MATH GRADE 5 Page of
Units: Unit 1: Understanding the Place Value System Unit 2: Understanding Volume and ?? Unit 3: More Operations on Fractions Unit 4: Coordinate Geometry and Classifying Figures 
Unit Title  Unit 1: Understanding the Place Value System  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 write and interpret numerical expressions, understand place value system, and perform operations with multidigit numbers and decimals to hundredths.(CRP2)(9.2.8.B.3) Students will evaluate, write and interpret numerical expressions that contain parentheses, brackets and braces. Students will explain and represent place value to its right, powers of 10 by using whole number exponents. Students will multiply and divide a whole number of up to a four digits by a whole number of up to two digits. To show understanding of concept, students will create an equation, array, or area model. Students will compare two decimals to thousandths and represent decimals using number names, expanded form and standard form. Students will use these skills to evaluate, communicate, and collaborate while making connections between abstract concepts and realworld applications. Topic 1  Understand Place Value Topic 2  Add and Subtract Decimals to Hundredths Topic 3  Fluently Multiply MultiDigit Whole Numbers Topic 4  Use Models and Strategies to Multiply Decimals Topic 5  Use Models and Strategies to Divide Whole Numbers Topic 13  Write and Interpret Numerical Expressions  
Learning Targets  
Essential Questions  Topic 1  How are whole numbers and decimals written, compared, and ordered? Topic 2  How can sums and differences of decimals be estimated? What are the standard procedures for adding and subtracting whole numbers and decimals? How can sums and differences be found mentally? Topic 3  What are the standard procedures for estimating and finding products of multidigit numbers? Topic 4  What are the standard procedures for estimating and finding products involving decimals? Topic 5  What is the standard procedure for division and why does it work? Topic 13  How is the value of a numerical expression found?  
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:
efficiency.
based on place value, properties of operations, and the relationship between multiplication and division.
 
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 Math Centers  
Supplemental Resources  5.OA.A.1 Using Operations and Parentheses 5.OA.A.1 Watch out for Parentheses 1 5.NBT.A.1 Millions and Billions of People 5.NBT.A.3 Placing Thousandths on the Number Line 
Standards  
Content Statement  Mathematical Practice Standards  
 MP.1 Make sense of problems and persevere in solving them. MP.5 Use appropriate tools strategically. MP.8 Look for and express regularity in repeated reasoning.  
For example, express the calculation “add 8 and 7, then multiply by 2” as 2 × (8 + 7). Recognize that 3 × (18932 + 921) is three times as large as 18932 + 921, without having to calculate the indicated sum or product.  MP.1 Make sense of problems and persevere in solving them. 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.6 Attend to precision. MP.7 Look for and make use of structure.  
*(benchmarked)  MP.2 Reason abstractly and quantitatively. 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.2 Reason abstractly and quantitatively. MP.3 Construct viable arguments and critique the reasoning of others. MP.4 Model with mathematics. MP.5 Use appropriate tools strategically. MP.7 Look for and make use of structure.  
5.NBT.A.3a. Read and write decimals to thousandths using baseten numerals, number names, and expanded form, e.g., 347.392 = 3 × 100 + 4 × 10 + 7 × 1 + 3 × (1/10) + 9 × (1/100) + 2 × (1/1000). 5.NBT.A.3b. Compare two decimals to thousandths based on meanings of the digits in each place, using >, =, and < symbols to record the results of comparisons.  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.2 Reason abstractly and quantitatively. MP.6 Attend to precision. 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.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.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.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: 5LS11, 5LS21, 5PS31, 5ESS22, 5ESS31, 5ESS21, 5ESS31 
 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 Problemsolving Reading Mat Center Games Math and Science Activity Visual Learning Math Tools Math Games Higher Order Thinking Questions Leveled Homework and Practice Another Look Homework Video Adaptive Homework and Practice Today’s Challenge Math Diagnosis and Intervention System Practice Buddy Ell Toolkit 
Unit Title  Unit 2:Understanding Volume and Operations on Fractions  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 understand concepts of volume, perform operations with whole numbers and decimals, use equivalent fractions as a strategy to add and subtract fractions, and apply and extend previous understandings of multiplication and division. (CRP8)(9.2.8.B.4) When working with volume, students will be able to measure and show volume by counting cubic units. Students will also apply formulas and strategies to solve real world and mathematical problems involving volume. Students will fluently multiply and divide whole numbers with accuracy and efficiency. Students will add and subtract (including mixed numbers) with unlike denominators and determine if the answer to a word problem is reasonable using estimations with benchmark fractions. Students will interpret a fraction as a division of the numerator by the denominator, and interpret the product as parts of a whole using visual fraction models. Students will also model the area of a rectangle. Topic 7  Use Equivalent Fractions to Add and Subtract Fractions Topic 8  Apply Understanding of Multiplication to Multiply Fractions Topic 9  Apply Understanding of Division to Divide Fractions Topic 10  Understand Volume Concepts  
Learning Targets  
Essential Questions  Topic 7  How can sums and differences of fractions and mixed numbers be estimated? What are standard procedures for adding and subtracting fractions for adding and subtracting fractions and mixed numbers? Topic 8  What does it mean to multiply whole numbers and fractions? How can multiplication and whole numbers and fractions be shown using models and symbols? Topic 9  How are fractions related to division? How can you divide with whole numbers and unit fractions? Topic 10  What is the meaning of volume of a solid? How can the volume of a rectangular prism be found?  
