MATH  GRADE 3                                                                                        Page  of

Units:

Unit 1:  Multiplication, Division and Concepts of Area

Unit 2: Modeling Multiplication, Division and Fractions

Unit 3: Fractions as Numbers and Measurement

Unit 4:  Representing Data


Unit Title

Unit 1:  Multiplication, Division and Concepts of Area

Timeframe 

40 days 

Unit Summary

In this unit students will use critical thinking skills to interpret products of whole numbers as repeated addition and as the total number of objects (up to 100) in equal groups or arrays (CRP8). They will reason effectively and evaluate evidence to interpret quotient as a set of objects (up to 100) partitioned equally into a number of shares and as the number of equal shares. Students will use multiplication and division within 100 to articulate findings to word problems by modeling equal groups or arrays and by writing equations to represent equal groups or arrays. Work collaboratively to determine the unknown in a division or multiplication equation relating 3 whole numbers (within 100)(CRP12). Communicate constructively to share solutions to division problems with whole numbers by representing the problem as an unknown factor problem (CRP4). Apply technology effectively to measure areas by counting unit squares (cm2 , m2 , in2 , ft2 , and improvised units)(CRP11). Interact effectively with others to tile a rectangle to find its area and explain the relationship between tiling and multiplying side lengths to find the area of rectangles. Understand different viewpoints and perspectives while solving real world problems by multiplying side lengths to find areas of rectangles (CRP5). Demonstrate openness to new ideas, information, tools and ways of thinking to multiply one digit whole numbers by multiples of 10 (10-90)(CRP6).

Topic 1- Understand Multiplication and Division of Whole Numbers

Topic 2- Multiplication Facts: Use Patterns

Topic 3- Apply Properties: Multiplication Facts for 3,4,6,7,8

Topic 4- Use Multiplication to Divide; Division Facts

Topic 5- Fluently Multiply and Divide within 100

Topic 6- Connect Area to Multiplication and Addition

Topic 8- Use Strategies and Properties to Add Subtract

Topic 9- Fluently Add and Subtract Within 1,000

Topic 10- Multiply by Multiples of 10

Learning Targets

Essential Questions

Topic 1: What are the different meanings of multiplication and division?

Topic 2: How can unknown multiplication facts be found using patterns and properties?

Topic 3:  How can unknown multiplication facts be found using known facts?

Topic 4:  How can unknown division facts be found using known multiplication facts?

Topic 5:  What are strategies to solve multiplication and division facts?

Topic 6:  How can area be measured and found?

Topic 8:  How can sums and differences be estimated and found mentally?

Topic 9:  What are standard procedures for adding and subtracting whole numbers?

Topic 10:  What are ways to multiply by multiples of 10?

Enduring Understandings

Students will understand:

  • Represent and solve problems involving multiplication and division

  • Understand properties of multiplication and the relationship between multiplication and division

  • Understand concepts of area and relate area to multiplication and addition (Geometric measurement)

  • Use place value understanding and properties of operations to perform multi-digit arithmetic

Know

By the end of this unit, students will know:

  • Multiplication is a means to determine the total number of objects when there are a specific number of groups with the same

   number of objects in each group.

  •  Multiplication gives the same result as repeated addition.

  •  Product of two whole numbers is the total number of objects in a number of equal groups.

  •  Division is a means to finding equal groups of objects.

  •  Division gives the same result as repeated subtraction.

  •  Quotient of two whole numbers is the number of objects in each share when objects are grouped equally into shares.

  •  Quotient of two whole numbers is the number of shares when objects are grouped into equal shares of objects.

  •  Equal sign indicates that the value of the numerical expressions on each side are the same.  

  •  Unknown in an equation ( 4 x __ = 20 and 20 = ? x 4) represents a number.

  •  Unknown can be in different positions.

  •  Letters can represent numbers in equations.

  •  Division can be represented as a multiplication problem having an unknown factor.

  •  Relationships between factors, products, quotients, divisors and dividends.

  •  Area is the amount of space inside the boundary of a (closed) figure.

  •  Square with side length 1 unit, called “a unit square,” is said to have “one square unit” of area, and can be used to measure area.

  •  Plane figure which can be covered without gaps or overlaps by n unit squares is said to have an area of n square units area can be

   found by covering a figure with unit squares.

  •  Area of a figure can be determined using unit squares of other dimensions.

  •  Area of a rectangle is found by multiplying the side lengths.

  •  Area of a rectangle may be found by tiling.

  •  Rounding leads to an approximation or estimate.

  •  Multiples of 10 can be represented as a specific number of groups of ten.

Do

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

  •  Interpret products of whole numbers as a total number of objects.

  •  Use repeated addition to find the total number of objects arranged in an array and in equal groups and compare to the result of

   multiplication.

  •  Describe a context in which a total number of objects is represented by a product.

