Mathematics Grade 4: Year at a Glance 2016-2017 Q2 16-17 w YAG.pdf · outside of math, particularly science, students are given ... Grade 4 Quarter 2 Overview Module 3: Multi-digit

Curriculum and Instruction – Office of Mathematics Quarter 2 Grade 4

Shelby County Schools 2016/2017 Revised 9/02/16

1 of 21 !MajorContent ! SupportingContent " AdditionalContent

!MajorContent ! SupportingContent " AdditionalContent


Mathematics Grade 4: Year at a Glance

2016-2017

Module 1 Aug. 10-Sept. 14

Module 2 Sept. 15- 23

Module 3 Sept. 26-Dec. 2

Module 5 Dec. 5 - Feb. 14

Module 6 Feb. 16-March 22

Module 4 Mar. 23- Apr. 20

Module 7 Apr. 21-May 26

Place Value,

Rounding, and Algorithms for Addition and Subtraction

Unit Conversion

and Problem Solving with

Metric Measurements

Multi-Digit Multiplication and

Division

Fraction

Equivalence, Ordering and Operations

Decimal Fractions

Angle Measure and Plane Figures

Angle Measure and Plane Figures

Exploring

Measurement with

Multiplication

25 days 7 days 40 days 40 days 20 days 20 days 20 days 4.OA.A.3 4.MD.A.1 4.OA.A.1 4.NF.A.1 4.NF.C.5 4.MD.C.5 4.OA.A.1 4.NBT.A.1 4.MD.A.2 4.OA.A.2 4.NF.A.2 4.NF.C.6 4.MD.C.6 4.OA.A.2 4.NBT.A.2 4.OA.A.3 4.NF.A.3 4.NF.C.7 4.MD.C.7 4.OA.A.3 4.NBT.A.3 4.OA.B.4 4.NF.A.4 4.MD.A.2 4.G.1 4.NBT.B.4 4.NBT.B.5 4.OA.C.5 4.G.2 4.MD.1

4.NBT.B.6 4.MD.B.4 4.G.3 4.MD.2 4.MD.A.3

Key:

Major Clusters Supporting Clusters Additional Clusters

Note: Please use the suggested pacing as a guide. Use this guide as you prepare to teach a module for additional guidance in planning, pacing, and suggestions for omissions. Pacing and Preparation Guide (Omissions)






Introduction In 2014, the Shelby County Schools Board of Education adopted a set of ambitious, yet attainable goals for school and student performance. The District is committed to these goals, as further described in our strategic plan, Destination2025. By 2025,

• 80% of our students will graduate from high school college or career ready • 90% of students will graduate on time • 100% of our students who graduate college or career ready will enroll in a post-secondary opportunity

In order to

achieve these ambitious goals, we

must collectively work to provide our students with high

quality, college

and career ready aligned instruction.

The Tennessee State Standards

provide a common

set of expectations for what students will know and be able to do at the end of a grade. College and career readiness is rooted in the knowledge and skills students need to succeed in post-secondary study or careers. The TN State Standards represent three fundamental shifts in mathematics instruction: focus, coherence and rigor.

Focus

• The Standards call for a greater focus in mathematics. Rather than racing to cover topics in a mile-wide, inch-deep curriculum, the Standards require us to significantly narrow and deepen the way time and energy is spent in the math classroom. We focus deeply on the major work of each grade so that students can gain strong foundations: solid conceptual understanding, a high degree of procedural skill and fluency, and the ability to apply the math they know to solve problems inside and outside the math classroom.

• For grades K–8, each grade's time spent in instruction must meet or exceed the following percentages for the major work of the grade. • 85% or more time spent in instruction in each grade

Kindergarten, 1, and 2 align exclusively to the major work of the grade.

• 75% or more time spent in instruction in each grade 3, 4, and 5 align exclusively to the major work of the grade.

• Supporting Content - informaiont that supports the understanding and implementation of the major work of the grade.

• Additional Content - content that does not explicitly connect to the major work of the grade yet it is required for proficiency.

Coherence

• Thinking across grades: • The Standards are designed around coherent

progressions from grade to grade. Learning is carefully connected across grades so that students can build new understanding on to foundations built in previous years. Each standard is not a new event, but an extension of previous learning.

• Linking to major topics: •  Instead of allowing additional or supporting topics to

detract from the focus of the grade, these concepts serve the grade level focus. For example, instead of data displays as an end in themselves, they are an opportunity to do grade-level word problems.

Rigor • Conceptual understanding:

• The Standards call for conceptual understanding of key concepts, such as place value and ratios. Students must be able to access concepts from a number of perspectives so that they are able to see math as more than a set of mnemonics or discrete procedures.

