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 multi-digit 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 real-world applications.

Topic 1 - Understand Place Value

Topic 2 - Add and Subtract Decimals to Hundredths

Topic 3 - Fluently Multiply Multi-Digit 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 multi-digit 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:

  • Write and interpret numerical expressions
  • Understand the place value system
  • Perform operations with multi-digit whole numbers and with decimals to hundredths

Know

By the end of this unit, students will know:

  •  Standard convention for performing operations (Order of operations, including grouping symbols)
  •  Order of operations, including grouping symbols.  
  •  Quantitative relationships exist between the digits in place value positions of a multi-digit number.
  •  Scientific notation and exponents
  •  Multiple representations of whole numbers

Do

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

  •  Evaluate numerical expressions that include grouping symbols (parentheses, brackets or braces).
  •  Evaluate numerical expressions that include nested grouping symbols (for example, 3 x [5 + (7 - 3)]).
  •  Write a simple numerical expression when given a verbal description.
  •  Interpret the quantitative relationships in numerical expressions without evaluating (simplifying) the expression.
  •  Explain that a digit in one place represents 1/10 of what it would represent in the place to its left.
  •  Explain that a digit in one place represents ten times what it would represent in the place to its right.
  •  Explain patterns in the number of zeros of the product when multiplying a whole number by powers of 10.
  •  Write powers of 10 using whole-number exponents.
  •  Multiply a whole number of up to a four digits by a whole number of up two digits using the standard algorithm with accuracy and

   efficiency.

  •  Divide to find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors using strategies  

   based on place value, properties of operations, and the relationship between multiplication and division.

  •  Represent these operations with equations, rectangular arrays, and area models.
  •  Explain the calculation by referring to the model (equation, array, or area model).
  •  Read and write decimals to thousandths using base-ten numerals.
  •  Read and write decimals to thousandths using number names.
  •  Read and write decimals to thousandths using expanded form.
  •  Compare two decimals to thousandths using >, =, and < symbols.
  •  Compare decimals when each is presented in a different form (base-ten numeral, number name, and expanded form).
  •  Round decimals to any place value.

Evidence of Learning

Formative

Summative/ Benchmark

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

Alternative Assessments

  • Placement Test

  • ExamView Test Generator

  • Math and Science Project
  • End of Year Assessment
  • Benchmark Assessment

Learning Activities

  • Evaluate numerical expressions that contain parentheses, brackets and braces.
  • Write numerical expressions when given a verbal description or word problem; interpret numerical expressions without evaluating them.
  • Explain that a digit in one place represents 1/10 of what it would represent in the place to its left and ten times what it would represent in the place to its right.
  • Explain patterns in the number of zeros in the product when a whole number is multiplied by a power of 10; represent powers of 10 using whole-number exponents.
  • Use the standard algorithm to multiply a whole number of up to a four digits by a whole number of up two digits.
  • Calculate whole number quotients of whole numbers with 4-digit dividends and 2-digit divisors; explain and represent calculations with equations, rectangular arrays, and area models.
  • Compare two decimals to thousandths using >, =, and < for numbers presented as base ten numerals, number names, and/or in expanded form.
  • Round decimals to any place value

Materials / Equipment / Resources

Core Instructional

Materials and Texts

enVisionmath 2.0 ( Hardcopy and electronic edition)

  • Teacher Edition
  • Student Edition
  • Math and Science Project
  • Vocabulary Cards and Activities
  • Fluency Practice Activity
  • Digital Resources

Google Classroom

Seesaw

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 Which number is it?

5.NBT.A.1 Millions and Billions of People

5.NBT.A.3 Placing Thousandths on the Number Line

5.NBT.A.4 Rounding to Tenths and Hundredths

5.NBT.B.5 Elmer's Multiplication Error

Standards

Content Statement

Mathematical Practice Standards

  • 5.OA.A.1. Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols.

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.

  • 5.OA.A.2. Write simple expressions that record calculations with numbers, and interpret numerical expressions without evaluating them.

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.8   Look for and express regularity in repeated reasoning

  • 5.NBT.A.1. Recognize that in a multi-digit number, a digit in one place represents 10 times as much as it represents in the place to its right and 1/10 of what it represents in the place to its left.

