Mathematics: Grade 5 Year at a Glance- 2016-2017 Q2 16-17 w YAG.pdf · Quarter 2 Grade 5 ... Unit 2 Module Sept.8-Nov. 3 Unit 3 Module ... math they know to solve problems inside

Curriculum and Instruction – Mathematics Quarter 2 Grade 5

Shelby County Schools 2016/2017 Revised 5/27/16

1 of 25 !MajorContent ! SupportingContent " AdditionalContent

!MajorContent ! SupportingContent " AdditionalContent


Mathematics: Grade 5 Year at a Glance- 2016-2017

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)

Unit 1 Module

Aug. 10- Sept. 7

Unit 2 Module

Sept.8-Nov. 3

Unit 3 Module

Nov. 4-Dec. 8

Unit 4 Module

Dec. 9- Feb. 20

Unit 5 Module

Feb. 21- Mar. 31

Unit 6 Module

Apr. 3- May 26

Place Value and Decimal Fractions

Multi-Digit Whole Number and

Decimal Fraction Operations

Addition and Subtraction of

Fractions

Multiplication and Division of

Fractions and Decimal Fractions

Addition and Multiplication with Volume and Area

Problem Solving with the

Coordinate Plane

5.NBT.A.1 5.OA.A.1 5.NF.A.1 5.OA.1 5.NF.B.4b 5.OA.A.2

5.NBT.A.2 5.OA.A.2 5.NF.A.2 5.OA.2 5.NF.6 5.OA.B.3

5.NBT.A.3 5.NBT.A.1 5.NBT.B.7 5.MD.C.3 5.G.A.1

5.NBT.A.4 5.NBT.A.2 5.NF.B.3 5.MD.C.4 5.G.A.2

5.NBT.B.7 5.NBT.B.5 5.NF.B.4a 5.MD.C.5

5.MD.A.1 5.NBT.B.6 5.NF.B.5 5.G.B.3

5.NBT.B.7 5.NF.B.6 5.G.B.4

5.MD.A.1 5.NF.7

5.MD.1

5.MD.2






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.






The Standards for Mathematical Practice descri

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.

Mathematical Practice Standards Mathematical Practice Standards 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.

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.

•  It is important to understand that the shifts require us to pursue each component of rigor with EQUAL intensity.






be 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:

Purpose of Mathematics Curriculum Maps

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






This Map is meant to help teachers and their support providers (e.g., coaches, leaders) on their path to effective, college and career ready (CCR) aligned instruction and our pursuit of Destination 2025. It is a resource for organizing instruction around the TN State Standards, which define what to teach and what students need to learn at each grade level. The map is designed to reinforce the grade/course-specific standards and content—the major work of the grade (scope)—and provides suggested sequencing, pacing, time frames, and aligned resources. Our hope is that by curating and organizing a variety of standards-aligned resources, teachers will be able to spend less time wondering what to teach and searching for quality materials (though they may both select from and/or supplement those included here) and have more time to plan, teach, assess, and reflect with colleagues to continuously improve practice and best meet the needs of their students. The map is meant to support effective planning and instruction to rigorous standards. It is not meant to replace teacher planning, prescribe pacing or instructional practice. In fact, our goal is not to merely “cover the curriculum,” but rather to “uncover” it by developing students’ deep understanding of the content and mastery of the standards. Teachers who are knowledgeable about and intentionally align the learning target (standards and objectives), topic, text(s), task,, and needs (and assessment) of the learners are best-positioned to make decisions about how to support student learning toward such mastery. Teachers are therefore expected--with the support of their colleagues, coaches, leaders, and other support providers--to exercise their professional judgment aligned to our shared vision of effective instruction, the Teacher Effectiveness Measure (TEM) and related best practices. However, while the framework allows for flexibility and encourages each teacher/teacher team to make it their own, our expectations for student learning are non-negotiable. We must ensure all of our children have access to rigor—high-quality teaching and learning to grade level specific standards, including purposeful support of literacy and language learning across the content areas. Additional Instructional Support Shelby County Schools adopted our current math textbooks for grades K-5 in 2010-2011. The textbook adoption process at that time followed the requirements set forth by the Tennessee Department of Education and took into consideration all texts approved by the TDOE as appropriate. We now have new standards, therefore, the textbook(s) have been vetted using the Instructional Materials Evaluation Tool (IMET). This tool was developed in partnership with Achieve, the Council of Chief State Officers (CCSSO) and the Council of Great City Schools. The review revealed some gaps in the content, scope, sequencing, and rigor (including the balance of conceptual knowledge development and application of these concepts), of our current materials. The additional materials purposefully address the identified gaps in alignment to meet the expectations of the CCR standards and related instructional shifts while still incorporating the current materials to which schools have access. Materials selected for inclusion in the Curriculum Maps, both those from the textbooks and external/supplemental resources (e.g., EngageNY), have been evaluated by district staff to ensure that they meet the IMET criteria. How to Use the Maps






