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Subject to revision Major Content Supporting Content Additional Content

Curriculum and Instruction – Office of Mathematics

2nd Nine Weeks Grade 5

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 standards-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 Ready Standards are 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.

Shelby County Schools 2015/2016Revised 8/17/15

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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 thay 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 onto 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.




While the academic standards establish desired learning outcomes, the curriculum provides instructional planning designed to help students reach these outcomes. Educators will use this guide and the standards as a roadmap for curriculum and instruction. The sequence of learning is strategically positioned so that necessary foundational skills are spiraled in order to facilitate student mastery of the standards.

These standards emphasize thinking, problem-solving and creativity through next generation assessments that go beyond multiple-choice tests to increase college and career readiness among Tennessee students. In addition, assessment blueprints (http://www.tn.gov/education/article/tnready-blueprints) have been designed to show educators a summary of what will be assessed in each grade, including the approximate number of items that will address each standard. Blueprints also detail which standards will be assessed on Part I of TNReady and which will be assessed on Part II.

Our collective goal is to ensure our students graduate ready for college and career. The Standards for Mathematical Practice describe varieties of expertise that mathematics educators at all levels should seek to develop in their students. These practices rest on important “processes and proficiencies” with longstanding importance in mathematics education. The first of these are the NCTM process standards of problem solving, reasoning and proof, communication, representation and connections.


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Problem Solving

Reasoning and Proof

CommunicationRepresentation

Connecton

http://www.tn.gov/education/article/tnready-blueprints




The second are the strands of mathematical proficiency specified in the National Research Council’s report Adding It Up: adaptive reasoning, strategic competence, conceptual understanding (comprehension of mathematical concepts, operations and relations) procedural fluency

(skill in carrying out procedures flexibly, accurately, efficiently and appropriately), and productive disposition (habitual inclination to see mathematics and sensible, useful and worthwhile, coupled with a belief in diligence and one’s own efficacy). Throughout the year, students should continue to develop proficiency with the eight Standards for Mathematical Practice.

How to Use the Mathematic Curriculum Maps

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 instructional practice in alignment with the three College and Career Ready shifts, as described above, in instruction for Mathematics.

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 standards and teaching practices that teachers should consistently access:


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Mathematical Practices

Make sense of problems and persevere in solving them

Reason abstractly and quatitatively

Construct viable arguments and

crituqe the reasoning of

others

Model with mathematics

Use appropriate tools

strategically

Attend to precision

Look for and make use of

structure

Look for and express

regularity in repeated reasoning




Curriculum Maps:

Locate the TDOE Standards in the left column. Analyze the language of the standards and match each standard to a learning target in the second column.

Each standard is identified as the following: Major Work, Supporting Content or Additional content. In any single grade, students and teachers should spend the majority of their time on the major work of the grade. Consult your enVision Teachers’ Edition (TE) and other cited references to map out your week(s) of instruction. Plan your weekly and daily objectives, using the learning target statements to help. Best practices tell us that making objectives

measureable increases student mastery. Include daily fluency practice. Study the suggested performance assessments (tasks) and match them to your objectives. Review the CLIP Connections found in the right hand column. Make plans to address the Academic Vocabulary in your instruction. Examine the other standards and skills you will need to address in order to ensure mastery of the indicated standard. Using your enVision TE and other resources cited in the curriculum map, plan your week using the SCS lesson plan template.

Remember to include differentiated activities to address the needs of all students.


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The TNCore Mathematics StandardsThe 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 Teaching Practiceshttps://mathprojectsjournal.files.wordpress.com/2015/05/nctm-teaching-practices.pdf

NCTM – Mathematics Teaching Practices

https://mathprojectsjournal.files.wordpress.com/2015/05/nctm-teaching-practices.pdf

https://mathprojectsjournal.files.wordpress.com/2015/05/nctm-teaching-practices.pdf

https://www.tn.gov/education/article/mathematics-standards

https://www.tn.gov/education/article/mathematics-standards




Grade 5: Quarter 2

Topic 5: Dividing by Two-Digit Divisors (cont.)Topic 7: Multiplying and Dividing DecimalsTopic 9: Fractions and DecimalsTopic 10: Adding and Subtracting Fractions and Mixed NumbersTopic 11: Multiplying Fractions & Mixed Numbers (to be continued in Q4)

Overview

We begin Quarter 2 with a continuation of division by two digit divisors. This concept begins concretely with place value rods as an introduction to division with multi-digit whole numbers (5.NBT.6). Students round dividends and two-digit divisors to nearby multiples of 10 in order to estimate single-digit quotients (e.g., 431 ÷ 58 ≈ 420 ÷ 60 = 7) and then multi-digit quotients. This work is done horizontally, outside the context of the written vertical method. The series of lessons in Topic 5 leads students to divide multi-digit dividends by two-digit divisors using the written vertical method. Each lesson moves to a new level of difficulty with a sequence beginning with divisors that are multiples of 10 to non-multiples of 10. There is a connection from the first quarter in which time was devoted to single-digit quotients with and without remainders before progressing to two- and three-digit quotients (5.NBT.6).

