NYS Math Standards Grade 5 Crosswalk - New York State .

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ClusterWrite and interpretnumericalexpressions.New York State Next Generation Mathematics Learning StandardsGrade 5 CrosswalkOperations and Algebraic ThinkingNYS P-12 CCLSNYS Next Generation Learning Standard5.OA.1 Use parentheses, brackets, or braces in numericalexpressions, and evaluate expressions with these symbols.NY-5.OA.1 Apply the order of operations to evaluate numericalexpressions.e.g., 6 8 2(6 8) 2Note: Exponents and nested grouping symbols are not included.Analyze patterns andrelationships.5.OA.2 Write simple expressions that record calculationswith numbers, and interpret numerical expressions withoutevaluating them. For example, express the calculation “add8 and 7, then multiply by 2” as 2 (8 7). Recognize that 3 (18932 921) is three times as large as 18932 921,without having to calculate the indicated sum or product.NY-5.OA.2 Write simple expressions that record calculations withnumbers, and interpret numerical expressions without evaluating them.5.OA.3 Generate two numerical patterns using two givenrules. Identify apparent relationships between correspondingterms. Form ordered pairs consisting of corresponding termsfrom the two patterns, and graph the ordered pairs on acoordinate plane. For example, given the rule “Add 3” andthe starting number 0, and given the rule “Add 6” and thestarting number 0, generate terms in the resulting sequences,and observe that the terms in one sequence are twice thecorresponding terms in the other sequence. Explaininformally why this is so.NY-5.OA.3 Generate two numerical patterns using two given rules.Identify apparent relationships between corresponding terms. Formordered pairs consisting of corresponding terms from the two patterns,and graph the ordered pairs on a coordinate plane.NYSED Grade 5 Draft Updated June 2019e.g., Express the calculation “add 8 and 7, then multiply by 2” as (8 7) 2. Recognize that 3 (18,932 921) is three times as large as18,932 921, without having to calculate the indicated sum or product.e.g., Given the rule “Add 3” and the starting number 0, and given therule “Add 6” and the starting number 0, generate terms in the resultingsequences, and observe that the terms in one sequence are twice thecorresponding terms in the other sequence. Explain informally why thisis so.

New York State Next Generation Mathematics Learning StandardsGrade 5 CrosswalkNumber and Operations in Base TenNYS P-12 CCLSNYS Next Generation Learning StandardClusterUnderstand the placevalue system.5.NBT. 1 Recognize that in a multi-digit number, a digit inone place represents 10 times as much as it represents in theplace to its right and 1/10 of what it represents in the place toits left.NY-5.NBT. 1 Recognize that in a multi-digit number, a digit in oneplace represents 10 times as much as it represents in the place to its1right and of what it represents in the place to its left.5.NBT.2 Explain patterns in the number of zeros of theproduct when multiplying a number by powers of 10, andexplain patterns in the placement of the decimal point whena decimal is multiplied or divided by a power of 10. Usewhole number exponents to denote powers of 10.NY-5.NBT.2 Use whole-number exponents to denote powers of 10.Explain patterns in the number of zeros of the product whenmultiplying a number by powers of 10, and explain patterns in theplacement of the decimal point when a decimal is multiplied or dividedby a power of 10.5.NBT.3 Read, write, and compare decimals to thousandths.NY-5.NBT.3 Read, write, and compare decimals to thousandths.a. Read and write decimals to thousandths using base-tennumerals, number names, and expanded form,e.g., 347.392 3 100 4 10 7 1 3 (1/10) 9 (1/100) 2 NY-5.NBT.3a Read and write decimals to thousandths using base-tennumerals, number names, and expanded form.e.g.,(1/1000).10𝟏𝟏𝟏 47.392 4 10 7 1 3 47.392 (4 10) (7 1) (3 47.392 (4 10) (7 1) (3 0.1) (9 0.01) (2 0.001)𝟏𝟎 9 𝟏𝟏𝟎𝟏𝟎𝟎 2 ) (9 𝟏𝟎𝟎𝟎𝟏𝟏𝟎𝟎) (2 𝟏)𝟏𝟎𝟎𝟎b. Compare two decimals to thousandths based on meaningsof the digits in each place, using , , and symbols torecord the results of comparisons.NY-5.NBT.3b Compare two decimals to thousandths based onmeanings of the digits in each place, using , , and symbols torecord the results of comparisons.5.NBT.4 Use place value understanding to round decimals toany place.NY-5.NBT.4 Use place value understanding to round decimals to anyplace.NYSED Grade 5 Draft Updated June 2019

