Units: Unit 1:  Multiplication, Division and Concepts of AreaUnit 2: Modeling Multiplication, Division and FractionsUnit 3: Fractions as Numbers and MeasurementUnit 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:

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

Know

By the end of this unit, students will know:

• #### 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:

• #### 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

• ## 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

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

 Modifications/Accommodations (IEPs, ELLs, 504s, G/T & BASIC SKILLS) Quick CheckIntervention Activity Problem-solving Reading MatCenter Games Math and Science ActivityVisual Learning Math ToolsMath Games Higher Order Thinking QuestionsLeveled Homework and PracticeAnother Look Homework VideoAdaptive 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:

• #### Reason with shapes and their attributes

Know

By the end of this unit, students will know:

• #### 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:

• #### 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

• ## 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

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

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

 Modifications/Accommodations (IEPs, ELLs, 504s, G/T & BASIC SKILLS) Quick CheckIntervention Activity Problem-solving Reading MatCenter Games Math and Science ActivityVisual Learning Math ToolsMath Games Higher Order Thinking QuestionsLeveled Homework and PracticeAnother Look Homework VideoAdaptive 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:

• #### Multiply and divide within 100

Know

By the end of this unit, students will know:

• #### Rectangles that have same area can have different perimeters.

Do

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

• #### 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

• ## 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

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

 Modifications/Accommodations (IEPs, ELLs, 504s, G/T & BASIC SKILLS) Quick CheckIntervention Activity Problem-solving Reading MatCenter Games Math and Science ActivityVisual Learning Math ToolsMath Games Higher Order Thinking QuestionsLeveled Homework and PracticeAnother Look Homework VideoAdaptive 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:

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

Know

By the end of this unit, students will know:

• #### 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:

• #### 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

• ## 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

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