• Procedural skill and fluency: • The Standards call for speed and accuracy in calculation.

Students are given opportunities to practice core functions such as single-digit multiplication so that they have access to more complex concepts and procedures.

• Application: • The Standards call for students to use math flexibly for

applications in problem-solving contexts. In content areas outside of math, particularly science, students are given the opportunity to use math to make meaning of and access content.






The Standards for Mathematical Practice describe varieties of expertise, habits of minds and productive dispositions that mathematics educators at all levels should seek to develop in their students. These practices rest on important National Council of Teachers of Mathematics (NCTM) “processes and proficiencies” with longstanding importance in mathematics education. Throughout the year, students should continue to develop proficiency with the eight Standards for Mathematical Practice. This curriculum map is designed to help teachers make effective decisions about what mathematical content to teach so that, ultimately our students, can reach Destination 2025. To reach our collective student achievement goals, we know that teachers must change their practice so that it is in alignment with the three mathematics instructional shifts. Throughout this curriculum map, you will see resources as well as links to tasks that will support you in ensuring that students are able to reach the demands of the standards in your classroom. In addition to the resources embedded in the map, there are some high-leverage resources around the content standards and mathematical practice standards that teachers should consistently access:

MathematicalPractices

1. Make sense of problems and persevere in solving them

2. Reason abstractly and quatitatively

3. Construct viable arguments and

crituqe the reasoning of others

4. Model with mathematics

5. Use appropriate tools strategically

6. Attend to precision

7. Look for and make use of

structure

8. Look for and express regularity

in repeated reasoning






Purpose of Mathematics Curriculum Maps The Shelby County Schools curriculum maps are intended to guide planning, pacing, and sequencing, reinforcing the major work of the grade/subject. Curriculum maps are NOT meant to replace teacher preparation or judgment; however, it does serve as a resource for good first teaching and making instructional decisions based on best practices, and student learning needs and progress. Teachers should consistently use student data differentiate and scaffold instruction to meet the needs of students. The curriculum maps should be referenced each week as you plan your daily lessons, as well as daily when instructional support and resources are needed to adjust instruction based on the needs of your students. Additional Instructional Support The curriculum maps continue to provide references to envision lessons that support covered standards. Since this resource was developed for previous TN State Standards, it was necessary to evaluate and provide additional resources to support teachers and students.The2016-17 Curriculum Maps include the addition of the open resource curriculum that can be found at engageny.org. The curriculum and resources developed by Great Minds for engageny have consistently been rated as “exemplifying quality” by districts and organizations across the country, meaning they are highly aligned to college and career standards and instructional shifts.

How to Use the Mathematics Curriculum Maps Tennessee State Standards

The TN Mathematics Standards The Tennessee Mathematics Standards: https://www.tn.gov/education/article/mathematics-standards

Teachers can access the Tennessee State standards, which are featured throughout this curriculum map and represent college and career ready learning at reach respective grade level.

Standards for Mathematical Practice Standards for Mathematical Practice https://drive.google.com/file/d/0B926oAMrdzI4RUpMd1pGdEJTYkE/view

Teachers can access the Mathematical Practice Standards, which are featured throughout this curriculum map. This link contains more a more detailed explanation of each practice along with implications for instructions.






TN State Standards are located in the left column. Each content standard is identified as the following: Major Work, Supporting Content or Additional Content.; a key can be found at the bottom of the map. The major work of the grade should comprise 65-85% of your instructional time. Supporting Content are standards the supports student’s learning of the major work. Therefore, you will see supporting and additional standards taught in conjunction with major work It is the teachers' responsibility to examine the standards and skills needed in order to ensure student mastery of the indicated standard. Content Weekly and daily objectives/learning targets should be included in you plans. These can be found under the column titled content. The enduring understandings will help clarify the “big picture” of the standard. The essential questions break that picture down into smaller questions and the learning targets/objectives provide specific outcomes for that standard(s). Best practices tell us that making objectives measureable increases student mastery. Instructional Support and Resources District and web-based resources have been provided in the Instructional Support and Resources column. The additional resources provided are supplementary and should be used as needed for content support and differentiation. In order to assist with planning, a list of fluency activities have been included for each lesson. It is expected that fluency practice will be a part of daily instruction. (Note: Fluency practice is NOT intended to be speed drills, but rather an intentional sequence to support student automaticity. Conceptual Understanding MUST underpin the work of fluency.