In Topic 7, students’ understandings of the patterns in the base ten system are extended from Grade 4’s work with place value to include decimals to the thousandths place. In Grade 5, students deepen their knowledge through a more generalized understanding of the relationships between and among adjacent places on the place value chart, e.g., 1 tenth times any digit on the place value chart moves the digit one place value to the right (5.NBT.1). Students will then apply these new understandings as they reason about and perform decimal operations through the hundredths place. They will connect their knowledge from the previous quarter of conceptual exploration of the multiplicative patterns of the base ten system using place value disks and a place value chart.

Now in Grade 5, students use exponents and the unit fraction to represent expanded form, e.g., 2 × 102 + 3 × (1/10) + 4 × (1/100) = 200.34 (5.NBT.C.3, NBT.A.2). Further, students’ reason about differences in the values of like place value units and express those comparisons with


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symbols (>, <, and =). Students generalize their knowledge of rounding whole numbers to round decimal numbers covered in the previous quarter initially using a vertical number line to interpret

Students use the relationships of adjacent units and generalize whole number algorithms to decimal fraction operations (5.NBT.6, 5.NBT.7). Topic 7 bridges the gap between Grade 4 work with multiplication and the standard algorithm by focusingon an intermediate step—reasoning about multiplyinga decimal by a one-digit whole number. The areamodel, with which students have had extensiveexperience since Grade 3, is used as a scaffold for this work. In Topic 7 students explored with a similar exploration of division of decimal numbers by one-digit whole number divisors (5.NBT.6) and solidify their skills with an understanding of the algorithm.

In Topic 9, 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. Students’ understanding of addition and subtraction of fractions extends in Topic 9 with fraction equivalence and decimals. This concept 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. Furthermore, equivalence is evidenced when adding fractions with the same denominator. The sum may be decomposed into parts (or recomposed into an equal sum). This also carries forward work with decimal place value Topic 7, 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 10, 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. 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.


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Addition and Subtraction of Fractions

Quarter 2 concludes with Topic 11, where students interpret finding a fraction of a set (34 of 24) as multiplication of a whole number by a fraction (

34

× 24) and use diagrams to support their understandings (5.NF.4a). This, in turn, will help students to see division by a whole number as being

equivalent to multiplication by its reciprocal. That is, division by 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. (5.NFB.6) Students will continue this topic of study in quarter 3.

Focus Grade Level Standards(Note: Related Foundational Standards are noted in parenthesis after standard)

Cluster 5.NBT.A: Understands the place value system 5.NBT.A.1 Recognize that in a multi-digit number, a digit in one place represents 10 times as much as it represents in the place to its right

and 1/10 of what it represents in the place to its left. (3.NBT.3, 4.NGT.A.1, 4.NBT.A.2) 5.NBT.A.2 Explain patterns in the number of zeros of the product when multiplying a number by powers of 10. (3.NBT.3, 4.NGT.A.1,

4.NBT.A.2, 5.NBT.A.1)


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http://www.corestandards.org/Math/Content/5/NBT/#CCSS.Math.Content.5.NBT.A.2





5.NBT.A.3.a Read and write decimals to thousandths using base-ten numerals, number names, and expanded form. (4.NG.C.5, 4.NF.C.6, 4.NF.C.7)

Cluster 5.NBT.B: Perform operations with multi-digit whole numbers and with decimals to hundredths. 5.NBT.B.6 Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors. (3.OA.A.2, 3.OA.C.7,

4.NBT.B.6) 5.NBT.B.7 Add, subtract, multiply, and divide decimals to hundredths, using concrete models. (4.NF.C.6, 4.NBT.B.6, 5.NGT.B.5,

5.NBT.B.6)

Cluster 5.NF.A: Use equivalent fractions as a strategy to add and subtract fractions. 5.NF.A.1 Add and subtract fractions with unlike denominators. (3.NG.A.2, 3.NG.A.3, 4.NG.B.3) 5.NF.A.2 Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike

denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. (4.NG.B.S, 5.NG.A.1)