Enduring Understandings  Students will understand:
 
Know  By the end of this unit, students will know:
volume.
 
Do  By the end of this unit, students will be able to:
showing that they are the same.
same.Explain how both volume formulas relate to counting the cubes in one layer and multiplying that value by the number of layers (height).
that has unlike denominators.
model, (3/4) x 5 can be represented by 3 parts, after partitioning 5 objects into 4 equal parts].
rectangle, tile the rectangle using ¼ inch tiles].
 
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 Math Centers  
Supplemental Resources  5.MD.C.5 Breaking Apart Composite Solids 5.MD.C.5a using Volume to Understand the Associative Property of Multiplication 5.NF.B.4b Chavone's Bathroom Tiles 
Standards  
Content Statement  Mathematical Practice Standards  
5.MD.C.5a. A cube with side length 1 unit, called a “unit cube,” is said to have “one cubic unit” of volume, and can be used to measure volume. 5.MD.C.5b. A solid figure which can be packed without gaps or overlaps using n unit cubes is said to have a volume of n cubic units.
 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.6 Attend to precision. MP.7 Look for and make use of structure.  
5.MD.C.5a. Find the volume of a right rectangular prism with wholenumber side lengths by packing it with unit cubes, and show that the volume is the same as would be found by multiplying the edge lengths, equivalently by multiplying the height by the area of the base. Represent threefold wholenumber products as volumes, e.g., to represent the associative property of multiplication. 5.MD.C.5b. Apply the formulas V = l × w × h and V = B × h for rectangular prisms to find volumes of right rectangular prisms with whole number edge lengths in the context of solving real world and mathematical problems. 5.MD.C.5c. Recognize volume as additive. Find volumes of solid figures composed of two nonoverlapping right rectangular prisms by adding the volumes of the nonoverlapping parts, applying this technique to solve real world problems.  MP.1 Make sense of problems and persevere in solving them. MP.2 Reason abstractly and quantitatively. MP.3 Construct viable arguments and critique the reasoning of others. 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.2 Reason abstractly and quantitatively. MP.3 Construct viable arguments and critique the reasoning of others. MP.4 Model with mathematics. MP.5 Use appropriate tools strategically. MP.7 Look for and make use of structure.  
 MP.1 Make sense of problems and persevere in solving them. MP.2 Reason abstractly and quantitatively. MP.3 Construct viable arguments and critique the reasoning of others. 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.  
For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2.  MP.1 Make sense of problems and persevere in solving them. MP.2 Reason abstractly and quantitatively. MP.3 Construct viable arguments and critique the reasoning of others. 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.  
For example, interpret 3/4 as the result of dividing 3 by 4, noting that 3/4 multiplied by 4 equals 3, and that when 3 wholes are shared equally among 4 people each person has a share of size 3/4. If 9 people want to share a 50pound sack of rice equally by weight, how many pounds of rice should each person get? Between what two whole numbers does your answer lie?  MP.1 Make sense of problems and persevere in solving them. MP.2 Reason abstractly and quantitatively. MP.3 Construct viable arguments and critique the reasoning of others. 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.  