MP.2   Reason abstractly and quantitatively.

MP.6   Attend to precision.

 MP.7   Look for and make use of structure.

  • 5.NBT.A.2. Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and explain patterns in the placement of the decimal point when a decimal is multiplied or divided by a power of 10. Use whole-number exponents to denote powers of 10.

MP.2   Reason abstractly and quantitatively.

MP.6   Attend to precision.

 MP.7   Look for and make use of structure.

  • 5.NBT.B.5. Fluently multiply multi-digit whole numbers using the standard algorithm.

*(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.

  • 5.NBT.B.6. Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models.

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.3. Read, write, and compare decimals to thousandths.

5.NBT.A.3a. Read and write decimals to thousandths using base-ten 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.

  • 5.NBT.A.4. Use place value understanding to round decimals to any place.

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:

5-LS1-1, 5-LS2-1, 5-PS3-1, 5-ESS2-2, 5-ESS3-1, 5-ESS2-1, 5-ESS3-1

  • 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

Problem-solving 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:

  • Understand concepts of volume
  • Perform operations with multi-digit whole numbers and with decimals to hundredths
  • Use equivalent fractions as a strategy to add and subtract fractions
  • Volume is additive: volumes of composite solids can be determined by adding the volumes of each solid.

Know

By the end of this unit, students will know:

  •  Volume is the amount of space inside a solid (3-dimensional) figure.
  •  Cubes with side length of 1 unit, called “a unit cube,” is said to have “one cubic unit” of volume, and can be used to measure

   volume.

  •  Solid figures which can be packed without gaps or overlaps using n unit cubes is said to have a volume of n cubic units.
  •  Volume of a solid can be determined using unit cubes of other dimensions.
  •  Equivalent fractions can be used to add and subtract fractions.
  •  Fractions represent division.

Do

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

  •  Count unit cubes in order to measure the volume of a solid.
  •  Use unit cubes of centimeters, inches, and/or other units to measure volume.
  •  Pack right rectangular prisms with cubes to find volume and multiply side lengths of the right rectangular prism to find volume,

   showing that they are the same.

  •  Pack right rectangular prisms with cubes to find volume and multiply height by the area of the base, showing that they are the

   same.Explain how both volume formulas relate to counting the cubes in one layer and multiplying that value by the number of

   layers (height).

  •  Write the volume of an object as the product of three whole numbers.
  •  Solve real-world and mathematical problems using the formulas V = l × w × h and V = B × h.
  •  Find the volume of a composite solid composed of two right rectangular prisms.
  •  Multiply multi-digit whole numbers with accuracy and efficiency.
  •  Produce an equivalent sum (or difference) of fractions with like denominators from the original sum (or difference) of fractions

    that has unlike denominators.

  •  Add and subtract fractions with unlike denominators by replacing given fractions with equivalent fractions.
  •  Add and subtract fractions, including mixed numbers, with unlike denominators to solve word problems.
  •  Represent calculations and solutions with visual fraction models and equations
  •  Estimate answers using benchmark fractions and explain whether the answer is reasonable.
  •  Estimate answers by reasoning about the size of the fractions and explain whether the answer is reasonable.
  •  Represent a fraction as a division statement (a/b = a ÷ b).
  •  Divide whole numbers in order to solve real world problems, representing the quotient as a fraction or a mixed number.
  •  Represent word problems involving division of whole numbers using visual fraction models and equations.
  •  For whole number or fraction q, represent (a/b) × q as a parts of a partition of q into b equal parts [e.g. using a visual fraction

    model, (3/4) x 5 can be represented by 3 parts, after partitioning 5 objects into 4 equal parts].

  •  For whole number or fraction q, represent (a/b) × q as a × q ÷ b [e.g. showing that (2/5) x 3 is equivalent to (2 x 3) ÷ 5].
  •  From a story context, interpret (a/b) × q as a parts of a partition of q into b equal parts.
  •  Tile a rectangle having fractional side lengths using unit squares of the appropriate unit fraction [e.g. given a 3 ¼ inch  x 7 ¾ inch

    rectangle, tile the rectangle using ¼ inch tiles].