Cluster 5.NF.B: Apply and extend previous understandings of multiplication and division to multiply and divide fractions. 5.NF.B.3. Interpret a fraction as division of the numerator by the denominator (Introduction) 5.NF.B.4 Apply and extend previous understandings of multiplication to multiply a fraction or whole number by a fraction. (3.MD.C.7,

4.NG.B.4) 5.NF.B.4.a Interpret the product (a/b)×q as a parts of a partition of q into b equal parts; equivalently, as the result of a sequence of operations a ×

q ÷ b. (3.MD.C.7, 4.NG.B.4) 5.NF.B.6 Solve real world problems involving multiplication of fractions and mixed numbers. (3.MD.C.7, 4.NF.B.4, 5.NF.B.4)

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

and properties of operations. 3.MD.C.7: Understand concepts of area and relate area to multiplication and to addition.


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http://www.corestandards.org/Math/Content/5/NF/#CCSS.Math.Content.5.NF.B.6




http://www.corestandards.org/Math/Content/5/NF/#CCSS.Math.Content.5.NF.A.1

http://www.corestandards.org/Math/Content/5/NBT/#CCSS.Math.Content.5.NBT.B.7


http://www.corestandards.org/Math/Content/3/MD/C/7/

http://www.corestandards.org/Math/Content/3/NBT/A/3/

http://www.corestandards.org/Math/Content/5/NF/A/2/

http://www.corestandards.org/Math/Content/5/NBT/A/3/a/




3.OA.A.2 Interpret whole-number quotients of whole numbers, e.g., interpret 56 ÷ 8 as the number of objects in each share when 56 objects are partitioned equally into 8 shares, or as a number of shares when 56 objects are partitioned into equal shares of 8 objects each. For example, describe a context in which a number of shares or a number of groups can be expressed as 56 ÷ 8. 3.OA.C.7 Fluently multiply and divide within 100, using strategies such as the relationship between multiplication and division (e.g., knowing

that 8 x 5 = 40, one knows 40 ÷ 5 = 8) or properties of operations. By the end of Grade 3, know from memory all products of two one-digit numbers. 3.NF.A.2

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

4.NBT.A.1 Recognize that in a multi-digit whole number, a digit in one place represents ten times what it represents in the place to its right.

4.NBT.A.2 Read and write multi-digit whole numbers using base-ten numerals, number names, and expanded form. Compare two multi-digit numbers based on meanings of the digits in each place, using >, =, and < symbols to record the results 4.NBT.B.6 Find whole-number quotients and remainders with up to four-digit 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 by using equations, rectangular arrays, and/or area models.

4.NF.B.3 Understand a fraction a/b with a > 1 as a sum of fractions 1/b. 4.NF.B.4.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 5 × (1/4),

recording the conclusion by the equation 5/4 = 5 × (1/4). 4.NF.B.4.b Understand a multiple of a/b as a multiple of 1/b, and use this understanding to multiply a fraction by a whole number. For example,

use a visual fraction model to express 3 × (2/5) as 6 × (1/5), recognizing this product as 6/5. (In general, n × (a/b) = (n × a)/b.) 4.NF.B.4.c Solve word problems involving multiplication of a fraction by a whole number, e.g., by using visual fraction models and equations to

represent the problem. For example, if each person at a party will eat 3/8 of a pound of roast beef, and there will be 5 people at the party, how many pounds of roast beef will be needed? Between what two whole numbers does your answer lie?

4.NF.C.5 Express a fraction with denominator 10 as an equivalent fraction with denominator 100, and use this technique to add two fractions with respective denominators 10 and 100. For example, express 3/10 as 30/100, and add 3/10 + 4/100 = 34/100.

4.NF.C.6 Use decimal notation for fractions with denominators 10 or 100. For example, rewrite 0.62 as 62/100; describe a length as 0.62 meters; locate 0.62 on a number line diagram.

4.NF.C.7 Compare two decimals to hundredths by reasoning about their size. Recognize that comparisons are valid only when the two decimals refer to the same whole. Record the results of comparisons with the symbols >, =, or <, and justify the conclusions, e.g., by using a visual model.