Grade 4 Quarter 2 Overview Module 3: Multi-digit Multiplication and Division Module 5: Fraction Equivalence, Ordering, and Operations Overview Module 3 continues with students using place value understanding and visual representations to solve multiplication and division problems with multi-digit numbers. As a key area of focus for Grade 4, this module moves slowly but comprehensively to develop students’ ability to reason about the methods and models chosen to solve problems with multi-digit factors and dividends. In Topic E, students synthesize their Grade 3 knowledge of division types (group size unknown and number of groups unknown) with their new, deeper understanding of place value.






Students focus on interpreting the remainder within division problems, both in word problems and long division (4.OA.3). A remainder of 1, as exemplified below, represents a leftover flower in the first situation and a remainder of 1 ten in the second situation.1 While we have no reason to subdivide a remaining flower, there are good reasons to subdivide a remaining ten. Students apply this simple idea to divide two-digit numbers unit by unit: dividing the tens units first, finding the remainder (the number of tens unable to be divided), and decomposing remaining tens into ones to then be divided. Students represent division with single-digit divisors using arrays and the area model before practicing with place value disks. The standard division algorithm2 is practiced using place value knowledge, decomposing unit by unit. Finally, students use the area model to solve division problems, first with and then without remainders (4.NBT.6). In Topic F, armed with an understanding of remainders, students explore factors, multiples, and prime and composite numbers within 100 (4.OA.4), gaining valuable insights into patterns of divisibility as they test for primes and find factors and multiples. This prepares them for Topic G’s work with multi-digit dividends.

1Notethatcaremustbetakenintheinterpretationofremainders.Considerthefactthat7÷3isnotequalto5÷2becausetheremainderof1isinreferencetoadifferentwholeamount(213isnotequalto212).2StudentsbecomefluentwiththestandarddivisionalgorithminGrade6(6.NS.2).Foradequatepracticeinreachingfluency,studentsareintroducedto,butnotassessedon,thedivisionalgorithminGrade4asageneralmethodforsolvingdivisionproblems.






Topic G extends the practice of division with three- and four-digit dividends using place value understanding. A connection to Topic B is made initially with dividing multiples of 10, 100, and 1,000 by single-digit numbers. Place value disks support students visually as they decompose each unit before dividing. Students then practice using the standard algorithm to record long division. They solve word problems and make connections to the area model as was done with two-digit dividends (4.NBT.6, 4.OA.3). The module closes as students multiply two-digit by two-digit numbers. Students use their place value understanding and understanding of the area model to empower them to multiply by larger numbers (as pictured to the right). Topic H culminates at the most abstract level by explicitly connecting the partial products appearing in the area model to the distributive property and recording the calculation vertically (4.NBT.5). Students see that partial products written vertically are the same as those obtained via the distributive property: 4 twenty-sixes + 30 twenty-sixes = 104 + 780 = 884. As students progress through this module, they are able to apply the multiplication and division algorithms because of their in-depth experience with the place value system and multiple conceptual models. This helps to prepare them for fluency with the multiplication algorithm in Grade 5 and the division algorithm in Grade 6. Students are encouraged in Grade 4 to continue using models to solve when appropriate. In Module 5, students build on their Grade 3 work with unit fractions as they explore fraction equivalence and extend this understanding to mixed numbers. This leads to the comparison of fractions and mixed numbers and the representation of both in a variety of models. Benchmark fractions play an important part in students’ ability to generalize and reason about relative fraction and mixed number sizes. Students then have the opportunity to apply what they know to be true for whole number operations to the new concepts of fraction and mixed number operations. Students begin Topic A by decomposing fractions and creating tape diagrams to represent them as sums of fractions with the same denominator in different ways (e.g., 35 = 15 + 15 + 15 = 15 + 25 ) (4.NF.3b). They proceed to see that representing a fraction as the repeated addition of a unit fraction is the same as multiplying that unit fraction by a whole number. This is already a familiar fact in other contexts.

For example, just as 3 twos = 2 + 2 + 2 = 3 × 2, so does 3 fourths = 14 + 14 + 14 = 3 × 14.

The






introduction of multiplication as a record of the decomposition of a fraction (4.NF.4a) early in the module allows students to become familiar with the notation before they work with more complex problems. As students continue working with decomposition, they represent familiar unit fractions as the sum of smaller unit fractions. A folded paper activity allows them to see that, when the number of fractional parts in a whole increases, the size of the parts decreases. They proceed to investigate this concept with the use of tape diagrams and area models. Reasoning enables them to explain why two different fractions can represent the same portion of a whole (4.NF.1).

In Topic B, students use tape diagrams and area models to analyze their work from earlier in the module and begin using multiplication to create an equivalent fraction that comprises smaller units, e.g., 23 = 2 × 43 × 4 = 812 (4.NF.1). Based on the use of multiplication, they reason that division can be used to create a fraction that comprises larger units (or a single unit) equivalent to a given fraction (e.g., 812 = 8 ÷ 412 ÷ 4 = 23). Their work is justified using area models and tape diagrams and, conversely, multiplication is used to test for and/or verify equivalence. Students use the tape diagram to transition to modeling equivalence on the number line.