  •  Show that the area found by tiling with unit fraction tiles is the same as would be found by multiplying the side lengths.

Evidence of Learning

Formative

Summative/ Benchmark

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

Alternative Assessments

  • Placement Test

  • ExamView Test Generator

  • Math and Science Project
  • End of Year Assessment
  • Benchmark Assessment

Learning Activities

  • Measure volume by counting the total number cubic units required to fill a figure without gaps or overlaps.
  • Show that the volume of a right rectangular prism found by counting all the unit cubes is the same as the formulas V = l × w × h or V = B × h.
  • Apply formulas to solve real world and mathematical problems involving volumes of right rectangular prisms that have whole number edge lengths.
  • Find the volume of a composite solid figure composed of two non-overlapping right rectangular prisms, applying this strategy to solve real-world problems.
  • Fluently multiply multi-digit whole numbers with accuracy and efficiency.
  • Add and subtract fractions (including mixed numbers) with unlike denominators by replacing the given fractions with equivalent fractions having like denominators.
  • Solve word problems involving adding or subtracting fractions with unlike denominators, and determine if the answer to the word problem is reasonable, using estimations with benchmark fractions.
  • Interpret a fraction as a division of the numerator by the denominator; solve word problems in which division of whole numbers leads to fractions or mixed numbers as solutions.
  • For whole number or fraction q, interpret the product (a/b) x q as a parts of a whole partitioned into b equal parts added q times (e.g. using a visual fraction model).
  • Tile a rectangle with unit fraction squares to find the area and multiply side lengths to find the area of the rectangle, showing that the areas are the same.

Materials / Equipment / Resources

Core Instructional

Materials and Texts

enVisionmath 2.0 ( Hardcopy and electronic edition)

  • Teacher Edition
  • Student Edition
  • Math and Science Project
  • Vocabulary Cards and Activities
  • Fluency Practice Activity
  • Digital Resources

Google Classroom

Seesaw

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.MD.C.5b Cari's Aquarium

5.MD.C Box of Clay

5.NF.A.1 Making S'Mores

5.NF.A.2 Do These Add Up?

5.NF.A Measuring Cups

5.NF.B.3 How Much Pie?

5.NF.B.4b Chavone's Bathroom Tiles

Standards

Content Statement

Mathematical Practice Standards

  • 5.MD.C.3. Recognize volume as an attribute of solid figures and understand concepts of volume measurement.

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.

  • 5.MD.C.4. Measure volumes by counting unit cubes, using cubic cm, cubic in, cubic ft, and non-standard 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.5. Relate volume to the operations of multiplication and addition and solve real world and mathematical problems involving volume.

5.MD.C.5a. Find the volume of a right rectangular prism with whole-number 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 whole-number 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 non-overlapping right rectangular prisms by adding the volumes of the non-overlapping 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.

  • 5.NBT.B.5. Fluently multiply multi-digit whole numbers using the standard algorithm. *(benchmarked)

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.A.1. Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators.     For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/1 (in general, a/b + c/d = (ad + bc)/bd).

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.A.2. Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers.

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.

  • 5.NF.B.3. Interpret a fraction as division of the numerator by the denominator (a/b = a ÷ b). Solve word problems involving division of whole numbers leading to answers in the form of fractions or mixed numbers, e.g., by using visual fraction models or equations to represent the problem.

 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 50-pound 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.4. Apply and extend previous understandings of multiplication to multiply a fraction or whole number by a fraction.

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:

5-PS1-4, 5-PS1-S, 5-LS1-1, 5-LS2-1, 5-PS3-1

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.

DELETE OUT THOSE NOT APPLICABLE TO THIS UNIT

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

Problem-solving 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 multi-digit 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 real-world 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 non-zero 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 real-world 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 whole-number 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 multi-step problems.

