Units:

Unit 1:  Operations and Reasoning about Ratios

Unit 2:  Expressions and 3-D Geometry

Unit 3:  Equations, The Rational Number System and 2-D  Geometry

Unit 4:  Variability, Distributions, and Relationships between Quantities

Unit Title

Unit 1:  Operations and Reasoning about Ratios

Timeframe 

40 days

Unit Summary

In this unit students will explain why knowledge and skills acquired in the elementary grades lay the foundation for future academic and career success, apply appropriate academic and technical skills to working with whole numbers, fractions, decimals, and rates and ratios (CRP11).  Students will be able to compute quotients of fractions.  Students will be able to construct visual fraction models to represent quotients of fractions and use the relationship between multiplication and division to explain division of fractions.  They will solve real-world problems involving quotients of fractions and interpret the solutions in the context given (CRP2).  Student will fluently divide multi-digit numbers using the standard algorithms, as well as fluently add, subtract, multiply and divide multi-digit decimals. (9.2.8.B.3 )Students will collaborate at school to help ready them for future careers (CRP12).  This will enable them to act as a responsible and contributing citizen and employee (CRP1).  Students will use ratio and rate language to explain the relationship between two quantities, in addition to describing a unit rate.  Students will solve real world and mathematical problems using ratio and rate reasoning that include making tables of equivalent ratios, solving unit rate problems, finding percent of a quantity as a rate per 100.  Students will use ratio and rate reasoning to convert measurement units and to transform units appropriately when multiplying or dividing quantities (CRP4).  Students will find the greatest common factor of two whole numbers less than or equal to 100 and the least common multiple of two numbers less than or equal to 12.

Topic 1: Use positive and rational numbers.  

Topic 5: Understand and use ratio and rate.

Topic 6: Understand and use percent

Learning Targets

Essential Questions

Topic 1 - How do operations with integers relate to the same operations with rational numbers?  How can you determine the correct operation to use to solve problems?

Enduring Understandings

Students will understand:

• Apply and extend previous understandings of multiplication and division to divide fractions by fractions

• Compute fluently with multi-digit numbers and find common factors and multiples

• Understand ratio concepts and use ratio reasoning to solve problems

Know

By the end of this unit, students will know:

•  A ratio shows relative sizes or values of two quantities.

Do

By the end of this unit, students will be able to:

•  Divide a fraction by a fraction.
•  Represent division of fractions using visual models.
•  Interpret quotients of fractions in the context of the problem.
•  Compute quotients of fractions in order to solve word problems.
•  Write equations to solve word problems involving division of fraction by a fraction.
•  Use the relationship between multiplication and division to explain division of fractions.
•  Use the standard algorithm to divide multi-digit numbers with speed and accuracy.
•  Describe a ratio relationship between two quantities using ratio language.
•  A rate is a ratio comparing two different types of quantities.
•  Determine the unit rate given a ratio relationship
•  Describe a unit rate relationship between two quantities using rate language.
•  Use ratio and rate reasoning to create tables of equivalent ratios relating quantities with whole number measurements, find

   missing values in tables and plot pairs of values.

•  Compare ratios using tables of equivalent ratios.
•  Solve real world and mathematical problems involving unit rate (including unit price and constant speed).
•  Calculate a percent of a quantity and solve problems by finding the whole when given the part and the percent.
•  Convert measurement units using ratio reasoning.
•  Transform units appropriately when multiplying and dividing quantities.
•  Add and subtract multi-digit decimals with accuracy and efficiency.
•  Multiply and divide multi-digit decimals with accuracy and efficiency.
•  Create lists of factors for two whole numbers less than or equal to 100; find the largest factor common to both lists.
•  Create lists of multiples for two whole numbers less than or equal to 12; find the smallest multiple common to both lists.

Evidence of Learning

Formative

• Lesson Quiz
• Formative Assessment Strategies 
• 53 Ways to Check for Understanding
• Fluency Practice Activity
• Mid-Topic Assessment
• Topic Readiness Assessment

Summative/ Benchmark

• Topic Assessment
• Topic Performance Task
• MAP - Math Assessment

Alternative Assessments

• ExamView Test Generator

• STEM Project
• End of Year Assessment

Learning Activities

• Compute quotients of fractions.
• Construct visual fraction models to represent quotients of fractions and use the relationship between multiplication and division to explain division of fractions.
• Solve real-world problems involving quotients of fractions and interpret the solutions in the context given.
• Fluently divide multi-digit numbers using the standard algorithms.
• Explain the relationship of two quantities in given ratio using ratio language.
• Use rate language, in the context of the ratio relationship, to describe a unit rate.
• Create and complete tables of equivalent ratios to sole real world and mathematical problems using ratio and rate reasoning that include making tables of equivalent ratios, solving unit rate problems, finding percent of a quantity as a rate per 100.
• Use ratio and rate reasoning to convert measurement units and to transform units appropriately when multiplying or dividing quantities.
• Fluently add, subtract, multiply and divide multi-digit decimals.
• Find the greatest common factor of two whole numbers less than or equal to 100 and the least common multiple of two numbers less than or equal to 12.

Materials / Equipment / Resources

Core Instructional

Materials and Texts

enVisionmath 2.0 ( Hardcopy and electronic edition)

• Teacher Edition
• Student Edition
• Fluency Practice Activity
• Digital Resources

Google Classroom

Seesaw

Equipment

Chromebooks

Smartboards

Supplemental Resources

6.NS.A.1 Traffic Jam

6.RP.A.1 Games at Recess

6.RP.A.2 Price per pound and pounds per dollar

6.RP.A.3 Voting for Three, Variation 1

6.RP.A.3c Shirt Sale

6.NS.B.3 Reasoning about Multiplication and Division and Place Value, Part 1

6.NS.B.4 Factors and Common Factors

6.NS.B.4 Multiples and Common Multiples

Standards

Content Statement

Mathematical Practice Standards

• 6.NS.A.1. Interpret and compute quotients of fractions, and solve word problems involving division of fractions by fractions, e.g., by using visual fraction models and equations to represent the problem.

For example, create a story context for (2/3) ÷ (3/4) and use a visual fraction model to show the quotient; use the relationship between multiplication and division to explain that (2/3) ÷ (3/4) = 8/9 because 3/4 of 8/9 is 2/3. (In general, (a/b) ÷ (c/d) = ad/bc.) How much chocolate will each person get if 3 people share 1/2 lb of chocolate equally? How many 3/4-cup servings are in 2/3 of a cup of yogurt? How wide is a rectangular strip of land with length 3/4 mi and area 1/2 square mi?

MP.4   Model with mathematics.

• 6.NS.B.2. Fluently divide multi-digit numbers using the standard algorithm.

• 6.RP.A.1. Understand the concept of a ratio and use ratio language to describe a ratio relationship between two quantities.

For example, "The ratio of wings to beaks in the bird house at the zoo was 2:1, because for every 2 wings there was 1 beak." "For every vote candidate A received, candidate C received nearly three votes."

MP.2   Reason abstractly and quantitatively.

• 6.RP.A.2. Understand the concept of a unit rate a/b associated with a ratio a:b with b ≠ 0, and use rate language in the context of a ratio relationship.

For example, "This recipe has a ratio of 3 cups of flour to 4 cups of sugar, so there is 3/4 cup of flour for each cup of sugar." "We paid $75 for 15 hamburgers, which is a rate of $5 per hamburger."

MP.2   Reason abstractly and quantitatively.

• 6.RP.A.3. Use ratio and rate reasoning to solve real-world and mathematical problems, e.g., by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations. *(benchmarked)

6.RP.A.3a. Make tables of equivalent ratios relating quantities with whole number measurements, find missing values in the tables, and plot the pairs of values on the coordinate plane. Use tables to compare ratios.

6.RP.A.3b. Solve unit rate problems including those involving unit pricing and constant speed.

For example, if it took 7 hours to mow 4 lawns, then at that rate, how many lawns could be mowed in 35 hours? At what rate were lawns being mowed?

6.RP.A.3c. Find a percent of a quantity as a rate per 100 (e.g., 30% of a quantity means 30/100 times the quantity); solve problems involving finding the whole, given a part and the percent.

6.RP.A.3d. Use ratio reasoning to convert measurement units; manipulate and transform units appropriately when multiplying or dividing quantities.