They see that, by multiplying, any unit fraction length can be partitioned into n equal lengths and that doing so multiplies both the total number of fractional units (the denominator) and number of selected units (the numerator) by n. They also see that there are times when fractional units can be grouped together, or divided, into larger fractional units. When that occurs, both the total number of fractional units and number of selected units are divided by the same number.

In Grade 3, students compared fractions using fraction strips and number lines with the same denominators. In Topic C, they expand on comparing fractions by reasoning about fractions with unlike denominators. Students use the relationship between the numerator and denominator of a fraction to compare to a known benchmark (e.g., 0, 12 , or 1) on the number line. Alternatively, students compare using the same numerators. They find that the fraction with the greater denominator is the lesser fraction since the size of the fractional unit is smaller as the whole is decomposed into more equal parts (e.g., 15 > 110; therefore 35 >310). Throughout the process, their reasoning is supported using tape diagrams and number lines in cases where one numerator or denominator is a factor of the other, such as 15 and 110 or 23 and 56. When the units are unrelated, students use area models and multiplication, the general method pictured below to the left, whereby

ComparisonUsingLikeDenominators

ComparisonUsingLikeNumerators






two fractions are expressed in terms of the same denominators. Students also reason that comparing fractions can only be done when referring to the same whole, and they record their comparisons using the comparison symbols <, >, and = (4.NF.2).

Overview recap

Focus Grade Level Standard Type of Rigor Foundational Standards

4.OA.3 Procedural Skill and Fluency 3.OA.8, 4.NBT.3, 4.NBT.6

4.OA.4 Conceptual 3.OA.7

4.NBT.1 Conceptual 2.NBT.1

4.NBT.5 Procedural Skill and Fluency 2.NBT.1, 3.OA.1, 3.OA.2, 3.OA.B, 3.NBT.A.3, 3.OA.5, 3.OA.7, 4.NBT.1

4.NBT.6 Procedural Skill and Fluency, Conceptual 3.OA.1, 3.OA.2, 3.OA.B, 2.NBT.1, 3.OA.5, 3.OA.7, 4.NBT.1, 4.NBT.6

4.MD.3 Application 3.MD.8, 3.OA.4






4.NF.3b Conceptual 3.NF.1, 3.NF.2, 4.NF.1,1.OA.3,1.OA.4,1.OA.8,2.OA.1, 2.G.3, 2.MD.2, 2.MD.6, 3.NF.3, 4.0A.2, K.OA.2, 1.OA.7, 1.NBT.4, 1.NBT.5, 1.NBT.6

4.NF.4a Application Introductory

4.NF.1 Conceptual 3.NF.3, 4.OA.2, 3.NF.1, 3.NF.2, 3.OA.3

Fluency NCTM Position

Procedural fluency is a critical component of mathematical proficiency. Procedural fluency is the ability to apply procedures accurately, efficiently, and flexibly; to transfer procedures to different problems and contexts; to build or modify procedures from other procedures; and to recognize when one strategy or procedure is more appropriate to apply than another. To develop procedural fluency, students need experience in integrating concepts and procedures and building on familiar procedures as they create their own informal strategies and procedures. Students need opportunities to justify both informal strategies and commonly used procedures mathematically, to support and justify their choices of appropriate procedures, and to strengthen their understanding and skill through distributed practice.

Fluency is designed to promote automaticity by engaging students in daily practice. Automaticity is critical so that students avoid using lower-level skills when they are addressing higher-level problems. The automaticity prepares students with the computational foundation to enable deep understanding in flexible ways. Therefore, it is recommended that students participate in fluency practice daily using the resources provided in the curriculum maps. Special care should be taken so that it is not seen as punitive for students that might need more time to master fluency.

The fluency standard for 4th grade listed below should be incorporated throughout your instruction over the course of the school year. The engageny lessons include fluency exercises that can be used in conjunction with building conceptual understanding.

! 4.NBT.B.4 Add/Subtract within 1,000,000

Note: Fluency is only one of the three required aspects of rigor. Each of these components have equal importance in a mathematics curriculum.






