Wayne County Public Schools

Wayne County Public Schools Revised July, 2015 Curriculum Guide for Grade 5 Mathematics 2010 NC Standard Course of Study for Mathematics Grade 5 Overview  Operations and Algebraic Thinking o Write and interpret numerical expressions. o Analyze patterns and relationships --- generate 2 numerical patterns using 2 given rules; form ordered pairs from the 2 patterns; graph the ordered pairs on a coordinate plane (first quadrant).  Number and Operations in Base Ten o Understand the place value system – read/write/compare decimals to thousandths . o Perform 4 operations (+, -, x, /) with multi-digit whole numbers and with decimals to hundredths.  Number and Operations- Fractions o Use equivalent fractions as a strategy to add and subtract fractions – add and subtract with unlike denominators. o Apply and extend previous understandings of multiplication and division to multiply and divide fractions – Note: Division is limited to dividing unit fractions by whole numbers and whole numbers by unit fractions; division of a fraction by a fraction is not a requirement at grade 5.  Measurement and Data o Convert like measurement units within a given measurement system. o Represent and interpret data – use line plots to display a data set of measurements in fractions of a unit (½, ¼, ⅛). o Geometric measurement: Understand concepts of volume and relate volume to multiplication and to addition –- a cube with side length 1 unit is called a unit cube and can be used to measure volume; apply the formulas: V=lxwxh; V= bxh.  Geometry o Graph points on the coordinate plane to solve real-world and mathematical problems -- first quadrant. o Classify two-dimensional figures into categories based on their properties. Resources: NC SCoS K – 12 Mathematics Standards: http://www.ncpublicschools.org/docs/acre/standards/common-core/standards-k-12.pdf

NC DPI NC COMMON CORE INSTRUCTIONAL SUPPORT TOOLS Home page: http://www.ncpublicschools.org/acre/standards/common-core-tools/ *** NC DPI Grade 5 Math Unpacking Document: http://www.dpi.state.nc.us/docs/acre/standards/common-core-tools/unpacking/math/5th.pdf

*** NC Math Wiki: Elementary Resources http://maccss.ncdpi.wikispaces.net/Elementary

NC DPI Grade 5 Quick Reference Guide: http://aplus.ncdpi.wikispaces.net/file/view/ReferenceGuide_5th_grade.pdf

Building Conceptual Understanding and Fluency through Games: Grade 5 Games: http://maccss.ncdpi.wikispaces.net/file/view/5thgrade_GAMES_8.22.14.pdf/519547634/4thgrade_GAMES_8.22.14.pdf

Textbook Series: enVision Math Common Core,  2012, Scott Foresman-Addison Wesley Investigations in Number, Data, and Space, Pearson Publishing Investigations and the Common Core State Standards in Math Home Page: http://investigations.terc.edu/components/CCSS/CommonCore.cfm Math Common Core State Standards Grade 4 Correlation: http://investigations.terc.edu/library/common_core/G4_InvCCSS_Corr.pdf

Council of Chief State School Officers (CCSSO)Common Core State Standards Resources: http://www.ncpublicschools.org/docs/acre/standards/common-core-tools/ccsso.pdf