MP.2   Reason abstractly and quantitatively.

MP.4   Model with mathematics.

MP.5   Use appropriate tools strategically

MP.6   Attend to precision.

MP.7   Look for and make use of structure.

MP.8   Look for and express regularity in repeated reasoning

• 6.NS.B.3. Fluently add, subtract, multiply, and divide multi-digit decimals using the standard algorithm for each operation.

• 6.NS.B.4. Find the greatest common factor of two whole numbers less than or equal to 100 and the least common multiple of two whole numbers less than or equal to 12.

MP.7   Look for and make use of structure.

21st Century Skills and Themes

Interdisciplinary Connections

Career Ready Practices

9.2 Career Awareness, Exploration, and

      Preparation 

ELA:

NJSLSA.R1. Read closely to determine what the text says explicitly and to make logical inferences and relevant connections from it; cite specific textual evidence when writing or speaking to support conclusions drawn from the text.

NJSLSA.R4. Interpret words and phrases as they are used in a text, including determining technical, connotative, and figurative meanings, and analyze how specific word choices shape meaning or tone.

NJSLSA.R5. Analyze the structure of texts, including how specific sentences, paragraphs, and larger portions of the text (e.g., a section, chapter, scene, or stanza) relate to each other and the whole.

NJSLSA.R7. Integrate and evaluate content presented in diverse media and formats, including visually and quantitatively, as well as in words.

NJSLSA.R8. Delineate and evaluate the argument and specific claims in a text, including the validity of the reasoning as well as the relevance and sufficiency of the evidence.

NJSLSA.R10. Read and comprehend complex literary and informational texts independently and proficiently with scaffolding as needed.

NJSLSA.W1. Write arguments to support claims in an analysis of substantive topics or texts, using valid reasoning and relevant and sufficient evidence.

NJSLSA.W2. Write informative/explanatory texts to examine and convey complex ideas and information clearly and accurately through the effective selection, organization, and analysis of content.

NJSLSA.SL1. Prepare for and participate effectively in a range of conversations and collaborations with diverse partners, building on others’ ideas and expressing their own clearly and persuasively.

NJSLSA.SL2. Integrate and evaluate information presented in diverse media and formats, including visually, quantitatively, and orally.

NJSLSA.SL4. Present information, findings, and supporting evidence such that listeners can follow the line of reasoning and the organization, development, and style are appropriate to task, purpose, and audience.

NJSLSA.SL5. Make strategic use of digital media and visual displays of data to express information and enhance understanding of presentations.

Science:

DELETE OUT THOSE NOT APPLICABLE TO THIS UNIT

• CRP1. Act as a responsible and contributing citizen and employee.
• CRP2. Apply appropriate academic and technical skills.
• CRP3. Attend to personal health and financial well-being.
• CRP4.Communicate clearly and effectively and with reason.
• CRP5.Consider the environmental, social and economic impacts of decisions.
• 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.
• CRP9.Model integrity, ethical leadership and effective management.
• CRP10. Plan education and career paths aligned to personal goals.
• CRP11. Use technology to enhance productivity.
• CRP12.Work productively in teams while using cultural global competence.

By the end of 8th grade,

• 9.2.8.B.1 Research careers within the 16 Career Clusters and determine attributes of career success.
• 9.2.8.B.2 Develop a Personalized Student Learning Plan with the assistance of an adult mentor that includes information about career areas of interest, goals and an educational plan.
• 9.2.8.B.3 Evaluate communication, collaboration, and leadership skills that can be developed through school, home, work, and extracurricular activities for use in a career.
• 9.2.8.B.4 Evaluate how traditional and nontraditional careers have evolved regionally, nationally, and globally.
• 9.2.8.B.5 Analyze labor market trends using state and federal labor market information and other resources available online.
• 9.2.8.B.6 Demonstrate understanding of the necessary preparation and legal requirements to enter the workforce.
• 9.2.8.B.7 Evaluate the impact of online activities and social media on employer decisions.

Technology Standards - 8.1

3 -5th Grade

A. Technology Operations and Concepts: Students demonstrate a sound understanding of technology concepts, systems and operations.

• Understand and use technology systems.

8.1.5.A.1 Select and use the appropriate digital tools and resources to accomplish a variety of tasks including solving problems.

• Select and use applications effectively and productively.

8.1.5.A.2. Format a document using a word processing application to enhance text and include graphics, symbols and/ or pictures.

8.1.5.A.3 Use a graphic organizer to organize information about problem or issue.

8.1.5.A.4 Graph data using a spreadsheet, analyze and produce a report that explains the analysis of the data.

8.1.5.A.5 Create and use a database to answer basic questions.

8.1.5.A.6 Export data from a database into a spreadsheet; analyze and produce a report that explains the analysis of the data.

B. Creativity and Innovation: Students demonstrate creative thinking, construct knowledge and develop innovative products and process using technology.

• Apply existing knowledge to generate new ideas, products, or processes.
• Create original works as a means of personal or group expression.

8.1.5.B.1 Collaborative to produce a digital story about a significant local event or issue based on first-person interviews.

C. Communication and Collaboration: Students use digital media and environments to communicate and work collaboratively, including at a distance, to support individual learning and contribute to the learning of others.

• Interact, collaborate, and publish with peers, experts, or others by employing a variety of digital environments and media.
• Communicate information and ideas to multiple audiences using a variety of media and formats.
• Develop cultural understanding and global awareness by engaging with learners of other cultures.
• Contribute to project teams to produce original works or solve problems.

8.1.5.C.1 Engage in online discussions with learners of other cultures to investigate a worldwide issue from multiple perspectives and sources, evaluate findings and present possible solutions, using digital tools and online resources for all steps.

D. Digital Citizenship: Students understand human, cultural, and societal issues related to technology and practice legal and ethical behavior.

• Advocate and practice safe, legal, and responsible use of information and technology.

8.1.5.D.1 Understand the need for and use of copyrights.

• Demonstrate personal responsibility for lifelong learning.

8.1.5.D.2 Analyze the resource citations in online materials for proper use.

8.1.5.D.3 Demonstrate an understanding of the need to practice cyber safety, cyber security, and cyber ethics when using technologies and social media.

• Exhibit leadership for digital citizenship.

8.1.5.D.4  Understand digital citizenship and demonstrate an understanding of the personal consequences of inappropriate use of technology and social media.

E: Research and Information Fluency: Students apply digital tools to gather, evaluate, and use information.

• Plan strategies to guide inquiry.
• Locate, organize, analyze, evaluate, synthesize, and ethically use information from a variety of sources and media.
• Evaluate and select information sources and digital tools based on the appropriateness for specific tasks.

8.1.5.E.1  Use digital tools to research and evaluate the accuracy of, relevance to, and appropriateness of using print and non-print electronic information sources to complete a variety of tasks.

F: Critical thinking, problem solving, and decision making: Students use critical thinking skills to plan and conduct research, manage projects, solve problems, and make informed decisions using appropriate digital tools and resources.

• Identify and define authentic problems and significant questions for investigation.
• Plan and manage activities to develop a solution or complete a project.
• Collect and analyze data to identify solutions and/or make informed decisions.
• Use multiple processes and diverse perspectives to explore alternative solutions.

8.1.5.F.1 Apply digital tools to collect, organize, and analyze data that support a scientific finding.

Modifications/Accommodations

(IEPs, ELLs, 504s, G/T & BASIC SKILLS)

Quick Check

Intervention Activity

Center Games

Math and Science Activity

Visual Learning

Math Tools

Math Games

Higher Order Thinking Questions

Leveled Homework and Practice

Listen and Look for Lesson Video

Virtual Nerd Videos

Adaptive Homework and Practice

Today’s Challenge

Math Diagnosis and Intervention System

ELL Toolkit

Unit Title

Unit 2:  Expressions and 3-D Geometry

Timeframe 

40 days

Unit Summary

In this unit students will explain why knowledge and skills acquired in the elementary grades lay the foundation for future academic and career success and apply appropriate academic and technical skills to working with algebraic and geometric concepts.  Students will use mathematical language to write and evaluate numerical and algebraic expressions involving whole number exponents (including evaluating formulas).