Overview An overview is provided for each quarter. The information given is intended to aid teachers, coaches and administrators develop an understanding of the content the students will learn in the quarter, how the content addresses prior knowledge and future learning, and may provide specific examples of student work. Tennessee State Standards 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 Teachers are expected to carefully craft weekly and daily learning objectives/ based on their knowledge of TEM Teach 1. In addition, teachers should include related best practices based upon the TN State Standards, related shifts, and knowledge of students from a variety of sources (e.g., student work samples, MAP, performance in the major work of the grade) . Support for the development of these lesson objectives 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 clearly communicating and making objectives measureable leads to greater student mastery. Instructional Resources District and web-based resources have been provided in the Instructional Resources column. At the end of each module you will find instructional/performance tasks, i-Ready lessons and additional resources that align with the standards in that module. The additional resources provided are supplementary and should be used as needed for content support and differentiation. Vocabulary and Fluency The inclusion of vocabulary serves as a resource for teacher planning, and for building a common language across K-12 mathematics. One of the goals for CCSS is to create a common language, and the expectation is that teachers will embed this language throughout their daily lessons.

In order to aid your planning we have included a list of fluency activities for each lesson. It is expected that fluency practice will be a part of your 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 5 Quarter 2 Overview






Module 2: Multi- Digit Whole Number and Decimal Fraction Operations Module 3: Place Value and Decimal Fractions Module 4: Multiplication and Division of Fractions and Decimal Fractions Overview Module 2 continues with students applying the patterns of the base ten system to mental strategies and the multiplication and division algorithms. In Topic G, students use their understanding to divide decimals by two-digit divisors in a sequence similar to that of Topic F with whole numbers (5.NBT.7). In Topic H, students apply the work of the module to solve multi-step word problems using multi-digit division with unknowns representing either the group size or number of groups. In this topic, an emphasis on checking the reasonableness of their answers draws on skills learned throughout the module, including refining their knowledge of place value, rounding, and estimation. In Module 3, students’ understanding of addition and subtraction of fractions extends from earlier work with fraction equivalence and decimals. This module marks a significant shift away from the elementary grades’ centrality of base ten units to the study and use of the full set of fractional units from Grade 5 forward, especially as applied to algebra. In Topic A, students revisit the foundational Grade 4 standards addressing equivalence. When equivalent, fractions represent the same amount of area of a rectangle and the same point on the number line. These equivalencies can also be represented symbolically.

Furthermore, equivalence is evidenced when adding fractions with the same denominator. The sum may be decomposed into parts (or recomposed into an equal sum). An example is shown as follows:

23=13+13

78=38+38+18

62=22+22+22=1+1+1=3

85=55+35=135

23=2×43×4=812






73=63+13=2×33+13=2+13=213

This also carries forward work with decimal place value from Modules 1 and 2, confirming that like units can be composed and decomposed.

5 tenths + 7 tenths = 12 tenths = 1 and 2 tenths

5 eighths + 7 eighths = 12 eighths = 1 and 4 eighths

In Topic B, students move forward to see that fraction addition and subtraction are analogous to whole number addition and subtraction. Students add and subtract fractions with unlike denominators (5.NF.1) by replacing different fractional units with an equivalent fraction or like unit.