Topic 3 - Fluently Multiply Multi-Digit 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 multi-digit 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:

  • Apply and extend previous understandings of multiplication and division
  • Understand the place value system
  • Perform operations with multi-digit whole numbers and with decimals to hundredths
  • Convert like measurement units within a given measurement system

Know

By the end of this unit, students will know:

  •  Multiplication as resizing (scaling)

Do

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

  •  Multiply fractional side lengths to find areas of rectangles.
  •  Represent fraction products as rectangular areas.
  •  Multiply a fraction by a whole number.
  •  Multiply a fraction by a fraction, in general, if q is a fraction c/d, then (a/b) x (c/d) = a(1/b) × c(1/d) =  ac × (1/b)(1/d) =

   ac(1/bd) = ac/bd.

  •  Compare the size of a product to the size of one of its factors, considering the size of the other factor (at least one factor is a

   fraction).

  •  Explain why multiplying a given number by a fraction greater than 1 results in a product greater than the given number.
  •  Explaining why multiplying a given number by a fraction less than 1 results in a product smaller than the given number.
  •  Explain that multiplying a given number by a fraction equivalent to 1 does not change the product.
  •  Multiply fractions and mixed numbers in order to solve real world problems.
  •  Represent the solution to these real world problems with visual fraction models and equations.
  •  Use a story context to interpret division of a unit fraction by a whole number.
  •  Divide of a unit fraction by a whole number and represent with visual fraction models.
  •  Use a story context to interpret division of a whole number by a unit fraction.
  •  Divide of a whole number by a unit fraction and represent with visual fraction models.
  •  Divide unit fractions by whole numbers to solve real-world problems, using visual fraction models and equations to represent the

   problem.

  •  Divide whole numbers by unit fractions to solve real-world problems, using visual fraction models and equations to represent the

   problem

  •  Explain patterns in the placement of the decimal point when multiplying or dividing a decimal by powers of 10.
  •  Write powers of 10 using whole-number exponents.
  •  Add and subtract decimals to hundredths using concrete models and drawings.
  •  Multiply and divide decimals to hundredths using concrete models and drawings.
  •  Add, subtract, multiply, and divide decimals to hundredths using strategies based on place value, properties of operations,

   and/or the relationship between addition and subtraction.

  •  Relate the strategy to the written method and explain the reasoning used.
  •  Convert from one measurement unit to another within a given measurement system (e.g., convert 5 cm to 0.05 m, convert minutes

   to hours).

  •  Solve multi-step, real world problems that require conversions.

Evidence of Learning

Formative

Summative/ Benchmark

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

Alternative Assessments

  • Placement Test

  • ExamView Test Generator

  • Math and Science Project
  • End of Year Assessment
  • Benchmark Assessment

Learning Activities

  • Multiply fractions by whole numbers and fractions by fractions, drawing visual models to represent products, showing  (a/b) x (c/d) = ab(1/bd), and creating story contexts.
  • 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.
  • Solve real-world problems involving multiplication of fractions (including mixed numbers), using visual fraction models or equations to represent the problem.
  • Divide a unit fraction by a non-zero 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.
  • Solve real-world problems involving division of unit fractions by whole numbers or whole numbers by unit fractions.
  • Explain patterns in the placement of the decimal point when a decimal is multiplied or divided by a power of 10; represent powers of 10 using whole-number exponents.
  • 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.
  • Convert standard measurement units within the same system (e.g., centimeters to meters) in order to solve multi-step problems.

Materials / Equipment / Resources

Core Instructional

Materials and Texts

enVisionmath 2.0 ( Hardcopy and electronic edition)

  • Teacher Edition
  • Student Edition
  • Math and Science Project
  • Vocabulary Cards and Activities
  • Fluency Practice Activity
  • Digital Resources

Google Classroom

Seesaw

Equipment

Chromebooks

Smartboards

Math Centers

Supplemental Resources

5.NF.B.4b New Park

5.NF.B.5 Comparing Heights of Buildings

5.NF.B.5 Grass Seedlings

5.NF.B.5b Mrs. Gray's Homework Assignment

5.NF.B.6 To Multiply or not to multiply?

5.NF.B.7 Banana Pudding

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.4. Apply and extend previous understandings of multiplication to multiply a fraction or whole number by a fraction.

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.5. Interpret multiplication as scaling (resizing), by:

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.

  • 5.NF.B.6. Solve real world problems involving multiplication of fractions and mixed numbers, e.g., by using visual fraction models or equations to represent the problem.