Students will apply properties of operations (factor, distribute, and combine like terms) to generate equivalent expressions and to identify when two expressions are equivalent.  Students will find the volume of a right rectangular prism with fractional edge lengths by packing it with unit cubes and show that the volume is the same as it would be if found by multiplying the edge lengths; apply volume formulas to right rectangular prisms with fractional edge lengths.  Students will represent three dimensional figures objects with nets made of rectangles and triangles, and use the nets to find the surface area of the figures in order to solve real world and mathematical problems. (CRP2) (CRP8). Students will utilize critical thinking to make sense of problems and persevere in solving them. Students will understand how geometric concepts apply to the 16 Career Clusters and can lead to career success (9.2.8.B.1) (CRP3).

Topic 3: Numeric and Algebraic Expressions.  

Topic 4: Represent and solve equations and inequalities.  

Topic 7: Solve area, surface area and volume problems.

Learning Targets

Essential Questions

Enduring Understandings

Students will understand:

• Apply and extend previous understandings of arithmetic to algebraic expressions

• Reason about and solve one-variable equations and inequalities

• Solve real-world and mathematical problems involving area, surface area, and volume

Know

By the end of this unit, students will know:

•  Properties of operations: distributive property, combining like terms

•  A variable can represent an unknown number or any number in a set of numbers.

Do

By the end of this unit, students will be able to:

•  Write numerical expressions (involving whole number exponents) from verbal descriptions.

•  Evaluate numerical expressions involving whole number exponents.

•  Write algebraic expressions from verbal descriptions.

•  Use mathematical terms (sum, term, product, factor, quotient, coefficient) to identify the parts of an expression.

•  Evaluate algebraic expressions and formulas, including those involving exponents.

•  Combine like terms to generate an equivalent expression.

•  Factor to generate an equivalent expression.

•  Multiply (apply the distributive property) to generate an equivalent expression.

•  Write expressions for solving real-world problems.

•  Pack a right rectangular prism with fractional edge lengths with unit fraction cubes.

•  Show that the volume found by packing is the same as would be found by multiplying the edge lengths of the prism.

•  Apply volume formulas,  V = l w h and V = b h, to right rectangular prisms with fractional edge lengths.

•  Represent three dimensional objects with nets made up of rectangles and triangles.

•  Find surface area of three-dimensional objects using nets.

•  Folve real world and mathematical problems involving surface area using nets.

Evidence of Learning

Formative

• Lesson Quiz
• Formative Assessment Strategies 
• 53 Ways to Check for Understanding
• Fluency Practice Activity
• Mid-Topic Assessment
• Topic Readiness Assessment

Summative/ Benchmark

• Topic Assessment
• Topic Performance Task
• MAP - Math Assessment

Alternative Assessments

• ExamView Test Generator

• STEM Project
• End of Year Assessment

Learning Activities

• Write and evaluate numerical expressions involving whole number exponents.
• Use mathematical language to identify parts of an expression.
• Write and evaluate algebraic expressions involving exponents (include evaluating formulas).
• Apply properties of operations (factor, distribute, and combine like terms) to generate equivalent expressions and to identify when two expressions are equivalent.
• Use variables to represent numbers and write expressions when solving real world or mathematical problems.
• Find the volume of a right rectangular prism with fractional edge lengths by packing it with unit cubes and show that the volume is the same as it would be if found by multiplying the edge lengths; apply volume formulas to right rectangular prisms with fractional edge lengths.
• Represent three dimensional figures objects with nets made of rectangles and triangles, and use the nets to find the surface area of the figures in order to solve real world and mathematical problems.

Materials / Equipment / Resources

Core Instructional

Materials and Texts

enVisionmath 2.0 ( Hardcopy and electronic edition)

• Teacher Edition
• Student Edition
• Fluency Practice Activity
• Digital Resources

Google Classroom

Seesaw

Equipment

Chromebooks

Smartboards

Supplemental Resources

6.EE.A.1 The Djinni's Offer

6.EE.A.2 Rectangle Perimeter 1

6.EE.A.4 Rectangle Perimeter 2

6.EE.A.4 Equivalent Expressions

6.G.A.2 Volumes with Fractional Edge Lengths

6.G.A.4 Nets for Pyramids and Prisms

Standards

Content Statement

Mathematical Practice Standards

• 6.EE.A.1. Write and evaluate numerical expressions involving whole-number exponents

MP.2   Reason abstractly and quantitatively.

MP.7   Look for and make use of structure.

• 6.EE.A.2. Write, read, and evaluate expressions in which letters stand for numbers

6.EE.A.2a. Write expressions that record operations with numbers and with letters standing for numbers. For example, express the calculation "Subtract y from 5" as 5 - y.

6.EE.A.2b. Identify parts of an expression using mathematical terms (sum, term, product, factor, quotient, coefficient); view one or more parts of an expression as a single entity. For example, describe the expression 2 (8 + 7) as a product of two factors; view (8 + 7) as both a single entity and a sum of two terms

6.EE.A.2c. Evaluate expressions at specific values of their variables. Include expressions that arise from formulas used in real-world problems. Perform arithmetic operations, including those involving whole-number exponents, in the conventional order when there are no parentheses to specify a particular order (Order of Operations). For example, use the formulas V = s3 and A = 6s2 to find the volume and surface area of a cube with sides of length s = ½

MP.2   Reason abstractly and quantitatively.

MP.7   Look for and make use of structure.

• 6.EE.A.3. Apply the properties of operations to generate equivalent expressions.

For example, apply the distributive property to the expression 3 (2 + x) to produce the equivalent expression 6 + 3x; apply the distributive property to the expression 24x + 18y to produce the equivalent expression 6 (4x + 3y); apply properties of operations to y + y + y to produce the equivalent expression 3y

• 6.EE.A.4. Identify when two expressions are equivalent (i.e., when the two expressions name the same number regardless of which value is substituted into them).

For example, the expressions y + y + y and 3y are equivalent because they name the same number regardless of which number y stands for

MP.2   Reason abstractly and quantitatively.

MP.7   Look for and make use of structure.

• 6.EE.B.6. Use variables to represent numbers and write expressions when solving a real-world or mathematical problem; understand that a variable can represent an unknown number, or, depending on the purpose at hand, any number in a specified set.

MP.2   Reason abstractly and quantitatively.

MP.6   Attend to precision.

MP.7   Look for and make use of structure.

• 6.G.A.2. Find the volume of a right rectangular prism with fractional edge lengths by packing it with unit cubes of the appropriate unit fraction edge lengths, and show that the volume is the same as would be found by multiplying the edge lengths of the prism. Apply the formulas V = l w h and V = B h to find volumes of right rectangular prisms with fractional edge lengths in the context of solving real-world and mathematical problems.

MP. 2   Reason abstractly and quantitatively.

• 6.G.A.4.  Represent three-dimensional figures using nets made up of rectangles and triangles, and use the nets to find the surface area of these figures. Apply these techniques in the context of solving real-world and mathematical problems.

MP.1   Make sense of problems and persevere in solving them.

MP.4   Model with mathematics.

MP.5   Use appropriate tools strategically

21st Century Skills and Themes

Interdisciplinary Connections

Career Ready Practices

9.2 Career Awareness, Exploration, and

      Preparation 

ELA:

NJSLSA.R1. Read closely to determine what the text says explicitly and to make logical inferences and relevant connections from it; cite specific textual evidence when writing or speaking to support conclusions drawn from the text.

NJSLSA.R4. Interpret words and phrases as they are used in a text, including determining technical, connotative, and figurative meanings, and analyze how specific word choices shape meaning or tone.

NJSLSA.R5. Analyze the structure of texts, including how specific sentences, paragraphs, and larger portions of the text (e.g., a section, chapter, scene, or stanza) relate to each other and the whole.

NJSLSA.R7. Integrate and evaluate content presented in diverse media and formats, including visually and quantitatively, as well as in words.

NJSLSA.R8. Delineate and evaluate the argument and specific claims in a text, including the validity of the reasoning as well as the relevance and sufficiency of the evidence.

NJSLSA.R10. Read and comprehend complex literary and informational texts independently and proficiently with scaffolding as needed.

NJSLSA.W1. Write arguments to support claims in an analysis of substantive topics or texts, using valid reasoning and relevant and sufficient evidence.

NJSLSA.W2. Write informative/explanatory texts to examine and convey complex ideas and information clearly and accurately through the effective selection, organization, and analysis of content.