1 fourth + 2 thirds = 3 twelfths + 8 twelfths = 11 twelfths

14+23=312+812=1112

This is not a new concept, but certainly a new level of complexity. Students have added equivalent or like units since kindergarten, adding frogs to frogs, ones to ones, tens to tens, etc.

1 boy + 2 girls = 1 child + 2 children = 3 children

1 liter – 375 mL = 1,000 mL – 375 mL = 625 mL Throughout the module, a concrete to pictorial to abstract approach is used to convey this simple concept. Topic A uses paper strips and number line diagrams to clearly show equivalence. After a brief concrete experience with folding paper, Topic B primarily uses the rectangular fractional model because it is useful for creating smaller like units by means of partitioning (e.g., thirds and fourths are changed to twelfths to create equivalent fractions as in the diagram below). In Topic C, students move away from the pictorial altogether as they are empowered to write equations clarified by the model.

14+23=1×34×3+2×43×4=312+812=1112






Topic C also uses the number line when adding and subtracting fractions greater than or equal to 1 so that students begin to see and manipulate fractions in relation to larger whole numbers and to each other. The number line allows students to pictorially represent larger whole numbers. For example, “Between which two whole numbers does the sum of 1 34 and 535 lie?”

This leads to an understanding of and skill with solving more complex problems, which are often embedded within multi-step word problems:

Cristina and Matt’s goal is to collect a total of 312 gallons of sap from the maple trees. Cristina collected 134 gallons. Matt collected 535 gallons. By how much did they beat their goal?

134+535−312=3+3×54×5+3×45×4−1×102×10 =3+1520+1220−1020=31720

Cristina and Matt beat their goal by 31720 gallons. Word problems are a part of every lesson. Students are encouraged to draw tape diagrams, which encourage

them to recognize part–whole relationships with fractions that they have seen with whole numbers since Grade 1. In Topic D, students strategize to solve multi-term problems and more intensely assess the reasonableness of their solutions to equations and word problems with fractional units (5.NF.2).

“I know my answer makes sense because the total amount of sap they collected is about 7 and a half gallons. Then, when we subtract 3 gallons, that is about 4 and a half. Then, 1 half less than that is about 4. 31720 is just a little less than 4.”

____<134+535<____






Module 4 is where students learn to multiply fractions and decimal fractions and begin working with fraction division. Topic A opens the 38-day module with an exploration of fractional measurement. Students construct line plots by measuring the same objects using three different rulers accurate to 12, 14, and 18 of an inch (5.MD.2). Students compare the line plots and explain how changing the accuracy of the unit of measure affects the distribution of points. This is foundational to the understanding that measurement is inherently imprecise because it is limited by the accuracy of the tool at hand. Students use their knowledge of fraction operations to explore questions that arise from the plotted data. The interpretation of a fraction as division is inherent in this exploration. For measuring to the quarter inch, one inch must be divided into four equal parts, or 1 ÷ 4. This reminder of the meaning of a fraction as a point on a number line, coupled with the embedded, informal exploration of fractions as division, provides a bridge to Topic B’s more formal treatment of fractions as division. Topic B focuses on interpreting fractions as division. Equal sharing with area models (both concrete and pictorial) provides students with an opportunity to understand division of whole numbers with answers in the form of fractions or mixed numbers (e.g., seven brownies shared by three girls, three pizzas shared by four people). Discussion also includes an interpretation of remainders as a fraction (5.NF.3). Tape diagrams provide a linear model of these problems. Moreover, students see that, by renaming larger units in terms of smaller units, division resulting in a fraction is similar to whole number division. Topic B continues as students solve real-world problems (5.NF.3) and generate story contexts for visual models. The topic concludes with students making connections between models and equations while reasoning about their results (e.g., between what two whole numbers does the answer lie?). In Topic C, students interpret finding a fraction of a set (34 of 24) as multiplication of a whole number by a fraction (34 × 24) and use tape diagrams to support their understandings (5.NF.4a). This, in turn, leads students to see division by a whole number as being equivalent to multiplication by its reciprocal. That is, division by

