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Glen Ridge Public Schools - Mathematics Curriculum

Course Title: Pre-Algebra 7

Subject: Mathematics

Grade Level: 7th Grade

Duration: One Academic Year

Prerequisite: Math 6

Elective or Required: Required Content Course

Mathematics Mission Statement:

Since Mathematical and Computational thinking are an integral part of our lives and 21st century learning, students must be actively involved in their mathematics education with problem solving being an essential part of the curriculum. The mathematics and computer science curricula will emphasize thinking skills through a balance of computation, intuition, common sense, logic, analysis and technology.

Students will be engaged and challenged in a developmentally appropriate, student-centered learning environment. Students will communicate mathematical ideas effectively and apply those ideas by using manipulatives, computational skills, mathematical models and technology in order to solve practical problems.

To achieve these goals, students will be taught a standards-based curriculum that is aligned with the National Common Core Standards in Mathematics and the New Jersey Core Curriculum Content Standards in Technology and 21st Century Life and Careers.

Course Description:

Pre-Algebra 7 students will develop fundamental mathematical ideas and methods through a student-centered based curricula. These methods provide a strong foundation in algebraic and geometric concepts. This course emphasizes problem solving strategies and applies the use of mental math and estimation to determine a the validity of a solution. Concepts covered in this course include algebraic reasoning, number sense, numeric relationships, geometric properties, data analysis and statistical thinking.

Author: Erika Taylor Date Submitted: Summer, 2012Text: Holt McDougal Mathematics Grade 7, 2012 by Bennett, Burger, Chard, Hall, Kennedy, Renfro, Roby, Scheer, & Waits

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Course Name: Pre-Algebra 7

Unit #1: Number Sense Chapter 1: Algebraic Reasoning & Chapter 2: Integers & Rational Numbers

Approximate Number of Weeks: 5 Weeks

Essential Questions: • How are velocity and speed related? • Is the sum of two integers positive, negative, or zero? How can you tell? • How are adding and subtracting integers related? • Is the product/quotient of two integers positive, negative, or zero? How Can you tell?• How are multiplying and dividing integers related? Different?• How can you use a number line to order rational numbers?• How does adding and subtracting rational numbers compare with adding and

subtracting integers?• How is multiplying and dividing rational numbers similar to multiplying and dividing

integers?• How can you use inverse operations to solve an equation?

Common Core Standards: CC.7.NS.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 diagram.

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

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

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

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

CC.7.EE.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.

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CC.7.EE.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.

Upon completion of this unit students will be able to: • Use the order of operations to simplify numerical expressions (CC.7.NS.1).• Identify properties of rational numbers and use them to simplify numerical expressions

(CC.7.NS.1, CC.7.EE.2, CC.7.EE.3).• Evaluate algebraic expressions (CC.7.NS.1).• Translate words into numbers, variables, and operations (CC.7.EE.2, CC.7.EE.4).• Simplify algebraic expressions (CC.7.EE.1, CC.7.EE.4).

• Compare and order integers and determine absolute value (CC.7.NS.1).• Add integers (CC.7.NS.1, CC.7.NS.3, CC.7.EE.3).• Use additive inverses and absolute value in real-world situations (CC.7.NS.1).• Subtract Integers (CC.7.NS.1).• Multiply and divide integers (CC.7.NS.2, CC.7.EE.2).• Solve one-step equations with integers (CC.7.NS.1, CC.7.EE.4).• Write fractions as decimals and vice versa, and determine whether a decimal is

terminating or repeating (CC.7.NS.2, CC.7.NS.3).• Compare and order fractions and decimals (CC.7.NS.2, CC.7.NS.3).

Interdisciplinary Standards (NJCCCS.org)

Standard 9.1 21st-Century Life & Career Skills All students will demonstrate the creative, critical thinking, collaboration, and problem-solving skills needed to function successfully as both global citizens and workers in diverse ethnic and organizational cultures.

Standard 8.1 – Computer and Information LiteracyAll students will use computer applications to gather and organize information and to solve problems.