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.7. Apply and extend previous understandings of division to divide unit fractions by whole numbers and whole numbers by unit fractions. *(benchmarked)

5.NF.B.7a. Interpret division of a unit fraction by a non-zero 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 non-zero 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 1/3-cup 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.

  • 5.NBT.A.2. Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and explain patterns in the placement of the decimal point when a decimal is multiplied or divided by a power of 10. Use whole-number exponents to denote powers of 10.

MP.2   Reason abstractly and quantitatively.

MP.6   Attend to precision.

 MP.7   Look for and make use of structure.

  • 5.NBT.B.7. 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; relate the strategy to a written method and explain the reasoning used.  *(benchmarked)

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.MD.A.1. Convert among different-sized standard measurement units within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world 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.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:

5-ESS2-2, 5-ESS3-1,

5-LS1-1, 5-LS2-1, 5-PS3-1, 5-PS1-3, 5-PS1-1, 5-PS1-4, 5-PS1-2, 5-ESS2-1, 5-ESS3-1

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.

DELETE OUT THOSE NOT APPLICABLE TO THIS UNIT

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)

Intervention Activity

Problem-solving 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 real-world and mathematical problems, analyze patterns and relationships, classify two-dimensional figures into categories based on their properties, represent and interpret data, perform operations with multi-digit 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 two-dimensional 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 multi-digit 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 Multi-Digit 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 Two-Dimensional Figures

Learning Targets

Essential Questions

Topic 3 - What are the standard procedures for estimating and finding products of multi-digit 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:

  •  Graph points on the coordinate plane to solve real-world and mathematical problems
  •  Analyze patterns and relationships
  •  Classify two dimensional figures into categories based on their properties
  •  Represent and interpret data
  •  Perform operations with multi-digit whole numbers and with decimals to hundredths
  •  Apply and extend previous understanding of multiplication and division

Know

By the end of this unit, students will know:

  •  Coordinate plane as perpendicular number lines.
  •  Perpendicular number lines (axes) define a coordinate system.
  •  Intersection of the lines (origin) coincides with the 0 on each number line.
  •  Given points in the plane is located using an ordered pair of numbers (coordinates).
  •  First numbers in an ordered pair indicates how far to travel from the origin in the direction of the x-axis.
  •  Second numbers in an ordered pair indicate how far to travel in the direction of the y-axis.
  •  Attributes belonging to a category of two-dimensional figures also belong to all subcategories of that category.

Do

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

  •  Graph points defined by whole number coordinates in the first quadrant of the coordinate plane in order to represent real world

   and mathematical problems.

  •  Interpret coordinates in context.
  •  Use two rules to create two numerical patterns.
  •  Compare corresponding terms (e.g. compare the first terms in each list, compare the second terms in each list, etc).
  •  Identify the relationship between corresponding terms and write ordered pairs.
  •  Graph the ordered pairs.
  •  Classify two-dimensional figures (triangles, quadrilaterals) based on shared attributes (e.g. parallel sides, number of sides, angle

   size, side length, etc.).

  •  Arrange the categories/subcategories of figures (e.g. squares, rectangles, trapezoids, etc) in a hierarchy based on attributes.
  •  Identify attributes of a two-dimensional shape based on attributes of the categories to which it belongs.
  •  Use measurement information to create a line plot.
  •  Using measurement information presented in line plots, add, subtract, multiply and divide fractions in order to solve problems.
  •  Multiply multi-digit whole numbers with accuracy and efficiency.
  •  Add and subtract decimals to hundredths using concrete models and drawings.
  •  Multiply and divide decimals to hundredths using concrete models and drawings.
  •  Add, subtract, multiply, and divide decimals to hundredths using strategies based on place value, properties of operations,

   and/or the relationship between addition and subtraction.

  •  Relate the strategy to the written method and explain the reasoning used.
  •  Use a story context to interpret division of a unit fraction by a whole number.
  •  Use a story context to interpret division of a whole number by a unit fraction.
  •  Divide unit fractions by whole numbers to solve real world problems, using visual fraction models and equations to represent the

   problem.

  •  Divide whole numbers by unit fractions to solve real world problems, using visual fraction models and equations to represent the

   problem.