5.NF.B.4a. Interpret the product (a/b) × q as a parts of a partition of q into b equal parts; equivalently, as the result of a sequence of operations a × q ÷ b. For example, use a visual fraction model to show (2/3) × 4 = 8/3, and create a story context for this equation. Do the same with (2/3) × (4/5) = 8/15. (In general, (a/b) × (c/d) = ac/bd.) 5.NF.B.4b. Find the area of a rectangle with fractional side lengths by tiling it with unit squares of the appropriate unit fraction side lengths, and show that the area is the same as would be found by multiplying the side lengths. Multiply fractional side lengths to find areas of rectangles, and represent fraction products as rectangular areas.  MP.1 Make sense of problems and persevere in solving them. MP.2 Reason abstractly and quantitatively. MP.3 Construct viable arguments and critique the reasoning of others. 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.  
21st Century Skills and Themes  
Interdisciplinary Connections  Career Ready Practices  9.2 Career Awareness, Exploration, and Preparation 
ELA: 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.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.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: 5PS14, 5PS1S, 5LS11, 5LS21, 5PS31  DELETE OUT THOSE NOT APPLICABLE TO THIS UNIT
 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 Problemsolving Reading Mat Center Games Math and Science Activity Visual Learning Math Tools Math Games Higher Order Thinking Questions Leveled Homework and Practice Another Look Homework Video Adaptive Homework and Practice Today’s Challenge Math Diagnosis and Intervention System Practice Buddy Ell Toolkit 
Unit Title  Unit 3: More Operations on Fractions  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 apply and extend previous understandings of multiplication and division, understand the place value system, perform operations with multidigit whole numbers and with decimals to hundredths and convert like measurement units within a given measurement system. (CRP6) (9.2.8.B.5) Students will multiply fractional side lengths to find areas of rectangles, multiply a fraction by a whole number and by a fraction and be able to draw visual models to represent products. Students will also explain how a product is related to the magnitude of the factors, including cases in which one factor is a fraction greater than 1 and cases in which one factor is a fraction less than 1. Students will solve realworld problems involving multiplication of fractions (including mixed numbers), using visual fraction models or equations to represent the problem. Students will divide a unit fraction by a nonzero whole number and interpret by creating a story context or visual fraction model, divide a whole number by a unit fraction and interpret by creating a story context or visual fraction model and solve realworld problems involving division of unit fractions by whole numbers or whole numbers by unit fractions. Students will explain patterns in the placement of the decimal point when a decimal is multiplied or divided by a power of 10 and representing powers of 10 using wholenumber exponents. Students will add, subtract, multiply and divide decimals to hundredths using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; explain the reasoning used, relating the strategy to the written method. Students will convert standard measurement units within the same system (e.g., centimeters to meters) in order to solve multistep problems. Topic 3  Fluently Multiply MultiDigit Whole Numbers Topic 4  Use Models and Strategies to Multiply Decimals Topic 6  Use Models and Strategies to Divide Decimals Topic 7  Use Equivalent Fractions to Add and Subtract Fractions Topic 8  Apply Understanding of Multiplication to Multiply Fractions Topic 9  Apply Understanding of Division to Divide Fractions Topic 11  Convert Measurement  
Learning Targets  
Essential Questions  Topic 3  What are the standard procedures for estimating and finding products of multidigit numbers? Topic 4  What are the standard procedures for estimating and finding products involving decimals? Topic 6  What are the standard procedures for estimating and finding quotients involving decimals? Topic 7  How can sums and differences of fractions and mixed numbers be estimated? What are standard procedures for adding and subtracting fractions for adding and subtracting fractions and mixed numbers? Topic 8  What does it mean to multiply whole numbers and fractions? How can multiplication and whole numbers and fractions be shown using models and symbols? Topic 9  How are fractions related to division? How can you divide with whole numbers and unit fractions? Topic 11  What are customary measurement units and how are they related? What are metric measurement units and how are they related?  
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:
ac(1/bd) = ac/bd.
fraction).
problem.
problem
and/or the relationship between addition and subtraction.
to hours).