Standard 8.2 – Technology EducationAll students will develop an understanding of the nature and impact of technology, engineering, technological design, and the designed world as they relate to the individual, society, and the environment.

Activities/ Technology:• Order of Operations Lab TI-84 (Holt, 1-1 Exploration, page 11)• Numeric Property Group Presentation - Investigate & Share • Activity 3: Finding Speed & Velocity (Big Ideas Text, page 3)• Algebra Tile Operations Labs (Intro/Combining Like Terms, Addition, Subtraction,

Multiplication & Division, Solving One-Step Equations)• Human Rational Number Line (Big Ideas Activity 1, page 50)• Math Card War - Rational Numbers (Big Ideas Activity 2, page 51)

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• Financial Literacy (Big Ideas Activity 3, page 57)• Math Card War - One-Step Equations (Big Ideas Activity 3, page 77)• Countdown to Mastery (Holt, page CC8 to CC31)• Problem Solving/ Real-Life Applications • Powerpoint & Video Tutors from Holt

Enrichment Activities: • Magic Square - Order of Operations (Holt, page TE-19)• Integer 24 Game • Fraction/Decimal 24 Game • Taking Math Deeper (Big Ideas)• Practice C - Level Worksheets (Holt)• Challenge Worksheets (Holt)• On Core Test Preparation Questions (Houghton Mifflin)

Methods of Assessment/Evaluation:Technology Assessment

Closure Assessments

Summative Assessments

Formative Assessments

Unit Specific Assessments

Smart Board Lessons (clickers)

Entry/ Exit Slips

Portfolio Think/Pair/Share

Math Chat (Big Ideas, T-40)

Brain Pop Videos

Wall Wisher Questions

Chapter/Unit Tests

Entry/ Exit Slips

Graphic Organizer (Big Ideas, page T-40)

Discovery Education/ United Streaming

Thumbs Up/ Thumbs Down

Midterms/Finals

Whiteboards Rational Number Venn Diagram (Big Ideas, Key Ideas, page 52)

Calculator Labs Think/Pair/Share

Unit Projects Classwork/ Homework

3*2*1/KWL Quiz Games/ Board Games

Real World Applications

Revisit Essential Questions (Objectives)

Song/Rap Writing

Manipulatives

Dry Erase Boards

Labs Center Activities

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Technology Assessment

Closure Assessments




Lab Reflection Questions

Give a Choice of an Assessment

3*2*1/KWL

Quick Write Journals/ Open Ended Questions

Verbal Assessment

Rhetorical Questions

Unit Projects

Error Analysis

Math Games

Notebook/ Binder Quiz

Resources:• Online Textbook Information: my.hrw.com • Teacher Webpage • Big Ideas Math Text, Common Core Curriculum• On Core Mathematics, Middle School Grade 7, Houghton Mifflin Harcourt • The Middle School Mathematician, Terri Breeden & Kathryn Dillard• Teaching Middle Grades with TI Technology, Prentice Hall Mathematics • Technology:

• mathsnacks.org• mathtv.com• mathbits.com• mathworksheetsgo.com• catchupmath.com/math-games/

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Unit #2: Numeric RelationshipsChapter 3: Applying Rational Numbers, Chapter 4: Proportional Relationships, &

Chapter 6: Percents


Essential Questions: • How does adding and subtracting rational numbers compare with adding and

subtracting integers?• How does multiplying and dividing rational numbers compare with multiplying and

dividing integers?• How does solving one-step equations containing integers compare to solving one-step

equations containing rational numbers?• How do you find and compare unit rates?• How do rates help you describe real-life problems?• How do you compare two rates graphically?• How can proportions help you decide when things are fair?• How can you use tables and equations to identify and describe proportional

relationships?• How can you write a proportion that solves a problem in real life?• How can you use ratio tables and cross products to solve proportions in science?• How can you use models to estimate percent questions?• How do you use percents to solve problems?

Common Core Standards: CC.7.RP.1: Compute unit rates associated with ratios of fraction, including ratios of lengths, areas and other quantities measured in like or different units.

CC.7.RP.2: Recognize and represent proportional relationships between quantities.