  •  Interpret the product in the context of a real-world problem.

  •  Interpret division of whole numbers as a number of equal shares or the number of groups when objects are divided equally.

  •  Use repeated subtraction to find the number of shares or the number of groups and compare to the result of division.

  •  Describe a context in which the number of shares or number of groups is represented with division.

  •  Interpret the quotient in the context of a real-world problem.

  •  Multiply to solve word problems involving  equal groups and arrays.

  •  Divide to solve word problems involving  equal groups and arrays.

  •  Represent a word problem with a drawing showing equal groups, arrays, equal shares, and/or total objects.

  •  Represent a word problem with an equation.

  •  Determine which operation is needed to find the unknown.

  •  Multiply or divide, within 100, to find the unknown whole number in a multiplication or division equation.

  •  Write division number sentences as unknown factor problems.

  •  Solve division of whole numbers by finding the unknown factor.

  •  Count unit squares in order to measure the area of a figure.

  •  Use unit squares of centimeters, meters, inches, feet, and other units to measure area.

  •  Tile a rectangle with unit squares.

  •  Multiply side lengths of a rectangle to find its area and compare the result to that found by tiling the rectangle with unit squares.

  •  Solve real world and mathematical problems involving measurement.

  •  Represent a rectangular area as the product of whole-numbers.

  •  Use number lines and a hundreds charts to explain rounding numbers to the nearest 10 and 100.

  •  Round a whole number to the nearest 10.

  •  Round a whole number to the nearest 100.

  •  Multiply to determine the total number of groups of ten.

  •  Multiply one-digit whole numbers by multiples of 10

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

  • Interpret products of whole numbers as repeated addition and as the total number of objects (up to 100) in equal groups or arrays.
  • Interpret the quotient as a set of objects (up to 100) partitioned equally into a number of shares and as the number of equal shares.
  • Use multiplication and division within 100 to solve word problems by modeling equal groups or arrays and by writing equations to represent equal groups or arrays
  • Determine the unknown in a division or multiplication equation relating 3 whole numbers (within 100)
  • Solve division of whole numbers by representing the problem as an unknown factor problem.
  • Measure areas by counting unit squares (cm2, m2, in2, ft2, and improvised units).
  • Tile a rectangle to find its area and explain the relationship between tiling and multiplying side lengths to find the area of rectangles; solve real world problems by multiplying side lengths to find areas of rectangles.
  • Round whole numbers to the nearest 10 or 100.
  • Multiply one digit whole numbers by multiples of 10 (10-90).

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

3.OA.A.2 Fish Tanks

3.OA.A.3 Analyzing Word Problems Involving Multiplication

3.OA.A.4 Finding the unknown in a division equation

3.MD.C.6 Finding the Area of Polygons

3.MD.C.7a India's Bathroom Tiles

3.NBT.A.1 Rounding to 50 or 500

3.NBT.A.1 Rounding to the Nearest Ten and Hundred

3.NBT.A.3 How Many Colored Pencils

Standards

Content Statement

Mathematical Practice Standards

  • 3.OA.A.1.  Interpret products of whole numbers, e.g., interpret 5 x 7 as the total number of objects in 5 groups of 7 objects each.  For example, describe and/or represent a context in which a total number of objects can be expressed as 5 x 7.

MP 2   Reason abstractly and quantitatively.

MP.4   Model with mathematics.

  • 3.OA.A.2. Interpret whole-number quotients of whole numbers, e.g., interpret 56 ÷ 8 as the number of objects in each share when 56 objects are partitioned equally into 8 shares, or as a number of shares when 56 objects are partitioned into equal shares of 8 objects each. For example, describe and/or represent a context in which a number of shares or a number of groups can be expressed as 56 ÷ 8.

MP 2   Reason abstractly and quantitatively.

MP.4   Model with mathematics.


  • 3.OA.A.3. Use multiplication and division within 100 to solve word problems in situations involving equal groups, arrays, and measurement quantities, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem.  *(benchmarked)

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

MP.4   Model with mathematics.

  • 3.OA.A.4. Determine the unknown whole number in a multiplication or division equation relating three whole numbers. For example, determine the unknown number that makes the equation true in each of the equations 8 × ? = 48, 5 =  ÷ 3,  6 × 6 = ?.

MP 2   Reason abstractly and quantitatively.         

MP.7   Look for and make use of structure.

  • 3.OA.B.6. Understand division as an unknown-factor problem. For example, find 32 ÷ 8 by finding the number that makes 32 when multiplied by 8.

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

MP.6   Attend to precision.

MP.7   Look for and make use of structure.

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

3.MD.C.5a. A square with side length 1 unit, called “a unit square,” is said to have “one square unit” of area, and can be used to measure area.

3.MD.C.5b. A plane figure which can be covered without gaps or overlaps by n unit squares is said to have an area of n square units.