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


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http://www.corestandards.org/

http://www.corestandards.org/Math/Content/4/NF/C/7/



http://www.corestandards.org/Math/Content/4/NF/B/4/c/

http://www.corestandards.org/Math/Content/4/NF/B/4/b/

http://www.corestandards.org/Math/Content/4/NF/B/4/a/

http://www.corestandards.org/Math/Content/4/NF/B/3/

http://www.corestandards.org/Math/Content/4/NBT/B/6/

http://www.corestandards.org/Math/Content/4/NBT/A/2/


http://www.corestandards.org/Math/Content/3/OA/#CCSS.Math.Content.3.OA.C.7

http://www.corestandards.org/Math/Content/3/OA/A/2/




Fluency Practice

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 practice in ways that get their adrenaline flowing. Automaticity is critical so that students avoid using up too many of their attention resources with 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. It should be high-paced and energetic, celebrating improvement and focusing on recognizing patterns and connections within the material. Special care should be taken so that it is not seen as punitive for students that might need more time to master fluency.

Standards for Mathematical Practice

The eight Standards for Mathematical Practice are an important component of the mathematics standards for each grade and course, K-12. The Standards for Mathematical Practice describe the varieties of expertise, habits of minds, and productive dispositions that educators seek to develop in all students.


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TN State Standards Essential Understandings Content & Tasks CLIP ConnectionsTopic 5: Dividing by Two-Digit Divisors

(Allow 1week for instruction, review and assessment– continued from Quarter 1)Cluster 5.NBT.B: Perform operations with multi-digit whole numbers and with decimals to hundredths. 5.NBT.B.6 Find whole-number quotients of

whole numbers with up to four-digit dividends and two-digit divisors.


Enduring Understandings1. There are no remainders dealing

quantities that must be kept as a whole.2. Computational fluency includes

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

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

4. In many cases, there are multiple algorithms for finding a mathematical solution, and those algorithms are frequently associated with different cultures.

5. Context is critical when using estimation.

Essential Questions1. When are remainders okay and when are

they not?2. What makes a computational strategy

both effective and efficient?3. How does the size of the number affect

the outcome of the operation?4. How can we decide when to use an exact

answer and when to use an estimate?

Learning Targets

Division5-5 1-Digit Quotients5-6 2-Digit Quotients5-7 Estimating and Dividing Greater Numbers

Supplemental Engage NY Activitieshttps://www.engageny.org/resource/grade-5-mathematics-module-2

Mental Strategies for Multi-Digit Whole Number Division(See Topic E Lessons 16-18 zip fie)Partial Quotients and Multi-Digit Whole Number Division(See Topic F Lessons 19-23 zip file)

Fluency Resources:http://www.caboces.org/iss/resources/school-library-system/common-core-workbooks(See Grade 5 - Sprints – Grade 5 – Module 2)

http://biloxischools.schoolwires.net/Page/5285

http://maccss.ncdpi.wikispaces.net/5th+Grade+Instructional+Resources

Academic Vocabularymultiplication/multiply, division/divide, quotients, dividends, (properties) rules about how numbers work, reasoning

Explain Your Thinking• Do you Understand? (see daily lesson)

• Writing to Explain (See Problem Solving Section of each lesson)

Reading Comprehension & Problem SolvingTeaching Tool 1 (See TE p. 120 F for more information)

Literature ConnectionsWorldScapes Readers: Everest Adventures

Additional Literature ConnectionsThe Great Divide Dayle Ann DoddsA Remainder of One Elinor Pinczes


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Make sense of problems and persevere in solving them. Reason abstractly and quantitatively. Construct viable arguments and critique the reasoning of others. Model with mathematics. Use appropriate tools strategically. Attend to precision. Look for and make use of structure. Look for and express regularity in repeated reasoning.

Resources: https://www.engageny.org/resource/grade-5 -

mathematics https://www.pearsonsuccessnet.com/snpapp/iText/

getTeacherHomepage.do?newServiceId=6000&newPageId=10100

http://www.nctm.org/Standards-and-Positions/ Position-Statements/Procedural-Fluency-in-Mathematics/






http://www.caboces.org/iss/resources/school-library-system/common-core-workbooks



https://www.engageny.org/resource/grade-5-mathematics-module-2







http://www.nctm.org/Standards-and-Positions/Position-Statements/Procedural-Fluency-in-Mathematics/



https://www.pearsonsuccessnet.com/snpapp/iText/getTeacherHomepage.do?newServiceId=6000&newPageId=10100



https://www.engageny.org/resource/grade-2-mathematics

https://www.engageny.org/resource/grade-2-mathematics




TN State Standards Essential Understandings Content & Tasks CLIP Connections I can demonstrate division of whole

number with four-digit dividends and two-digit divisors using place value, rectangular arrays, area models, and other strategies. (5.NBT.B.6)

I can solve division of whole numbers with four-digit dividends and two-digit divisors using properties of operations and equations. (5.NBT.B.6)

I can explain my chosen strategy. (5.NBT.B.6)

Fluency Practice Daily

(Click on resource Building Conceptual Understanding and Fluency Through Games)

Topic 7: Multiplying and Dividing Decimals(Allow 2 weeks for instruction, review and assessment)

Cluster 5.NBT.A: Understands the place value system 5.NBT.A.1 Recognize that in a multi-digit

number, a digit in one place represents 10 times as much as it represents in the place to its right and 1/10 of what it represents in the place to its left.