1÷7=77÷7=175÷3=53






2, for example, is the same as multiplication by 12. Students also use the commutative property to relate a fraction of a set to the Grade 4 repeated addition interpretation of multiplication by a fraction. This offers opportunities for students to reason about various strategies for multiplying fractions and whole numbers. Students apply their knowledge of a fraction of a set and previous conversion experiences (with scaffolding from a conversion chart, if necessary) to find a fraction of a measurement, thus converting a larger unit to an equivalent smaller unit (e.g., 13 minutes = 20 seconds and 2 14 feet = 27 inches). Overview recap

Focus Grade Level Standard Type of Rigor Foundational Standards

5.OA.1 Conceptual Introductory 5.OA.2 Application 5.OA.1






5.NBT.1 Conceptual 2.NBT.1, 4.NF.1, 4.NF.2, 4.NF.5, 4.NF.6, 4.NF.7, 4.NBT.1

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

4.NBT.5, 5.NBT.1

5.NBT.6 Conceptual, Application 3.NBT.2, 4.NBT.1, 3.OA.5, 3.OA.7, 4.NF.5, 4.NF.6, 4.NBT.5, 4.NBT,4, 4.NBT,6, 5.NBT.1, 5.NBT,5, 5.NBT.2

5.NBT.7 Procedural Skill and Fluency 3.NBT.2, 4.NBT.1, 4.NF.5, 4.NF.6, 4.NF.1, 4.NF.4, 3.NF.1, 3.OA.6, 4.NBT.4, 5.NBT.1, 5.F.1, 5.NF.4, 5.NF.7, 5.NF

5.MD.1

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 5th 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.

! 5.NBT.B.5 Fluently multiply multi-digit whole numbers using the standard algorithm. 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 RESOURCES VOCABULARY & FLUENCY Module 2 Multi-Digit Whole Number and Decimal Fraction Operations

(Allow 2 weeks for instruction, review and assessment)

Domain: Operations and Algebraic Thinking Cluster: Write and interpret numerical expressions.

Enduring Understandings • Multiplication is related to both addition

Vocabulary Conversion factor, Decimal fraction, Multiplier, Parentheses






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

" 5.OA.2 Write simple expressions that record calculations with numbers, and interpret numerical expressions without evaluating them. For example, express the calculation “add 8 and 7, then multiply by2” as 2x(8+7). Recognize that 3x(18932+ 921) is three times as large as 18932 + 921, without having to calculate the indicated sum or product.

Domain: Number and Operations in Base Ten Cluster: Understand the place value system. !5.NBT.1 Recognize that in a multi-digit number, a digit in one place represents 10 times as much as it represents in the place to its right and 1/10 of what it represents in the place to its left. !5.NBT.2 Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and explain patterns in the placement of the decimal point when a decimal is multiplied or divided by a power of 10. Use whole-number exponents to denote power of 10. Domain: Number and Operations in Base Ten Cluster: Perform operations with multi-digit whole numbers and with decimals to hundredths. !5.NBT.5 Fluently multiply multi-digit whole numbers using the standard algorithm. !5.NBT.6 Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular

and division. • Computational fluency includes

understanding not only the meaning but also the appropriate use of numerical operations.

• The magnitude of numbers affects the outcome of operations on them.

• Context is critical when using estimation. Essential Questions • How does multiplication relate to the

other operations? • What makes a computational strategy

both effective and efficient? • How does the size of the number affect

the outcome of the operation? • How can we decide when to use an exact

answer and when to use an estimate? Learning Targets Topic G Lesson 24: I can divide decimal dividends by multiples of 10, reasoning about the placement of the decimal point and making connections to a written method. (5.NBT.2, 5.NBT.7) Lesson 25: I can use basic facts to approximate decimal quotients with two-digit divisors, reasoning about the placement of the decimal point. (5.NBT.2, 5.NBT.7) Lesson 26-27: I can solve division word problems involving multi-digit division with group size unknown and the number of groups unknown. (5.NBT.2, 5.NBT.7)

engageny Module 2: Multi-Digit Whole Number and Decimal Fraction Operations Topic G Lesson 24 Lesson 25 Lesson 26-27