  • 3.MD.C.6. Measure areas by counting unit squares (square cm, square m, square in, square ft, and non-standard units).

MP 2   Reason abstractly and quantitatively.                        

MP.4   Model with mathematics.              

MP.5   Use appropriate tools strategically.

MP.7   Look for and make use of structure.

  • 3.MD.C.7.  Relate area to the operations of multiplication and addition.

3.MD.C.7a. Find the area of a rectangle with whole-number side lengths by tiling it, and show that the area is the same as would be found by multiplying the side lengths.

3.MD.C.7b. Multiply side lengths to find areas of rectangles with whole-number side lengths in the context of solving real world and mathematical problems, and represent whole-number products as rectangular areas in mathematical reasoning.

MP.4   Model with mathematics.

MP.5   Use appropriate tools strategically.

  • 3.NBT.A.1. Round whole numbers to the nearest 10 or 100.

MP 2   Reason abstractly and quantitatively.

  • 3.NBT.A.3. Multiply one-digit whole numbers by multiples of 10 in the range   10 to 90 (e.g., 9 × 80, 5 × 60) using strategies based on place value and properties of operations.

MP 2   Reason abstractly and quantitatively.

21st Century Skills and Themes

Interdisciplinary Connections

Career Ready Practices

9.2 Career Awareness, Exploration, and

      Preparation  

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

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

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

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

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

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

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

NJSLSA.SL1. Prepare for andparticipate 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:

ESS2.D, 3-ESS2-1,3-ESS2-2, 3-ESS3-1, 3-LS3-1, C-LS3-2, 3-PS2-1, 3-PS2-2, 3-LS4-1, 3-LS4-4,  3-LS2-1, 3-LS4-3

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 4th grade,

  • 9.2.4.A.1 Identify reasons why people work, different types of work, and how work can help a person achieve personal and professional goals.  
  • 9.2.4.A.2 Identify various life roles and civic and work‐related activities in the school, home, and community.
  • 9.2.4.A.3 Investigate both traditional and nontraditional careers and relate information to personal likes and dislikes.
  • 9.2.4.A.4 Explain why knowledge and skills acquired in the elementary grades lay the foundation for future academic and career success.

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: Modeling Multiplication, Division and Fractions 

Timeframe 

40 days

Unit Summary

Use critical thinking skills to multiply and divide within 100 to solve word problems involving measurement quantities (area) using drawings (CRP8).  Multiply one-digit whole numbers by applying the properties of operations (commutative, associative, and distributive properties) and communicate answers effectively (CRP2).  Apply technology effectively to tile an area model to represent the distributive property (CRP11). Use creativity and critical thinking skills to solve real-world problems involving finding areas of rectilinear figures by decomposing them into non-overlapping rectangles and adding the areas of the non-overlapping parts (CRP8). Fluently multiply and divide within 40 using strategies such as the relationship between multiplication and division (CRP4).  Write equations when solving two-step word problems, using a symbol for an unknown.  Interact effectively with others to find the value of an unknown in an equation involving any of the four operations and use estimation strategies to assess the reasonableness of answers (CRP12). Reason effectively to recognize arithmetic patterns, including patterns in addition or multiplication tables, and explain the patterns using properties of operations (CRP4). Fluently add and subtract (with regrouping) two 2-digit whole numbers within 100. Work independently and/or in diverse teams to partition shapes into parts with equal areas and express the area of each part as a unit fraction; interpret the unit fraction 1/b as the quantity formed by 1 of b equal parts of a whole and the fraction a/b as the quantity formed by a parts of size 1/b (CRP6).

Topic 1- Understand Multiplication and Division of Whole Numbers

Topic 2- Multiplication Facts: Use Patterns

Topic 3- Apply Properties: Multiplication Facts for 3,4,6,7,8

Topic 4- Use Multiplication to Divide; Division Facts

Topic 5- Fluently Multiply and Divide within 100

Topic 6- Connect Area to Multiplication and Addition

Topic 8- Use Strategies and Properties to Add Subtract

Topic 9- Fluently Add and Subtract Within 1,000

Topic 11- Use Operations with Whole Numbers to Solve Problems

Learning Targets

Essential Questions

 

Enduring Understandings

Students will understand:

  • Represent and solve problems involving multiplication and division

  • Understand properties of multiplication and the relationship between multiplication and division

  • Geometric measurement: understand concepts of area and relate area to multiplication and to addition

  • Multiply and divide within 100

  • Solve problems involving the four operations, and identify and explain patterns in arithmetic

  • Use place value understanding and properties of operations to perform multi-digit arithmetic

  • Develop understanding of fractions as numbers.

  • Reason with shapes and their attributes

Know

By the end of this unit, students will know:

  •  Properties are rules about relationships between numbers.

  •  Changing the order of factors does not change the result of multiplication.