5.NBT.A.2 Explain patterns in the number of zeros of the product when multiplying a number by powers of 10.

Cluster 5.NBT.B: Perform operations with multi-digit whole numbers and with decimals to hundredths. 5.NBT.B.7 Add, subtract, multiply, and

divide decimals to hundredths, using concrete models.


Enduring Understandings1. Identification of patterns can be used to

determine the reasonableness of answers.

2. Computational fluency includes understanding not only the meaning, but also the appropriate use of numerical operations.

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

4. Context is critical when using estimation.

Essential Questions1. How can identification of patterns assist

me when dividing decimals?2. What makes a computational strategy

both effective and efficient?3. How does the size of the number affect

the outcome of an operation?4. How can we decide when to use an exact

answer and when to use an estimate?

Learning Targets

Decimals7-1 Multiplying Decimals a Decimal by a

Whole Number7-3 Estimating the Product of a Decimal and

a Whole Number7-4 Multiplying Two Decimals7-4A Number Sense: Decimal Multiplication7-4B Models for Multiplying Decimals7-5 Dividing Decimals by 10, 100, or 1,0007-6 Dividing a Decimal by a Whole Number7-6A Number Sense: Decimal Division7-7 Estimation: Decimals Divided by Whole

Numbers7-8 Dividing a Decimal by a Decimal

enVision Math Transitioning to Common Core Student Lesson: 7-4A Number Sense: Decimal Multiplication 7-4B Models for Multiplying Decimals7-6A Number Sense: Decimal Division

Supplemental Engage NY Activitieshttps://www.engageny.org/resource/grade-

Academic Vocabularymultiplication/multiply, division/divide, decimal, decimal point, tenths, hundredths, thousandths, products, quotients, dividends, rectangular arrays, area models, addition/add, subtraction/subtract

Explain Your Thinking• Do you Understand? (see Guided Practice)


Task Bank (TNCore 5th Grade Task Arc)Decimal Operations: Multiplication and Divisionhttp://tncore.org/sites/www/Uploads/MathTasks_9.13/5thGradeTaskArc.pdf

Reading Comprehension & Problem SolvingTeaching Tool 1 (See TE p. 168 F for more information)


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http://tncore.org/math/instructional_resources/grades/grade5.aspx





http://tncore.org/sites/www/Uploads/MathTasks_9.13/5thGradeTaskArc.pdf

http://tncore.org/sites/www/Uploads/MathTasks_9.13/5thGradeTaskArc.pdf






TN State Standards Essential Understandings Content & Tasks CLIP Connections I can recognize that each place to the left

is 10 times larger in a multi-digit number (5.NBT.A.1)

I can recognize that each place to the right if 1/10 as much in a multi-digit number. (5.NBT.A.1)

I can express powers of 10 using whole-number exponents. (5.NBT.A.2)

I can illustrate and explain a pattern for how the number of zeros of a product – when multiplying a whole number by a power of 10 – relates to the power of 10. (5.NBT.A.2)

I can illustrate and explain a pattern for how multiplying or dividing any decimal by a power of 10 relates to the placement of the decimal point. (5.NBT.A.2)

I can add, subtract, multiply, and divide decimals to hundredths using strategies based on place value, properties of operations, or other strategies. (5.NBT.B.7)

I can explain and illustrate strategies using concrete models or drawing when adding, subtracting, multiplying, and dividing decimals to hundredths.


5-mathematics-module-2

Decimal Multi-Digit Multiplication(See Topic C Lessons 10-12 zip file)

Partial Quotients and Multi-Digit Decimal Division(See Topic G Lessons 24-27 zip file)



http://maccss.ncdpi.wikispaces.net/5th+Grade+Instructional+Resources(Click on resource Building Conceptual Understanding and Fluency Through Games)

Literature ConnectionsWorldScapes Readers: Keeping Records

Additional Literature ConnectionsThe Best of Times Greg TangThe Grapes of Math Greg Tang

Topic 9: Fractions & Decimals(Allow 2 weeks for instruction, review and assessment)

Cluster 5.NF.A: 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, including cases of unlike denominators, e.g., by

Enduring Understandings1. The denominator determines how many

parts make the whole; that is why quantities must have the same denominator to be combined.