 
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 Math Centers  
Supplemental Resources  5.NF.B.5 Comparing Heights of Buildings 5.NF.B.5b Mrs. Gray's Homework Assignment 5.NF.B.6 To Multiply or not to multiply? 5.NBT.A.2 Multiplying Decimals by 10 5.NBT.A.2 Marta's Multiplication Error 5.NBT.B.7 The Value of Education 5.MD.A.1, 5.NF.B.3 Converting Fractions of a Unit into a Smaller Unit 
Standards  
Content Statement  Mathematical Practice Standards  
5.NF.B.4b. Find the area of a rectangle with fractional side lengths by tiling it with unit squares of the appropriate unit fraction side lengths, and show that the area is the same as would be found by multiplying the side lengths. Multiply fractional side lengths to find areas of rectangles, and represent fraction products as rectangular areas.  MP.1 Make sense of problems and persevere in solving them. MP.2 Reason abstractly and quantitatively. MP.3 Construct viable arguments and critique the reasoning of others. 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.  
5.NF.B.5a. Comparing the size of a product to the size of one factor on the basis of the size of the other factor, without performing the indicated multiplication. 5.NF.B.5b. Explaining why multiplying a given number by a fraction greater than 1 results in a product greater than the given number (recognizing multiplication by whole numbers greater than 1 as a familiar case); explaining why multiplying a given number by a fraction less than 1 results in a product smaller than the given number; and relating the principle of fraction equivalence a/b = (n×a)/(n×b) to the effect of multiplying a/b by 1.  MP.2 Reason abstractly and quantitatively. MP.4 Model with mathematics. MP.6 Attend to precision. MP.7 Look for and make use of structure.  
 MP.4 Model with mathematics. MP.1 Make sense of problems and persevere in solving them. MP.2 Reason abstractly and quantitatively. MP.3 Construct viable arguments and critique the reasoning of others. 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.  
5.NF.B.7a. Interpret division of a unit fraction by a nonzero whole number, and compute such quotients. For example, create a story context for (1/3) ÷ 4, and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that (1/3) ÷ 4 = 1/12 because (1/12) × 4 = 1/3. 5.NF.B.7b. Interpret division of a whole number by a unit fraction, and compute such quotients. For example, create a story context for 4 ÷ (1/5), and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that 4 ÷ (1/5) = 20 because 20 × (1/5) = 4. 5.NF.B.7c. Solve real world problems involving division of unit fractions by nonzero whole numbers and division of whole numbers by unit fractions, e.g., by using visual fraction models and equations to represent the problem. For example, how much chocolate will each person get if 3 people share 1/2 lb of chocolate equally? How many 1/3cup servings are in 2 cups of raisins?  MP.1 Make sense of problems and persevere in solving them. MP.2 Reason abstractly and quantitatively. MP.3 Construct viable arguments and critique the reasoning of others. 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.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.3 Construct viable arguments and critique the reasoning of others. MP.4 Model with mathematics. MP.5 Use appropriate tools strategically. MP.7 Look for and make use of structure.  
 MP.1 Make sense of problems and persevere in solving them. MP.2 Reason abstractly and quantitatively. MP.5 Use appropriate tools strategically. MP.6 Attend to precision.  
21st Century Skills and Themes  
Interdisciplinary Connections  Career Ready Practices  9.2 Career Awareness, Exploration, and Preparation 
ELA: 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.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.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: 5ESS22, 5ESS31, 5LS11, 5LS21, 5PS31, 5PS13, 5PS11, 5PS14, 5PS12, 5ESS21, 5ESS31  DELETE OUT THOSE NOT APPLICABLE TO THIS UNIT
 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)  
Intervention Activity Problemsolving Reading Mat Center Games Math and Science Activity Visual Learning Math Tools Math Games Higher Order Thinking Questions Leveled Homework and Practice Another Look Homework Video Adaptive Homework and Practice Today’s Challenge Math Diagnosis and Intervention System Practice Buddy Ell Toolkit 