NJSLSA.SL1. Prepare for and participate effectively in a range of conversations and collaborations with diverse partners, building on others’ ideas and expressing their own clearly and persuasively.

NJSLSA.SL2. Integrate and evaluate information presented in diverse media and formats, including visually, quantitatively, and orally.

NJSLSA.SL4. Present information, findings, and supporting evidence such that listeners can follow the line of reasoning and the organization, development, and style are appropriate to task, purpose, and audience.

NJSLSA.SL5. Make strategic use of digital media and visual displays of data to express information and enhance understanding of presentations.

Science:

DELETE OUT THOSE NOT APPLICABLE TO THIS UNIT

• CRP1. Act as a responsible and contributing citizen and employee.
• CRP2. Apply appropriate academic and technical skills.
• CRP3. Attend to personal health and financial well-being.
• CRP4.Communicate clearly and effectively and with reason.
• CRP5.Consider the environmental, social and economic impacts of decisions.
• 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.
• CRP9.Model integrity, ethical leadership and effective management.
• CRP10. Plan education and career paths aligned to personal goals.
• CRP11. Use technology to enhance productivity.
• CRP12.Work productively in teams while using cultural global competence.

By the end of 8th grade,

• 9.2.8.B.1 Research careers within the 16 Career Clusters and determine attributes of career success.
• 9.2.8.B.2 Develop a Personalized Student Learning Plan with the assistance of an adult mentor that includes information about career areas of interest, goals and an educational plan.
• 9.2.8.B.3 Evaluate communication, collaboration, and leadership skills that can be developed through school, home, work, and extracurricular activities for use in a career.
• 9.2.8.B.4 Evaluate how traditional and nontraditional careers have evolved regionally, nationally, and globally.
• 9.2.8.B.5 Analyze labor market trends using state and federal labor market information and other resources available online.
• 9.2.8.B.6 Demonstrate understanding of the necessary preparation and legal requirements to enter the workforce.
• 9.2.8.B.7 Evaluate the impact of online activities and social media on employer decisions.

Technology Standards - 8.1

3 -5th Grade

A. Technology Operations and Concepts: Students demonstrate a sound understanding of technology concepts, systems and operations.

• Understand and use technology systems.

8.1.5.A.1 Select and use the appropriate digital tools and resources to accomplish a variety of tasks including solving problems.

• Select and use applications effectively and productively.

8.1.5.A.2. Format a document using a word processing application to enhance text and include graphics, symbols and/ or pictures.

8.1.5.A.3 Use a graphic organizer to organize information about problem or issue.

8.1.5.A.4 Graph data using a spreadsheet, analyze and produce a report that explains the analysis of the data.

8.1.5.A.5 Create and use a database to answer basic questions.

8.1.5.A.6 Export data from a database into a spreadsheet; analyze and produce a report that explains the analysis of the data.

B. Creativity and Innovation: Students demonstrate creative thinking, construct knowledge and develop innovative products and process using technology.

• Apply existing knowledge to generate new ideas, products, or processes.
• Create original works as a means of personal or group expression.

8.1.5.B.1 Collaborative to produce a digital story about a significant local event or issue based on first-person interviews.

C. Communication and Collaboration: Students use digital media and environments to communicate and work collaboratively, including at a distance, to support individual learning and contribute to the learning of others.

• Interact, collaborate, and publish with peers, experts, or others by employing a variety of digital environments and media.
• Communicate information and ideas to multiple audiences using a variety of media and formats.
• Develop cultural understanding and global awareness by engaging with learners of other cultures.
• Contribute to project teams to produce original works or solve problems.

8.1.5.C.1 Engage in online discussions with learners of other cultures to investigate a worldwide issue from multiple perspectives and sources, evaluate findings and present possible solutions, using digital tools and online resources for all steps.

D. Digital Citizenship: Students understand human, cultural, and societal issues related to technology and practice legal and ethical behavior.

• Advocate and practice safe, legal, and responsible use of information and technology.

8.1.5.D.1 Understand the need for and use of copyrights.

• Demonstrate personal responsibility for lifelong learning.

8.1.5.D.2 Analyze the resource citations in online materials for proper use.

8.1.5.D.3 Demonstrate an understanding of the need to practice cyber safety, cyber security, and cyber ethics when using technologies and social media.

• Exhibit leadership for digital citizenship.

8.1.5.D.4  Understand digital citizenship and demonstrate an understanding of the personal consequences of inappropriate use of technology and social media.

E: Research and Information Fluency: Students apply digital tools to gather, evaluate, and use information.

• Plan strategies to guide inquiry.
• Locate, organize, analyze, evaluate, synthesize, and ethically use information from a variety of sources and media.
• Evaluate and select information sources and digital tools based on the appropriateness for specific tasks.

8.1.5.E.1  Use digital tools to research and evaluate the accuracy of, relevance to, and appropriateness of using print and non-print electronic information sources to complete a variety of tasks.

F: Critical thinking, problem solving, and decision making: Students use critical thinking skills to plan and conduct research, manage projects, solve problems, and make informed decisions using appropriate digital tools and resources.

• Identify and define authentic problems and significant questions for investigation.
• Plan and manage activities to develop a solution or complete a project.
• Collect and analyze data to identify solutions and/or make informed decisions.
• Use multiple processes and diverse perspectives to explore alternative solutions.

8.1.5.F.1 Apply digital tools to collect, organize, and analyze data that support a scientific finding.

Modifications/Accommodations

(IEPs, ELLs, 504s, G/T & BASIC SKILLS)

Quick Check

Intervention Activity

Center Games

Math and Science Activity

Visual Learning

Math Tools

Math Games

Higher Order Thinking Questions

Leveled Homework and Practice

Listen and Look for Lesson Video

Virtual Nerd Videos

Adaptive Homework and Practice

Today’s Challenge

Math Diagnosis and Intervention System

ELL Toolkit

Unit Title

Unit 3:  Equations, The Rational Number System

          and 2-D  Geometry

Timeframe 

40 days

Unit Summary

In this unit students will explain why knowledge and skills acquired in the elementary grades lay the foundation for future academic and career success and apply appropriate academic and technical skills to working with equations, the rational number system and 2-D geometry.

Students will use substitution to determine whether a given number makes an equation or inequality true (CRP3).  Students will solve real world problems by writing and solving equations of the form x + p = q and px = q (p, q, and x are non-negative rational numbers). (CRP8)  Use positive and negative numbers to represent quantities in real-world situations, explaining the meaning of zero in the context of the real-world situation. Locate rational numbers and their opposites on horizontal and vertical number line; explain their relation of the opposites to zero.  Plot pairs of positive and negative rational numbers in the coordinate plane; describe two ordered pairs that differ only by signs as reflections across one or both axes. Use statements of inequality to determine relative positions of two rational numbers on a number line; write and explain statements of order for rational numbers in real-world contexts.  Explain the meaning of absolute value of a rational number as distance from zero on the number line and as magnitude for a positive or negative quantity in a real-world situation.(CRP4) Write an inequality of the form x > c or x < c to represent a constraint or condition in a real world or mathematical problem and represent them on a number line.  Solve real world and mathematical problems by graphing points in all four quadrants of the coordinate plane. Use the absolute value of the differences of their coordinates to find distances between points with the same first coordinate or same second coordinate.  Find the area of right triangles, other triangles, special quadrilaterals and polygons by composing into rectangles or decomposing into triangles and other shapes to solve real world or mathematical problems.

Topic 2: Integers and rational numbers.  

Topic 4: Represent and solve equations and inequalities.

Topic 7: Solve area, surface area and volume problems.

Learning Targets

Essential Questions

Topic 2- What are integers and rational numbers?  How are points graphed on a coordinate plane?

Enduring Understandings

Students will understand:

• Reason about and solve one-variable equations and inequalities

• Apply and extend previous understandings of numbers to the system of rational numbers

• Solve real-world and mathematical problems involving area, surface area, and volume

Know

By the end of this unit, students will know:

•  Solving an equation or inequality is a process of answering the question: determine which values from a specified set, if any, make

   the equation or inequality true.

•  An equation is defined by two expressions that are equivalent to one another.

•  Positive and negative numbers, used together, describe quantities having opposite directions or opposite values.

•  Opposite signs of numbers indicate locations on opposite sides of 0 on the number line.