Familiar Terms and Symbols Decimal, digit, divisor, equation, equivalence, equivalent, estimate, exponent, multiple, pattern, product, quotient, remainder, renaming, rounding, unit form Fluency Practice: Please see engageNY full module download for suggested fluency pacing and activities. Lesson 24 Rename Tenths and Hundredths Divide Decimals Divide by Two-Digit Numbers Lesson 25 Rename Tenths and Hundredths Divide Decimals by Ten Divide Decimals by Multiples of 10 Lesson 26-27 Rename Tenths and Hundredths Divide Decimals by Multiples of 10 Estimate the Quotient Unit Conversions Divide Decimals by Two-Digit Numbers 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)






arrays, and/or area models. !5.NBT.7 Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Domain: Measurement and Data Cluster: Convert like measurement units within a given measurement system. ! 5.MD.1 Convert among different-sized

standard measurement units within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems.

Learning Targets Topic H Lesson 28-29 Solve division word problems involving multi-digit division with group size unknown and the number of groups unknown. (5.NBT.2, 5.NBT.7)

Topic H Lesson 28-29 End-of-Module Assessment 1-3 Decimal Place Value 1-4 Comparing and Ordering Decimals 1-5 Problem Solving Look for a Pattern Number Sense 2-1 Mental Math 2-2 Rounding Whole Numbers and Decimals 2-3 Estimating Sums and Differences 2-4 Problem Solving – Draw a Picture and

Write an Equation Tasks: Kipton’s Scale

Fluency Practice Lesson 28-29 Multiples of 10 Unit Conversions Divide Decimals by Two-Digit Numbers






Learning Targets Topic H Lesson 28-29 Solve division word problems involving multi-digit division with group size unknown and the number of groups unknown. (5.NBT.2, 5.NBT.7)

Topic H Lesson 28-29 End-of-Module Assessment 1-3 Decimal Place Value 1-4 Comparing and Ordering Decimals 1-5 Problem Solving Look for a Pattern Number Sense 2-1 Mental Math 2-2 Rounding Whole Numbers and Decimals 2-3 Estimating Sums and Differences 2-4 Problem Solving – Draw a Picture and

Write an Equation Tasks: Kipton’s Scale Multiplying Decimals by 10 The Value of Education Coordinating I-Ready Lessons:

Fluency Practice Lesson 28-29 Multiples of 10 Unit Conversions Divide Decimals by Two-Digit Numbers

Module 3 Addition and Subtraction of Fractions (Allow 4 weeks for instruction, review and assessment)

Domain: Number and Operations-Fractions Cluster: Use equivalent fractions as a strategy to add and subtract fractions. ! 5.NF.A.1 Add and subtract fractions with

unlike denominators. # 5.NF.A.2 Solve word problems involving

addition and subtraction of fractions referring to the same whole.

Enduring Understandings One representation may sometimes be more helpful than another; and, used together multiple representations give a fuller understanding of a problem. Essential Questions How do mathematical ideas interconnect and build on one another to produce a coherent whole?

Learning Targets Topic A Lesson 1: I can make equivalent fractions with the number line, the area model, and numbers. (4.NF.1)

engageny Module 3 Addition and Subtraction of Fractions

Learning Targets Topic A: Equivalent Fractions Lesson 1 Lesson 2 Videos:

Familiar Terns and Symbols Between, denominator, equivalent fraction, fraction, fraction greater than or equal to 1, fraction written in the largest possible unit, fractional unit, hundredth, kilometer, meter, centimeter, liter, milliliter, kilogram, gram, mile, yard, foot, inch, gallon, quart, pint, cup, pound, ounce, hour, minute, second, more than halfway and less than halfway, number sentence, numerator, one tenth, tenth, whole unit, <, >, = Fluency Practice:






Topic B Lesson 3: Add fractions with unlike units using the strategy of creating equivalent fractions. (5.NF.1, 5.NF.2) Lesson 4: Add fractions with sums between 1 and 2. (5.NF.1, 5.NF.2) Lesson 5: Subtract fractions with unlike units using the strategy of creating equivalent fractions. (5.NF.1, 5.NF.2) Lesson 6: Subtract fractions from numbers between 1 and 2. (5.NF.1, 5.NF.2) Lesson 7: Solve two-step word problems. (5.NF.1, 5.NF.2)

Topic B: Making Like Units Pictorially Lesson 3 Lesson 4 Lesson 5 Lesson 6 Lesson 7 Mid-Module Assessment Videos: • Findingacommondenominator

usingareamodels• Addingfractionswithunlike

denominatorsusingareamodels• Subtractingfractionswithunlike

denominatorsusingareamodels

Fluency Practice: Lesson 3 Sprint: Equivalent Fractions Adding Like Fractions Fractions as Division Lesson 4 Adding Fractions to Make One Whole Skip-Counting by yard Lesson 5 Sprint: Subtracting Fractions From a Whole Lesson 6 Name the Fraction to Complete the Whole Taking from the Whole Fraction Units to Ones and Fractions Lesson 7 Sprint: Circle the Equivalent Fraction

Topic C Lesson 8: Add fractions to and subtract fractions from whole numbers using equivalence and the number line as strategies. (5.NF.1, 5.NF.2) Lesson 9: Add fractions making like units numerically. (5.NF.1, 5.NF.2) Lesson 10: Add fractions with sums greater than 2. (5.NF.1, 5.NF.2) Lesson 11: Subtract fractions making like units numerically. (5.NF.1, 5.NF.2) Lesson 12: Subtract fractions greater than or equal to 1. (5.NF.1, 5.NF.2)

Topic C: Making Like Units Numerically Lesson 8 Lesson 9 Lesson 10 Lesson 11Lesson 12 Videos: • Adding mixed numbers using area

models and renaming as improper fractions

• Subtracting mixed numbers using area models

Fluency Practice: Lesson 8 Adding Whole Numbers and Fractions Subtracting Fractions from Whole Numbers Lesson 9 Adding and Subtracting Fractions with Like Units Sprint: Adding and Subtracting Fractions with Like Units Lesson 10 Sprint: Add and Subtract Whole Numbers and Ones with Fraction Units Lesson 11 Subtracting Fractions from Whole Numbers Adding and Subtracting Fractions with Like






Topic C Lesson 8: Add fractions to and subtract fractions from whole numbers using equivalence and the number line as strategies. (5.NF.1, 5.NF.2) Lesson 9: Add fractions making like units numerically. (5.NF.1, 5.NF.2) Lesson 10: Add fractions with sums greater than 2. (5.NF.1, 5.NF.2) Lesson 11: Subtract fractions making like units numerically. (5.NF.1, 5.NF.2) Lesson 12: Subtract fractions greater than or equal to 1. (5.NF.1, 5.NF.2)

Topic C: Making Like Units Numerically Lesson 8 Lesson 9 Lesson 10 Lesson 11Lesson 12 Videos: • Adding mixed numbers using area

models and renaming as improper fractions

• Subtracting mixed numbers using area models

Fluency Practice: Lesson 8 Adding Whole Numbers and Fractions Subtracting Fractions from Whole Numbers Lesson 9 Adding and Subtracting Fractions with Like Units Sprint: Adding and Subtracting Fractions with Like Units Lesson 10 Sprint: Add and Subtract Whole Numbers and Ones with Fraction Units Lesson 11 Subtracting Fractions from Whole Numbers Adding and Subtracting Fractions with Like Units Lesson 12 Sprint: Subtracting Fractions with Like and Unlike Units

Topic D Lesson 13: Use fraction benchmark numbers to assess reasonableness of addition and subtraction equations. (5.NF.1, 5.NF.2) Lesson 14: Strategize to solve multi-term problems. (5.NF.1, 5.NF.2) Lesson 15: Solve multi-step word problems; assess reasonableness of solutions using benchmark numb. (5.NF.1, 5.NF.2) Lesson 16: Explore part-to-whole relationships. (5.NF.1, 5.NF.2)