ClusterPerform operationswith multi-digitwhole numbers andwith decimals tohundredths.New York State Next Generation Mathematics Learning StandardsGrade 5 CrosswalkNumber and Operations in Base TenNYS P-12 CCLSNYS Next Generation Learning Standard5.NBT.5 Fluently multiply multi-digit whole numbers usingthe standard algorithm.NY-5.NBT.5 Fluently multiply multi-digit whole numbers using astandard algorithm.5.NBT.6 Find whole-number quotients of whole numberswith up to four-digit dividends and two-digit divisors, usingstrategies 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.NY-5.NBT.6 Find whole-number quotients of whole numbers with upto four-digit dividends and two-digit divisors, using strategies based onplace value, the properties of operations, and/or the relationshipbetween multiplication and division. Illustrate and explain thecalculation by using equations, rectangular arrays, and/or area models.Notes on and/or: Students should be taught to use strategies based on place value, theproperties of operations, and the relationship between multiplication anddivision; however, when solving any problem, students can choose anystrategy. Students should be taught to use equations, rectangular arrays, and areamodels; however, when illustrating and explaining any calculation,students can choose any strategy.5.NBT.7 Add, subtract, multiply, and divide decimals tohundredths, using concrete models or drawings andstrategies based on place value, properties of operations,and/or the relationship between addition and subtraction;relate the strategy to a written method and explain thereasoning used.NY-5.NBT.7 Using concrete models or drawings and strategies basedon place value, properties of operations, and/or the relationshipbetween operations: add and subtract decimals to hundredths; multiply and divide decimals to hundredths.Relate the strategy to a written method and explain the reasoning used.Notes on and/or: Students should be taught to use concrete models and drawings; aswell as strategies based on place value, properties of operations, and the relationshipbetween operations. When solving any problem, students can choose to use aconcrete model or a drawing. Their strategy must be based on place value, propertiesof operations, or the relationship between operations.Note: Division problems are limited to those that allow for the use of concrete modelsor drawings, strategies based on properties of operations, and/or the relationshipbetween operations (e.g., 0.25 0.05). Problems should not be so complex as torequire the use of an algorithm (e.g., 0.37 0.05).NYSED Grade 5 Draft Updated June 2019

ClusterUse equivalentfractions as a strategyto add and subtractfractions.New York State Next Generation Mathematics Learning StandardsGrade 5 CrosswalkNumber and Operations - FractionsNYS P-12 CCLSNYS Next Generation Learning Standard5.NF.1 Add and subtract fractions with unlike denominators(including mixed numbers) by replacing given fractions withequivalent fractions in such a way as to produce anequivalent sum or difference of fractions with likedenominators. For example, 2/3 5/4 8/12 15/12 23/12. (In general, a/b c/d (ad bc)/bd.)NY-5.NF.1 Add and subtract fractions with unlike denominators(including mixed numbers) by replacing given fractions withequivalent fractions in such a way as to produce an equivalent sum ordifference of fractions with like denominators.e.g., 5.NF.2 Solve word problems involving addition andsubtraction of fractions referring to the same whole,including cases of unlike denominators, e.g., by using visualfraction models or equations to represent the problem. Usebenchmark fractions and number sense of fractions toestimate mentally and assess the reasonableness of answers.For example, recognize an incorrect result 2/5 1/2 3/7,by observing that 3/7 1/2.1323 2954 398 1229 151259 2312NY-5.NF.2 Solve word problems involving addition and subtraction offractions referring to the same whole, including cases of unlikedenominators.e.g., using visual fraction models or equations to represent the problem.Use benchmark fractions and number sense of fractions to estimatementally and assess the reasonableness of answers.21331e.g., Recognize an incorrect result 5 2 7 by observing that 7 2.NYSED Grade 5 Draft Updated June 2019