CC.7.RP.3: Use proportional relationships to solve multistep ratio and percent problems.

CC.7.NS.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 diagram.

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

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

CC.7.EE.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.

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CC.7.EE.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.


CC.7.G.1: Solve problems involving scale drawings of geometric figures, including computing actual lengths and areas from scale drawing and reproducing a scale drawing at a different scale.

Upon completion of this unit students will be able to: • Add and subtract decimals (CC.7.NS.1, CC.7.NS.3).• Multiply decimals (CC.7.NS.1, CC.7.NS.2, CC.7.NS.3).• Divide decimals by integers and integers by decimals (CC.7.NS.2).• Solve one-step equations that contain decimals (CC.7.NS.2, CC.7.EE.4).• Add and subtract fractions (CC.7.NS.1, CC.7.NS.3).• Multiply fractions and mixed numbers (CC.7.NS.1, CC.7.NS.2, CC.7.NS.3). • Divide fractions and mixed numbers (CC.7.NS.2, CC.7.NS.3).• Solve one-step equations that contain fractions (CC.7.EE.4).

• Find and compare unit rates and unit price (CC.7.RP.1, CC.7.RP.2).• Find equivalent ratios and identify proportions (CC.7.RP.2, CC.7.NS.3).• Solve proportions using cross products (CC.7. RP.1, CC.7.RP.2).• Use ratios to determine if two figures are similar (CC.7.RP.2, CC.7.NS.3). • Use similar figures to find unknown measures (CC.7.RP.2, CC.7.G.1).• Understand ratios and proportions in scale drawings and use ratios and proportions

with scale (CC.7.NS.3, CC.7.G.1).

• Write decimals and fractions as percents (CC.7.EE.3). • Estimate percents (CC.7.EE.3). • Use properties of rational numbers to write expressions and equations (CC.7.NS.1,

CC.7.NS. 2, CC.7.EE.2, CC.7.EE.3).• Solve problems involving percent of change (CC.7.RP.3, CC.7.EE.2, CC.7.EE.3). • Find commission, sales tax, and percent of earnings (CC.7.RP.3).• Compute simple interest (CC.7.RP.3)

Interdisciplinary Standards (NJCCCS.org)Standard 9.3 - Career Awareness, Exploration, and Preparation All students will apply knowledge about and engage in the process of career awareness, exploration, and preparation in order to navigate the globally competitive work environment of the information age.

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Standard 6.1 U.S. History: America in the WorldAll students will acquire the knowledge and skills to think analytically about how past and present interactions of people, cultures, and the environment shape the American heritage. Such knowledge and skills enable students to make informed decisions that reflect fundamental rights and core democratic values as productive citizens in local, national, and global communities.

Activities/ Technology:• Science - Comparison of Fahrenheit & Celsius (Holt, Reaching All Learners, page

T-105)• Ratio Concentration (Holt, Game Time, page 182)• Ratios TI-84 Lab (Prentice Hall Mathematics, page 57)• Unit Rates TI-84 Lab (Prentice Hall Mathematics, page 35)• Precent of Change TI-84 Lab (Prentice Hall Mathematics, page 59)• Make Scale Drawings & Models Lab (Holt, pages 176-177)• Use Scale Drawings Lab (Holt, pages 178-179)• Comparing Unit Rates (Big Ideas, Activity 1/2, page 104)• Determining Fairness (Big Ideas, Activity 3, page 111)• Problem Solving Connections: Car or Motorcycle? (Houghton Mifflin On Core 7, page

51)• Solving a Proportion in Science (Big Ideas, Activity 1, page 122)• The Game of Criss Cross (Big Ideas, Activity 2, page 123)• What is Your Answer? Puzzle (Big Ideas, Question #4, page 123)• Communicator Percent Activity (LLTeach Activity Book)• Percent Dominos Game (Room 213 Closet) • Fraction Dominos (The Middle School Mathematician, pages 21-22)• The National Debt (Big Ideas, Activity 3, page 179)• Percents of Increase or Decrease Review Game (Big Ideas, page T-186)• Problem Solving/ Real-Life Applications • Powerpoint & Video Tutors from Holt