References:

• https://www.engageny.org/ • http://www.corestandards.org/ • http://www.nctm.org/ • http://achievethecore.org/

TN STATE STANDARDS CONTENT INSTRUCTIONAL SUPPORT VOCABULARY/FLUENCY Module 3 Multi-Digit Multiplication and Division

(Allow 5-6 weeks for instruction, review and assessment) Domain: Operations and Algebraic Thinking Cluster: 4.OA.1 Use the Four Operations with whole numbers to solve problems ! 4.OA.1 Interpret a multiplication equation as a comparison, e.g., interpret 35=5x7 as a statement that 35 is 5 times as many as 7 and 7 times as many as 5. Represent verbal statements of multiplicative comparisons as multiplication equations. ! 4.OA.2 Multiply or divide to solve word problems involving multiplicative comparison, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem, distinguishing multiplicative comparison from additive comparison ! 4.OA.3 Solve multistep word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems

Enduring Understandings • Basic facts and place value patterns can

be used to divide multiples of 10 and 100 by 1-digit numbers

• The remainder when dividing must be less than the divisor. The nature of the question asked determines how to interpret and use the remainder.

• The relationship between multiplication, division, and estimation can be used to determine the place value of the largest digit in a quotient.

• Every counting number is divisible by 1 and itself, and some counting numbers are also divisible by other numbers.

• Some counting numbers have exactly two factors; others have more than two.

. Essential Questions • How can you use place value and

patterns to help you divide mentally? • What does it mean when you divide and

some are left over?

Module 3: Multi-Digit Multiplication and Division Topic E: Division of Tens and Ones with Successive Remainders Lesson 14

Vocabulary Associative property, composite number, distributive property, divisible, divisor, formula, long division, partial product, prime number, remainder Familiar Terms and Symbols Algorithm, Area, Area model, Array, bundling,

grouping, reaming, changing, compare, distribute, divide, division, equation, factors, mixed units, multiple, multiply, multiplication, perimeter, place value, product, quotient, rectangular array, rows, columns, __times as many__as ____ Fluency Practice: Please see engageNY full module download for suggested fluency pacing and activities. Lesson 14:






TN STATE STANDARDS CONTENT INSTRUCTIONAL SUPPORT VOCABULARY/FLUENCY using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. Domain: Operations and Algebraic Thinking Cluster: 4.OA. Gain Familiarity with factors and multiples ! 4.OA.4 Find all factor pairs for a whole

number in the range 1-100. Recognize that a whole number is a multiple of each of its factors. Determine whether a given whole number in the range 1-100 is a multiple of a given one-digit number. Determine whether a given whole number in the range 1-100 is prime or composite.

Domain: Numbers and Operations in Base Ten Cluster: Use place value understanding and properties of operations to perform multi-digit arithmetic ! 4.NBT.5 Multiply a whole number of up to four digits by a one digit whole number, and multiply two two-digit numbers, using strategies based on place value and the properties of operations. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. ! 4.NBT.6 Find whole-number quotients and remainders with up to four dividends and one-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation

• What do you do when there are not enough hundreds to divide?

• How can you use multiplication to find all the factors of a number?

• How can you sort numbers by their factors?

• What hidden questions lie within a multiple-step problem?

Objectives/Learning Targets Topic E Lesson 14: I can solve division word problems with remainders. (4.NBT.6) Lesson 15: I can understand and solve division problems with a remainder using the array and area models. (4.NBT.6) Lesson 16: I can understand and solve two-digit dividend division problems with a remainder in the ones place by using place value disks. (4.NBT.6) Lesson 17: I can represent and solve division problems requiring decomposing a remainder in the tens. (4.NBT.6) Lesson 18: I can find whole number quotients and remainders. (4.NBT.6) Lesson 19: I can explain remainders by using place value understanding and models. (4.NBT.6) Lesson 20: I can solve division problems without remainders using the area model. (4.NBT.6) Lesson 21: I can solve division problems with remainders using the area model.(4.NBT.6)

Lesson 15 Lesson 16 Lesson 17 Lesson 18 Lesson 19 Lesson 20 Lesson 21

Group Count to Divide Number Sentences in an Array Divide with Remainders Lesson 15: Show values with Number Disks Divide with Remainders Number Sentences in an Array Lesson 16: Group Count Divide with Remainders Lesson 17: Group Count Divide Mentally Divide Using the Standard Algorithm Lesson 18: Group Count Divide Mentally Divide Using the Standard Algorithm Lesson 19: Sprint: Mental Division Divide Using the Standard Algorithm Lesson 20: Divide Using the Standard Algorithm Find Unknown Factors Mental Multiplication Lesson 21: Sprint: Division with Remainders Find Unknown Factors






TN STATE STANDARDS CONTENT INSTRUCTIONAL SUPPORT VOCABULARY/FLUENCY

Objectives/Learning Targets Topic F Lesson 22: I can find factor pairs for numbers to 100, and use understanding of factors to define prime and composite. (4.OA.4) Lesson 23: I can use division and the associative property to test for factors and observe patterns. (4.OA.4) Lesson 24: I can determine if a whole number is a multiple of another number. (4.OA.4) Lesson 25: I can explore properties of prime and composite numbers to 100 by using multiples. (4.OA.4)