CCSS : Standards for Mathematical Practice

Note: These 8 Standards for Mathematical Practice play a critical role in student understanding of the content standards set forth in the NC Standard Course of Study for Mathematics, grades K – 12. 1. Make sense of problems and persevere in solving them. 2. Reason abstractly and quantitatively. 3. Construct viable arguments and critique 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. Fifth Grade – Common Core State Standards-- MATH Operations and Algebraic Thinking (Weight of Standard: 5 – 10%) 5.OA Write and interpret numerical expressions. Critical Areas 5. OA.1 Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols. 1. Developing fluency with addition and subtraction of fractions, and 5. OA.2 Write simple expressions that record calculations with numbers, and interpret numerical expressions developing understanding of the multiplication of fractions and of division without evaluating them. For example, express the calculation “add 8 and 7, then multiply by 2” as of fractions in limited cases (unit fractions divided by whole numbers and 2 × (8 + 7). Recognize that 3 × (18932 + 921) is three times as large as 18932 + 921, without having whole numbers divided by unit fractions) – Students apply their to calculate the indicated sum or product. understanding of fractions and fraction models to represent the addition and subtraction of fractions with unlike denominators as equivalent calculations Analyze patterns and relationships. with like denominators. They develop fluency in calculating sums and 5. OA.3 Generate two numerical patterns using two given rules. Identify apparent relationships between differences of fractions, and make reasonable estimates of them. Students also corresponding terms. Form ordered pairs consisting of corresponding terms from the two patterns, use the meaning of fractions, of multiplication and division, and the relationship and graph the ordered pairs on a coordinate plane. For example, given the rule “Add 3” and the between multiplication and division to understand and explain why the starting number 0, and given the rule “Add 6” and the starting number 0, generate terms in the procedures for multiplying and dividing fractions make sense. (Note: This is resulting sequences, and observe that the terms in one sequence are twice the corresponding terms in limited to the case of dividing unit fractions by whole numbers and whole the other sequence. Explain informally why this is so. numbers by unit fractions.) 2. Extending division to 2-digit divisors, integrating decimal fractions into Number and Operations in Base Ten (Weight of Standard: 22 – 27%) 5.NBT the place value system and developing understanding of operations with Understand the place value system. decimals to hundredths, and developing fluency with whole number and 5. NBT.1 Recognize that in a multi-digit number, a digit in one place represents 10 times as much as it decimal operations – Students develop understanding of why division represents in the place to its right and 1/10 of what it represents in the place to its left. procedures work based on the meaning of base-ten numerals and properties 5. NBT.2 Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, of operations. They finalize fluency with multi-digit addition, subtraction, and explain patterns in the placement of the decimal point when a decimal is multiplied or divided multiplication, and division. They apply their understandings of models for by a power of 10. Use whole-number exponents to denote powers of 10. decimals, decimal notation, and properties of operations to add and subtract 5. NBT.3: Read, write, and compare decimals to thousandths. decimals to hundredths. They develop fluency in these computations, and a. Read and write decimals to thousandths using base-ten numerals, number names, and expanded form, make reasonable estimates of their results. Students use the relationship e.g., 347.392 = 3 × 100 + 4 × 10 + 7 × 1 + 3 × (1/10) + 9 × (1/100) + 2 × (1/1000). between decimals and fractions, as well as the relationship between finite b. Compare two decimals to thousandths based on meanings of the digits in each place, using >, =, and decimals and whole numbers (i.e., a finite decimal multiplied by an appropriate < symbols to record the results of comparisons. power of 10 is a whole number), to understand and explain why the procedures 5. NBT.4 Use place value understanding to round decimals to any place. for multiplying and dividing finite decimals make sense. They compute products and quotients of decimals to hundredths efficiently and accurately. Perform operations with multi-digit whole numbers and with decimals to hundredths. 3. Developing understanding of volume – Students recognize volume as an 5. NBT.5 Fluently multiply multi-digit whole numbers using the standard algorithm. attribute of three-dimensional space. They understand that volume can be 5. NBT.6 Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit quantified by finding the total number of same-size units of volume required divisors, using strategies based on place value, the properties of operations, and/or the relationship to fill the space without gaps or overlaps. They understand that a 1-unit by between multiplication and division. Illustrate and explain the calculation by using equations, 1-unit by 1-unit cube is the standard unit for measuring volume. They select rectangular arrays, and/or area models. appropriate units, strategies, and tools for solving problems that involve 5. NBT.7 Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and estimating and measuring volume. They decompose three-dimensional shapes strategies based on place value, properties of operations, and/or the relationship between addition and find volumes of right rectangular prisms by viewing them as decomposed and subtraction; relate the strategy to a written method and explain the reasoning used. into layers of arrays of cubes. They measure necessary attributes of shapes in order to determine volumes to solve real world and mathematical problems. Number and Operations – Fractions (Weight of Standard: 47 – 52%) 5.NF Use equivalent fractions as a strategy to add and subtract fractions. Mathematical Practices 5. NF.1 Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given 1. Make sense of problems and persevere in solving them. fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. 2. Reason abstractly and quantitatively. In general, a/b + c/d = (ad + bc)/bd. 3. Construct viable arguments and critique the reasoning of others. 5. NF.2 Solve word problems involving addition and subtraction of fractions referring to the same whole, 4. Model with mathematics. including cases of unlike denominators, e.g., by using visual fraction models or equations to represent 5. Use appropriate tools strategically. the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess 6. Attend to precision. the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by 7. Look for and make use of structure. observing that 3/7 < 1/2. 