Unit Title  Unit 4: Coordinate Geometry and Classifying Figures  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 graph points on the coordinate plane to solve realworld and mathematical problems, analyze patterns and relationships, classify twodimensional figures into categories based on their properties, represent and interpret data, perform operations with multidigit whole numbers and with decimals to hundredths and apply and extend previous understanding of multiplication and division. (CRP7) (9.2.8.B.2) Students will be able to represent real world and mathematical problems by graphing points defined by whole number coordinates in the first quadrant of the coordinate plane, and interpret coordinate values of points in the context of the situation. Students will be able to generate two numerical patterns from two given rules, identify the relationship between corresponding terms, create ordered pairs and graph the ordered pairs. Students will be able to classify twodimensional figures in a hierarchy based on properties. Students will make a line plot to display a data set in measurements in fractions of a unit and use it to solve problems involving the four operations on fractions and unlike denominators. Students will fluently multiply multidigit whole numbers with accuracy and efficiency. Students will add, subtract, multiply, and divide decimals to hundredths using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; explain the reasoning used, relating the strategy to the written method. Topic 3  Fluently Multiply MultiDigit Whole Numbers Topic 6  Use Models and Strategies to Divide Decimals Topic 12  Represent and Interpret Data Topic 13  Write and Interpret Numerical Expressions Topic 14  Graph Points on the Coordinate Plane Topic 15  Algebra: Analyze Patterns and Relationships Topic 16  Geometric Measurement: Classify TwoDimensional Figures  
Learning Targets  
Essential Questions  Topic 3  What are the standard procedures for estimating and finding products of multidigit numbers? Topic 6  What are the standard procedures for estimating and finding quotients involving decimals? Topic 12  How can line plots be used to represent data and answer questions? Topic 13  How is the value of a numerical expression found? Topic 14  How are points plotted? How are relationships shown on a graph? Topic 15  How can number patterns be analyzed and graphed? How can number patterns and graphs be used to solve problems? Topic 16  How can triangles and quadrilaterals be described, classified, and named?  
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:
and mathematical problems.
size, side length, etc.).
and/or the relationship between addition and subtraction.
problem.
problem.
problem.
 
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 Math Centers  
Supplemental Resources  5.G.A.1 Battle Ship Using Grid Paper 5.G.A.2 Meerkat Coordinate Plane Task 5.G.B.3 Always, Sometimes, Never 5.G.B.4 What is a Trapezoid? (Part 2) 5.MD.B.2 5.NF.A.1 Fractions on a Line Plot 
Standards  
Content Statement  Mathematical Practice Standards  
 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.6 Attend to precision. MP.7 Look for and make use of structure.  
 MP.2 Reason abstractly and quantitatively. MP.7 Look for and make use of structure.  
For example, all rectangles have four right angles and squares are rectangles, so all squares have four right angles.
 MP.2 Reason abstractly and quantitatively. MP.3 Construct viable arguments and critique the reasoning of others. MP.5 Use appropriate tools strategically. MP.6 Attend to precision. MP.7 Look for and make use of structure.  
For example, given different measurements of liquid in identical beakers, find the amount of liquid each beaker would contain if the total amount in all the beakers were redistributed equally.  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.6 Attend to precision. MP.7 Look for and make use of structure.  
 MP.2 Reason abstractly and quantitatively. MP.3 Construct viable arguments and critique the reasoning of others. MP.4 Model with mathematics. MP.5 Use appropriate tools strategically. MP.7 Look for and make use of structure.  
 MP.2 Reason abstractly and quantitatively. MP.3 Construct viable arguments and critique the reasoning of others. MP.4 Model with mathematics. MP.5 Use appropriate tools strategically. MP.7 Look for and make use of structure.  
5.NF.B.7c. Solve real world problems involving division of unit fractions by nonzero whole numbers and division of whole numbers by unit fractions, e.g., by using visual fraction models and equations to represent the problem. For example, how much chocolate will each person get if 3 people share 1/2 lb of chocolate equally? How many 1/3cup servings are in 2 cups of raisins?  MP.1 Make sense of problems and persevere in solving them. MP.2 Reason abstractly and quantitatively. MP.3 Construct viable arguments and critique the reasoning of others. 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.  
21st Century Skills and Themes  
Interdisciplinary Connections  Career Ready Practices  9.2 Career Awareness, Exploration, and Preparation 
ELA: 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.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.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: 5ESS22, 5ESS31,5PS13, 5PS11,5LS11,5LS21,5PS31,5PS21,5ESS11, 5ESS12  DELETE OUT THOSE NOT APPLICABLE TO THIS UNIT
 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 Problemsolving Reading Mat Center Games Math and Science Activity Visual Learning Math Tools Math Games Higher Order Thinking Questions Leveled Homework and Practice Another Look Homework Video Adaptive Homework and Practice Today’s Challenge Math Diagnosis and Intervention System Practice Buddy Ell Toolkit 