Enrichment Activities: • Real World Connections (Holt, Chapter 4, page 181)• Taking Math Deeper (Big Ideas)• Practice C - Level Worksheets (Holt)• Challenge Worksheets (Holt)• On Core Test Preparation Questions (Houghton Mifflin)

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Methods of Assessment/Evaluation: Technology Assessment

Closure Assessments





Entry/ Exit Slips


Information Wheel (Big Ideas, pages 128, T-128)

Brain Pop Videos


Chapter/Unit Tests

Entry/ Exit Slips

Error Notebook (Big Ideas, page T-129)



Midterms/Finals

Whiteboards Summary Triangle (Big Ideas, page 170)






Song/Rap Writing

Manipulatives

Dry Erase Boards




3*2*1/KWL


Verbal Assessment


Unit Projects

Error Analysis

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Closure Assessments




Math Games




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Unit #3: Data AnalysisChapter 7: Collecting, Displaying & Analyzing Data & Chapter 10: Probability


Essential Questions: • How can you use graphs to represent and analyze proportional relationships?• How do you use a survey to make conclusions about the general population?• How can you predict the results of spinning a spinner?• How can you find a theoretical probability? Experimental probability?• What are the differences/similarities between theoretical and experimental

probabilities?• What is the difference between independent and dependent events?• How do you find the probability of a compound event?

Common Core Standards: CC.7.SP.1: Understand that statistics can be used to gain information about a population by examining a sample of the population; generalizations about a population from a sample are valid only if the sample is representative of that population. Understand that random sampling tends to produce representative samples and support valid inferences.

CC.7.SP.2: Use data from a random sample to draw inferences about a population with an unknown characteristic of interest. Generate multiple samples (or simulated samples) of the same size to gauge the variation in estimates or predictions.

CC.7.SP.3: Informally assess the degree of visual overlap of the two numerical data distributions with similar variabilities, measuring the difference between the centers by expressing it as a multiple of a measure of variability.

CC.7.SP.4: Use measures of center and measures of variability for numerical data from random samples to draw informal comparative inferences about two populations.

CC.7.SP.5: Understand that the probability of a chance event is a number between 0 and 1 that expresses the likelihood of the event occurring. Larger numbers indicate greater likelihood. A probability near 0 indicates an unlikely event, a probability around 1/2 indicates an event that is neither unlikely nor likely, and a probability near 1 indicates a likely event.

CC.7.SP.6: Approximate the probability of a chance event by collecting data on the chance process that produces it and observing its long-run relative frequency, and predict the approximate relative frequency given the probability.

CC.7.SP.7: Develop a probability model and use it to find probabilities of events. Compare probabilities from a model observed to observed frequencies; if the agreement is not good, explain possible sources of the discrepancy.

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CC.7.SP.8: Find probabilities of compound events using organized lists ,tables, tree diagrams, and simulations.

Upon completion of this unit students will be able to:• Find the mean, median, mode and range of a data set (CC.7.SP.4).• Display and analyze data in box-and-whisker plots (CC.7.SP.2, CC.7.SP.3, CC.7.SP.

4).• Compare and analyze sampling methods (CC.7.SP.1).

• Use informal measures of probabilities (CC.7.SP.5).• Find experimental probability (CC.7.SP.6, CC.7.SP.7).• Use counting methods to determine possible outcomes (CC.7.SP.8).• Find the theoretical probability of an event (CC.7.SP.6, CC.7.SP.8). • Use probability to predict events (CC.7.SP.6, CC.7.SP.6, CC.7.SP.8). • Find the probability of independent and dependent events (CC.7.SP.8).• Find probabilities of compound events (CC.7.SP.8).

Interdisciplinary Standards (NJCCCS.org)Standard 9.1 21st-Century Life & Career Skills All students will demonstrate the creative, critical thinking, collaboration, and problem-solving skills needed to function successfully as both global citizens and workers in diverse ethnic and organizational cultures.

Standard 9.3 - Career Awareness, Exploration, and Preparation All students will apply knowledge about and engage in the process of career awareness, exploration, and preparation in order to navigate the globally competitive work environment of the information age.