ClusterApply and extendprevious understandingsof multiplications anddivision to multiply anddivide fractions.New York State Next Generation Mathematics Learning StandardsGrade 5 CrosswalkNumber and Operations - FractionsNYS P-12 CCLSNYS Next Generation Learning Standard5.NF.3 Interpret a fraction as division of the numeratorby the denominator(a/b a b). Solve word problems involving division ofwhole numbers leading to answers in the form offractions or mixed numbers, e.g., by using visual fractionmodels or equations to represent the problem. Forexample, interpret 3/4 as the result of dividing 3 by 4,noting that 3/4 multiplied by 4 equals 3, and that when 3wholes are shared equally among 4 people, each personhas a share of size 3/4. If 9 people want to share a 50pound sack of rice equally by weight, how many poundsof rice should each person get? Between what two wholenumbers does your answer lie?NY-5.NF.3 Interpret a fraction as division of the numerator by the𝑎denominator ( a b).𝑏33e.g., Interpret as the result of dividing 3 by 4, noting that multiplied44by 4 equals 3, and that when 3 wholes are shared equally among 43people each person has a share of size .4Solve word problems involving division of whole numbers leading toanswers in the form of fractions or mixed numbers.e.g., using visual fraction models or equations to represent the problem.e.g., If 9 people want to share a 50-pound sack of rice equally byweight, how many pounds of rice should each person get? Betweenwhat two whole numbers does your answer lie?NYSED Grade 5 Draft Updated June 2019

ClusterApply and extendprevious understandingsof multiplications anddivision to multiply anddivide fractions.New York State Next Generation Mathematics Learning StandardsGrade 5 CrosswalkNumber and Operations - FractionsNYS P-12 CCLSNYS Next Generation Learning Standard5.NF.4 Apply and extend previous understandings ofmultiplication to multiply a fraction or whole number bya fraction.NY-5.NF.4 Apply and extend previous understandings ofmultiplication to multiply a fraction by a whole number or a fraction.a. Interpret the product (a/b) q as a parts of a partitionof q into b equal parts; equivalently, as the result of asequence of operations a q b. For example, use avisual fraction model to show (2/3) 4 8/3, and createa story context for this equation. Do the same with (2/3) (4/5) 8/15. (In general, (a/b) (c/d) ac/bd.)NY-5.NF.4a Interpret the product q as a parts of a partition of q𝑏into b equal parts; equivalently, as the result of a sequence ofoperations a q b.𝑎28e.g., Use a visual fraction model to show 4 , and create a story324353context for this equation. Do the same with b. Find the area of a rectangle with fractional sidelengths by tiling it with unit squares of the appropriateunit fraction side lengths, and show that the area is thesame as would be found by multiplying the side lengths.Multiply fractional side lengths to find areas ofrectangles, and represent fraction products as rectangularareas.NYSED Grade 5 Draft Updated June 2019815.NY-5.NF.4b Find the area of a rectangle with fractional side lengths bytiling it with rectangles of the appropriate unit fraction side lengths,and show that the area is the same as would be found by multiplyingthe side lengths. Multiply fractional side lengths to find areas ofrectangles, and represent fraction products as rectangular areas.e.g.,

ClusterApply and extendprevious understandingsof multiplications anddivision to multiply anddivide fractions.New York State Next Generation Mathematics Learning StandardsGrade 5 CrosswalkNumber and Operations - FractionsNYS P-12 CCLSNYS Next Generation Learning Standard5.NF.5 Interpret multiplication as scaling (resizing), by:NY-5.NF.5 Interpret multiplication as scaling (resizing).a. Comparing the size of a product to the size of one factor on thebasis of the size of the other factor, without performing theindicated multiplication.NY-5.NF.5a Compare the size of a product to the size ofone factor on the basis of the size of the other factor,without performing the indicated multiplication.𝟏e.g., In the case of 10 x 5, 5 is half of 10 and 5 is 10𝟏𝟐times larger than .𝟐b. Explaining why multiplying a given number by a fraction greaterthan 1 results in a product greater than the given number(recognizing multiplication by whole numbers greater than 1 as afamiliar case); explaining why multiplying a given number by afraction less than 1 results in a product smaller than the givennumber; and relating the principle of fraction equivalence a/b (n a)/(n b) to the effect of multiplying a/b by 1.NY-5.NF.5b Explain why multiplying a given number by afraction greater than 1 results in a product greater than thegiven number (recognizing multiplication by wholenumbers greater than 1 as a familiar case). Explain whymultiplying a given number by a fraction less than 1 resultsin a product smaller than the given number. Relate the𝒂𝒂𝒏principle of fraction equivalence to the effect of𝒃𝑎𝒃𝒏multiplying by 1.𝑏e.g.,𝟑Explain why 4 is greater than 4.𝟐𝟏Explain why 4 is less than 4.𝟏𝟑5.NF.6 Solve real world problems involving multiplication offractions and mixed numbers, e.g., by using visual fraction modelsor equations to represent the problem.𝟐𝟐𝟏𝟐𝟔𝟑𝟐is equivalent to because 𝟐 .𝟔NY-5.NF.6 Solve real world problems involvingmultiplication of fractions and mixed numbers.e.g., using visual fraction models or equations to representthe problem.NYSED Grade 5 Draft Updated June 2019