  •  Changing the order of numbers does change the result of division.

  •  Area of a rectangle with whole-number side lengths a and b + c is the sum of  a × b and a × c. 

  •  Area models can be used to represent the distributive property.

  •  Areas of rectilinear figures can be determined by decomposing them into non-overlapping rectangles and adding the areas of the

   parts.

  •  Letters or symbols in an equation represent an unknown quantity.

  •  Addition and multiplication tables reveal arithmetic patterns.

  •  Patterns may be related to whether a number is even or odd.

  •  Patterns exist in rows, columns and diagonals of addition tables and multiplication tables.

  •  Decomposing numbers into equal addends may reveal patterns.

  •  Wholes, when partitioned into equal parts, contain parts representing a unit fraction and each part is the same size.

  •  Each part has the same name and represents a unit fraction (one-half, one-third, one-fourth, one-sixth, one-eighth).

  •  The denominator is the total number of parts in the whole.

  •  The numerator is the number of parts in a given fraction.

  •  Fraction 1/b is the quantity formed by 1 part when a whole is partitioned into b equal parts.

  •  Fraction a/b as the quantity formed by a parts of size 1/b (e.g. 10/2 is 10 parts and each part is of size ½).

Do

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

  •  Multiply to solve word problems involving arrays and measurement quantities (area).

  •  Mivide to solve word problems involving arrays and measurement quantities (area).

  •  Represent a word problem with a drawing or array.

  •  Represent a word problem with an equation.

  •  Multiply whole numbers using the commutative property as a strategy.

  •  Multiply whole numbers using the associative property as a strategy.

  •  Use tiling to show that the area of a rectangle with whole-number side lengths a and b + c is the sum of a × b and a × c. 

  •  Multiply whole numbers using the distributive property as a strategy.

  •  Decompose rectilinear figures into non-overlapping rectangles.

  •  Find areas of non-overlapping rectangles and add to find the area of the rectilinear figure.

  •  Solve real world problems involving area of rectilinear figures.

  •  Multiply and divide within 40 with accuracy and efficiency.

  •  Represent the solution to two-step word problems with equations.

  •  Use a symbol to represent an unknown in an equation.

  •  Use rounding as an estimation strategy.

  •  Explain, using an estimation strategy, whether an answer is reasonable.

  •  Explain arithmetic patterns using properties of operations.

  •  Add and subtract two 2-digit whole numbers within 100 with accuracy and efficiency.

  •  Partition rectangles, and other shapes, into halves, thirds, fourths, sixths and eighths.

  •  Identify the fractional name of each part.

  •  Model and explain that a fraction a/b is the quantity formed by a parts of size 1/b (For example, 10/2 is 10 parts and each part is  of size ½).

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

  • Use multiplication and division within 100 to solve word problems involving measurement quantities (area) using drawings.
  • Multiply one-digit whole numbers by applying the properties of operations (commutative, associative, and distributive properties).
  • Use tiling and an area model to represent the distributive property.
  • Solve real-world problems involving finding areas of rectilinear figures by decomposing them into non-overlapping rectangles and adding the areas of the non-overlapping parts.
  • Fluently multiply and divide within 40 using strategies such as the relationship between multiplication and division.
  • Write equations when solving two-step word problems, using a symbol for an unknown; find the value of an unknown in an equation involving any of the four operations and use estimation strategies to assess the reasonableness of answers.
  • Recognize arithmetic patterns, including patterns in addition or multiplication tables, and explain the patterns using properties of operations.
  • Fluently add and subtract (with regrouping) two 2-digit whole numbers within 100.
  • Partition shapes into parts with equal areas and express the area of each part as a unit fraction; interpret the unit fraction 1/b as the quantity formed by 1 of b equal parts of a whole and the fraction a/b as the quantity formed by a parts of size 1/b.

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

3.OA.A.3 Two Interpretations of Division

3.OA.B.5 Valid Equalities? (Part 2)

3.MD.C.7c Introducing the Distributive Property

3.OA.C.7 Kiri's Multiplication Matching Game

3.OA.D.8 The Class Trip

3.OA.D.9 Addition Patterns

3.NF.A.1 Naming the Whole for a Fraction

3.G.A.2 Representing Half of a Circle

Standards

Content Statement

Mathematical Practice Standards

  • 3.OA.A.3. Use multiplication and division within 100 to solve word problems in situations involving equal groups, arrays, and measurement quantities, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem.  *(benchmarked)

        

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

MP.4   Model with mathematics.

  • 3.OA.B.5. Apply properties of operations as strategies to multiply and divide.

Examples: If 6 × 4 = 24 is known, then 4 × 6 = 24 is also known. (Commutative property of multiplication.) 3 × 5 × 2 can be found by 3 × 5 = 15, then 15 × 2 = 30, or by 5× 2 = 10, then 3 × 10 = 30. (Associative property of multiplication.) Knowing that 8 × 5 = 40 and 8 × 2 =16, one can find 8 × 7 as 8 × (5 + 2) = (8 × 5) + (8 × 2) = 40 + 16 = 56. (Distributive property.)