Standard 6.1 U.S. History: America in the WorldAll students will acquire the knowledge and skills to think analytically about how past and present interactions of people, cultures, and the environment shape the American heritage. Such knowledge and skills enable students to make informed decisions that reflect fundamental rights and core democratic values as productive citizens in local, national, and global communities.

Standard 6.2 World History, Global Studies

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All students will acquire the knowledge and skills to think analytically and systematically about how past interactions of people, cultures, and the environment affect issues across time and cultures. Such knowledge and skills enable students to make informed decisions as socially and ethically responsible world citizens in the 21st century.

Activities/ Technology:• Mean Solitaire (Great Graphs, page 91)• GPA (Great Graphs, page 97)• Explore Box-and-Whisker Plots Lab (Holt, page 284-285)• Box-and-Whisker Plot TI-84 Lab (Prentice Hall Mathematics, page 65)• Explore Samples Lab (Holt, page 290)• Use Random Samples Lab (Holt, pages 292-293)• Conduct a Survey (Big Ideas, Activity 2, page 368)• Using Samples to Compare Populations (Big Ideas, Activity 2, page 373B)• Motivate Spinner Activity (Big Ideas, page T-384)• Experimental & Theoretical Probability Lab (Holt, pages 430-431)• M&M Lab (see appendix, pages 27-31)• Rolling Number Cubes TI-84 Lab (Prentice Hall Mathematics, page 37)• Dependent/Independent Events (Big Ideas, Activity 1/2, page 404)• Problem Solving/ Real-Life Applications • Powerpoint & Video Tutors from Holt

Enrichment Activities: • Real World Connections (Holt, Chapter 7, page 295)• Taking Math Deeper (Big Ideas)• Practice C - Level Worksheets (Holt)• Challenge Worksheets (Holt)• On Core Test Preparation Questions (Houghton Mifflin)


Closure Assessments





Entry/ Exit Slips


Information Frame (Big Ideas, page 360)

Brain Pop Videos


Chapter/Unit Tests

Entry/ Exit Slips

100% Quiz (Big Ideas, page T-397)



Midterms/Finals

Whiteboards

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Closure Assessments









Song/Rap Writing

Manipulatives

Dry Erase Boards




3*2*1/KWL


Verbal Assessment


Unit Projects

Error Analysis

Math Games



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Unit #4: Geometric PropertiesChapter 8: Geometric Figures & Chapter 9: Measurement & Geometry


Essential Questions: • How can you draw shapes that satisfy given conditions?• How can you identify cross sections of three-dimensional figures?• How can you use angle pairs to solve problems?• How do you find the circumference of a circle?• How do you find the area of a circle?• How do you find the area of composite figures?• How do you find the surface area of a figure made of prisms? • How can you use a net to find the surface area of a prism? Cylinder?• How do you find the volume of a figure made up of cubes and prisms?

Common Core Standards: CC.7.RP.2: Recognize and represent proportional relationships between quantities.

CC.7.RP.3: Use proportional relationships to solve multistep ratio and percent problems.

CC.7.G.2: Draw (freehand, with ruler and protractor, and with technology) geometric shapes with given conditions. Focus on constructing triangles from three measures of angles or sides, noticing when the conditions determine a unique triangle, more than one triangle, or no triangle.

CC.7.G.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.

CC.7.G.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.

CC.7.G.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.

CC.7.G.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.

Upon completion of this unit students will be able to: • Identify and describe geometric figures. • Identify angles and angle pairs (CC.7.G.5).

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• Identify parallel, perpendicular, and skew lines, and angles formed by transversals (CC.7.G.5).

• Find the measures of angles in polygons (CC.7.RP.2, CC.7.G.5).• Identify congruent figures and use congruence to solve problems (CC. 7.G.2).

• Find the perimeter of a polygon and the circumference of a circle (CC.7.RP.3, CC.7.G.4).