8. Look for and express regularity in repeated reasoning. Apply and extend previous understandings of multiplication and division to multiply and divide Measurement and Data (Weight of Standard: 10 – 15%) 5.MD fractions. Convert like measurement units within a given measurement system. 5. NF.3 Interpret a fraction as division of the numerator by the denominator (a/b = a ÷ b). 5. MD.1 Convert among different-sized standard measurement units within a given measurement Solve word problems involving division of whole numbers leading to answers in system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, the form of fractions or mixed numbers, e.g., by using visual fraction models or real world problems. 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 Represent and interpret data. are shared equally among 4 people each person has a share of size 3/4. If 9 people want 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). to share a 50-pound sack of rice equally by weight, how many pounds of rice should Use operations on fractions for this grade to solve problems involving information each person get? Between which two whole numbers does your answer lie? presented in line plots. For example, given different measurements of liquid in identical 5. NF.4 Apply and extend previous understandings of multiplication to multiply a fraction or beakers, find the amount of liquid each beaker would contain if the total amount in all whole number by a fraction. the a. Interpret the product (a/b) × q as a parts of a partition of q into b equal parts; beakers were redistributed equally. 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 Geometric measurement: understand concepts of volume and relate volume to multiplication equation. Do the same with (2/3) × (4/5) = 8/15. (In general, (a/b) × (c/d) = ac/bd.) and to addition. b. Find the area of a rectangle with fractional side lengths by tiling it with unit squares 5. MD.3 Recognize volume as an attribute of solid figures and understand concepts of volume of the appropriate unit fraction side lengths, and show that the area is the same as measurement. would be found by multiplying the side lengths. Multiply fractional side lengths to a. A cube with side length 1 unit, called a “unit cube,” is said to have “one cubic unit” find areas of rectangles, and represent fraction products as rectangular areas. of volume, and can be used to measure volume. 5. NF.5: Interpret multiplication as scaling (resizing), by: b. A solid figure which can be packed without gaps or overlaps using n unit cubes is a. Comparing the size of a product to the size of one factor on the basis of the size of the said to have a volume of n cubic units. other factor, without performing the indicated multiplication. 5. MD.4 Measure volumes by counting unit cubes, using cubic cm, cubic in, cubic ft, and b. Explaining why multiplying a given number by a fraction greater than 1 results in a improvised units. product greater than the given number (recognizing multiplication by whole 5. MD.5 Relate volume to the operations of multiplication and addition and solve real world and numbers greater than 1 as a familiar case); explaining why multiplying a given mathematical problems involving volume. number by a fraction less than 1 results in a product smaller than the given number; a. Find the volume of a right rectangular prism with whole-number side lengths by and relating the principle of fraction equivalence a/b = (n×a)/(n×b) to the effect of packing it with unit cubes, and show that the volume is the same as would be multiplying a/b by 1. found by multiplying the edge lengths, equivalently by multiplying the height by 5. NF.6 Solve real world problems involving multiplication of fractions and mixed numbers, the area of the base. Represent threefold whole number products as volumes, e.g., e.g., by using visual fraction models or equations to represent the problem. to represent the associative property of multiplication. 5. NF.7 Apply and extend previous understandings of division to divide unit fractions by b. Apply the formulas V = l × w × h and V = b × h for rectangular prisms to find whole numbers and whole numbers by unit fractions. (Note: Students able to volumes of right rectangular prisms with whole-number edge lengths in the context multiply fractions in general can develop strategies to divide fractions in general, of solving real world and mathematical problems. by reasoning about the relationship between multiplication and division. But c. Recognize volume as additive. Find volumes of solid figures composed of two division of a fraction by a fraction is not a requirement at this grade.) non-overlapping right rectangular prisms by adding the volumes of the non-overlapping a. Interpret division of a unit fraction by a non-zero whole number, and compute parts, applying this technique to solve real world problems. 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 Geometry (Weight of Standard: 2 – 7%) 5.G and division to explain that (1/3) ÷ 4 = 1/12 because (1/12) × 4 = 1/3. Graph points on the coordinate plane to solve real-world and mathematical problems. b. Interpret division of a whole number by a unit fraction, and compute such quotients. 5. G.1 Use a pair of perpendicular number lines, called axes, to define a coordinate system, with the For example, create a story context for 4 ÷ (1/5), and use a visual fraction model to intersection of the lines (the origin) arranged to coincide with the 0 on each line and a show the quotient. Use the relationship between multiplication and division to explain given point in the plane located by using an ordered pair of numbers, called its coordinates. that 4 ÷ (1/5) = 20 because 20 × (1/5) = 4. Understand that the first number indicates how far to travel from the origin in the direction c. Solve real world problems involving division of unit fractions by non-zero whole of one axis, and the second number indicates how far to travel in the direction of the second numbers and division of whole numbers by unit fractions, e.g., by using visual axis, with the convention that the names of the two axes and the coordinates correspond fraction models and equations to represent the problem. For example, how much (e.g., x-axis and x-coordinate, y-axis and y-coordinate). chocolate will each person get if 3 people share 1/2 lb of chocolate equally? How 5. G.2 Represent real world and mathematical problems by graphing points in the first quadrant of many 1/3-cup servings are in 2 cups of raisins? the coordinate plane, and interpret coordinate values of points in the context of the situation. Classify two-dimensional figures into categories based on their properties. 5. G.3 Understand that attributes belonging to a category of two-dimensional figures also belong to all subcategories of that category. For example, all rectangles have four right angles and squares are rectangles, so all squares have four right angles. 5. G.4 Classify two-dimensional figures in a hierarchy based on properties. Major Work of the Grade