Topic F: Reasoning with Divisibility Lesson 22 Lesson 23 Lesson 24 Lesson 25

Fluency Practice: Topic F Lesson 22: Divide Using the Area Model Find the Unknown Factor Mental Multiplication Lesson 23: Use Arrays to Find Factors Multiply Two Factors Prime and Composite Lesson 24: Group Counting Prime or Composite? Test for Factors Lesson 25: Test for Factors Multiples Are Infinite List Multiples and Factors

by using equations, rectangular arrays, and/or area models. Domain: Measurement and Data Cluster: Solve Problems involving measurement and conversion of measurements from a larger unit to a smaller unit. ! 4.MD.3 Apply the area and perimeter

formula for rectangles in real world and mathematical problems. For example, find the width of a rectangular room given the area of the flooring and the length, by viewing he area formula as a multiplication equation with an unknown factor.

Objectives/Learning Targets Topic G Lesson 26: I can divide multiples of 10, 100, and 1,000 by single-digit numbers. (4.OA.3, 4.NBT.6) Lesson 27: I can represent and solve division problems with up to a three-digit dividend numerically and with place value disks requiring decomposing a remainder in the hundreds place. (4.OA.3, 4.NBT.6) Lesson 28: I can represent and solve three-digit dividend division with divisors of 2, 3, 4, and 5 numerically. (4.OA.3, 4.NBT.6) Lesson 29: I can represent numerically four-

Topic G: Division of Thousands, Hundreds Tens, and Ones Lesson 26 Lesson 27 Lesson 28 Lesson 29 Lesson 30 Lesson 31 Lesson 32 Lesson 33

Fluency Practice Lesson 26: Show values with Number Disks Group Counting List Multiples and Factors List Prime Numbers Lesson 27: Sprint: Circle the prime Number Divide with Number Disks Lesson 28: Multiply by Units Divide Different Units Group Count






TN STATE STANDARDS CONTENT INSTRUCTIONAL SUPPORT VOCABULARY/FLUENCY digit dividend division with divisors of 2, 3, 4, and 5, decomposing a remainder up to three times. (4.OA.3, 4.NBT.6) Lesson 30: I can solve division problems with a zero in the dividend or with a zero in the quotient. (4.OA.3, 4.NBT.6) Lesson 31: I can Interpret division word problems as either number of groups unknown or group size unknown. (4.OA.3, 4.NBT.6) Lesson 32: I can interpret and find whole number quotients and remainders to solve one-step division word problems with larger divisors of 6, 7, 8, and 9. (4.OA.3, 4.NBT.6) Lesson 33: I can explain the connection of the area model of division to the long division algorithm for three- and four-digit dividends. (4.OA.3, 4.NBT.6)

Divide Three-Digit Numbers by 2 Lesson 29: Multiply by Units Divide Different Units Divide to Find Half Lesson 30: Multiply Using the Standard Algorithm Divide Using Different Units Find the Quotient and Remainder Lesson 31: Sprint: Divide Different Units Group Size or Number of Groups Unknown Lesson 32: Quadrilaterals Multiply Units Group Count Lesson 33: Quadrilaterals Group Count Multiply Units

Objectives/Learning Targets Topic H Lesson 34: I can multiply two-digit multiples of 10 by two-digit numbers using a place value chart. (4.NBT.5) Lesson 35: I can multiply two-digit multiples of 10 by two-digit numbers using the area model. (4.NBT.5) Lesson 36: I can multiply two-digit by two-digit

Topic H: Multiplication of Two-Digit by Two-Digit Numbers Lesson 34 Lesson 35 Lesson 36 Lesson 37-38 End-of-Module Assessment

Fluency Practice: Lesson 34: Draw a Unit Fraction List Multiples and Factors List Prime Numbers Lesson 35: Draw and Label Unit Fractions Divide Three Different Ways Multiply by Multiples of 10 Lesson 36:






TN STATE STANDARDS CONTENT INSTRUCTIONAL SUPPORT VOCABULARY/FLUENCY numbers using four partial products. (4.NBT.5) Lesson 37-38: I can transition from four partial products to the standard algorithm for two-digit by two-digit multiplication. (4.NBT.5)

Draw and Label Unit Fractions Divide Three Different Ways Lesson 37-38: Decompose 90 and 180 Multiply by Multiples of 10 Written Vertically