• Find the area of circles (CC.7.G.4). • Find the area of irregular figures (CC.7.G.6). • Identify various three-dimensional figures and sketch and describe cross-sections of

three-dimensional figures (CC.7.G.3). • Find the volume of prisms and cylinders (CC.7.G.6). • Find the surface area of prisms and cylinders (CC.7.G.6).

Interdisciplinary Standards (NJCCCS.org)Standard 9.1 21st-Century Life & Career Skills All students will demonstrate the creative, critical thinking, collaboration, and problem-solving skills needed to function successfully as both global citizens and workers in diverse ethnic and organizational cultures.



Activities/ Technology:• Problem Solving Connections - Buying a Home (On Core Mathematics, pages

103-106)• Finding Surface Area (Big Ideas, Activity 2, page 257)• Finding Surface Area (Big Ideas, Activity 1/2, page 262)• Classifying Triangles TI-84 Lab (Prentice Hall Mathematics, page 41)• Nets of Prisms TI-84 Lab (Prentice Hall Mathematics, page 43)• Pythagorean Theorem TI-84 Lab (Prentice Hall Mathematics, page 53)• Points, Lines & Angles (The Middle School Mathematician, page 97)• Geometry Flash Cards (The Middle School Mathematician, pages 98-99)• Congruent Figures TI-84 Lab (Prentice Hall Mathematics, page 69)• Construct Bisectors & Congruent Angles Lab (Holt, pages 326-327)• Construct Triangles & Given Side Lengths Lab (Holt, pages 334-335)• Construct Triangles with Given Angle Measures Lab (Holt, pages 342-343)

Enrichment Activities: • Game Time - Networks (Holt, page 346)

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• Taking Math Deeper (Big Ideas)• Practice C - Level Worksheets (Holt)• Challenge Worksheets (Holt)• On Core Test Preparation Questions (Houghton Mifflin)


Closure Assessments





Entry/ Exit Slips


Math Chat (Big Ideas, page T-338)

Brain Pop Videos


Chapter/Unit Tests

Entry/ Exit Slips

Graphic Organizers (Big Ideas, page T-338)



Midterms/Finals

Whiteboards






Song/Rap Writing

Manipulatives

Dry Erase Boards




3*2*1/KWL


Verbal Assessment

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Closure Assessments





Unit Projects

Error Analysis

Math Games


Resources:• Online Textbook Information: my.hrw.com • Teacher Webpage • Big Ideas Math Text, Common Core Curriculum• On Core Mathematics, Middle School Grade 7, Houghton Mifflin Harcourt • The Middle School Mathematician, Terri Breeden & Kathryn Dillard• Teaching Middle Grades with TI Technology, Prentice Hall Mathematics • Great Graphs & Sensational Statistics, Lynette Long• Technology:


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Unit #5: Algebraic Reasoning Chapter 5: Graphs & Chapter 11: Multi-Step Equations & Inequalities


Essential Questions: • How can you use ordered pairs to locate points in a coordinate plane?• How do you add, subtract, factor and multiply algebraic expressions?• How do you solve equations that contain multiple operations?• In a two-step equation, which step should you do first?• How do you solve inequalities that involve one operation?• How do you solve inequalities that involve multiple operations?• How do you solve problems by using expressions, equations, and inequalities?

Common Core Standards: CC.7.RP.1: Compute unit rates associated with ratios of fraction, including ratios of lengths, areas and other quantities measured in like or different units.

CC.7.RP.2: Recognize and represent proportional relationships between quantities.

CC.7.NS.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 diagram.

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


Upon completion of this unit students will be able to: • Plot and identify ordered pairs in a coordinate plane. • Relate graphs to situations. • Determine the slope of a line and recognize constant and variable rates of change

(CC.7.RP.1, CC.7.RP.2). • Identify, write and graph an equation of direct variation (CC.7.RP.2, CC.7.NS.1).

• Solve two-step equations (CC.7.EE.1).• Solve multi-step equations (CC.7.EE.1, CC.7.EE.4). • Solve equations that have variables on both sides (CC.7.EE.1, CC.7.EE.4).• Compare algebraic and numeric solution methods (CC.7.EE.4). • Read and write inequalities and graph them on a number line. • Solve one-step inequalities by adding or subtracting (CC.7.EE.4). • Solve one-step inequalities by multiplying or dividing (CC.7.EE.4). • Solve simple two-step inequalities (CC.7.EE.4).