Fifth Grade Major Clusters Supporting/Additional Clusters Number and Operations in Base Ten Operations and Algebraic Thinking  Understand the place value system.  Write and interpret numerical expressions.

 Perform operations with multi-digit whole  Analyze patterns and relationships. numbers and with decimals to hundredths. Measurement and Data Number and Operations—Fractions  Convert like measurement units within a  Use equivalent fractions as a strategy to given measurement system. add and subtract fractions.  Represent and interpret data.  Apply and extend previous understandings of multiplication and division to multiply and divide fractions. Geometry  Graph points on the coordinate plane to solve real-world and mathematical prob- Measurement and Data lems.  Geometric measurement: understand concepts of volume and relate volume to mul-  Classify two-dimensional figures into cate- tiplication and to addition. gories based on their properties.

Wayne County Public Schools Revisions (07/2015) to Pacing Guide are denoted in RED. 2010 North Carolina Standard Course of Study: Mathematics Grade 5 Math At A Glance Note: All teachers should have Investigations Teacher Resources; they were part of the enVision Math Textbook Adoption in 2012. Revisions (08/2015) to Pacing Guide are denoted in Purple. Domain First Quarter Second Quarter Third Quarter Fourth Quarter Operations & 5.OA.1 5.OA.1 5.OA.3 5.OA.2 5.OA.2 Algebraic Review All OA Standards Thinking (5% – 10%) As of 3-10-15, 3 items are from the OA Domain on the NC READY Math 5 EOG. Number and 5.NBT.1 Review All NBT Standards Operations in 5.NBT.2 5.NBT.6 with a Focus on 5.NBT.6 & 5.NBT.7 Base Ten 5.NBT.3 5.NBT.7 As of 3-10-15, 11 items are from the NBT Domain 5.NBT.4 (22%- 27%) on the NC READY Math 5 EOG. 5.NBT.5 5.NBT.7 The NBT Domain is a Major Work of the Grade! Number and 5.NF.2, 5,NF.3 - Continue 5.NF.3; 5.NF.4; 5.NF.5; 5.NF.6; 5NF.7 - Continue Operations - 5.NF.1 5.NF.1, 5.NF.2, 5.NF.3 5.NF.4 a & b 5.NF.7 - Focus 5.NF.2 Fractions 5.NF.5 Review All NF Standards (47%– 52%) 5.NF.6 As of 3-10-15, 22 items are from the NF Domain on 5.NF.7 the NC READY Math 5 EOG. The NF Domain is a Major Work of the Grade! Measurement 5.MD.3; 5.MD.4; 5.MD.5 and Data 5.MD.1 Review All MD Standards 5.MD.2 (10% – 15%) with a Focus on 5.MD.1, 5.MD.B.2 & 5.MD.5 As of 3-10-15, 5 items are from the MD Domain on the NC READY Math 5 EOG. Geometry 5.G.1; 5.G.2 (2% – 7%) 5.G.3; 5.G.4 As of 3-10-15, 2 items are from the Geometry Do- main on the NC READY Math 5 EOG. Note: Understanding concepts of volume and relating volume to multiplication & addition are a Major Work of the Grade! Always use NC 5.OA.1; 5.OA.2; 5.NBT.6 5.OA.1; 5.OA.2 5.OA.1; 5.OA.2; 5.OA.3 DPI’s Grade 5 Topic 8: Numerical expressions Topic 4: Dividing by 1-Digit Divisors; Topic 8: Numerical expressions, Topic 8: Numerical expressions, Patterns & Relationships Topic 5: Dividing by 2-Digit divisors Math Unpacking 5.NBT.1; 5.NBT.2; 5;NBT.3 5.NBT.7 5.NF.3; 5.NF.4; 5.NF.6; 5.NF.7 Document Topic 1: Place Value 5.NBT.7 Topic 6: Multiplying Decimals Topic 11: Multiplying & Dividing Fractions & Mixed Num- Topic 2: Adding & Subtracting Decimals Topic 7: Dividing Decimals bers 5.NBT.4