2. One representation may sometimes be more helpful than another; and, used together multiple representations give a

Fractions and Decimals9-1 Meanings of Fractions9-2 Fractions and Division9-3 Mixed Numbers and Improper Fractions9-4 Equivalent Fractions9-5 Comparing and Ordering Fractions and

Mixed Numbers9-6 Common Factors and Greatest

Academic Vocabularyfraction, equivalent, addition/add, sum, subtraction/subtract, difference, unlike denominator, numerator, benchmark fraction, estimate, reasonableness, mixed numbers



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TN State Standards Essential Understandings Content & Tasks CLIP Connectionsusing visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers.

Cluster 5.NF.B: Apply and extend previous understandings of multiplication and division to multiply and divide fractions.

5.NF.B.3. Interpret a fraction as division of the numerator by the denominator

Cluster 5.NBT.A: Understand the place value system. 5.NBT.A.3.a Read and write decimals to

thousandths using base-ten numerals, number names, and expanded form.


fuller understanding of a problem.

Essential Questions1. Why can’t you add and subtract fractions

with unlike denominators in their current form?

2. How do mathematical ideas interconnect and build on one another to produce a coherent whole?

Learning Targets I can determine common multiples of

unlike denominators. (5.NF.A.1) I can create equivalent fractions using

common multiples. (5.NF.A.1) I can add and subtract fractions with

unlike denominators (including mixed numbers) using equivalent fractions. (5.NF.A.1)

I can solve addition and subtraction word problems involving fractions using visual models or equations. (5.NF.A.2)

I can use estimation strategies, benchmark fractions, and number sense to check if my answer is reasonable. (5.NF.A.2)

I can explain that fractions can be represented as a division of a numerator by a denominator and illustrate why a÷ bcan be represented by the fraction a/b. (5.NF.B.3)

I can solve word problems involving division of whole numbers and interpret the quotient – which could be a whole number, mixed number, or fraction – in the context of the problem. (5.NF.B.3)

I can explain or illustrate my solution strategy using visual fraction models or

Common Factor9-7 Fractions in Simplest Form9-8 Tenths and Hundredths9-9 Thousandths9-10 Fractions and Decimals on the Number

Line


Fractions as Division(See Topic B Lessons 2-5 zip file)





Task Bank (TNCore 5th Grade Task)Apple Orchardhttp://tncore.org/sites/www/Uploads/Math_Tasks_July2013/Grade%205,%20apple%20orchard.pdf

Reading Comprehension & Problem SolvingTeaching Tool 1

Literature ConnectionsWorldScapes Readers: The Mighty Mekong

Additional Literature ConnectionsThe Hershey’s Fraction Book by Jerry PallottaEating Fractions by Bruce McMillanWorking With Fractions by David AdlerI f You Were a Fraction by Trisha Shaskan


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http://tncore.org/sites/www/Uploads/Math_Tasks_July2013/Grade%205,%20apple%20orchard.pdf














http://www.corestandards.org/Math/Content/5/NBT/A/3/a/




TN State Standards Essential Understandings Content & Tasks CLIP Connectionsequations that represent the problem. (5.NF.B.3)

I can read and write decimals to the thousandths in word form, based-ten numerals, and expanded form. (5.NBT.A.3.a)

Fluency Practice DailyTopic 10: Adding & Subtraction Fractions & Mixed Numbers

(Allow 2 weeks for instruction, review and assessment)Cluster 5.NF.A : 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 UnderstandingsOne representation may sometimes be more helpful than another; and, used together multiple representations give a fuller understanding of a problem.

Essential QuestionsHow do mathematical ideas interconnect and build on one another to produce a coherent whole?

Learning Targets I can determine common multiples of

unlike denominators. (5.NF.A.1) I can create equivalent fractions using

common multiples. (5.NF.A.1) I can add and subtract fractions with

unlike denominators (including mixed numbers) using equivalent fractions. (5.NF.A.1)

I can solve addition and subtraction word problems involving fractions using visual models or equations. (5.NF.A.2)

I can use estimation strategies, benchmark fractions, and number sense to check if my answer is reasonable. (5.NF.A.2)

Adding and Subtracting Fractions10-1: Adding and Subtracting Fractions with

Like Denominators10-1A: Estimating Sums and Differences of

Fractions10-2: Common Multiples and Least Common

Multiple10-3: Adding Fractions with Unlike

Denominators10-4: Subtracting Fractions with Unlike

Denominators10-5: Adding Mixed Numbers10-5A : Modeling Addition and Subtraction of Mixed Numbers10-6: Subtracting Mixed Numbers10-7A : More Adding and Subtracting of Mixed