Topic D: Further Applications Lesson 13 Lesson 14 Lesson 15 Lesson 16 End-of-Module Assessment

Fluency Practice Lesson 13 FromFractionstoDecimalsAdding and Subtracting Fractions with Unlike Units Lesson 14 Sprint: Make Larger Units (Simplifying Fractions) Happy Counting with Mixed Numbers Lesson 15 Sprint: Circle the Smallest Fraction Sprint Lesson 16 Break Apart the Whole Make a Like Unit Add Fractions with Answers Greater than 1






enVision Resource: (enVision may be used to support the needs of your students, but should not be used independently of the mathematics curriculum) 10-1: Adding and Subtracting Fractions with

Like Denominators 10-1A: Estimating Sums and Differences of

Fractions 10-2: Common Multiples and Least Common

Multiple 10-3: Adding Fractions with Unlike

Denominators 10-4: Subtracting Fractions with Unlike

Denominators 10-5: Adding Mixed Numbers 10-5A : Modeling Addition and Subtraction of Mixed Numbers 10-6: Subtracting Mixed Numbers 10-7A : More Adding and Subtracting of Mixed

Numbers Tasks: Cindy’s Cats Part and Whole Coordinating I-Ready Lessons:

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)

Module 4 Multiplication and Division of Fractions and Decimal Fractions (Allow 3 weeks for instruction, review and assessment)






Domain: Operations and Algebraic Thinking Cluster: Write and Interpret Numerical Expressions

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

" 5.OA.2 Write simple expressions that record calculations with numbers, and interpret numerical expressions without evaluating them. For example, express the calculation “add 8 and 7, then multiply by 2” as 2 × (8 +7). Recognize that 3 × (18932 + 921) is three times as large as 18932 + 921, without having to calculate the indicated sum or product

Domain: Number and Operations Base Ten Cluster: Perform operations with multi-digit whole numbers and with decimals to hundredths.

! 5.NBT.7 Add subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used Domain: Number and Operations- Fractions Cluster: Apply and extend previous understandings of multiplication and division to multiply and divide fractions. ! 5.NF.3 Interpret a fraction as division of the numerator by the denominator (a/b = a ÷ b). Solve word problems involving division of whole numbers leading to answers in the form

Enduring Understandings • Fractions can be interpreted as division. • Equal sharing with area models provides

opportunities to understand division of whole numbers with answers in the form of fractions or mixed numbers.

• Fractions and decimals allow for quantities to be expressed with greater precision than with just whole numbers.

Essential Questions • How do mathematical ideas interconnect

and build on one another to produce a coherent whole?

• Why express quantities, measurements, and number relationships in different ways?

Learning Targets Topic A Lesson 1:

Topic A: Line Plots of Fraction Measurements Lesson 1

Vocabulary Decimal divisor, simplify Familiar Terms and Symbols Commutative property, conversion factor,

decimal fraction, denominator, distribute, divide, division, equation, equivalent fraction, expression, factors, foot, mile, yard, inch, gallon, quart, pound, pint, cup, ounce, hour, minute, second, fraction greater than or equal to 1

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






of fractions or mixed numbers, e.g., by using visual fraction models or equations to represent the problem. For example, interpret 3/4 as the result of dividing 3 by 4, noting that 3/4 multiplied by 4 equals 3, and that when 3 wholes are shared equally among 4 people each person has a share of size 3/4. If 9 people want to share a 50‐pound sack of rice equally by weight, how many pounds of rice should each person get? Between what two whole numbers does your answer lie? ! 5.NF.4 Apply and extend previous understandings of multiplication to multiply a fraction or whole number by a fraction. a. Interpret the product of (a/b) × q as a parts of a partition of q into b equal parts; equivalently, as the result of a sequence of operations a × q ÷ b. For example, use a visual fraction model to show (2/3) × 4 = 8/3, and create a story context for this equation. Do the same with (2/3) × (4/5) = 8/15. (In general, (a/b) × (c/d) = ac/bd.) ! 5.NF.5 Interpret multiplication as scaling (resizing), by: a. Comparing the size of a product to the size of one factor on the basis of the size of the other factor, without performing the indicated multiplication b. Explaining why multiplying a given number by a fraction greater than 1 results in a product greater than the given number (recognizing multiplication by whole numbers greater than 1 as a familiar case); explaining why multiplying a given number by a fraction less than 1 results in a product smaller than the given number; and relating the principle of fraction