Supplement Topic 2: Adding & Subtracting Decimals 5.NF.1;5.NF.2 5.NF.3; 5.NF.4; 5.NF.5; 5.NF.6; 5.NF.7 5.G.1; 5.G.2 with Textbook Topic 9: Adding & Subtracting Fractions Topic 11: Multiplying & Dividing Topic 16: Coordinate Geometry 5.NBT.5 as Appropriate. Topic 10: Adding & Subtracting Mixed Num- Fractions & Mixed Numbers Topic 3: Multiplying Whole Numbers Textbook bers 5.G.3; 5.G.4 5.MD.3; 5.MD.4; 5.MD.5 Topic 15: Classifying Plane Figures envision Math 5.NF.1;5.NF.2 5.NF.3 Topic 12: Volume of Solids Common Core, Topic 9: Adding & Subtracting Fractions Topic 11: Multiplying & Dividing Fractions © 2012 Topic 10: Adding & Subtracting Mixed Num- & Mixed Numbers bers 5.MD.1; 5.MD.2 Topic 13: Units of Measure; Topic 14: Data Wayne County Public Schools Revisions (07/2015) to Pacing Guide are denoted in RED. 2010 North Carolina Standard Course of Study: Mathematics Grade 5 Math At A Glance with Abbreviated Standards Note: All teachers should have Investigations Teacher Resources; they were part of the enVision Math Textbook Adoption in 2012. Revisions (08/2015) to Pacing Guide are denoted in Purple. Domain First Quarter Second Quarter Third Quarter Fourth Quarter Operations & Alge- 5.OA.1 Use parentheses, brackets, or braces in numeri- 5.OA.1 Use parentheses, brackets, or braces in 5.OA.3 Analyze patterns and rela- braic Thinking cal expressions to evaluate the expressions --- order of numerical expressions to evaluate the expres- tionships. (5% – 10%) operations; parentheses only for grouping. sions. – order of operations. Generate 2 number patterns using 2 given rules; 5.OA.2 Write simple expressions that record calcula- 5.OA.2 Write simple expressions that record identify relationships between corresponding tions with numbers & interpret numerical expressions calculations with numbers & interpret terms from the number patterns; form ordered pairs & graph on a coordinate plane. without evaluating them. numerical expressions without evaluating them. Number and Opera- 5.NBT.1 Recognize that in a multi-digit number, a digit 5.NBT.6 Find whole-number quotients of whole tions in Base Ten --- in one place represents 10 times as much as it represents in numbers by dividing 4-digit numbers(dividends) by its place to the right and 1/10 of what it represents to the 2-digit numbers (divisors); illustrate and explain a di- Includes Deci- left. vision problem using equations, rectangular arrays, mals to Hundredths and/or area models. 5.NBT.2 Explain patterns in the number of 0’s of the (+, -, x, ÷) &Thou- product when multiplying a number by powers of 10; use 5.NBT.7 Add/subtract decimals to hundredths, using 5.NBT.7 Add/ subtract/ multiply/ divide sandths (read, write, com- whole number exponents to show powers of 10. concrete models or drawings and strategies based on decimals to hundredths, using concrete pare) place value, properties of operations, and/or the rela- models or drawings and strategies based on 5.NBT.3 Read, write, and compare decimals to thou- (22%- 27%) tionship between addition and subtraction. sandths, using base-10 numerals, number names, and ex- place value, properties of operations, and/or -Extend division to 2-digit divi- panded form. the relationship between addition and sub- sors; traction, multiplication and division. - Integrate decimal fractions into 5.NBT.4 Use place value understanding to round deci- the place value system & develop understanding of operations with mals to any place. decimals to hundredths; 5.NBT.5 Multiply multi-digit whole numbers fluent- - Develop fluency with whole number and decimal operations. ly using the standard algorithm. Number and Opera- 5.NF.1; 5.NF.2 5.NF.1; 5.NF.2 Use equivalent fractions as a strategy 5.NF.2 Continue to solve word problems 5.NF.3; 5.NF.4; 5.NF.5; 5.NF.6; Use equivalent fractions as a strategy to add and sub- to add and subtract fractions with unlike denomina- that involve + and – of fractions referring to 5NF.7 tions - Frac- tract fractions with unlike denominators. tors. Develop fluency with + & - of fractions. the same whole. Apply and extend previous under- 5.NF.1 Add & subtract fractions with unlike de- 5.NF.1 Continue … Add & subtract fractions with 5.NF.3 Continue to solve word problems standings of multiplication and divi- tions nominators – including mixed numbers. unlike denominators – including mixed numbers. where the division of whole numbers may sion to multiply and divide fractions (47%– 52%) 5.NF.2 Solve word problems that involve + and – of 5.NF.2 Continue … Solve word problems that in- lead to an answer with fractions or mixed 5.NF.6 Continue to solve word fractions referring to the same whole; use bench- volve + and – of fractions referring to the same number. problems that involve multiplica- Develop fluency with + mark fractions & number sense of fractions to esti- whole; use benchmark fractions & number sense of 5.NF.4 Multiply fractions or whole numbers tion of fractions and mixed num- & - of fractions; mate the reasonableness of answers to fraction fractions to estimate the reasonableness of answers by a fraction. 5.NF.4a &b bers by using visual fraction mod- - Develop understanding problems; use visual fraction models or equations. to fraction problems; use visual fraction models or 5.NF.5 Interpret multiplication as scaling els or equations to represent the of the x of fractions; equations. (resizing), similar to a scale on a map. problem. - Develop understanding 5.NF.6 Solve word problems that involve 5.NF.7 Focus on dividing unit frac- 5.NF.3 Interpret a fraction as division of the nu- of ÷ of fractions in lim- multiplication of fractions and mixed num- tions by whole numbers or whole merator by the denominator; solve word problems ited cases --- unit frac- bers by using visual fraction models or numbers by unit fractions; solve where the division of whole numbers may lead to tions divided by whole equations to represent the problem. word problems. 5.NF.7 a,b,c answers that are fractions or mixed numbers. numbers and whole 5.NF.7 Divide unit fractions by whole num- numbers divided by bers or whole numbers by unit fractions; unit fractions. solve word problems. 5.NF.7 a,b,c Measurement and 5.MD.1; 5.MD.2 5.MD.3; 5.MD.4; 5.MD.5 --Volume 5.MD.B.2 Data Convert like measurement units within a given mea- -Geometric measurement: understand concepts of Use +, -, x, ÷ of fractions to solve volume and relate volume to multiplication and to ad- (10% – 15%) surement system; use measurement conversions to solve problems involving information multi-step real-world problems. dition. presented on a line plot. -Measure volume by counting unit cubes; Make a line plot to show a data set of measurements Note: The line plot should also in- -Use V formula of a right rectangular prism; Develop understanding involving fractions of a unit --- (1/2, ¼, 1/8). clude mixed numbers in grade 5. of volume. Note: The line plot should also include mixed. - Recognize volume as additive (nonoverlapping parts/figures). Geometry 5.G.1; 5.G.2 Graph points on the coordinate plane (1st quadrant) to solve real-world (2% – 7%) and mathematical problems; represent real- world problems by graphing points in the first quadrant of a coordinate plane. 5.G.3; 5.G.4 Classify two-dimensional figures into categories based on their properties. Always use NC DPI’s 5.OA.1; 5.OA.2; 5.NBT.6 5.OA.1; 5.OA.2 5.OA.1; 5.OA.2; 5.OA.3 Grade 5 Math Unpack- Topic 8: Numerical expressions Topic 4: Dividing by 1-Digit Divisors; Topic 8: Numerical expressions, Topic 8: Numerical expressions, Patterns Topic 5: Dividing by 2-Digit divisors & Relationships ing Document 5.NBT.1; 5.NBT.2; 5;NBT.3 5.NBT.7 Topic 1: Place Value 5.NBT.7 Topic 6: Multiplying Decimals 5.NF.3; 5.NF.4; 5.NF.6; 5.NF.7 Supplement with Text- Topic 2: Adding & Subtracting Decimals Topic 7: Dividing Decimals Topic 11: Multiplying & Dividing 5.NBT.4 Fractions & Mixed Numbers book as Appropriate. 5.NF.1;5.NF.2 Topic 2: Adding & Subtracting Decimals 5.NF.3; 5.NF.4; 5.NF.5; 5.NF.6; 5.NF.7 Textbook Topic 9: Adding & Subtracting Fractions 5.G.1; 5.G.2 Topic 11: Multiplying & Dividing envision Math Com- 5.NBT.5 Topic 10: Adding & Subtracting Mixed Numbers Topic 16: Coordinate Geometry Fractions & Mixed Numbers mon Core, © 2012 Topic 3: Multiplying Whole Numbers 5.NF.3 5.G.3; 5.G.4 5.NF.1;5.NF.2 Topic 11: Multiplying & Dividing Fractions & Mixed 5.MD.3; 5.MD.4; 5.MD.5 Topic 15: Classifying Plane Figures Topic 9: Adding & Subtracting Fractions Numbers Topic 12: Volume of Solids Topic 10: Adding & Subtracting Mixed Numbers 5.MD.1; 5.MD.2 Topic 13: Units of Measure; Topic 14: Data