  •  Use a story context to interpret division of a unit fraction by a whole number.
  •  Use a story context to interpret division of a whole number by a unit fraction.
  •  Divide unit fractions by whole numbers to solve real world problems, using visual fraction models and equations to represent the

   problem.

  •  Divide whole numbers by unit fractions to solve real world problems, using visual fraction models and equations to represent the problem.

Evidence of Learning

Formative

Summative/ Benchmark

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

Alternative Assessments

  • Placement Test

  • ExamView Test Generator

  • Math and Science Project
  • End of Year Assessment
  • Benchmark Assessment

Learning Activities

  • 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.
  • Generate two numerical patterns from two given rules, identify the relationship between corresponding terms, create ordered pairs and graph the ordered pairs.
  • Classify two- dimensional figures in a hierarchy based on properties.
  • Make a line plot to display a data set in measurements in fractions of a unit (1/2, 1/4, 1/8) and use it to solve problems involving the four operations on fractions with unlike denominators.
  • Fluently multiply multi-digit whole numbers with accuracy and efficiency.
  • 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.
  • Solve real world problems involving division of unit fractions by whole numbers or whole numbers by unit fractions.

Materials / Equipment / Resources

Core Instructional

Materials and Texts

enVisionmath 2.0 ( Hardcopy and electronic edition)

  • Teacher Edition
  • Student Edition
  • Math and Science Project
  • Vocabulary Cards and Activities
  • Fluency Practice Activity
  • Digital Resources

Google Classroom

Seesaw

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.OA.B.3 Sidewalk Patterns

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

5.NBT.B.7, 5.NF.B.3 What is 23 divided by 5?

5.NF.B.7c Salad Dressing

Standards

Content Statement

Mathematical Practice Standards

  • 5.G.A.1. Use a pair of perpendicular number lines, called axes, to define a coordinate system, with the intersection of the lines (the origin) arranged to coincide with the 0 on each line and a given point in the plane located by using an ordered pair of numbers, called its coordinates. Understand that the first number indicates how far to travel from the origin in the direction of one axis, and the second number indicates how far to travel in the direction of the second axis, with the convention that the names of the two axes and the coordinates correspond (e.g., x-axis and x-coordinate, y-axis and y-coordinate).

  • 5.G.A.2. Represent real world and mathematical problems by graphing points in the first quadrant of the coordinate plane, and interpret coordinate values of points in the context of the situation.

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.OA.A.3. Generate two numerical patterns using two given rules. Identify apparent relationships between corresponding terms. Form ordered pairs consisting of corresponding terms from the two patterns, and graph the ordered pairs on a coordinate plane. For example, given the rule “Add 3” and the starting number 0, and given the rule “Add 6” and the starting number 0, generate terms in the resulting sequences, and observe that the terms in one sequence are twice the corresponding terms in the other sequence. Explain informally why this is so.

MP.2   Reason abstractly and quantitatively.

MP.7   Look for and make use of structure.

  • 5.G.B.3. Understand that attributes belonging to a category of two-dimensional figures also belong to all subcategories of that category.

 For example, all rectangles have four right angles and squares are rectangles, so all squares have four right angles.

 

  • 5.G.B.4. Classify two-dimensional figures in a hierarchy based on properties.

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.

  • 5.MD.B.2. Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8). Use operations on fractions for this grade to solve problems involving information presented in line plots.

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.

  • 5.NBT.B.5. Fluently multiply multi-digit whole numbers using the standard algorithm. *(benchmarked)

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.B.7. 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; relate the strategy to a written method and explain the reasoning used. *(benchmarked)

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.7. Apply and extend previous understandings of division to divide unit fractions by whole numbers and whole numbers by unit fractions.*(benchmarked)

5.NF.B.7c. Solve real world problems involving division of unit fractions by non-zero 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 1/3-cup 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:

5-ESS2-2, 5-ESS3-1,5-PS1-3, 5-PS1-1,5-LS1-1,5-LS2-1,5-PS3-1,5-PS2-1,5-ESS1-1, 5-ESS1-2

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.

DELETE OUT THOSE NOT APPLICABLE TO THIS UNIT

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

Problem-solving 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