Numbers

enVision Math Transitioning to Common Core Student Lesson:10-1A Estimating Sums and Differences of Fractions10-5A Modeling Addition and Subtraction of Mixed Numbers10-7A More Adding and Subtracting of Mixed Numbers

Supplemental Engage NY Activities

Academic Vocabularyfraction, equivalent, addition/add, sum, subtraction/subtract, difference, unlike denominator, numerator, benchmark fraction, estimate, reasonableness, mixed numbers



Task Bank (TNCore 5th Grade Tasks)Jenna’s Homeworkhttp://tncore.org/sites/www/Uploads/Gr%205%20Jenna%27s%20Homework.pdf

Reading Comprehension & Problem SolvingTeaching Tool 1 (See TE p. 254F for more information)

Literature ConnectionsWorldScapes Readers: Cruising the Caribbean

Additional Literature ConnectionsThe Wishing Club A Story about Fractions by


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http://tncore.org/sites/www/Uploads/Gr%205%20Jenna's%20Homework.pdf







TN State Standards Essential Understandings Content & Tasks CLIP ConnectionsFluency Practice Daily https://www.engageny.org/resource/grade-

5-mathematics-module-3

Making Like Units Pictorially(See Topic B Lessons 3-7 zip file)Making Like Units Numerically(See Topic C Lessons 8-12 zip file)Further Applications(See Topic D Lessons 12-16 zip file)




Donna NapoliPolar Bear Math by Cindy Bickel

Topic 11: Multiplying Fractions & Mixed Numbers(Allow 2 weeks 1 day for instruction, review and assessment – will continue in Quarter 3)

Focus Cluster 5.NF.B: Apply and extend previous understandings of multiplication and division to multiply and divide fractions. 5.NF.B.4 Apply and extend previous

understandings of multiplication to multiply a fraction or whole number by a fraction.

5.NF.B.4.a Interpret the product(a/b)×q as a parts of a partition of q into b equal parts;

Enduring Understandings1. Improper fractions can assist when

multiplying and dividing mixed numbers.2. One representation may sometimes be

more helpful than another; and, used together multiple representations give a fuller understanding of a problem.

3. Fractions and decimals allow for quantities to be expressed with greater

Multiplying Fractions11-1 Multiplying Fractions and Whole

Numbers11-2 Multiplying Two Fractions11-2A Estimating Products

enVision Math Transitioning to Common Core Student Lesson:

Academic Vocabularyfraction, numerator, denominator, operations, multiplication/multiply, division/divide, mixed numbers, product, quotient, partition, equal parts, equivalent, factor, unit fraction, area, side lengths, fractional sides lengths, comparing, scaling

Explain Your Thinking


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TN State Standards Essential Understandings Content & Tasks CLIP Connectionsequivalently, as the result of a sequence of operations a × q ÷ b

5.NF.B.6 Solve real world problems involving multiplication of fractions and mixed numbers.


precision than with just whole numbers.

Essential Questions1. How do you determine which form of a

number is most appropriate?2. How do mathematical ideas interconnect

and build on one another to produce a coherent whole?

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

Learning Targets I can create story contexts for

problems involving multiplication of a fraction and a whole number or multiplication of 2 fractions. (5.NF.B.4)

I can interpret multiplication with fractions in the same way that I interpret multiplication with whole numbers. (5.NF.B.4.a)

I can solve real world problems involving multiplication of fractions and mixed numbers and interpret the product in the context of the problem. (5.NF.B.6)

I can explain or illustrate my solution strategy using visual fraction models or equations that represent the problem. (5.NF.B.6)


11-2A Estimating Products


Multiplication of a Whole Number by a Fraction(See Topic C Lessons 6-9 zip file)Fraction Expressions and Word Problems(See Topic D Lessons 10-12 zip file)Multiplication of a Fraction by a Fraction(See Topic E Lessons 13-20 zip file)




• Do you Understand? (see Guided Practice)


Task Bank (TNCore 5th Grade Tasks)Arthttp://tncore.org/sites/www/Uploads/Gr5_Art_Task.pdf

Multiplication with Fractions: Finding Portions of Numbershttp://tncore.org/sites/www/Uploads/Aug_23/MATH/gr5_guide_arc.pdf

Reading Comprehension & Problem SolvingTeaching Tool 1 (See TE p. 276F for more information)