•  The opposite of the opposite of a number is the number itself (e.g. the opposite of three is -3. The opposite of the opposite of

   three, -(-3), is equal to the original number, 3).

•  Signs of numbers in ordered pairs indicate their locations in quadrants of the coordinate plane.

•  When two ordered pairs differ only by signs, the locations of the points are related by reflections across one or both axes.

•  The absolute value of a rational number is its distance from 0 on the number line.

•  An inequality may represent a constraint (or a condition) in a real-world problem.

•  Infinity (x > c and x < c have an infinite number of solutions).

Do

By the end of this unit, students will be able to:

•  Substitute a number into an equation to determine whether it makes an equation true.

•  Substitute a number into an inequality to determine whether it makes the inequality true.

•  Solve real world problems by writing and solving equations of the form x + p = q (p, q, and x are non-negative and rational).

•  Solve real world problems by writing and solving equations of the form px = q  (p, q, and x are non-negative and rational).

•  Represent quantities with positive and negative numbers in real-world contexts.

•  Interpret positive and negative numbers in real-world contexts.

•  Explain the meaning of zero, in context, in each real-world situation.

•  Position rational numbers on horizontal and vertical number lines.

•  Position pairs of rational numbers on a coordinate plane.

•  Explain the conditions for which pairs of points are reflections across an axes in the coordinate plane.

•  Locate numbers and their opposites on the number line and explain their relation to 0.

•  Given an inequality, determine the position of one rational number relative to another.

•  Write a inequality and explain statements of order for rational numbers in real world situations.

•  Represent real-world constraint or condition by writing an inequality of the form x > c or x < c.

•  Graph inequalities of the form x > c or x < c on number lines.raph points in all four quadrants of the coordinate plane in order to

   solve real-world and mathematical problems.

•  Draw polygons in the coordinate plane.

•  Use absolute value to find distances between points with the same first coordinate or the same second coordinate.

•  Use coordinates to solve real-world distance, perimeter, and area problems.

•  Compose rectangles in order to find the area of triangles, special quadrilaterals and polygons.

•  Decompose triangles, special quadrilaterals, and polygons into triangles and other shapes in order to find their area.

•  Dompose rectangles and decompose into triangles in order to solve real-world problems.

Evidence of Learning

Formative

• Lesson Quiz
• Formative Assessment Strategies 
• 53 Ways to Check for Understanding
• Fluency Practice Activity
• Mid-Topic Assessment
• Topic Readiness Assessment

Summative/ Benchmark

• Topic Assessment
• Topic Performance Task
• MAP - Math Assessment

Alternative Assessments

• ExamView Test Generator

• STEM Project
• End of Year Assessment

Learning Activities

• Use substitution to determine whether a given number makes an equation or inequality true.

• Solve real world problems by writing and solving equations of the form x + p = q and px = q (p, q, and x are non-negative rational numbers).
• Use positive and negative numbers to represent quantities in real-world situations, explaining the meaning of zero in the context of the real-world situation.
• Locate rational numbers and their opposites on horizontal and vertical number line; explain their relation of the opposites to zero.
• Plot pairs of positive and negative rational numbers in the coordinate plane; describe two ordered pairs that differ only by signs as reflections across one or both axes.
• Use statements of inequality to determine relative positions of two rational numbers on a number line; write and explain statements of order for rational numbers in real-world contexts.
• Explain the meaning of absolute value of a rational number as distance from zero on the number line and as magnitude for a positive or negative quantity in a real-world situation.
• Write an inequality of the form x > c or x < c to represent a constraint or condition in a real world or mathematical problem and represent them on a number line.
• Solve real world and mathematical problems by graphing points in all four quadrants of the coordinate plane. Use the absolute value of the differences of their coordinates to find distances between points with the same first coordinate or same second coordinate.
• Find the area of right triangles, other triangles, special quadrilaterals and polygons by composing into rectangles or decomposing into triangles and other shapes to solve real world or mathematical problems.

Materials / Equipment / Resources

Core Instructional

Materials and Texts

enVisionmath 2.0 ( Hardcopy and electronic edition)

• Teacher Edition
• Student Edition
• Fluency Practice Activity
• Digital Resources

Google Classroom

Seesaw

Equipment

Chromebooks

Smartboards

Supplemental Resources

6.EE.B.5 Make Use of Structure

6.EE.B.7 Morning Walk

6.NS.C.5 Warmer in Miami

6.NS.C.6 Mile High

6.NS.C.7 Jumping Flea

6.NS.C.7a Fractions on the Number Line

6.NS.C.7b Comparing Temperatures

6.EE.B.8 Fishing Adventures 1

6.NS.C.8 Nome, Alaska

6.G.A.1, 6.G.A.3 Polygons in the Coordinate Plane

Standards

Content Statement

Mathematical Practice Standards

• 6.EE.B.5. Understand solving an equation or inequality as a process of answering a question: which values from a specified set, if any, make the equation or inequality true? Use substitution to determine whether a given number in a specified set makes an equation or inequality true.

MP.5   Use appropriate tools strategically.

MP.6   Attend to precision.

• 6.EE.B.7. Solve real-world and mathematical problems by writing and solving equations of the form x + p = q and px = q for cases in which p, q and x are all nonnegative rational numbers.

MP.1   Make sense of problems and persevere in solving them.

MP.2   Reason abstractly and quantitatively.

MP.6   Attend to precision.

MP.7   Look for and make use of structure.

• 6.NS.C.5. Understand that positive and negative numbers are used together to describe quantities having opposite directions or values (e.g., temperature above/below zero, elevation above/below sea level, credits/debits, positive/negative electric charge); use positive and negative numbers to represent quantities in real-world contexts, explaining the meaning of 0 in each situation.

MP.2   Reason abstractly and quantitatively.

MP.5   Use appropriate tools strategically

• 6.NS.C.6. Understand a rational number as a point on the number line. Extend number line diagrams and coordinate axes familiar from previous grades to represent points on the line and in the plane with negative number coordinates.

6.NS.C.6a. Recognize opposite signs of numbers as indicating locations on opposite sides of 0 on the number line; recognize that the opposite of the opposite of a number is the number itself, e.g., –(–3) = 3, and that 0 is its own opposite.

6.NS.C.6b. Understand signs of numbers in ordered pairs as indicating locations in quadrants of the coordinate plane; recognize that when two ordered pairs differ only by signs, the locations of the points are related by reflections across one or both axes.

6.NS.C.6c. Find and position integers and other rational numbers on a horizontal or vertical number line diagram; find and position pairs of integers and other rational numbers on a coordinate plane.

 MP.5   Use appropriate tools strategically.

 MP.8   Look for and express regularity in repeated reasoning.

• 6.NS.C.7. Understand ordering and absolute value of rational numbers.

6.NS.C.7a.  Interpret statements of inequality as statements about the relative position of two numbers on a number line diagram. For example, interpret –3 > –7 as a statement that –3 is located to the right of –7 on a number line oriented from left to right.

6.NS.C.7b. Write, interpret, and explain statements of order for rational numbers in real-world contexts. For example, write –3 oC > –7 oC to express the fact that –3 oC is warmer than –7 oC.

6.NS.C.7c. Understand the absolute value of a rational number as its distance from 0 on the number line; interpret absolute value as magnitude for a positive or negative quantity in a real-world situation. For example, for an account balance of –30 dollars, write |–30| = 30 to describe the size of the debt in dollars.

6.NS.C.7d. Distinguish comparisons of absolute value from statements about order. For example, recognize that an account balance less than –30 dollars represents a debt greater than 30 dollars.

MP.2   Reason abstractly and quantitatively.

MP.3   Construct viable arguments and critique the reasoning of others.

MP.5   Use appropriate tools strategically

• 6.EE.B.8. Write an inequality of the form x > c or x < c to represent a constraint or condition in a real-world or mathematical problem. Recognize that inequalities of the form x > c or x < c have infinitely many solutions; represent solutions of such inequalities on number line diagrams

MP.2   Reason abstractly and quantitatively.

MP.6   Attend to precision.

MP.7   Look for and make use of structure.

• 6.NS.C.8. Solve real-world and mathematical problems by graphing points in all four quadrants of the coordinate plane. Include use of coordinates and absolute value to find distances between points with the same first coordinate or the same second coordinate.