Wayne County Public Schools Revisions (07/2015) to Pacing Guide are denoted in RED. 2010 North Carolina Standard Course of Study: Mathematics Grade 5 Math Pacing Guide with Complete Standards Note: All teachers should have Investigations Teacher Resources; they were part of the enVision Math Textbook Adoption in 2012. Domain First Quarter Second Quarter Third Quarter Fourth Quarter Operations & 5.OA.1 Use parentheses, brackets, or 5.OA.1 Use parentheses, brackets, 5.OA.3 Generate two numerical Algebraic braces in numerical expressions, and or braces in numerical expressions, patterns using two given rules. evaluate expressions with these symbols. and evaluate expressions with these Identify apparent relationships Thinking Note: Students begin working more for- mally with expressions. Expressions symbols. between corresponding terms. (5% – 10%) should not contain nested grouping sym- Form ordered pairs consisting of 5.OA.1 - 5.OA.2 bols, and they should be no more complex corresponding terms from the two than the expressions one finds in an appli- patterns, and graph the ordered Write & interpret nu- cation of the associative or distributive merical expressions us- property. The numbers in expressions need pairs on a coordinate plane. ing properties of opera- not always be whole numbers. tions & order of opera- 5.OA.2 Write simple expressions Review All OA Standards tions. 5.OA.2 Write simple expressions that record calculations with numbers, and that record calculations with num- 5.OA.3 interpret numerical expressions without bers, and interpret numerical ex- As of 3-10-15, 3 items are from the Analyze patterns & re- evaluating them. pressions without evaluating them. OA Domain on the lationships. NC READY Math 5 EOG. Number and 5.NBT.1 Recognize that in a multi-digit Operations in number, a digit in one place represents 10 times as much as it represents in the place Review All NBT Standards Base Ten - In- to its right and 1/10 of what it represents in the place to its left. with a Focus on 5.NBT.6 & 5.NBT.7 cludes Decimals 5.NBT.2 Explain patterns in the num- to Hundredths (+, -, x, ber of 0’s of the product when multiply- As of 3-10-15, 11 items are from ing a number by powers of 10, and ex- ÷) &Thousandths (read, the NBT Domain on the plain patterns in the placement of the write, compare) NC READY Math 5 EOG. decimal point when a decimal is multi- (22%- 27%) plied or divided by a power of 10. The NBT Domain is a Use whole-number exponents to denote 5.NBT.1-5.NBT.4 powers of 10. 5.NBT.6 Find whole-number quotients Major Work of the Grade! Understand the place 5.NBT.3 Read, write, and compare of whole numbers with up to 4-digit divi- value system to read, decimals to thousandths. dends and 2-digit divisors, using strate- write, compare, and a. Read & write decimals to thousandths gies based on place value, the properties order decimals to using base-ten numerals (standard form), of operations, and/or the relationship be- thousandths. number names (written form), and expand- tween multiplication and division. ed form. b. Compare two decimals to thousandths Illustrate and explain the calculation by based on meanings of the digits in each using equations, rectangular arrays, place, using >, =, < symbols to record the re- and/or area models. sults of comparisons. 5.NBT.4 Use place value understanding 5.NBT.7 Add, subtract , multiply, and di- to round decimals to any place. vide decimals to hundredths, using con- 5.NBT.7 Add, subtract, multiply, 5.NBT.5-5.NBT.7 5.NBT.5 Fluently multiply multi-digit Perform operations crete models or drawings and strategies and divide decimals to hundredths, whole numbers using the standard algo- based on place value, properties of opera- using concrete models or drawings with multi-digit rithm. Underlying this algorithm are the and strategies based on place value, whole numbers and properties of operations and the base-ten tions, and/or the relationship between + properties of operations, and/or the with decimals to system. and -; relate the strategy to a written Note: The size of the numbers should not ex- relationship between + and -; relate hundredths. ceed a 4-digit factor by a 2-digit factor unless method and explain the reasoning used. students are using previously learned strate- the strategy to a written method and gies such as properties of operations. explain the reasoning used. Domain First Quarter Second Quarter Third Quarter Fourth Quarter Number and 5.NF.1 Add & subtract fractions 5.NF.1 Continue … Add & subtract 5.NF.4 Apply and extend previous 5.NF.4; 5.NF.5; 5.NF.6 Continue with unlike denominators (includ- fractions with unlike denominators (in- understandings of multiplication - Apply & extend previous understandings Operations - ing mixed numbers) by replacing cluding mixed numbers) by replacing of multiplication to multiply a fraction or to multiply a fraction or whole num- whole number by a fraction. Fractions given fractions with equivalent given fractions with equivalent fractions ber by a fraction. - Multiplication as scaling (resizing) fractions in such a way as to pro- in such a way as to produce an equiva- a. Interpret the product (a/b) x q - Solve real world problems involving (47%– 52%) duce an equivalent sum or differ- lent sum or difference of fractions with as a parts of a partition of q into b multiplication of fractions & mixed num- ence of fractions with like denomi- like denominators. equal parts; equivalently, as the re- bers. 5.NF.1-5.NF.2 nators. In general, In general, a/b + c/d = (ad + bc)/bd. sult of a sequence of operations: a a/b + c/d = (ad + bc)/bd. x q ÷ b. Use equivalent th fractions as a strat- Note: -- builds on the work in 4 In general, (a/b) x (c/d) = ac/bd. egy to add and sub- grade where students add frac- 5.NF.2 Continue … Solve word prob- b. Find the area of a rectangle tract fractions with tions with like denominators. lems involving addition & subtraction of with fractional side lengths by tiling unlike denomina- fractions referring to the same whole, it with unit squares of the appropri- tors. 5.NF.2 Solve word problems in- including cases of unlike denominators, ate unit fraction side lengths, and volving addition & subtraction of e.g., by using visual fraction models or show that the area is the same as fractions referring to the same equations to represent the problem. would be found by multiplying the 5.NF.3-5.NF.7 whole, including cases of unlike Use benchmark fractions and number Apply and extend side lengths. Multiply fractional denominators, e.g., by using visual sense of fractions to estimate mentally side lengths to find areas of rectan- previous under- fraction models or equations to and assess the reasonableness of an- standings of multi- gles, and represent fraction prod- represent the problem. swers. ucts as rectangular areas. plication and divi- Use benchmark fractions and sion to multiply & number sense of fractions to esti- 5.NF.3 Interpret a fraction as division 5.NF.5 Interpret multiplication as divide fractions . mate mentally and assess the rea- of the numerator by the denominator scaling (resizing) by: Note: In grade 5 … sonableness of answers. (a/b=a ÷ b). a. Comparing the size of a prod- Multiply a fraction Solve word problems involving division uct to the size of one factor on the or whole number of whole numbers leading to answers in basis of the size of the other factor, by a fraction. the form of fractions or mixed numbers, without performing the indicated Divide unit frac- e.g., by using visual fraction models or multiplication. tions by whole equations to represent the problem. b. Explaining why multiplying a numbers & Divide Note: 5th grade students should connect given number by a fraction greater whole numbers by fraction with division (equal sharing). than 1 results in a product greater unit fractions. than the given number (recognizing multiplication by whole numbers greater that 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 equivalence a/b = (n x a)/(n x b) to the effect of multiplying a/b by 1. 5.NF.6 Solve real world problems 5.NF.6 Solve real world problems involving multiplication of frac- involving multiplication of fractions tions and mixed numbers, e.g., by and mixed numbers, e.g., by using using visual fraction models or visual fraction models or equations equations to represent the prob- to represent the problem. lem. 5.NF.7 Apply and extend previous 5.NF.7 Apply and extend previ- understandings of division to divide ous understandings of division to unit fractions by whole numbers and divide unit fractions by whole whole numbers by unit fractions. numbers and whole numbers by Note: Students able to multiply fractions in unit fractions. general can develop strategies to divide frac- Note: Students able to multiply fractions tions in general, by reasoning about the rela- in general can develop strategies to divide tionship between multiplication and division. fractions in general, by reasoning about But, division of a fraction by a frac- the relationship between multiplication tion is not a requirement at grade 5. and division. But, division of a frac- a. Interpret division of a unit fraction by a tion by a fraction is not a require- non-zero whole number, & compute such ment at grade 5. quotients. a. Interpret division of a unit fraction (1/b) ÷ d = 1/(b x d) because by a non-zero whole number, & compute such quotients. 1/(b x d) x d = (1/b) (1/b) ÷ d = 1/(b x d) because