*[Students need not use the formal terms for these properties.]

*[Limit to single digit factors and multipliers. 7 x 4 x 5 would exceed grade 3 expectations because it would result in a two-digit multiplier (28 x 5)]

  • 3.MD.C.7.  Relate area to the operations of multiplication and addition.

3.MD.C.7c. Use tiling to show in a concrete case that the area of a rectangle with whole-number side lengths a and b + c is the sum of a × b and a × c. Use area models to represent the distributive property in mathematical reasoning.

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.        

  • 3.MD.C.7.  Relate area to the operations of multiplication and addition.

3.MD.C.7d. Recognize area as additive. Find areas of rectilinear figures by decomposing them into non-overlapping rectangles and adding the areas of the non-overlapping parts, applying this technique to solve real world problems.

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.        

  • 3.OA.C.7. Fluently multiply and divide within 100, using strategies such as the relationship between multiplication and division (e.g., knowing that 8 × 5 = 40, one knows 40 ÷ 5 = 8) or properties of operations. By the end of Grade 3, know from memory all products of two one-digit numbers. *(benchmarked)

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.

  • 3.OA.D.8. Solve two-step word problems using the four operations. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. *(benchmarked)

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.

  • 3.OA.D.9.  Identify arithmetic patterns (including patterns in the addition table or multiplication table), and explain them using properties of operations.

For example, observe that 4 times a number is always even, and explain why 4 times a number can be decomposed into two equal addends. 

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

MP.6   Attend to precision.

MP.7   Look for and make use of structure.

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

  • 3.NBT.A.2. Fluently add and subtract within 1000 using strategies and algorithms based on place value, properties of operations, and/or the relationship between addition and subtraction.  *(benchmarked)

MP 2   Reason abstractly and quantitatively.

  • 3.NF.A.1.  Understand a fraction 1/b as the quantity formed by 1 part when a whole is partitioned into b equal parts; understand a fraction a/b as the quantity formed by a parts of size 1/b.

*[Grade 3 expectations in this domain are limited to fractions with denominators 2, 3, 4, 6, and 8.]

  • 3.G.A.2.  Partition shapes into parts with equal areas. Express the area of each part as a unit fraction of the whole. For example, partition a shape into 4 parts having equal area and describe the area of each part as 1/4 of the area of the shape.

 

MP 2   Reason abstractly and quantitatively.

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  

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

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

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

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

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

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

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

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

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

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

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

Science:

ESS2.D, 3-ESS2-1,3-ESS2-2, 3-ESS3-1, 3-LS3-1, C-LS3-2,

3-PS2-1,3-PS2-2, 3-LS2-1, 3-LS4-3, 3-LS4-1, 3-LS4-4

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 4th grade,

  • 9.2.4.A.1 Identify reasons why people work, different types of work, and how work can help a person achieve personal and professional goals.  
  • 9.2.4.A.2 Identify various life roles and civic and work‐related activities in the school, home, and community.
  • 9.2.4.A.3 Investigate both traditional and nontraditional careers and relate information to personal likes and dislikes.
  • 9.2.4.A.4 Explain why knowledge and skills acquired in the elementary grades lay the foundation for future academic and career success.

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: Fractions as Numbers and Measurement

Timeframe 

40 days

Unit Summary

Topic 12- Understand Fractions as Numbers

Topic 13- Fraction Equivalences and Comparison

Topic 14- Solve Time, Capacity, and Mass problems

Topic 15- Attributes of Two-Dimensional Shapes

Topic 16- Solve Perimeter Problem

Learning Targets

Essential Questions

Topic 12 - What are different interpretations of a fraction?

Topic 13 - What are different ways to compare fractions?

Topic 14 - How can time, capacity, and mass be measured and found?

Topic 15 - How can two-dimensional shapes be described, analyzed, and classified?

Topic 16 - How can perimeter be measured and found?

Enduring Understandings

Students will understand:

  • Develop understanding of fractions as numbers

  • Solve problems involving measurement and estimation of intervals of time, liquid volumes, and masses of objects

  • Reason with shapes and their attributes

  • Recognize perimeter as an attribute of plane figures and distinguish between linear and area measure

  • Multiply and divide within 100

Know

By the end of this unit, students will know:

  •  Fraction is a number and has its place on the number line.

  •  When placing unit fractions on a number line, the space between 0 and 1 is the whole and must be partitioned into equal parts.

  •  Each part of a whole has the same size (one-half, one-third, one-fourth, one-sixth or one-eighth).