ClusterApply and extendprevious understandingsof multiplications anddivision to multiply anddivide fractions.New York State Next Generation Mathematics Learning StandardsGrade 5 CrosswalkNumber and Operations - FractionsNYS P-12 CCLSNYS Next Generation Learning Standard5.NF.7 Apply and extend previous understandings ofdivision to divide unit fractions by whole numbers andwhole numbers by unit fractions.NY-5.NF.7 Apply and extend previous understandings of division todivide unit fractions by whole numbers and whole numbers by unitfractions.a. Interpret division of a unit fraction by a non-zerowhole number, and compute such quotients. For example,NY-5.NF.7a Interpret division of a unit fraction by a non-zero wholenumber, and compute such quotients.create a story context for (1/3) 4, and use a visual fraction model toshow the quotient. Use the relationship between multiplication anddivision to explain that (1/3) 4 1/12 because (1/12) 4 1/3.1e.g., Create a story context for 4 and use a visual fraction model to show3the quotient. Use the relationship between multiplication and division to1111explain that 4 because 4 .3b. Interpret division of a whole number by a unitfraction, and compute such quotients. For example, create astory context for 4 (1/5), and use a visual fraction model to show thequotient. Use the relationship between multiplication and division toexplain that 4 (1/5) 20 because 20 (1/5) 4.1212NY-5.NF.7b Interpret division of a whole number by a unit fraction,and compute such quotients.1e.g., Create a story context for 4 and use a visual fraction model to show5the quotient. Use the relationship between multiplication and division to11explain that 4 20 because 20 4.5c. Solve real world problems involving division of unitfractions by non-zero whole numbers and division ofwhole numbers by unit fractions, e.g., by using visualfraction models and equations to represent the problem.For example, how much chocolate will each person get if 3 peopleshare 1/2 lb of chocolate equally? How many 1/3-cup servings are in 2cups of raisins?Note: Students able to multiply fractions in general can developstrategies to divide fractions in general, by reasoning about therelationship between multiplication and division. But division of afraction by a fraction is not a requirement at this grade.NYSED Grade 5 Draft Updated June 201935NY-5.NF.7c Solve real-world problems involving division of unitfractions by non-zero whole numbers and division of whole numbersby unit fractions.e.g., using visual fraction models and equations to represent the problem.1e.g., How much chocolate will each person get if 3 people share lb. of12chocolate equally? How many -cup servings are in 2 cups of raisins?3Note: Students able to multiply fractions in general can develop strategies to dividefractions in general, by reasoning about the relationship between multiplication anddivision. But division of a fraction by a fraction is not a requirement until grade 6(NY-6. NS.1).

