GATEWAY REGIONAL HIGH SCHOOL

PACING GUIDE

# PURPOSE STATEMENT/PHILOSOPHY

The seventh grade mathematics curriculum is comprised of the following major concepts or “Big Ideas”: Integers; Rational Numbers; Equations and Expressions; Graphing; Ratios and Proportions; Percents; Solving Equations; Angles and Geometry Shapes; Area and Volume; and Probability and Random Samples. In addition, there are applications related to fraction and decimal manipulations. While knowledge of content is developed, students will be engaged in direct instruction activities, differentiated lessons, hands-on activities and cooperative learning activities that encourage mathematical problem solving.  The learning environment promotes mathematical reasoning, communication and higher order cognitive skills. Students will utilize technology such as calculators, lap top computers and scanners, cameras, and interactive white boards will be used to enhance instruction. Finally, evaluation of student performance will be accomplished through the use of primary, secondary, and support assessments. These may include but are not limited to tests, performance assessments, quizzes, informal assessments (both verbal and written), classroom observations, and homework.

PACING GUIDE

 GATEWAY GROUP CURRICULUM UNIT PLAN Content Area:  Mathematics Unit Title: Operations on Rational Numbers & Expressions Timeframe: 16 Days Lesson Components UNIT SUMMARY A summary of what the unit will contain and the learning students will be engaged in. Describe and model, on a horizontal and vertical number line, real-world situations in which rational numbers are combined.Apply the additive inverse property to subtraction problems and develop the argument that the distance between two points is the absolute value of the difference between their coordinates.Students will solve problems using all arithmetic operations involving integers.Explain why a divisor cannot be zero and why division of integers results in a rational number.Model the multiplication and division of signed numbers using real-world contexts, such as taking multiple steps backwards.Convert a rational number to a decimal using long division and explain in oral or written language why the decimal is either a terminating or repeating decimal.Apply properties of operations as strategies to add, subtract, multiply, and divide rational numbers.Solve mathematical and real-world problems involving addition, subtraction, multiplication, and division of rational numbers. LEARNING TARGETS ESSENTIAL QUESTIONSWhat is an integer?How can you develop an understanding of arithmetic operations with positive and negative integers?How do you graph a point on a coordinate grid?What is a variable expression?How do you evaluate an expression? ENDURING UNDERSTANDINGS An integer is the group of positive whole numbers, negative whole numbers, and zero.By creating an algorithm for addition, subtraction, multiplication, and division of integers.Use positive and negative number coordinates and arithmetic operations to locate and move points around a coordinate grid.A variable expression is a mathematical phrase that uses numbers, variables, and operation symbols.Use substitution and order of operations to find the value of expressions.

 Technology Standards: (See Pacing Guide for Specific Integration) Career Ready Practices:(See Pacing Guide for Specific Integration) Standard 8.1 Educational Technology:  All students will use digital tools to access manage, evaluate, and synthesize information in order to solve problems individually and collaborate and to create and communicate knowledge.A. Technology Operations and Concepts: Students demonstrate a sound understanding of technology concepts, systems and operations.8.1.8.A.2  Create a document (e.g. newsletter, reports, personalized learning plan, business letters or flyers) using one or more digital applications to be critiqued by professionals for usability.B. Creativity and Innovation: Students demonstrate creative thinking, construct knowledge and develop innovative products and process using technology.8.1.8.B.1 Synthesize and publish information about a local or global issue or event (ex. telecollaborative project, blog, school web).D. Digital Citizenship: Students understand human, cultural, and societal issues related to technology and practice legal and ethical behavior.8.1.8.D.1 Understand and model appropriate online behaviors related to cyber safety, cyber bullying, cyber security, and cyber ethics including appropriate use of social media.8.1.8.D.2 Demonstrate the application of appropriate citations to digital content.8.1.8.D.3 Demonstrate an understanding of fair use and Creative Commons to intellectual property.8.1.8.D.4 Assess the credibility and accuracy of digital content.8.1.8.D.5 Understand appropriate uses for social media and the negative consequences of misuse.E: Research and Information Fluency: Students apply digital tools to gather, evaluate, and use information.8.1.8.E.1 Effectively use a variety of search tools and filters in professional public databases to find information to solve a real world problem. CRP2. Apply appropriate academic and technical skills. CRP4. Communicate clearly and effectively and with reason. CRP6. Demonstrate creativity and innovation. CRP7. Employ valid and reliable research strategies. CRP8. Utilize critical thinking to make sense of problems and persevere in solving them. CRP11. Use technology to enhance productivity. CRP12. Work productively in teams while using cultural global competence.