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Interdisciplinary Standards (NJCCCS.org)Standard 9.3 - Career Awareness, Exploration, and Preparation All students will apply knowledge about and engage in the process of career awareness, exploration, and preparation in order to navigate the globally competitive work environment of the information age.



Activities/ Technology:• Plotting Points in a Coordinate Plane (Big Ideas - Record & Practice Journal, page 34)• Real-Life Application Coordinate Plane (Big Ideas - Example 3, page 37)• Algebra Tiles Labs (Solving Multi-Step Equations)• Problem Solving Connections - To Buy or not to buy? (On Core, page 81)• Tic-Tac-Five in a Row Game (The Middle School Mathematician, page 79)• Coordinate Hangman (The Middle School Mathematician, page 82)• Plotting Coordinate Pictures - Graph the Robot (superteacherworksheets.com)• Whatʼs the Point? Game (The Middle School Mathematician, page 87)• Geometric Ski Resort Game (The Middle School Mathematician, page 89)• Whatʼs My Line? Game (The Middle School Mathematician, page 91)• Equation of a Line TI-84 Lab (Prentice Hall Mathematics, page 39)• Graphing Proportional Relationships Lab (Holt, pages 204-205)

Enrichment Activities: • “I Have, Who Has?” - Algebra • Taking Math Deeper (Big Ideas)• Practice C - Level Worksheets (Holt)• Challenge Worksheets (Holt)• On Core Test Preparation Questions (Houghton Mifflin)


Closure Assessments





Entry/ Exit Slips


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Closure Assessments




Brain Pop Videos


Chapter/Unit Tests

Entry/ Exit Slips



Midterms/Finals

Whiteboards






Song/Rap Writing

Manipulatives

Dry Erase Boards




3*2*1/KWL


Verbal Assessment


Unit Projects

Error Analysis

Math Games


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Resources:• Online Textbook Information: my.hrw.com • Teacher Webpage • Big Ideas Math Text, Common Core Curriculum• On Core Mathematics, Middle School Grade 7, Houghton Mifflin Harcourt • The Middle School Mathematician, Terri Breeden & Kathryn Dillard• Teaching Middle Grades with TI Technology, Prentice Hall Mathematics • Great Graphs & Sensational Statistics, Lynette Long• Technology:


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AppendixAdditional Worksheets

Pre-Algebra 7 Course Outline With the Use of Holt McDougal Mathematics Grade 7 Text

Unit 1: Number Sense (MP 1 - 5 Weeks)

! Chapter 1: Algebraic Reasoning (2 Weeks)" " Order of Operations" " Properties of Numbers" " Variables and Algebraic Expressions" " Translating Words into Math" " Simplifying Algebraic Expressions

" Chapter 2: Integers & Rational Numbers (3 Weeks)" " Integers" " Adding Integers" " Additive Inverse & Absolute Value " " Subtracting Integers" " Multiplying & Dividing Integers" " Solving Equations Containing Integers" " Equivalent Fractions and Decimals" " Comparing & Ordering Rational Numbers

Unit 2: Numeric Relationships (MP 1/MP2 - 9 Weeks)

" Chapter 3: Applying Rational Numbers (3 weeks)" " Adding & Subtracting Decimals" " Multiplying Decimals" " Dividing Decimals" " Solving Equations Containing Decimals" " Adding & Subtracting Fractions" " Multiplying Fractions & Mixed Numbers" " Dividing Fractions & Mixed Numbers" " Solving Equations Containing Fractions

! Chapter 4: Proportional Relationships (3 Weeks) " " Rates" " Identifying & Writing Proportionals" " Solving Proportions" " Similar Figures & Proportions" " Using Similar Figures" " Scale Drawings & Scale Models

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! Chapter 6: Percents (3 Weeks)" " Fractions, Decimals & Percents" " Estimating with Percents (Mental Math)" " Using Properties with Rational Numbers" " Percent of Change" " Applications of Percents " " Simple Interest