  •  Parts of the whole that begin at 0 and ends at 1/b on the number line is the location of fraction 1/b (one-half, one-third, one-fourth, one-sixth, or one-eighth).

  •  Comparing fractions, each referencing the same whole.

  •  Fractions are equivalent if they are the same size.

  •  Fractions are equivalent if they are at the same point on a number line.

  •  Analog clocks represent hours as numbers and minutes are represented as tick marks.

  •  Mass may be measured in grams and kilograms.

  •  Mass is measured by weighing.

  •  Volume may be measured in liters.

  •  Volume may be measured with instruments such as beakers.

  •  Shapes in different categories share attributes.

  •  Quadrilaterals are closed figures with four sides.

  •  Rhombuses, rectangles, etc, and other quadrilaterals share attributes.

  •  Perimeter of a figure is equivalent to the sum of the length of all of the sides.

  •  Rectangles that have same perimeter can have different areas.

  •  Rectangles that have same area can have different perimeters.

Do

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

  •  Partition a number line into parts of equal sizes between 0 and 1 (halves, thirds, fourths sixths and eighths).

  •  Plot unit fractions on the number line.

  •  Identify multiple parts (of length 1/b) on the number line.

  •  Plot a fraction on the number line by marking off multiple parts of size 1/b.

  •  Plot fractions equivalent to whole numbers including 0 and up to 5.

  •  Find equivalent fractions (limited to fractions with denominators 2, 3, 4, 6, and 8).

  •  Explain why two fractions are equivalent; use a visual fraction model to support explanation.

  •  Write whole numbers as fractions.

  •  Identify fractions that are equivalent to whole numbers.

  •  Compare two fractions having the same numerator by reasoning about their size.

  •  Compare two fractions having the same denominator by reasoning about their size.

  •  Explain why comparing fractions that do not have the same whole is not valid (reason about their size and support reasoning with a

   model).

  •  Use <, =, and > symbols to write comparisons of fractions and justify conclusions with a visual fraction model.

  •  Generate simple equivalent fractions, explain why they are equivalent, and support the explanation with visual fraction models;

   locate them on the number line.

  •  Express whole numbers as fractions, identify fractions equivalent to whole numbers and locate them on the number lin

  •  Tell time to the nearest minute using digital and analog clocks.

  •  Write time to the nearest minute using analog clocks.

  •  Choose appropriate strategies to solve real world problems involving time.

  •  Use the number line as a visual model to determine intervals of time as jumps on a number line.

  •  Measure time intervals.

  •  Measure and read a scale to estimate volume.

  •  Measure and read a scale to estimate mass.

  •  Add, subtract, multiply, or divide to solve one-step word problems involving masses or volumes.

  •  Classify and sort shapes by attributes.

  •  Explain why rhombuses, rectangles, and squares are examples of quadrilaterals.

  •  Draw examples of quadrilaterals.

  •  Determine the perimeter of various plane shapes and irregular shapes given the side lengths.

  •  Determine the unknown side length give the perimeter and other sides.

  •  Show rectangles having the same perimeter and different areas.

  •  Show rectangles having different perimeters and the same area.

  •  Multiply and divide within 100 with accuracy and efficiency.

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

  •  Draw a number line depicting the position of 1/b (with b = 2, 3, 4, 6, or 8); represent the unit fraction ¼ on the number line by partitioning the number line between 0 and 1 into 4 equal lengths and name the point at the end of the first length as the position of the unit fraction ¼; apply the same method for placing points 1/2, 1/3, 1/6, and 1/8 on the number line.
  • Draw a number line depicting the position of fraction a/b (with b = 2, 4, 3, 6, or 8, and including whole numbers up to 5).
  • Compare two fractions having the same numerator; compare two fractions having the same denominator; reason about their size and use the symbols >, =, or < to record the comparison.
  • Tell and write time to the nearest minute, and solve word problems with addition and subtraction involving time intervals in minutes.
  • Solve one step word problems by estimating and measuring volume and mass using appropriate tools and standard units of grams, kilograms, and liters.
  • Recognize rhombuses, rectangles, and squares as examples of quadrilaterals, and draw examples of quadrilaterals that do not belong to any of these subcategories.
  • Solve real world and mathematical problems involving perimeters of polygons, including finding the perimeter given the side lengths, finding an unknown side length, and exhibiting rectangles with the same perimeter and different areas or with the same area and different perimeters.
  • Fluently multiply and divide within 100 using strategies such as the  
    relationship between multiplication and division.

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

3.NF.A.2 Closest to 1/2

3.NF.A.2 Find 1 Starting from 5/3

3.NF.A.2 Locating Fractions Greater than One on the Number Line

3.NF.A.3b, 3.G.A.2, 3.MD.C.6 Halves, thirds, and sixths

3.MD.A.1 Dajuana's Homework

3.MD.A.2 How Heavy?

