value equations and

inequalities • Chapter 3 Review

Lesson Check Practice WS 3.7 Pg. 211 #9-60 Text Pg. 222-227

Week 5 • Chapter 3 Exam • Chapter 4.1

Chapter 3 Exam Lesson Check Practice WS 4.1

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o Identify independent and dependent variables

o Analyze a graph containing two variables

o Sketch a graph that represents a situation

Pg. 237-238 #5-13

Week 6 • Chapter 4.2 o Identify independent and dependent

variables o Identify linear v. nonlinear functions

• Chapter 4.3 o Classify functions as linear or

nonlinear • Quiz

• Independent variable • Dependent variable • Function • Linear function • Nonlinear function

Lesson Check Practice WS 4.2 Pg. 243 #6-15 Lesson Check Practice WS 4.3 Pg. 250 #6-16

Week 7 • Chapter 4.4 o Graph function rules o Identify continuous and discrete

graphs • Chapter 4.5

o Create a function rule

• Continuous graph • Discrete graph

Lesson Check Practice WS 4.4 Pg. 257-258 #9-32 Lesson Check Practice WS 4.5 Pg. 265-266 #8-26

Week 8 • Chapter 4.6 o Identify relations and functions o Find the domain and range o Represent functions using function

notation • Chapter 4 Review • Chapter 4 Exam

• Relation • Domain • Range • Vertical line test • Function notation

Lesson Check Practice WS 4.6 Pg. 271-272 #8-25 Pg. 283-287 Chapter 4 Assessment

Week 9 • Classify angles such as vertical, adjacent, acute, right, obtuse, complementary and supplementary

NJSLS: Invest 4

• Vertex • Vertical angles • Adjacent angles • Acute angle

Glencoe Course 2 Geometry quizzes

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• Classify triangles based on angles and side lengths

• Find the missing side length or angle measure • Identify cross-sections of geometric figures

• Obtuse angle • Supplementary angles • Complementary angles • Acute triangle • Right triangle • Obtuse triangle • Scalene triangle • Isosceles triangle • Equilateral triangle • Congruent segments • Prism • Base • Pyramid • Plane • Coplanar • Parallel • Polyhedron • Edge • Face • Diagonal • Cylinder • Cone • Skew lines

Week 10 • Circumference and area of circles and semi-circles

• Area of composite figures • Volume of prisms • Volume of pyramids • Surface area of prisms • Surface area of pyramids • Volume and surface area of composite figures

Filling and Wrapping: Invest 3 & 4 NJSLS: Invest 4

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Week 11 • Geometry Review • Geometry Exam

Geometry Assessment

Resources/Technology Infusion Course Textbook: Pearson Common Core Edition 2012 Pearson Resources: Pearson Common Core Practice Workbook (Forms G and K), Student Companion (Pearson Online Access), Re-teaching worksheets (RTI), Additional Vocabulary Support (RTI), Find the error worksheets, Cumulative Review worksheets, Performance based tasks Online Resources: Pearson Student Access: www.pearsonsuccessnet.com Glencoe Student Intervention Workbook: http://glencoe.mheducation.com/sites/0078884802/student_view0/student_workbooks.html Kutasoftware: www.kutasoftware.com Interactive Lessons: https://illuminations.nctm.org Virtual Manipulatives: http://nlvm.usu.edu/en/nav/vlibrary.html Additional Worksheets: www.math-aids.com Performance Based Tasks: 7.EE.B.4 Fishing Adventures 2

7.EE.B.4, 7.NS.A.1 Bookstore Account

7.G.B.4 Wedges of a Circle

7.G.B.4 Eight Circles

7.G.B.6, 7.RP.A.3 Sand under the Swing Set

A.REI.B.3, A.REI.A.1 Reasoning with linear inequalities

A.CED.A.1 Planes and wheat

A-CED.A.1 Paying the rent

F.IF.B.4 Warming and Cooling

F.IF.B.4, F.IF.B.5 Average Cost F.IF.A.1 The Parking Lot

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Modifications for all learners 13. Providing manipulatives (Virtual Manipulatives) 14. Providing notes (Student Companion) 15. Use of graphic organizers (Student Companion) 16. Use of interactive math journals (Reflections) – “Do you Know How?” and “Do you Understand?” questions 17. Identify opportunities for individual and small group review and practice (Chapter reviews) 18. Test modifications as dictated by IEP/504 plan