Unit 3: Data Analysis (MP 2 - 5 Weeks)

! Chapter 7: Collecting, Displaying and Analyzing Data (2 Weeks)" " Mean, Median, Mode and Range" " Box-and-Whisker Plots" " Populations & Samples

" Chapter 10: Probability (3 Weeks)" " Probability " " Experimental Probability " " Sample Spaces" " Theoretical Probability " " Making Predictions" " Probability of Independent & Dependent Events" " *Combinations" " *Permutations" " *Probability of Compound Events

Unit 4: Geometric Properties (MP 3 - 6 Weeks)

" Chapter 8: Geometric Figures (3 Weeks)" " Building Blocks of Geometry " " Classifying Angles" " Line & Angle Relationships" " Angles in Polygons" " Congruent Figures" "! Chapter 9: Measurement and Geometry (3 Weeks)" " Perimeter & Circumference" " Area of Circles" " Area of Irregular Figures" " Introduction to 3D Figures" " Cross Sections" " Volume of Prisms & Cylinders" " Surface Area of Prisms & Cylinders " "Unit 5: Algebraic Reasoning (MP 4 - 7 Weeks)!

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! Chapter 5: Graphs (2 Weeks)" " The Coordinate Plane" " Interpreting Graphs" " Slope & Rates of Change" " Direct Variation

" Chapter 11: Multi-Step Equations & Inequalities (5 Weeks)" " Solving Two-Step Equations" " Solving Multi-Step Equations" " Solving Equations with Variables on Both Sides" " Examine Solutions Methods" " Inequalities" " Solving Inequalities by Adding or Subtracting" " Solving Inequalities by Multiplying or Dividing " " Solving Multi-Step Inequalities

"" "" "

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Name ____________________Date _____________________Period _________

Probability with M&Ms

In this activity, you will be drawing M&Ms from a bag to determine what the probability is of getting each color of M&M. You will record your results in a table.

Important Items:

•DO NOT EAT the M&Ms.

•REPLACE each M&M that you draw before drawing the next one. This makes your probability calculations easier.

•SHAKE the bag after you replace each M&M. This will help your draws be more “random” so that your data will be a good representation.

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Procedures:

1) Draw one M&M. Record the color in the table by marking a tally mark in the first row of the table.

2) Replace the M&M. Shake the bag.

3) Repeat steps 1 and 2 twenty-five times.

Brown Blue Red Orange Yellow Green

Tally Marks:

Total:

Probability (as a fraction):

Probability(as a decimal):

4) In the second row of the table, write down the total number of tally marks from each color.

5) Calculate the probability of drawing each color, based on the number of times you drew M&Ms (25) and the number of times you drew each color (tally total). Write these probabilities down in fraction form in the third row of the table and in decimal form in the last row of the table.

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6) Empty out your bag of M&Ms. In the table below, record the actual number of each color of M&M.

Brown Blue Red Orange Yellow Green

Actual Number:

Probability (as a fraction):

Probability(as a decimal):

7) Write down the total number of M&Ms in the bag: _______

(This number should be 50)

8) Calculate the probability of drawing each color, based on the total number of M&Ms in the bag and the actual number of each color. Write these probabilities down in fraction form in the second row of the table above, and then in decimal form in the last row.

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Summary:

Answer the following questions using the data you collected above and the vocabulary we have developed in class. Be sure to use complete sentences in your explanations.

9) Are your probabilities in the first table similar to your probabilities in the second table? Explain.

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10) Do you think your probabilities in the first table should be similar to your probabilities in the second table? Why or why not?

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11) One of these tables represents “experimental probability” and one represents “theoretical probability.” Which one do you think is which? What do you think “experimental probability” means? What do you think “theoretical probability” means?

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12) One of the tables above involves finding probability from a “sample” and one involves finding probability from a “population.” Which one do you think is which? What do you think a “sample” is? What do you think a “population” is?

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13) What changes could you make to the experiment in numbers 1-3 to produce more accurate results (results that are more similar to your theoretical probability)?

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