--- relationship between x & ÷. 1/(b x d) x d = (1/b) b. Interpret division of a whole number by --- relationship between x & ÷. a unit fraction, & compute such quotients. d ÷ (1/b ) = (b x d) because b. Interpret division of a whole number by a unit fraction, & compute such quo- (b x d) x (1/b) = d tients. d ÷ (1/b ) = (b x d) because --- relationship between x & ÷. c. Solve real world problems in- (b x d) x (1/b) = d volving division of unit fractions by --- relationship between x & ÷. non-zero whole numbers and division of whole numbers by unit frac- c. Solve real world problems in- tions, e.g., by using visual fraction volving division of unit fractions models and equations to represent by non-zero whole numbers and the problem. division of whole numbers by unit fractions, e.g., by using visual fraction models and equations to represent the problem. Review All NF Standards As of 3-10-15, 22 items are from the NF Domain on the NC READY Math 5 EOG. The NF Domain is a Major Work of the Grade!

Domain First Quarter Second Quarter Third Quarter Fourth Quarter Measurement 5.MD.1 Convert among different-sized 5.MD.3 Recognize volume as an at- standard measurement units within a tribute of solid figures and under- and Data given measurement system (e.g., stand concepts of volume measure- (10% – 15%) convert 5 cm to 0.05 m), and use these ment. conversions in solving multi-step, real a. A cube with side length 1 unit, called a 5.MD.1 world problems. “unit cube,” is said to have “one cubic unit” Review All MD Standards Note: Time could be used in this stan- of volume, and can be used to measure vol- Convert like mea- ume. with a Focus on 5.MD.1; 5.MD.B.2 surement units dard. b. A solid figure which can be packed & 5.MD.5 within a given mea- without gaps or overlaps using n unit cubes is surement system. said to have a volume on n cubic units. As of 3-10-15, 5 items are from the 5.MD.2 Make a line plot to display a MD Domain on the 5.MD.4 Measure volume by count- 5.MD.2 data set of measurements in fractions of NC READY Math 5 EOG. a unit ( ½, ¼, 1/8). Use operations on ing unit cubes, using cubic cm, cubic Represent and in- in, cubic ft, & improvised units. terpret data. fractions for this grade to solve problems involving information presented in line 5.MD.5 Relate volume to the oper- 5.MD.3-5.MD.5 plots. ations of multiplication and addition Geometric mea- Note: The line plot should also include and solve real world and mathemat- surement: under- mixed numbers in grade 5. ical problems involving volume. stand concepts of a. Find the volume of a right rec- volume and relate tangular prism with whole-number volume to multipli- side lengths by packing it with unit cation and to addi- cubes, and show that the volume is tion. the same as would be found by multiplying the edge lengths, equivalently by multiplying the height by the area of the base. Represent threefold whole-number products as volumes, e.g., to represent the associative property of multiplication. b. Apply the formulas V=l x w x h V=b x h for rectangular prisms to find volumes of right rectangular prisms with whole-number edge lengths in the context of solving real world and mathematical problems. c. Recognize volume as additive. Find volumes of solid figures composed of two non-overlapping right rectangular prisms by adding the volumes of the non-overlapping parts, applying this technique to solve real world problems. Domain First Quarter Second Quarter Third Quarter Fourth Quarter Geometry 5.G.1 Use a pair of perpendicular number lines, called axes, to define a co- (2% – 7%) ordinate system, with the intersection of the lines (the origin) arranged to coin- 5.G.1-5.G.2 cide with the 0 on each line and a given point in the plane located by using an Graph points on the ordered pair of numbers, called it coor- coordinate plane to dinates. Understand that the first num- solve real-world ber indicates how far to travel from the and mathematical origin in the direction of one axis, and problems. the second number indicates how far to travel in the direction of the second axis, with the convention that the names of the two axes and the coordinates corre- 5.G.3-5.G.4 spond (e.g., x-axis and x-coordinate, y- Classify 2-D figures axis and y-coordinate). into categories based on their 5.G.2 Represent real world and mathematical problems by graphing points in properties. the first quadrant of the coordinate Note: Polygon, tri- plane, and interpret coordinate values angle, quadrilateral of points in the context of the situation. , rhombus, rectan- 5.G.3 Understand that attributes be- gle, square, kite, longing to a category of two-dimensional trapezoid, penta- figures also belong to all subcategories gon, hexagon, of that category. half/quarter circle, 5.G.4 Classify two-dimensional figures circle in a hierarchy based on properties. As of 3-10-15, 2 items are from the Ge- ometry Domain on the NC READY Math 5 EOG. Note: Understanding concepts of volume and relating volume to multiplication & addition are a Major Work of the Grade! Always use NC 5.OA.1; 5.OA.2; 5.NBT.6 5.OA.1; 5.OA.2 5.OA.1; 5.OA.2; 5.OA.3 Topic 8: Numerical expressions Topic 4: Dividing by 1-Digit Divisors; Topic 8: Numerical expressions, Topic 8: Numerical expressions, Patterns & Rela- DPI’s Grade 5 Math Topic 5: Dividing by 2-Digit divisors tionships Unpacking Docu- 5.NBT.1; 5.NBT.2; 5;NBT.3 5.NBT.7 Topic 1: Place Value 5.NBT.7 Topic 6: Multiplying Decimals 5.NF.3; 5.NF.4; 5.NF.6; 5.NF.7 ment Topic 2: Adding & Subtracting Decimals Topic 7: Dividing Decimals Topic 11: Multiplying & Dividing Fractions & 5.NBT.4 Mixed Numbers Topic 2: Adding & Subtracting Decimals 5.NF.1;5.NF.2 5.NF.3; 5.NF.4; 5.NF.5; 5.NF.6; 5.NF.7 Supplement with Topic 9: Adding & Subtracting Fractions 5.G.1; 5.G.2 Topic 11: Multiplying & Dividing Textbook as Ap- 5.NBT.5 Topic 10: Adding & Subtracting Mixed Numbers Topic 16: Coordinate Geometry Topic 3: Multiplying Whole Numbers Fractions & Mixed Numbers propriate. 5.NF.3 5.G.3; 5.G.4 5.NF.1;5.NF.2 Topic 11: Multiplying & Dividing Fractions & Mixed 5.MD.3; 5.MD.4; 5.MD.5 Topic 15: Classifying Plane Figures Textbook Topic 9: Adding & Subtracting Fractions Numbers Topic 12: Volume of Solids envision Math Topic 10: Adding & Subtracting Mixed Numbers Common Core, © 5.MD.1; 5.MD.2 2012 Topic 13: Units of Measure; Topic 14: Data