GATEWAY GROUP CURRICULUM UNIT PLAN

Content Area:  Mathematics

Unit Title: Equations and Ratios and Proportions

Timeframe: 20 Days

Lesson Components

UNIT SUMMARY

A summary of what the unit will contain and the learning students will be engaged in.

• #### Draw, construct, and describe geometrical figures and describe the relationships between them.

LEARNING TARGETS

ESSENTIAL QUESTIONS

What is a ratio?

What operations can be used to make comparisons?

What is the relationship between ratios and similar figures?

How can we use proportions to solve problems?

What is a unit rate?

ENDURING UNDERSTANDINGS

A ratio is a comparison of two numbers by division.

Subtraction for difference statements.  Division for ratio statements. Multiplication to scale ratios.

The ratios of corresponding sides of similar figures are equal.

Pose problems in the form .

A rate in which the second number is 1 of a quantity.

 Technology Standards: (See Pacing Guide for Specific Integration) Career Ready Practices:(See Pacing Guide for Specific Integration) Standard 8.1 Educational Technology:  All students will use digital tools to access manage, evaluate, and synthesize information in order to solve problems individually and collaborate and to create and communicate knowledge.A. Technology Operations and Concepts: Students demonstrate a sound understanding of technology concepts, systems and operations.8.1.8.A.2  Create a document (e.g. newsletter, reports, personalized learning plan, business letters or flyers) using one or more digital applications to be critiqued by professionals for usability.B. Creativity and Innovation: Students demonstrate creative thinking, construct knowledge and develop innovative products and process using technology.8.1.8.B.1 Synthesize and publish information about a local or global issue or event (ex. telecollaborative project, blog, school web).D. Digital Citizenship: Students understand human, cultural, and societal issues related to technology and practice legal and ethical behavior.8.1.8.D.1 Understand and model appropriate online behaviors related to cyber safety, cyber bullying, cyber security, and cyber ethics including appropriate use of social media.8.1.8.D.2 Demonstrate the application of appropriate citations to digital content.8.1.8.D.3 Demonstrate an understanding of fair use and Creative Commons to intellectual property.8.1.8.D.4 Assess the credibility and accuracy of digital content.8.1.8.D.5 Understand appropriate uses for social media and the negative consequences of misuse.E: Research and Information Fluency: Students apply digital tools to gather, evaluate, and use information.8.1.8.E.1 Effectively use a variety of search tools and filters in professional public databases to find information to solve a real world problem. CRP2. Apply appropriate academic and technical skills. CRP4. Communicate clearly and effectively and with reason. CRP6. Demonstrate creativity and innovation. CRP7. Employ valid and reliable research strategies. CRP8. Utilize critical thinking to make sense of problems and persevere in solving them. CRP11. Use technology to enhance productivity. CRP12. Work productively in teams while using cultural global competence.

 GATEWAY GROUP CURRICULUM UNIT PLAN Content Area:  Mathematics Unit Title: Fractions, Decimals, and Percents Timeframe: 20 Days Lesson Components UNIT SUMMARY A summary of what the unit will contain and the learning students will be engaged in. Students will write and apply proportions to solve problems.Students will write ratios as fractions, decimals, and percents.Students will solve real world problems involving percents. LEARNING TARGETS ESSENTIAL QUESTIONSHow can percents be used to compare two quantities?What operations can be used to make comparisons?How can we use proportions to solve problems?What is a unit rate? ENDURING UNDERSTANDINGS Writing differences, ratios, fractions, and percents.Writing and solving proportions to solve different types percent problems.Subtraction for difference statements.  Division for ratio statements. Multiplication to scale ratios.