ALIGNMENT TO 21st CENTURY THEMES AND SKILLS

21st Century/ Interdisciplinary Themes: Bold all that apply 21st Century Skills: Bold all that apply 11. Global Awareness 12. Financial, Economic, Business and Entrepreneurial Literacy 13. Civic Literacy 14. Health Literacy 15. Environmental Literacy

15. Creativity & Innovation 16. Critical Thinking & Problem Solving 17. Communication & Collaboration 18. Media Literacy 19. Information Literacy 20. Information, Communication &Technology 21. Life & Career Skills

Special Notes:

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Montclair Public Schools Instructional Unit Content: Mathematics : Algebra A Grade: 7th Grade

Marking Period: 4 Unit 4 Slope, & Linear Equations Pacing: 10 weeks

CRITICAL AREAS OF FOCUS FOR UNIT 4 In this unit, students will work on identifying the rate of change between two variables, and then understanding that slope represents the rate of change between two variables. Students will then work on direct variation, making the correlation between direct variation and proportional relationships. Students will then work on slope, followed by creating linear equations using all three forms; slope-intercept form, point-slope form, and standard form. After identifying all three types of equations, students will proceed on to parallel and perpendicular lines. Finally, students will apply their knowledge of graphing equations to solving system of equations by graphing.

ESSENTIAL QUESTIONS • What does the slope of a line indicate in terms of the relationship between two variables? • What information does the equation of a line give you? • How can you make predictions based on a scatter plot?

TARGET STANDARDS

Math NJSLS Standard Emphasis

Mathematical Practice Standard

Benchmark Assessment (Place an X or N/A)

F.LE.A.1 Distinguish between situations that can be modeled with linear functions and with exponential functions.

Supporting Content

#1-8 X

A.CED.2 Create equations in two or more variables to represent relationships between quantities; Graph equations on coordinate axes with labels and scales

Major Content

#1-8

F.IF.C.7a Graph functions linear and quadratic functions and show intercepts, maxima, and minima

Supporting Content

#2, 5, 7-8

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F.LE.2 Construct linear and exponential functions-including arithmetic and geometric sequences-given a graph, a description of a relationship, or two input-output pairs

Supporting Content

#1-8

S.ID.C.7 Interpret the slope and the intercept of a linear model in the context of the data

Major Content

#1-8

A.REI.C.6 Solve systems of linear equations exactly and approximately, focusing on pairs of linear equations in two variables

Additional Content

#3-8

MATHEMATICAL PRACTICE STANDARDS Standard

# Standards for Mathematical Practice

1 Make sense of problems and preserve in solving them.

• Understand the correlation between slope and the rate of change between independent and dependent variables

2 Reason abstractly and quantitatively.

• Understand why slope is essentially rise over run. • Apply knowledge of parallel lines to justify why two parallel lines have the same slope.

3 Construct viable arguments and critique the reasoning of others. • Justify whether or not two lines are parallel, perpendicular, or neither.

4 Model with mathematics. • Graph systems of equations to show the point of intersection.

5 Use appropriate tools strategically. • Use graphing calculators to assist in graphing linear equations.

6 Attend to precision • Students must ensure all answers are in simplest form, and rounded to the correct value (if applicable).

7 Look for and make use of structure. • Use word problems to help interpret situations to set up a system of equations.

8 Look for and express regularity in repeated reasoning. • Justify your reasoning.

INTERDISCIPLINARY CONNECTIONS NJ CCCS Standard 8.1.8.A.1 Demonstrate knowledge of a real world problem using digital tools. 8.2.8.C.8 Develop a proposal for a chosen solution that include models (physical, graphical or mathematical) to communicate the

solution to peers. CRP1. Act as a responsible and contributing citizen and employee.

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CRP2. Apply appropriate academic and technical skills. CRP4. Communicate clearly and effectively and with reason. CRP8. Utilize critical thinking to make sense of problems and persevere in solving them. CRP11. Use technology to enhance productivity. 9.1.8.B.3 Evaluate communication, collaboration, and leadership skills that can be developed through school, home, work, and

extracurricular activities for use in a career.