3.MD.D Shapes and their Insides

Standards

Content Statement

Mathematical Practice Standards

  • 3.NF.A.2. Understand a fraction as a number on the number line; represent fractions on a number line diagram.

3.NF.A.2a. Represent a fraction 1/b on a number line diagram by defining the interval from 0 to 1 as the whole and partitioning it into b equal parts. Recognize that each part has size 1/b and that the endpoint of the part based at 0 locates the number 1/b on the number line.

3.NF.A.2b. Represent a fraction a/b on a number line diagram by marking off a lengths 1/b from 0. Recognize that the resulting interval has size a/b and that its endpoint locates the number a/b on the number line.

*[Grade 3 expectations in this domain are limited to fractions with denominators 2, 3, 4, 6, and 8.]

MP.5   Use appropriate tools strategically.

  • 3.NF.A.3. Explain equivalence of fractions in special cases, and compare fractions by reasoning about their size

3.NF.A.3a. Understand two fractions as equivalent (equal) if they are the same size, or the same point on a number line.

3.NF.A.3b. Recognize and generate simple equivalent fractions, e.g., 1/2 = 2/4, 4/6 = 2/3). Explain why the fractions are equivalent, e.g., by using a visual fraction model.

3.NF.A.3c. Express whole numbers as fractions, and recognize fractions that are equivalent to whole numbers. Examples: Express 3 in the form 3 = 3/1; recognize that 6/1 = 6; locate 4/4 and 1 at the same point of a number line diagram.

3.NF.A.3d. Compare two fractions with the same numerator or the same denominator by reasoning about their size. Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with the symbols >, =, or <, and justify the conclusions, e.g., by using a visual fraction model.

*[Grade 3 expectations in this domain are limited to fractions with denominators 2, 3, 4, 6, and 8.]

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.

  • 3.MD.A.1. Tell and write time to the nearest minute and measure time intervals in minutes. Solve word problems involving addition and subtraction of time intervals in minutes. (e.g., by representing the problem on a number line diagram)

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.

  • 3.MD.A.2. Measure and estimate liquid volumes and masses of objects using standard units of grams (g), kilograms (kg), and liters (l). Add, subtract, multiply, or divide to solve one-step word problems involving masses or volumes that are given in the same 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.

  • 3.G.A.1. Understand that shapes in different categories (e.g., rhombuses, rectangles, and others) may share attributes (e.g., having four sides), and that the shared attributes can define a larger category (e.g., quadrilaterals).  Recognize rhombuses, rectangles, and squares as examples of quadrilaterals, and draw examples of quadrilaterals.

MP.5   Use appropriate tools strategically.

MP.6   Attend to precision.        

MP.7   Look for and make use of structure.

  • 3.MD.D.8. Solve real world and mathematical problems involving perimeters of polygons, including finding the perimeter given the side lengths, finding an unknown side length, and exhibiting rectangles with the same perimeter and different areas or with the same area and different perimeters.

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.

  • 3.OA.C.7. Fluently multiply and divide within 100, using strategies such as the relationship between multiplication and division (e.g., knowing that 8 × 5 = 40, one knows 40 ÷ 5 = 8) or properties of operations. By the end of Grade 3, know from memory all products of two one-digit numbers. *(benchmarked)

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.

21st Century Skills and Themes

Interdisciplinary Connections

Career Ready Practices

9.2 Career Awareness, Exploration, and

      Preparation  

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

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

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

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

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

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

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

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

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

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

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

Science:

3-PS2-3, 3-PS2-4, 3-LS1.1, 3-LS14-2, 3-PS2-1,3-PS2-2,

3-LS4-1, 3-LS4-4,  3-LS2-1, 3-LS4-3

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 4th grade,

  • 9.2.4.A.1 Identify reasons why people work, different types of work, and how work can help a person achieve personal and professional goals.  
  • 9.2.4.A.2 Identify various life roles and civic and work‐related activities in the school, home, and community.
  • 9.2.4.A.3 Investigate both traditional and nontraditional careers and relate information to personal likes and dislikes.
  • 9.2.4.A.4 Explain why knowledge and skills acquired in the elementary grades lay the foundation for future academic and career success.

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 4:  Representing Data

Timeframe 

40 days

Unit Summary

Topic 7- Represent and Interpret Data

Topic 11- Use Operations with Whole Numbers to Solve Problems

Learning Targets

Essential Questions

Topic 7 - How can data be represented, interpreted, and analyzed?

Topic 11 - What are ways to solve two-step problems?

Enduring Understandings

Students will understand:

  • Represent and interpret data

  • Multiply and divide within 100

  • Use place value understanding and properties of operations to perform multi-digit arithmetic

  • Understand concepts of area and relate area to multiplication and to addition

Know

By the end of this unit, students will know:

  •  Graphs organize information and contain labels.

  •  Pictures and bars can represent numbers in graphs.