Literature ConnectionsWorldScapes Readers: The Mighty Mekong

Additional Literature ConnectionsThe Lion's Share - A Tale of Halving Cake and Eating It, Too Matthew McElligott

RESOURCE TOOLBOX


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http://tncore.org/sites/www/Uploads/Aug_23/MATH/gr5_guide_arc.pdf




http://tncore.org/sites/www/Uploads/Gr5_Art_Task.pdf



















Textbook ResourcesPearsonSCS All Things MathenVision Common Core Addendum Lessons

CalculatorTexas Instruments

CCSS/PARCCCore Standards Common Core Sheets Common Core ToolsMARSCommon Core LessonsEngage NY MathCommon Core onlineArizona Common Core MathDana CenterPARCC GamesInside Mathematics

Additional SitesIllustrative MathematicsNCTMTouchable Math TechnologyMath Dictionary and ChartsMath TasksCollection of Math websitesK-5 Teaching Math ResourcesMath PowerpointsPrint Resources

NCTM: Common Core Videoshttp://www.nctm.org/Standards-and-Positions/Common-Core-State-Standards/Teaching-and-Learning-Mathematics-with-the-Common-Core/TNCore: Videos for the TN State Standardshttp://tn.pbslearningmedia.org/collection/professional-learning-common-core/?topic_id=1078Achieve the Corehttp://achievethecore.org

Interactive ManipulativesEduplaceStem ResourcesIlluminationsInternet4ClassroomsMath ToolsIXL Math ActivitiesThinking BlocksVirtual Manipulatives

VideosTeacher TubeTech Coach Corner Powerpoints and ResourcesTeaching ChannelAchieve the CoreScholastic Math Study JamsMath TVLearn ZillionKhan Academy

Children’s LiteratureStuart J. MurphyMath WireElementary Math LiteratureThe Reading Nook

Achieve the Core Mini-Assessmentshttp://achievethecore.org/page/858/annotated-mini-assessmentsAchieve the Core: Aligned Instructional Materialshttp://achievethecore.org/aligned/?utm_source=Aligned%20Launch%20expanded%20partners_claires_email&utm_medium=email&utm_campaign=Aligned


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http://nlvm.usu.edu?

http://achievethecore.org/aligned/?utm_source=Aligned%20Launch%20expanded%20partners_claires_email&utm_medium=email&utm_campaign=Aligned



http://achievethecore.org/page/858/annotated-mini-assessments

http://achievethecore.org/page/858/annotated-mini-assessments

http://www.thereadingnook.com/math/

http://libguides.bgsu.edu/content.php?pid=46818

http://mathwire.com/literature/literature.html

http://www.stuartjmurphy.com/

https://www.khanacademy.org/

http://learnzillion.com/

http://www.mathtv.com/

http://studyjams.scholastic.com/

http://achievethecore.org/

http://www.teachingchannel.org/videos/Common-core-state-standards-for-math

http://techcoachcorner2.org/

http://www.teachertube.com/

http://www.thinkingblocks.com/

http://www.ixl.com/math/grade-5

http://www.bbc.co.uk/bitesize/ks2

http://www.internet4classrooms.com/

http://illuminations.nctm.org/

http://stemresources.com/

http://www.eduplace.com/math/mw

http://achievethecore.org/

http://tn.pbslearningmedia.org/collection/professional-learning-common-core/?topic_id=1078

http://tn.pbslearningmedia.org/collection/professional-learning-common-core/?topic_id=1078

http://www.nctm.org/Standards-and-Positions/Common-Core-State-Standards/Teaching-and-Learning-Mathematics-with-the-Common-Core/



http://www.senteacher.org/print/mathematics/

http://www.pppst.com/

http://www.k-5mathteachingresources.com/

http://guest.portaportal.com/mc2

https://grade5commoncoremath.wikispaces.hcpss.org/

http://amathsdictionaryforKids.com/mathsCharts.html

http://www.touchabletechnology.com/

http://www.nctm.org/standards/mathcommoncore/

http://www.illustrativemathematics.org/

http://www.insidemathematics.org/index.php/5th-grade

http://parccgames.com/

http://www.utdanacenter.org/

http://ime.math.arizona.edu/commoncore/

http://www.scoop.it/t/common-core-mathematics

http://www.engageny.org/

http://cc.betterlesson.com/

http://map.mathshell.org/materials/index.php

http://commoncoretools.me/

http://www.corestandards.org/Math

http://education.ti.com/

http://media.pearsoncmg.com/curriculum/math/envision2012/cc_support/G5/enVisionMATH_G5.html

http://scsallthingsmath.weebly.com/

http://www.pearsonsuccessnet.com/

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