     *(benchmarked)

• 6.G.A.3. Draw polygons in the coordinate plane given coordinates for the vertices; use coordinates to find the length of a side joining points with the same first coordinate or the same second coordinate. Apply these techniques in the context of solving real-world and mathematical problems.

MP.1   Make sense of problems and persevere in solving them.

MP.2   Reason abstractly and quantitatively.

MP.4   Model with mathematics.

MP.5   Use appropriate tools strategically.

• 6.G.A.1. Find the area of right triangles, other triangles, special quadrilaterals, and polygons by composing into rectangles or decomposing into triangles and other shapes; apply these techniques in the context of solving real-world and mathematical problems.

MP.1   Make sense of problems and persevere in solving them.

MP.2   Reason abstractly and quantitatively.

MP.5   Use appropriate tools strategically.

MP.7   Look for and make use of structure.

21st Century Skills and Themes

Interdisciplinary Connections

Career Ready Practices

9.2 Career Awareness, Exploration, and

      Preparation  

ELA:

NJSLSA.R1. Read closely to determine what the text says explicitly and to make logical inferences and relevant connections from it; cite specific textual evidence when writing or speaking to support conclusions drawn from the text.

NJSLSA.R4. Interpret words and phrases as they are used in a text, including determining technical, connotative, and figurative meanings, and analyze how specific word choices shape meaning or tone.

NJSLSA.R5. Analyze the structure of texts, including how specific sentences, paragraphs, and larger portions of the text (e.g., a section, chapter, scene, or stanza) relate to each other and the whole.

NJSLSA.R7. Integrate and evaluate content presented in diverse media and formats, including visually and quantitatively, as well as in words.

NJSLSA.R8. Delineate and evaluate the argument and specific claims in a text, including the validity of the reasoning as well as the relevance and sufficiency of the evidence.

NJSLSA.R10. Read and comprehend complex literary and informational texts independently and proficiently with scaffolding as needed.

NJSLSA.W1. Write arguments to support claims in an analysis of substantive topics or texts, using valid reasoning and relevant and sufficient evidence.

NJSLSA.W2. Write informative/explanatory texts to examine and convey complex ideas and information clearly and accurately through the effective selection, organization, and analysis of content.

NJSLSA.SL1. Prepare for and participate effectively in a range of conversations and collaborations with diverse partners, building on others’ ideas and expressing their own clearly and persuasively.

NJSLSA.SL2. Integrate and evaluate information presented in diverse media and formats, including visually, quantitatively, and orally.

NJSLSA.SL4. Present information, findings, and supporting evidence such that listeners can follow the line of reasoning and the organization, development, and style are appropriate to task, purpose, and audience.

NJSLSA.SL5. Make strategic use of digital media and visual displays of data to express information and enhance understanding of presentations.

Science:

DELETE OUT THOSE NOT APPLICABLE TO THIS UNIT

• CRP1. Act as a responsible and contributing citizen and employee.
• CRP2. Apply appropriate academic and technical skills.
• CRP3. Attend to personal health and financial well-being.
• CRP4.Communicate clearly and effectively and with reason.
• CRP5.Consider the environmental, social and economic impacts of decisions.
• 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.
• CRP9.Model integrity, ethical leadership and effective management.
• CRP10. Plan education and career paths aligned to personal goals.
• CRP11. Use technology to enhance productivity.
• CRP12.Work productively in teams while using cultural global competence.

By the end of 8th grade,

• 9.2.8.B.1 Research careers within the 16 Career Clusters and determine attributes of career success.
• 9.2.8.B.2 Develop a Personalized Student Learning Plan with the assistance of an adult mentor that includes information about career areas of interest, goals and an educational plan.
• 9.2.8.B.3 Evaluate communication, collaboration, and leadership skills that can be developed through school, home, work, and extracurricular activities for use in a career.
• 9.2.8.B.4 Evaluate how traditional and nontraditional careers have evolved regionally, nationally, and globally.
• 9.2.8.B.5 Analyze labor market trends using state and federal labor market information and other resources available online.
• 9.2.8.B.6 Demonstrate understanding of the necessary preparation and legal requirements to enter the workforce.
• 9.2.8.B.7 Evaluate the impact of online activities and social media on employer decisions.

Technology Standards - 8.1

3 -5th Grade

A. Technology Operations and Concepts: Students demonstrate a sound understanding of technology concepts, systems and operations.

• Understand and use technology systems.

8.1.5.A.1 Select and use the appropriate digital tools and resources to accomplish a variety of tasks including solving problems.

• Select and use applications effectively and productively.

8.1.5.A.2. Format a document using a word processing application to enhance text and include graphics, symbols and/ or pictures.

8.1.5.A.3 Use a graphic organizer to organize information about problem or issue.

8.1.5.A.4 Graph data using a spreadsheet, analyze and produce a report that explains the analysis of the data.

8.1.5.A.5 Create and use a database to answer basic questions.

8.1.5.A.6 Export data from a database into a spreadsheet; analyze and produce a report that explains the analysis of the data.

B. Creativity and Innovation: Students demonstrate creative thinking, construct knowledge and develop innovative products and process using technology.

• Apply existing knowledge to generate new ideas, products, or processes.
• Create original works as a means of personal or group expression.

8.1.5.B.1 Collaborative to produce a digital story about a significant local event or issue based on first-person interviews.

C. Communication and Collaboration: Students use digital media and environments to communicate and work collaboratively, including at a distance, to support individual learning and contribute to the learning of others.

• Interact, collaborate, and publish with peers, experts, or others by employing a variety of digital environments and media.
• Communicate information and ideas to multiple audiences using a variety of media and formats.
• Develop cultural understanding and global awareness by engaging with learners of other cultures.
• Contribute to project teams to produce original works or solve problems.

8.1.5.C.1 Engage in online discussions with learners of other cultures to investigate a worldwide issue from multiple perspectives and sources, evaluate findings and present possible solutions, using digital tools and online resources for all steps.

D. Digital Citizenship: Students understand human, cultural, and societal issues related to technology and practice legal and ethical behavior.

• Advocate and practice safe, legal, and responsible use of information and technology.

8.1.5.D.1 Understand the need for and use of copyrights.

• Demonstrate personal responsibility for lifelong learning.

8.1.5.D.2 Analyze the resource citations in online materials for proper use.

8.1.5.D.3 Demonstrate an understanding of the need to practice cyber safety, cyber security, and cyber ethics when using technologies and social media.

• Exhibit leadership for digital citizenship.

8.1.5.D.4  Understand digital citizenship and demonstrate an understanding of the personal consequences of inappropriate use of technology and social media.

E: Research and Information Fluency: Students apply digital tools to gather, evaluate, and use information.

• Plan strategies to guide inquiry.
• Locate, organize, analyze, evaluate, synthesize, and ethically use information from a variety of sources and media.
• Evaluate and select information sources and digital tools based on the appropriateness for specific tasks.

8.1.5.E.1  Use digital tools to research and evaluate the accuracy of, relevance to, and appropriateness of using print and non-print electronic information sources to complete a variety of tasks.

F: Critical thinking, problem solving, and decision making: Students use critical thinking skills to plan and conduct research, manage projects, solve problems, and make informed decisions using appropriate digital tools and resources.

• Identify and define authentic problems and significant questions for investigation.
• Plan and manage activities to develop a solution or complete a project.
• Collect and analyze data to identify solutions and/or make informed decisions.
• Use multiple processes and diverse perspectives to explore alternative solutions.

8.1.5.F.1 Apply digital tools to collect, organize, and analyze data that support a scientific finding.