  •  Different graphs may display different scales.

  •  Show measurements on a line plot displays the information in an organized way

  •  A letter or variable in an equation represents an unknown quantity.

  •  Areas of rectilinear figures can be determined decomposing the them into non-overlapping rectangles and adding the areas of the parts.

Do

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

  •  Draw scaled picture graphs.

  •  Draw scaled bar graphs.

  •  Analyze, interpret and create bar graphs and pictographs in real world situations.

  •  Solve “how many more” and “how many less” problems using scaled bar graphs.

  •  Measure length using rulers marked with inch, quarter inch and half inch

  •  Generate measurement data by measuring length and create a line plot of the data

  •  Accurately measure several small objects using a standard ruler and display findings on a line plot

  •  Display data on line plots with horizontal scales in whole numbers, halves, and quarters

  •  Multiply and divide within 100 with accuracy and efficiency.

  •  Represent two-step word problems with equation(s) containing unknowns.

  •  Perform operations in the conventional order (no parentheses).

  •  Use rounding as an estimation strategy.

  •  Explain, using an estimation strategy, whether an answer is reasonable.

  •  Add and subtract within 1000 with accuracy and efficiency.

  •  Decompose rectilinear figures into non-overlapping rectangles.

  •  Find areas of non-overlapping rectangles and add to find the area of the rectilinear figure.

  •  Solve real world problems involving area of rectilinear figures.

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

  • Draw scaled picture and scaled bar graphs to represent data with several categories.  Solve one and two-step word problems using scaled bar graphs.
  • Depict data measured in fourths and halves of an inch with a line plot with scales marked with appropriate units
  • Fluently multiply and divide within 100 using strategies such as the relationship between multiplication and division.
  • Write equation(s) containing an unknown and find the value of an unknown in an equation that is a representation of a two-step word problem (with any four operations); use estimation strategies to assess the reasonableness of answers.
  • Fluently add and subtract within 1000 using strategies and algorithms based on place value, properties of operations, and/or the relationship between addition and subtraction.
  • Solve real world problems involving finding areas of rectilinear figures by decomposing them into non-overlapping rectangles and adding the areas of the non-overlapping parts.

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

3.MD.C.7d Three Hidden Rectangles

3.OA.D.8 The Stamp Collection

3.NBT.A.2, 3.MD.B.3, 3.OA.A.3 Classroom Supplies

Standards

Content Statement

Mathematical Practice Standards

  • 3.MD.B.3.  Draw a scaled picture graph and a scaled bar graph to represent a data set with several categories. Solve one- and two-step “how many more” and “how many less” problems using information presented in scaled bar graphs. For example, draw a bar graph in which each square in the bar graph might represent 5 pets.

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

MP 2   Reason abstractly and quantitatively.
MP.4   Model with mathematics.

  • 3.MD.B.4.  Generate measurement data by measuring lengths using rulers marked with halves and fourths of an inch. Show the data by making a line plot, where the horizontal scale is marked off in appropriate units— whole numbers, halves, or quarters.

MP 2   Reason abstractly and quantitatively.

MP.5   Use appropriate tools strategically.

  • 3.OA.C.7. Fluently multiply and divide within 100, using strategies such as the relationship between multiplication and division (e.g., knowing that 8 × 5 = 40, one knows 40 ÷ 5 = 8) or properties of operations. By the end of Grade 3, know from memory all products of two one-digit numbers. *(benchmarked)

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.

  • 3.OA.D.8. Solve two-step word problems using the four operations. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. *(benchmarked)

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.

  • 3.NBT.A.2. Fluently add and subtract within 1000 using strategies and algorithms based on place value, properties of operations, and/or the relationship between addition and subtraction. *(benchmarked)

MP 2   Reason abstractly and quantitatively.

  • 3.MD.C.7.  Relate area to the operations of multiplication and addition.

3.MD.C.7d. Recognize area as additive. Find areas of rectilinear figures by decomposing them into non-overlapping rectangles and adding the areas of the non-overlapping parts, applying this technique to solve real world problems. *(benchmarked)

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.

21st Century Skills and Themes

Interdisciplinary Connections

Career Ready Practices

9.2 Career Awareness, Exploration, and

      Preparation  

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

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

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

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

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

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

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

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

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

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

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

Science:

ESS2.D, 3-ESS2-1,3-ESS2-2, 3-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 4th grade,

  • 9.2.4.A.1 Identify reasons why people work, different types of work, and how work can help a person achieve personal and professional goals.  
  • 9.2.4.A.2 Identify various life roles and civic and work‐related activities in the school, home, and community.
  • 9.2.4.A.3 Investigate both traditional and nontraditional careers and relate information to personal likes and dislikes.
  • 9.2.4.A.4 Explain why knowledge and skills acquired in the elementary grades lay the foundation for future academic and career success.

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