Tasks: Threatened and Endangered Thousands and Millions of Fourth Graders Coordinating i-Ready Lessons: • Multiplying two-digit numbers by one

digit numbers • Multiplying two-digit numbers by two-

digit numbers • Review Multiplying two-digit numbers by

one digit numbers • Multiplying by two-digit numbers enVision Resource: (enVision may be used to support the needs of your students, but should not be used independently of the mathematics curriculum) 8-1 Using Mental Math to Divide 8-2 Estimating Quotients 8-3 Dividing with Remainders 8-4 Division: Connecting Models and Symbols 8-5 Dividing 2-Digit by 1-Digit Numbers 8-6 Dividing 3-Digit by 1-Digit Numbers 8-7 Deciding Where to Start Dividing 8-8 Number Sense: Factors 8-9 Prime and Composite Numbers

Literature Connections WorldScape Readers: “All Tied Up” A Remainder of One Elinor Pinczes The Great Divide Dayle Ann Dobbs Other: Use this guide as you prepare to teach a module for additional guidance in planning, pacing, and suggestions for omissions. Pacing and Preparation Guide (Omissions)






TN STATE STANDARDS CONTENT INSTRUCTIONAL SUPPORT VOCABULARY/FLUENCY 8-10 Problem Solving: Multiple-Step

Problems Module 5 Fraction Equivalence, Ordering, and Operations (Allow 3 weeks for instruction, review and assessment)

Domain: Number and Operations-Fractions Cluster: Extend understanding of fraction equivalence and ordering. !4.NF.3 Understand a fraction a/b with a > 1 as a sum of fractions 1/b. a. Understand addition and subtraction of

fractions as joining and separating parts referring to the same whole.

b. Decompose a fraction into a sum of fractions with the same denominator in more than one way, recording each decomposition by an equation. Justify decompositions, e.g., by using a visual fraction model. Examples: 3/8 = 1/8 + 1/8 + 1/8 ; 3/8 = 1/8 + 2/8 ; 2 1/8 = 1 + 1 + 1/8 = 8/8 + 8/8 + 1/8.

!4.NF.4 Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. a. Understand a fraction a/b as a multiple of

1/b. For example, use a visual fraction model to represent 5/4 as the product 5x (1/4), recording the conclusion by the equation 5/4=5x (1/4).

Enduring Understandings • To add or subtract fractions with like

denominators, add or subtract the numerators and write the sum or difference over the common denominator.

• Information in a problem can often be shown using a diagram and can be used to solve the problem. Writing and completing a number sentence or equation can solve some problems.

Essential Questions • How can you add and subtract fractions

with like denominators? • What operation is needed to solve a

problem with fractions? Objectives/Learning Targets Topic A Lesson 1-2: I can Decompose fractions as a sum of unit fractions using tape diagrams. Lesson 3: I can Decompose non-unit fractions and represent them as a whole number times a unit fraction using tape diagrams. Lesson 4: I can Decompose fractions into sums of smaller unit fractions using tape diagrams Lesson 5: I can Decompose unit fractions using area models to show equivalence. Lesson 6: I can Decompose fractions using

Module 5: Multi-Digit Multiplication and Division Topic A: Decomposition and Fraction Equivalence Lesson 1 Lesson 2 Lesson 3 Lesson 4 Lesson 5 Lesson 6

Vocabulary benchmark, common denominator, denominator, fraction greater than 1, line plot, mixed number, numerator

Familiar Terms and Symbols

=, <, >, decompose, equivalent fractions, fraction, fractional unit, multiple, non-fractional unit, unit fraction, unit interval, whole

Fluency Practice: Please see engageNY full module download for suggested fluency pacing and activities. Lesson 1

Read a Tape Diagram Addition of Fractions in Unit Form

Lesson 2 Read Tape Diagrams Break Apart Fractions

Lesson 3 Multiply mentally Repeated addition and multiplication Add fraction

Lesson 4 Break apart fractions Count by equivalent fractions

Lesson 5






TN STATE STANDARDS CONTENT INSTRUCTIONAL SUPPORT VOCABULARY/FLUENCY area models to show equivalence.

Count by equivalent fractions Add fractions Break apart the unit fractions Lesson 6 Sprint: multiply whole numbers times fractions Find equivalent fractions

Objectives/Learning Targets Topic B Lesson 7-8: I can use the area model and multiplication to show the equivalence of two fractions Lesson 9-10: I can use the area model and division to show the equivalence of two fractions. Lesson 11: I can Explain fraction equivalence using a tape diagram and the number line, and relate that to the use of multiplication and division

Topic B: Fraction Equivalence Using Multiplication and Division Lesson 7 Lesson 8 Lesson 9 Lesson 10 Lesson 11

Lesson 7 Break Apart Fractions Count by Equivalent Fractions Draw Equivalent Fractions Lesson 8 Break Apart Fractions Count by Equivalent Fractions Draw Equivalent Fractions Lesson 9 Add and Subtract Find Equivalent Fractions Draw Equivalent Fractions Lesson 10 Add and Subtract Find Equivalent Fractions Draw Equivalent Fractions Lesson 11 Find the Quotient and Remainder Find Equivalent Fractions Draw Equivalent Fractions

Objectives/Learning Targets Topic C Lesson 12-13: Reason using benchmarks to compare two fractions on the number line.