Modifications/Accommodations

(IEPs, ELLs, 504s, G/T & BASIC SKILLS)

Quick Check

Intervention Activity

Center Games

Math and Science Activity

Visual Learning

Math Tools

Math Games

Higher Order Thinking Questions

Leveled Homework and Practice

Listen and Look for Lesson Video

Virtual Nerd Videos

Adaptive Homework and Practice

Today’s Challenge

Math Diagnosis and Intervention System

ELL Toolkit

Unit Title

Unit 4:  Variability, Distributions, and Relationships

          between Quantities

Timeframe 

40 days 

Unit Summary

In this unit, students will explain why knowledge and skills acquired in the elementary grades lay the foundation for future academic and career success and apply appropriate academic and technical skills to working with statistical variability, rates, and ratios.  Students will write an equation using two variables to represent two quantities that change in relationship to in another in a real world problem(CRP8).  Students will analyze the relationship between the dependent and independent variables and relate the equation to a given graph and to its table of values.  They will distinguish questions that are statistical from those that are not.  Students will display numerical data in plots on the number line and summarize in relation to their context.  Students will summarize numerical data in relation to their context by identifying the number of observations and describing how the data was measured.  They will calculate, and interpret measures of center and variability; report measures of center and variability appropriate to the shape of the distribution and context.  Students will create and complete tables of equivalent ratios to solve real world and mathematical problems using ratio and rate reasoning that include making tables of equivalent ratios, solving unit rate problems, finding percent of a quantity as a rate per 100(CRP5).  They will use ratio and rate reasoning to convert measurement units and to transform units appropriately when multiplying or dividing quantities.  Students will solve real world and mathematical problems by graphing points in all four quadrants of the coordinate plane(CRP2); use the absolute value of the differences of their coordinates to find distances between points with the same first coordinate or same second coordinates.

Topic 2: Integers and rational numbers.

Topic 5: Understand and use ratio and rate.

Topic 6: Understand and use percent.

Topic 8: Develop and understand statistics and probability.

Learning Targets

Essential Questions

Topic 2- What are integers and rational numbers?  How are points graphed on a coordinate plane?

Enduring Understandings

Students will understand:

• Represent and analyze quantitative relationships between dependent and independent variables

• Develop understanding of statistical variability

• Summarize and describe distributions

• Understand ratio concepts and use ratio reasoning to solve problems

• Apply and extend previous understandings of numbers to the system of rational numbers

Know

By the end of this unit, students will know:

•  Two quantities that change in relationship to one another may be represented with an equation in two variables, with a graph, an

   with a table of values.

•  Variability/Variation

•  A statistical question is one that anticipates variability in the data that is related to the question.

•  A data set has a distribution which can be described by its center, spread, and overall shape.

•  A measure of center summarizes, with a single number, the values of an entire data set.

•  A measure of variation describes, with a single number, how the values of a data set vary.

Do

By the end of this unit, students will be able to:

•  Represent two quantities that related to one another, with variables.

•  Write an equation in two variables.

•  Distinguish the dependent variable from the independent variable.

•  Analyze a given graph and table of values, and relate them to the equation.

•  Distinguish questions that are statistical (anticipate variability in data) from those that are not.

•  Distinguish center from variation.

•  Display numerical data in dot plots on a number line.

•  Display numerical data in histograms on a number line.

•  Display numerical data in box plots on a number line.

•  Determine the number of observations of a data set.

•  Describe the data in context, including how it was measured and the units of measurement.

•  Calculate measures of center, mean and median.

•  Calculate measures of spread, interquartile range and mean absolute deviation.

•  Describe the overall shape of a distribution (skewed left, skewed right, etc).

•  Identify striking deviations (outliers).

•  Choose measures of center and variability appropriate to the shape of the distribution and context.

•  Use ratio and rate reasoning to create tables of equivalent ratios relating quantities with whole number measurements, find

   missing values in tables and plot pairs of values.

•  Compare ratios using tables of equivalent ratios.

•  Solve real world and mathematical problems involving unit rate (including unit price and constant speed).

•  Calculate a percent of a quantity and solve problems by finding the whole when given the part and the percent.

•  Convert measurement units using ratio reasoning.

•  Transform units appropriately when multiplying and dividing quantities.

•  Graph points in all four quadrants of the coordinate plane in order to solve real-world and mathematical problems.

•  Draw polygons in the coordinate plane.

•  Use absolute value to find distances between points with the same first coordinate or the same second coordinate.

•  Use coordinates to solve real-world distance, perimeter, and area problems.

Evidence of Learning

Formative

• Lesson Quiz
• Formative Assessment Strategies 
• 53 Ways to Check for Understanding
• Fluency Practice Activity
• Mid-Topic Assessment
• Topic Readiness Assessment

Summative/ Benchmark

• Topic Assessment
• Topic Performance Task
• MAP - Math Assessment

Alternative Assessments

• ExamView Test Generator

• STEM Project
• End of Year Assessment

Learning Activities

• Write an equation using two variables (independent and dependent) to represent two quantities that change in relationship to one another in a real world problem.
• Analyze the relationship between the dependent and independent variables and relate the equation to a given graph and to its table of values.
• Distinguish questions that are statistical (anticipate variability in data) from those that are not.
• Display numerical data in plots on the number line (including dot plots, histograms, and box plots) and summarize in relation to their context.
• Summarize numerical data in relation to their context by identifying the number of observations and describing how the data was measured.
• Calculate, and interpret measures of center (mean and median) and variability (interquartile range and mean absolute deviation); report measures of center and variability appropriate to the shape of the distribution and context.
• Create and complete tables of equivalent ratios to sole real world and mathematical problems using ratio and rate reasoning that include making tables of equivalent ratios, solving unit rate problems, finding percent of a quantity as a rate per 100.
• Use ratio and rate reasoning to convert measurement units and to transform units appropriately when multiplying or dividing quantities.
• Solve real world and mathematical problems by graphing points in all four quadrants of the coordinate plane; use the absolute value of the differences of their coordinates to find distances between points with the same first coordinate or same second coordinate.

Materials / Equipment / Resources

Core Instructional

Materials and Texts

enVisionmath 2.0 ( Hardcopy and electronic edition)

• Teacher Edition
• Student Edition
• Fluency Practice Activity
• Digital Resources

Google Classroom

Seesaw

Equipment

Chromebooks

Smartboards

Supplemental Resources

6.EE.C.9 Families of Triangles

6.SP.A.1 Identifying Statistical Questions

6.SP.A.2, 6.SP.B.4 Puppy Weights

6.SP.A.3 Is It Center or Is It Variability?

6.SP.B.5c Number of Siblings

6.SP.B.5d Mean or Median?

Standards

Content Statement

Mathematical Practice Standards

• 6.EE.C.9. Use variables to represent two quantities in a real-world problem that change in relationship to one another; write an equation to express one quantity, thought of as the dependent variable, in terms of the other quantity, thought of as the independent variable. Analyze the relationship between the dependent and independent variables using graphs and tables, and relate these to the equation.

For example, in a problem involving motion at constant speed, list and graph ordered pairs of distances and times, and write the equation d = 65t to represent the relationship between distance and time.

MP.2   Reason abstractly and quantitatively.

MP.4   Model with mathematics.

MP.6   Attend to precision.

• 6.SP.A.1. Recognize a statistical question as one that anticipates variability in the data related to the question and accounts for it in the answers.

For example, “How old am I?” is not a statistical question, but “How old are the students in my school?” is a statistical question because one anticipates variability in students’ ages.

MP.2   Reason abstractly and quantitatively.

MP.6   Attend to precision

• 6.SP.A.2. Understand that a set of data collected to answer a statistical question has a distribution which can be described by its center, spread, and overall shape.

• 6.SP.A.3. Recognize that a measure of center for a numerical data set summarizes all of its values with a single number, while a measure of variation describes how its values vary with a single number.

• 6.SP.B.4. Display numerical data in plots on a number line, including dot plots, histograms, and box plots.

MP.4   Model with mathematics.

• 6.SP.B.5. Summarize numerical data sets in relation to their context, such as by:

6.SP.B.5a. Reporting the number of observations.

6.SP.B.5b. Describing the nature of the attribute under investigation, including how it was measured and its units of measurement.

6.SP.B.5c. Giving quantitative measures of center (median and/or mean) and variability (interquartile range and/or mean absolute deviation), as well as describing any overall pattern and any striking deviations from the overall pattern with reference to the context in which the data were gathered.

6.SP.B.5d. Relating the choice of measures of center and variability to the shape of the data distribution and the context in which the data were gathered.

MP.2   Reason abstractly and quantitatively.

MP.4   Model with mathematics.

MP.5   Use appropriate tools strategically.

• 6.RP.A.3. Use ratio and rate reasoning to solve real-world and mathematical problems, e.g., by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations.

     *(benchmarked)

6.RP.A.3a. Make tables of equivalent ratios relating quantities with whole number measurements, find missing values in the tables, and plot the pairs of values on the coordinate plane. Use tables to compare ratios.