Topic A: Line Plots of Fraction Measurements Lesson 1

Vocabulary Decimal divisor, simplify Familiar Terms and Symbols Commutative property, conversion factor,

decimal fraction, denominator, distribute, divide, division, equation, equivalent fraction, expression, factors, foot, mile, yard, inch, gallon, quart, pound, pint, cup, ounce, hour, minute, second, fraction greater than or equal to 1

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






equivalence a/b = (n×a)/(n×b) to the effect of multiplying a/b by 1. ! 5.NF.6 Solve real world problems involving multiplication of fractions and mixed numbers, e.g., by using visual fraction models or equations to represent the problem. ! 5.NF.7 Apply and extend previous understandings of division to divide unit fractions by whole numbers and whole numbers by unit fractions. (Students capable of multiplying fractions can generally develop strategies to divide fractions by reasoning about the relationship between multiplication and division. However, division of a fraction by a fraction is not a requirement at this grade level.) a. Interpret division of a unit fraction by a non-zero whole number, and compute such quotients. For example, create a story context for (1/3) ÷ 4, and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that (1/3) ÷ 4 = 1/12 because (1/12) × 4 = 1/3. b. Interpret division of a whole number by a unit fraction, and compute such quotients. For example, create a story context for 4 ÷ (1/5), and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that 4 ÷ (1/5) = 20 because 20 × (1/5) = 4. C. Solve real world problems involving division of unit fractions by non‐zero whole numbers and division of whole numbers by unit fractions, e.g., by using visual fraction models and equations to represent the problem. For example, how much chocolate






will each person get if 3 people share 1/2 lb of chocolate equally? How many 1/3-cup servings are in 2 cups of raisins? Domain: Measurement and Data Cluster: Convert like measurement units within a given measurement system. ! 5.MD.1 Convert among different-sized

standard measurement units within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems

Domain: Measurement and Data Cluster: Represent and Interpret Data ! 5.MD.2 Make a Line plot to display a data

set of measurements in fractions of a unit (1/2, 1/4, 1/8). Use operations on fractions for this grade to solve problems involving information presented in line plots. For example, given different measurements of liquid in identical beakers, find the amount of liquid each beaker would contain if the total amount in all the beakers were redistributed equally.

Topic C






Topic D Tasks: Task Bank (TNCore 5th Grade Task Arc) http://tncore.org/math/instructional_resources/grades/grade5.aspx

• Gretchen’s Garden • Multiplication with Fractions: Finding

Portions of Numbers enVision Resource: (enVision may be used to support the needs of your students, but should not be used independently.) Coordinating I-Ready Lessons:

• Multiplying a whole Number and a Fraction

• Multiply Fractions to Find Area • Understand Multiplication as Scaling • Multiplying Fractions • Understand Division with Unit

Fractions • Divide Unit Fractions in Word

Problems

*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)






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 TNReady Math Standards Achieve the Core

Videos Tech Coach Corner PowerPoint and Resources Teaching Channel Scholastic Math Study Jams Math TV

LearnZillion Khan Academy

Children’s Literature Stuart J. Murphy

Math Wire

Elementary Math Literature The Reading Nook

Interactive Manipulatives 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 http://www.k-5mathteachingresources.com/5th-grade-number-activities.html Edutoolbox ResourcesOther: 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 5 Year at a Glance- 2016-2017 Q2 16-17 w YAG.pdf · Quarter 2 Grade 5 ... Unit 2 Module Sept.8-Nov. 3 Unit 3 Module ... math they know to solve problems inside

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