Wayne County Public Schools 2010 NC Standard Course of Study for Mathematics Grade 5 Mathematics

Alignment of Textbook Topic Content to the Math CCSS : NOTE: Not all sections of each Topic are aligned to the 2010 NC Math SCoS – be sure to use ONLY the sections that are aligned to the 2010 NC Math SCoS .

Table of Topics Topic Number Topic Description CCSS Domain 1 Place Value Number and Operations in Base Ten NBT 2 Adding and Subtracting Decimals Number and Operations in Base Ten NBT 3 Multiplying Whole Numbers Number and Operations in Base Ten NBT 4 Dividing by 1-Digit Divisors Number and Operations in Base Ten NBT 5 Dividing by 2-Digit Divisors Number and Operations in Base Ten NBT 6 Multiplying Decimals Number and Operations in Base Ten NBT 7 Dividing Decimals Number and Operations in Base Ten NBT

8 Numerical Expressions, Patterns, and Relationships Operations and Algebraic Thinking OA

9 Adding and Subtracting Fractions Number and Operations -- Fractions NF 10 Adding and Subtracting Mixed Numbers Number and Operations -- Fractions NF 11 Multiplying and Dividing Fractions and Mixed Numbers Number and Operations -- Fractions NF

12 Volume of Solids Measurement and Data MD 13 Units of Measure Measurement and Data MD 14 Data Measurement and Data MD

15 Classifying Plane Figures Geometry G 16 Coordinate Geometry Geometry G

2010 NC SCoS: Mathematics K – 8 Continuum of Math Domains Domains K 1 2 3 4 5 6 7 8

Major Counting and Cardinality CC Major Major Major 30-35% 12-17% 5-10% Operations and Algebraic Thinking OA NBT Major Major Major 5-10% 22-27% 22-27% Number and Operations in Base Ten Support Major & Major & 22-27% 12-17% 10-15% Measurement and Data MD Support Support Support Support Support 10-15% 12-17% 2-7% 12-17% 22-27% 20-25% Geometry G

20-25% 27-32% 47-52% Number and Operations -- Fractions NF

Ratios and Proportional Relation- 12-17% 22-27% ships RP

27-32% 7-12% 2-7% The Number System NS

27-32% 22-27% 27-32% Expressions and Equations EE

7-12% 12-17% 15-20% Statistics and Probability SP

22-27% Functions F

For K – 2, the Major Work of the Grade is composed of Major Clusters and Supporting/Additional Clusters as denoted in chart. For grades 3 – 8, the % ranges are weight distributions determined by NC DPI – Division of Accountability Services, 3-10-15. NC EOG Information: http://www.ncpublicschools.org/accountability/testing/eog/math