 Technology Standards: (See Pacing Guide for Specific Integration) Career Ready Practices:(See Pacing Guide for Specific Integration) Standard 8.1 Educational Technology:  All students will use digital tools to access manage, evaluate, and synthesize information in order to solve problems individually and collaborate and to create and communicate knowledge.A. Technology Operations and Concepts: Students demonstrate a sound understanding of technology concepts, systems and operations.8.1.8.A.2  Create a document (e.g. newsletter, reports, personalized learning plan, business letters or flyers) using one or more digital applications to be critiqued by professionals for usability.B. Creativity and Innovation: Students demonstrate creative thinking, construct knowledge and develop innovative products and process using technology.8.1.8.B.1 Synthesize and publish information about a local or global issue or event (ex. telecollaborative project, blog, school web).D. Digital Citizenship: Students understand human, cultural, and societal issues related to technology and practice legal and ethical behavior.8.1.8.D.1 Understand and model appropriate online behaviors related to cyber safety, cyber bullying, cyber security, and cyber ethics including appropriate use of social media.8.1.8.D.2 Demonstrate the application of appropriate citations to digital content.8.1.8.D.3 Demonstrate an understanding of fair use and Creative Commons to intellectual property.8.1.8.D.4 Assess the credibility and accuracy of digital content.8.1.8.D.5 Understand appropriate uses for social media and the negative consequences of misuse.E: Research and Information Fluency: Students apply digital tools to gather, evaluate, and use information.8.1.8.E.1 Effectively use a variety of search tools and filters in professional public databases to find information to solve a real world problem. CRP2. Apply appropriate academic and technical skills. CRP4. Communicate clearly and effectively and with reason. CRP6. Demonstrate creativity and innovation. CRP7. Employ valid and reliable research strategies. CRP8. Utilize critical thinking to make sense of problems and persevere in solving them. CRP11. Use technology to enhance productivity. CRP12. Work productively in teams while using cultural global competence.

 GATEWAY GROUP CURRICULUM UNIT PLAN Content Area:  Mathematics Unit Title: Operations on Rational Numbers & Expressions Timeframe: 33 Days Lesson Components UNIT SUMMARY A summary of what the unit will contain and the learning students will be engaged in. Students will be able to develop a basic understanding of properties of numbers.Students will solve one-step and two-step equations and inequalities.Students will be able to graph equations/inequalities and to identify equations/inequalities by looking at graphs.Solve mathematical and real-world problems involving addition, subtraction, multiplication, and division of equations. LEARNING TARGETS ESSENTIAL QUESTIONSWhat are the properties of numbers?How do you solve a one-step equation or inequality?How do you graph an equation or inequality? ENDURING UNDERSTANDINGS The algebraic properties are Commutative, Associative, Distributive, and Inverse.By using inverses to simplify equations and inequalities.By using a number line and open and closed circles, graph the solutions to equations and inequalities

 Technology Standards: (See Pacing Guide for Specific Integration) Career Ready Practices:(See Pacing Guide for Specific Integration) Standard 8.1 Educational Technology:  All students will use digital tools to access manage, evaluate, and synthesize information in order to solve problems individually and collaborate and to create and communicate knowledge.A. Technology Operations and Concepts: Students demonstrate a sound understanding of technology concepts, systems and operations.8.1.8.A.2  Create a document (e.g. newsletter, reports, personalized learning plan, business letters or flyers) using one or more digital applications to be critiqued by professionals for usability.B. Creativity and Innovation: Students demonstrate creative thinking, construct knowledge and develop innovative products and process using technology.8.1.8.B.1 Synthesize and publish information about a local or global issue or event (ex. telecollaborative project, blog, school web).D. Digital Citizenship: Students understand human, cultural, and societal issues related to technology and practice legal and ethical behavior.8.1.8.D.1 Understand and model appropriate online behaviors related to cyber safety, cyber bullying, cyber security, and cyber ethics including appropriate use of social media.8.1.8.D.2 Demonstrate the application of appropriate citations to digital content.8.1.8.D.3 Demonstrate an understanding of fair use and Creative Commons to intellectual property.8.1.8.D.4 Assess the credibility and accuracy of digital content.8.1.8.D.5 Understand appropriate uses for social media and the negative consequences of misuse.E: Research and Information Fluency: Students apply digital tools to gather, evaluate, and use information.8.1.8.E.1 Effectively use a variety of search tools and filters in professional public databases to find information to solve a real world problem. CRP2. Apply appropriate academic and technical skills. CRP4. Communicate clearly and effectively and with reason. CRP6. Demonstrate creativity and innovation. CRP7. Employ valid and reliable research strategies. CRP8. Utilize critical thinking to make sense of problems and persevere in solving them. CRP11. Use technology to enhance productivity. CRP12. Work productively in teams while using cultural global competence.

GATEWAY GROUP CURRICULUM UNIT PLAN

Content Area:  Mathematics

Unit Title: Geometry

Timeframe: 51 Days

Lesson Components

UNIT SUMMARY

A summary of what the unit will contain and the learning students will be engaged in.