6.RP.A.3b. Solve unit rate problems including those involving unit pricing and constant speed. For example, if it took 7 hours to mow 4 lawns, then at that rate, how many lawns could be mowed in 35 hours? At what rate were lawns being mowed?

6.RP.A.3c. Find a percent of a quantity as a rate per 100 (e.g., 30% of a quantity means 30/100 times the quantity); solve problems involving finding the whole, given a part and the percent.

6.RP.A.3d. Use ratio reasoning to convert measurement units; manipulate and transform units appropriately when multiplying or dividing quantities.

MP.2   Reason abstractly and quantitatively.

MP.4   Model with mathematics.

MP.5   Use appropriate tools strategically

MP.6   Attend to precision.

MP.7   Look for and make use of structure.

MP.8   Look for and express regularity in repeated

           reasoning

• 6.NS.C.8. Solve real-world and mathematical problems by graphing points in all four quadrants of the coordinate plane. Include use of coordinates and absolute value to find distances between points with the same first coordinate or the same second coordinate.

MP.1   Make sense of problems and persevere in  

          solving them.

MP.2   Reason abstractly and quantitatively.

MP.5   Use appropriate tools strategically.

21st Century Skills and Themes

Interdisciplinary Connections

Career Ready Practices

9.2 Career Awareness, Exploration, and

       Preparation  

ELA:

NJSLSA.R1. Read closely to determine what the text says explicitly and to make logical inferences and relevant connections from it; cite specific textual evidence when writing or speaking to support conclusions drawn from the text.

NJSLSA.R4. Interpret words and phrases as they are used in a text, including determining technical, connotative, and figurative meanings, and analyze how specific word choices shape meaning or tone.

NJSLSA.R5. Analyze the structure of texts, including how specific sentences, paragraphs, and larger portions of the text (e.g., a section, chapter, scene, or stanza) relate to each other and the whole.

NJSLSA.R7. Integrate and evaluate content presented in diverse media and formats, including visually and quantitatively, as well as in words.

NJSLSA.R8. Delineate and evaluate the argument and specific claims in a text, including the validity of the reasoning as well as the relevance and sufficiency of the evidence.

NJSLSA.R10. Read and comprehend complex literary and informational texts independently and proficiently with scaffolding as needed.

NJSLSA.W1. Write arguments to support claims in an analysis of substantive topics or texts, using valid reasoning and relevant and sufficient evidence.

NJSLSA.W2. Write informative/explanatory texts to examine and convey complex ideas and information clearly and accurately through the effective selection, organization, and analysis of content.

NJSLSA.SL1. Prepare for and participate effectively in a range of conversations and collaborations with diverse partners, building on others’ ideas and expressing their own clearly and persuasively.

NJSLSA.SL2. Integrate and evaluate information presented in diverse media and formats, including visually, quantitatively, and orally.

NJSLSA.SL4. Present information, findings, and supporting evidence such that listeners can follow the line of reasoning and the organization, development, and style are appropriate to task, purpose, and audience.

NJSLSA.SL5. Make strategic use of digital media and visual displays of data to express information and enhance understanding of presentations.

Science:

DELETE OUT THOSE NOT APPLICABLE TO THIS UNIT

• CRP1. Act as a responsible and contributing citizen and employee.
• CRP2. Apply appropriate academic and technical skills.
• CRP3. Attend to personal health and financial well-being.
• CRP4.Communicate clearly and effectively and with reason.
• CRP5.Consider the environmental, social and economic impacts of decisions.
• 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.
• CRP9.Model integrity, ethical leadership and effective management.
• CRP10. Plan education and career paths aligned to personal goals.
• CRP11. Use technology to enhance productivity.
• CRP12.Work productively in teams while using cultural global competence.

By the end of 8th grade,

• 9.2.8.B.1 Research careers within the 16 Career Clusters and determine attributes of career success.
• 9.2.8.B.2 Develop a Personalized Student Learning Plan with the assistance of an adult mentor that includes information about career areas of interest, goals and an educational plan.
• 9.2.8.B.3 Evaluate communication, collaboration, and leadership skills that can be developed through school, home, work, and extracurricular activities for use in a career.
• 9.2.8.B.4 Evaluate how traditional and nontraditional careers have evolved regionally, nationally, and globally.
• 9.2.8.B.5 Analyze labor market trends using state and federal labor market information and other resources available online.
• 9.2.8.B.6 Demonstrate understanding of the necessary preparation and legal requirements to enter the workforce.
• 9.2.8.B.7 Evaluate the impact of online activities and social media on employer decisions.

Technology Standards - 8.1

3 -5th Grade

A. Technology Operations and Concepts: Students demonstrate a sound understanding of technology concepts, systems and operations.

• Understand and use technology systems.

8.1.5.A.1 Select and use the appropriate digital tools and resources to accomplish a variety of tasks including solving problems.

• Select and use applications effectively and productively.

8.1.5.A.2. Format a document using a word processing application to enhance text and include graphics, symbols and/ or pictures.

8.1.5.A.3 Use a graphic organizer to organize information about problem or issue.

8.1.5.A.4 Graph data using a spreadsheet, analyze and produce a report that explains the analysis of the data.

8.1.5.A.5 Create and use a database to answer basic questions.

8.1.5.A.6 Export data from a database into a spreadsheet; analyze and produce a report that explains the analysis of the data.

B. Creativity and Innovation: Students demonstrate creative thinking, construct knowledge and develop innovative products and process using technology.

• Apply existing knowledge to generate new ideas, products, or processes.
• Create original works as a means of personal or group expression.

8.1.5.B.1 Collaborative to produce a digital story about a significant local event or issue based on first-person interviews.

C. Communication and Collaboration: Students use digital media and environments to communicate and work collaboratively, including at a distance, to support individual learning and contribute to the learning of others.

• Interact, collaborate, and publish with peers, experts, or others by employing a variety of digital environments and media.
• Communicate information and ideas to multiple audiences using a variety of media and formats.
• Develop cultural understanding and global awareness by engaging with learners of other cultures.
• Contribute to project teams to produce original works or solve problems.

8.1.5.C.1 Engage in online discussions with learners of other cultures to investigate a worldwide issue from multiple perspectives and sources, evaluate findings and present possible solutions, using digital tools and online resources for all steps.

D. Digital Citizenship: Students understand human, cultural, and societal issues related to technology and practice legal and ethical behavior.

• Advocate and practice safe, legal, and responsible use of information and technology.

8.1.5.D.1 Understand the need for and use of copyrights.

• Demonstrate personal responsibility for lifelong learning.

8.1.5.D.2 Analyze the resource citations in online materials for proper use.

8.1.5.D.3 Demonstrate an understanding of the need to practice cyber safety, cyber security, and cyber ethics when using technologies and social media.

• Exhibit leadership for digital citizenship.

8.1.5.D.4  Understand digital citizenship and demonstrate an understanding of the personal consequences of inappropriate use of technology and social media.

E: Research and Information Fluency: Students apply digital tools to gather, evaluate, and use information.

• Plan strategies to guide inquiry.
• Locate, organize, analyze, evaluate, synthesize, and ethically use information from a variety of sources and media.
• Evaluate and select information sources and digital tools based on the appropriateness for specific tasks.

8.1.5.E.1  Use digital tools to research and evaluate the accuracy of, relevance to, and appropriateness of using print and non-print electronic information sources to complete a variety of tasks.

F: Critical thinking, problem solving, and decision making: Students use critical thinking skills to plan and conduct research, manage projects, solve problems, and make informed decisions using appropriate digital tools and resources.

• Identify and define authentic problems and significant questions for investigation.
• Plan and manage activities to develop a solution or complete a project.
• Collect and analyze data to identify solutions and/or make informed decisions.
• Use multiple processes and diverse perspectives to explore alternative solutions.

8.1.5.F.1 Apply digital tools to collect, organize, and analyze data that support a scientific finding.

Modifications/Accommodations

(IEPs, ELLs, 504s, G/T & BASIC SKILLS)

Quick Check

Intervention Activity

Center Games

Math and Science Activity

Visual Learning

Math Tools

Math Games

Higher Order Thinking Questions

Leveled Homework and Practice

Listen and Look for Lesson Video

Virtual Nerd Videos

Adaptive Homework and Practice

Today’s Challenge

Math Diagnosis and Intervention System

ELL Toolkit