Topic C: Fraction Comparison Lesson 12

Lesson 12 Add and Subtract Find Equivalent Fractions






TN STATE STANDARDS CONTENT INSTRUCTIONAL SUPPORT VOCABULARY/FLUENCY Lesson 14-15: Find common units to compare two fractions

Lesson 13 Lesson 14 Lesson 15

Construct a Number Line with Fractions Lesson 13 Divide three different ways Count by Equivalent Fractions Plot Fractions on a Number Line Lesson 14 Add and Subtract Fractions Compare Fractions Construct a Number Line with Fractions Lesson 15 Count by Equivalent Fractions Find Equivalent Fraction Compare Fractions

Tasks: Comparing Sums of Unit Fractions Cynthia's Perfect Punch Peaches TNCore 4th Grade Tasks Celebrate Chocolate Chips Salty Pretzel Ice Cream Treat Bag Closer to 1 12 Cookies Coordinating i-Ready Lessons • Understand Adding and Subtracting

Fractions • Add and Subtract Fractions • Add and Subtract Fractions in Word

Problems • Understand Fraction Multiplication

Other: Use this guide as you prepare to teach a module for additional guidance in planning, pacing, and suggestions for omissions. Pacing and Preparation Guide (Omissions)






TN STATE STANDARDS CONTENT INSTRUCTIONAL SUPPORT VOCABULARY/FLUENCY • Multiplying a Whole Number and a

Fraction enVision Resource: (enVision may be used to support the needs of your students, but should not be used independently of the mathematics curriculum) Adding and Subtracting Fractions 11-1A Decomposing and Composing Fractions 11-1 Adding and Subtracting Fractions with Like Denominator 11-5A Modeling Addition and Subtraction of Mixed Numbers 11-5B Adding Mixed Numbers 11-5C Subtracting Mixed Numbers Multiplying Fractions 11-5D – Fractions as Multiples of Unit fractions: Using Models 11-5E Multiplying a Fraction by a Whole Number: Using Models 11-5F - Multiplying a Fraction by a Whole Number






RESOURCE TOOLBOX The Resource Toolbox provides additional support for comprehension and mastery of grade-level skills and concepts. These resources were chosen as an accompaniment to

modules taught within this quarter. Incorporated materials may assist educators with grouping, enrichment, remediation, and differentiation. NWEA MAP Resources: https://teach.mapnwea.org/assist/help_map/ApplicationHelp.htm#UsingTestResults/MAPReportsFinder.htm - Sign in and Click the Learning Continuum Tab – this resources will help as you plan for intervention, and differentiating small group instruction on the skill you are currently teaching. (Four Ways to Impact Teaching with the Learning Continuum) https://support.nwea.org/khanrit - These Khan Academy lessons are aligned to RIT scores.

Textbook Resources engageNY Mathematics Modules envision Math

TN Core/CCSS TN Math Standards Achieve the Core

Videos NCTM Common Core Videos TN Core Online Math ResourcesLearnZillion CCSS Video Series

Children’s Literature The Reading Nook Math and Literature:A Match Made in the Classroom Math for Kids-Best Children’s Books Scholastic: Books and Programs to Improve Elementary Math

Interactive Manipulatives Interactive Content http://www.eduplace.com/ Illuminations Resources for Teaching Math Interactive Sites for Educators Math Playground: Common Core Standards Thinking Blocks: Computer and iPad based games PARCC Games IXL Math Virtual Manipulatives

Additional Sites Inside Mathematics Illustrative Mathematics Learn ZillionEngage NY Math Sheppard Software BBC Bitesize Singapore Math Math-Play-Com






Stem Resources Scholastic Math Study Jams

Other Illustrated Mathematics Dictionary for KidsUse this guide as you prepare to teach a module for additional guidance in planning, pacing, and suggestions for omissions. Pacing and Preparation Guide (Omissions)

Mathematics Grade 4: Year at a Glance 2016-2017 Q2 16-17 w YAG.pdf · outside of math, particularly science, students are given ... Grade 4 Quarter 2 Overview Module 3: Multi-digit

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