MATH GRADE 6 Page of
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 realworld problems involving quotients of fractions and interpret the solutions in the context given (CRP2). Student will fluently divide multidigit numbers using the standard algorithms, as well as fluently add, subtract, multiply and divide multidigit 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:
 
Know  By the end of this unit, students will know:
 
Do  By the end of this unit, students will be able to:
missing values in tables and plot pairs of values.
 
Evidence of Learning  
Formative 
 
Summative/ Benchmark 
 
Alternative Assessments 
 
Learning Activities  
 
Materials / Equipment / Resources  
Core Instructional Materials and Texts  enVisionmath 2.0 ( Hardcopy and electronic edition)
Google Classroom  
Equipment  Chromebooks Smartboards  
Supplemental Resources  6.RP.A.2 Price per pound and pounds per dollar 6.RP.A.3 Voting for Three, Variation 1 6.NS.B.3 Reasoning about Multiplication and Division and Place Value, Part 1 
Standards  
Content Statement  Mathematical Practice Standards  
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 3/4cup 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.  
 
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.  
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.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  
 
 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
 By the end of 8th grade,

Technology Standards  8.1  
3 5th Grade  
A. Technology Operations and Concepts: Students demonstrate a sound understanding of technology concepts, systems and operations.  
 8.1.5.A.1 Select and use the appropriate digital tools and resources to accomplish a variety of tasks including solving problems.
 
 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.  
 8.1.5.B.1 Collaborative to produce a digital story about a significant local event or issue based on firstperson 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.  
 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.  
 8.1.5.D.1 Understand the need for and use of copyrights.  
 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.
 
 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.  
 8.1.5.E.1 Use digital tools to research and evaluate the accuracy of, relevance to, and appropriateness of using print and nonprint 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.  
 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 3D 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:
 
Know  By the end of this unit, students will know:
 
Do  By the end of this unit, students will be able to:
 
Evidence of Learning  
Formative 
 
Summative/ Benchmark 
 
Alternative Assessments 
 
Learning Activities  
 
Materials / Equipment / Resources  
Core Instructional Materials and Texts  enVisionmath 2.0 ( Hardcopy and electronic edition)
Google Classroom  
Equipment  Chromebooks Smartboards  
Supplemental Resources  6.EE.A.2 Rectangle Perimeter 1 6.EE.A.4 Rectangle Perimeter 2 6.EE.A.4 Equivalent Expressions 
Standards  
Content Statement  Mathematical Practice Standards  
 MP.2 Reason abstractly and quantitatively. MP.7 Look for and make use of structure.  
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 realworld problems. Perform arithmetic operations, including those involving wholenumber 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.  
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
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.  
 MP.2 Reason abstractly and quantitatively. MP.6 Attend to precision. MP.7 Look for and make use of structure.  
 MP. 2 Reason abstractly and quantitatively.  
 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
 By the end of 8th grade,

Technology Standards  8.1  
3 5th Grade  
A. Technology Operations and Concepts: Students demonstrate a sound understanding of technology concepts, systems and operations.  
 8.1.5.A.1 Select and use the appropriate digital tools and resources to accomplish a variety of tasks including solving problems.
 
 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.  
 8.1.5.B.1 Collaborative to produce a digital story about a significant local event or issue based on firstperson 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.  
 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.  
 8.1.5.D.1 Understand the need for and use of copyrights.  
 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.
 
 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.  
 8.1.5.E.1 Use digital tools to research and evaluate the accuracy of, relevance to, and appropriateness of using print and nonprint 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.  
 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 Systemand 2D 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 2D 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 nonnegative rational numbers). (CRP8) Use positive and negative numbers to represent quantities in realworld situations, explaining the meaning of zero in the context of the realworld 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 realworld 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 realworld 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:
 
Know  By the end of this unit, students will know:
the equation or inequality true.
three, (3), is equal to the original number, 3).
 
Do  By the end of this unit, students will be able to:
solve realworld and mathematical problems.
 
Evidence of Learning  
Formative 
 
Summative/ Benchmark 
 
Alternative Assessments 
 
Learning Activities  
 
Materials / Equipment / Resources  
Core Instructional Materials and Texts  enVisionmath 2.0 ( Hardcopy and electronic edition)
Google Classroom  
Equipment  Chromebooks Smartboards  
Supplemental Resources  6.EE.B.5 Make Use of Structure 6.NS.C.7a Fractions on the Number Line 6.NS.C.7b Comparing Temperatures 6.G.A.1, 6.G.A.3 Polygons in the Coordinate Plane 
Standards  
Content Statement  Mathematical Practice Standards  
 MP.5 Use appropriate tools strategically. MP.6 Attend to precision.  
 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.  
 MP.2 Reason abstractly and quantitatively. MP.5 Use appropriate tools strategically  
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.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 realworld 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 realworld 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  
 MP.2 Reason abstractly and quantitatively. MP.6 Attend to precision. MP.7 Look for and make use of structure.  
*(benchmarked)
 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.  
 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
 By the end of 8th grade,

Technology Standards  8.1  
3 5th Grade  
A. Technology Operations and Concepts: Students demonstrate a sound understanding of technology concepts, systems and operations.  
 8.1.5.A.1 Select and use the appropriate digital tools and resources to accomplish a variety of tasks including solving problems.
 
 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.  
 8.1.5.B.1 Collaborative to produce a digital story about a significant local event or issue based on firstperson 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.  
 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.  
 8.1.5.D.1 Understand the need for and use of copyrights.  
 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.
 
 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.  
 8.1.5.E.1 Use digital tools to research and evaluate the accuracy of, relevance to, and appropriateness of using print and nonprint 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.  
 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 Relationshipsbetween Quantities  Timeframe  
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:
 
Know  By the end of this unit, students will know:
with a table of values.
 
Do  By the end of this unit, students will be able to:
missing values in tables and plot pairs of values.
 
Evidence of Learning  
Formative 
 
Summative/ Benchmark 
 
Alternative Assessments 
 
Learning Activities  
 
Materials / Equipment / Resources  
Core Instructional Materials and Texts  enVisionmath 2.0 ( Hardcopy and electronic edition)
Google Classroom  
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 
Standards  
Content Statement  Mathematical Practice Standards  
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.  
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  
 MP.4 Model with mathematics.  
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.  
*(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  
 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
 By the end of 8th grade,

Technology Standards  8.1  
3 5th Grade  
A. Technology Operations and Concepts: Students demonstrate a sound understanding of technology concepts, systems and operations.  
 8.1.5.A.1 Select and use the appropriate digital tools and resources to accomplish a variety of tasks including solving problems.
 
 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.  
 8.1.5.B.1 Collaborative to produce a digital story about a significant local event or issue based on firstperson 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.  
 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.  
 8.1.5.D.1 Understand the need for and use of copyrights.  
 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.
 
 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.  
 8.1.5.E.1 Use digital tools to research and evaluate the accuracy of, relevance to, and appropriateness of using print and nonprint 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.  
 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 