Students will identify special pairs of angles and lines. (supplementary, complementary, vertical, and adjacent)

Students will use angle measurements and line relationships to classify triangles and quadrilaterals.

Students will classify and identify corresponding parts of polygons.

Students will draw and construct two dimensional figures and slices from three dimensional figures.

Students will find the circumference of circles.

Students will experiment with transformations on a coordinate grid.

#### Solve real-life and mathematical problems using numerical and algebraic expressions and equations

LEARNING TARGETS

ESSENTIAL QUESTIONS

What are the special pairs of angles?

What are special pairs of lines?

How do you know if two polygons are congruent?

How do you find the circumference of a circle?

How do you graph a translation or reflection?

ENDURING UNDERSTANDINGS

They are supplementary, complementary, vertical, and adjacent angles.

Lines are intersecting, parallel, perpendicular, or skew.

By classifying triangles and quadrilaterals by their angle and side measurements.

By identifying relationships of the corresponding parts.

By using the diameter or radius measurement and pi.

By using algebraic rules on a coordinate grid.

 Technology Standards: (See Pacing Guide for Specific Integration) Career Ready Practices:(See Pacing Guide for Specific Integration) Standard 8.1 Educational Technology:  All students will use digital tools to access manage, evaluate, and synthesize information in order to solve problems individually and collaborate and to create and communicate knowledge.A. Technology Operations and Concepts: Students demonstrate a sound understanding of technology concepts, systems and operations.8.1.8.A.2  Create a document (e.g. newsletter, reports, personalized learning plan, business letters or flyers) using one or more digital applications to be critiqued by professionals for usability.B. Creativity and Innovation: Students demonstrate creative thinking, construct knowledge and develop innovative products and process using technology.8.1.8.B.1 Synthesize and publish information about a local or global issue or event (ex. telecollaborative project, blog, school web).D. Digital Citizenship: Students understand human, cultural, and societal issues related to technology and practice legal and ethical behavior.8.1.8.D.1 Understand and model appropriate online behaviors related to cyber safety, cyber bullying, cyber security, and cyber ethics including appropriate use of social media.8.1.8.D.2 Demonstrate the application of appropriate citations to digital content.8.1.8.D.3 Demonstrate an understanding of fair use and Creative Commons to intellectual property.8.1.8.D.4 Assess the credibility and accuracy of digital content.8.1.8.D.5 Understand appropriate uses for social media and the negative consequences of misuse.E: Research and Information Fluency: Students apply digital tools to gather, evaluate, and use information.8.1.8.E.1 Effectively use a variety of search tools and filters in professional public databases to find information to solve a real world problem. CRP2. Apply appropriate academic and technical skills. CRP4. Communicate clearly and effectively and with reason. CRP6. Demonstrate creativity and innovation. CRP7. Employ valid and reliable research strategies. CRP8. Utilize critical thinking to make sense of problems and persevere in solving them. CRP11. Use technology to enhance productivity. CRP12. Work productively in teams while using cultural global competence.

GATEWAY GROUP CURRICULUM UNIT PLAN

Content Area:  Mathematics

Unit Title: Geometry

Timeframe: 15 Days

Lesson Components

UNIT SUMMARY

A summary of what the unit will contain and the learning students will be engaged in.

Students will identify special pairs of angles and lines. (supplementary, complementary, vertical, and adjacent)

Students will use angle measurements and line relationships to classify triangles and quadrilaterals.

Students will classify and identify corresponding parts of polygons.

Students will draw and construct two dimensional figures and slices from three dimensional figures.

Students will find the circumference of circles.

Students will experiment with transformations on a coordinate grid.

#### Solve real-life and mathematical problems using numerical and algebraic expressions and equations

LEARNING TARGETS

ESSENTIAL QUESTIONS

What are the special pairs of angles?

What are special pairs of lines?

How do you know if two polygons are congruent?

How do you find the circumference of a circle?

How do you graph a translation or reflection?

ENDURING UNDERSTANDINGS

They are supplementary, complementary, vertical, and adjacent angles.

Lines are intersecting, parallel, perpendicular, or skew.

By classifying triangles and quadrilaterals by their angle and side measurements.

By identifying relationships of the corresponding parts.

By using the diameter or radius measurement and pi.

By using algebraic rules on a coordinate grid.