INSTRUCTIONAL PROGRESSION Weekly

Plan Concept CMP2 Connection Vocabulary Evidence of

Learning Week 1 • Chapter 5.1

o Identify rate of change o Identify/calculate slope

From a graph If given two points From an equation

o Special case slopes (horizontal & vertical)

• Chapter 5.2 o Direct variation equations o Solve for “k” in a direct variation

equation o Graph direct variation equations

Moving Straight Ahead

• Rate of change • Slope • Slope formula • Direct variation • Constant of variation • Proportional

relationship

Lesson Check Practice WS 5.1 & 5.2 Pg. 298-299 #8-38 Pg. 304-305 #9-33

Week 3 • Quiz • Chapter 5.3

o Identify the slope and y-intercept from a given equation

o Create equations in slope-intercept form using: A given slope and a point A graph Two points

o Graph a linear equation in slope-intercept form

Moving Straight Ahead

• Parent function • Linear equation • Y-intercept • Slope-intercept form • Point-slope form

Lesson Check Practice WS 5.3 Pg. 312-313 #7-44

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Week 4 • Chapter 5.4 o Create equations in point-slope form o Graph an equation that’s given in point

slope form o Create an equation in point-slope form

if given two points o Use a table to create a equation in

slope-intercept form • Quiz Review

Lesson Check Practice 5.4 WS Pg. 318-319 #8-26

Week 5 • Quiz • Chapter 5.5

o Standard form of linear equations o Finding x- and y-intercepts o Graphing lines given in standard form o Graphing horizontal and vertical lines o Converting between all three forms of

linear equations

• Standard form Lesson Check Practice 5.5 WS Pg. 326-327 #8-38, 52-57

Week 6 • Chapter 5.6 o Parallel and perpendicular lines o Writing equation for parallel and

perpendicular lines o Classify lines as parallel or

perpendicular • Chapter 5.7

o Scatter plots and correlation patterns o Creating a line of best fit

• Opposite reciprocals • Scatter plot • Positive correlation • Negative correlation • No correlation • Trend line • Interpolation • Extrapolation • Line of best fit • Correlation coefficient • Causation relationships

Lesson Check Practice WS 5.6 & 5.7 Pg. 334 #7-30 Pg. 341 #7-17

Week 7 • Chapter 5.8 o Absolute value functions o Graphing translations of absolute value

functions

• Absolute value function • Translation • Piecewise function • Step function

Week 8 • Chapter Review • Chapter Exam

Week 9 • Chapter 6.1 o Solving systems by graphing

• System of equations • Consistent

Lesson Check

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o Classify systems of equations • Independent • Dependent • Inconsistent

Practice WS 6.1 Pg. 367 #10-38

Week 10 • Final exam review • Final exam

Week 11 Resources/Technology Infusion

Course Textbook: Pearson Common Core Edition 2012 Pearson Resources: Pearson Common Core Practice Workbook (Forms G and K), Student Companion (Pearson Online Access), Re-teaching worksheets (RTI), Additional Vocabulary Support (RTI), Find the error worksheets, Cumulative Review worksheets, Performance based tasks Online Resources: Pearson Student Access: www.pearsonsuccessnet.com Glencoe Student Intervention Workbook: http://glencoe.mheducation.com/sites/0078884802/student_view0/student_workbooks.html Kutasoftware: www.kutasoftware.com Interactive Lessons: https://illuminations.nctm.org Virtual Manipulatives: http://nlvm.usu.edu/en/nav/vlibrary.html Additional Worksheets: www.math-aids.com Performance Based Tasks: A.CED.A.3 Dimes and Quarters

A.REI.C.5 Solving Two Equations in Two Unknowns

Modifications for all learners 19. Providing manipulatives (Virtual Manipulatives) 20. Providing notes (Student Companion) 21. Use of graphic organizers (Student Companion) 22. Use of interactive math journals (Reflections) – “Do you Know How?” and “Do you Understand?” questions 23. Identify opportunities for individual and small group review and practice (Chapter reviews) 24. Test modifications as dictated by IEP/504 plan

ALIGNMENT TO 21st CENTURY THEMES AND SKILLS

21st Century/ Interdisciplinary Themes: Bold all that apply 21st Century Skills: Bold all that apply 28 | P a g e

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16. Global Awareness 17. Financial, Economic, Business and Entrepreneurial Literacy 18. Civic Literacy 19. Health Literacy 20. Environmental Literacy

22. Creativity & Innovation 23. Critical Thinking & Problem Solving 24. Communication & Collaboration 25. Media Literacy 26. Information Literacy 27. Information, Communication &Technology 28. Life & Career Skills

Special Notes:

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