ClusterConvert likemeasurement unitswithin a givenmeasurement system.New York State Next Generation Mathematics Learning StandardsGrade 5 CrosswalkMeasurement and DataNYS P-12 CCLSNYS Next Generation Learning Standard5.MD.1 Convert among different-sized standardmeasurement units within a given measurement system(e.g., convert 5 cm to 0.05 m), and use these conversionsin solving multi-step, real world problems.NY-5.MD.1 Convert among different-sized standard measurementunits within a given measurement system when the conversion factoris given. Use these conversions in solving multi-step, real worldproblems.Notes: The known conversion factors from grade 4 include ft., in.;km, m, cm; hr., min., sec. and will not be given. All otherconversion factors will be given. Grade 5 expectations for decimal operations are limited towork with decimals to hundredths.Represent and interpretdata.5.MD.2 Make a line plot to display a data set ofmeasurements in fractions of a unit (1/2, 1/4, 1/8). Useoperations on fractions for this grade to solve problemsinvolving information presented in line plots. Forexample, given different measurements of liquid inidentical beakers, find the amount of liquid each beakerwould contain if the total amount in all the beakers wereredistributed equally.NYSED Grade 5 Draft Updated June 2019NY-5.MD.2 Make a line plot to display a data set of measurements in1 1 1fractions of a unit ( , , ). Use operations on fractions for this grade2 4 8to solve problems involving information presented in line plots.e.g., Given different measurements of liquid in identical beakers, makea line plot to display the data and find the total amount of liquid inall of the beakers.

ClusterGeometric measurement:understand concepts ofvolume and relatevolume to multiplicationand addition.New York State Next Generation Mathematics Learning StandardsGrade 5 CrosswalkMeasurement and DataNYS P-12 CCLSNYS Next Generation Learning Standard5.MD.3 Recognize volume as an attribute of solidfigures and understand concepts of volumemeasurement.NY-5.MD.3 Recognize volume as an attribute of solid figures andunderstand concepts of volume measurement.a. A cube with side length 1 unit, called a “unit cube,” issaid to have “one cubic unit” of volume, and can be usedto measure volume.NY-5.MD.3a Recognize that a cube with side length 1 unit, called a“unit cube,” is said to have “one cubic unit” of volume, and can beused to measure volume.b. A solid figure which can be packed without gaps oroverlaps using n unit cubes is said to have a volume of ncubic units.5.MD.4 Measure volumes by counting unit cubes, usingcubic cm, cubic in, cubic ft, and improvised units.NYSED Grade 5 Draft Updated June 2019NY-5.MD.3b Recognize that a solid figure which can be packedwithout gaps or overlaps using n unit cubes is said to have a volume ofn cubic units.NY-5.MD.4 Measure volumes by counting unit cubes, using cubic cm,cubic in., cubic ft., and improvised units.

ClusterGeometric measurement:understand concepts ofvolume and relatevolume to multiplicationand addition.New York State Next Generation Mathematics Learning StandardsGrade 5 CrosswalkMeasurement and DataNYS P-12 CCLSNYS Next Generation Learning Standard5.MD.5 Relate volume to the operations ofmultiplication and addition and solve real world andmathematical problems involving volume.NY-5.MD.5 Relate volume to the operations of multiplication andaddition and solve real world and mathematical problems involvingvolume.a. Find the volume of a right rectangular prism withwhole-number side lengths by packing it with unit cubes,and show that the volume is the same as would be foundby multiplying the edge lengths, equivalently bymultiplying the height by the area of the base. Representthreefold whole-number products as volumes, e.g., torepresent the associative property of multiplication.NY-5.MD.5a Find the volume of a right rectangular prism with wholenumber side lengths by packing it with unit cubes, and show that thevolume is the same as would be found by multiplying the edge lengths,equivalently by multiplying the height by the area of the base.b. Apply the formulas V l w h and V b h forrectangular prisms to find volumes of right rectangularprisms with whole-number edge lengths in the context ofsolving real world and mathematical problems.NY-5.MD.5b. Apply the formulas V l w h and V B h forrectangular prisms to find volumes of right rectangular prisms withwhole-number edge lengths in the context of solving real world andmathematical problems.c. Recognize volume as additive. Find volumes of solidfigures composed of two non-overlapping rightrectangular prisms by adding the volumes of the nonoverlapping parts, applying this technique to solve realworld problems.NY-5.MD.5c Recognize volume as additive. Find volumes of solidfigures composed of two non-overlapping right rectangular prisms byadding the volumes of the non-overlapping parts, applying thistechnique to solve real world problems.NYSED Grade 5 Draft Updated June 2019

ClusterGraph points on thecoordinate plane to solvereal-world andmathematical problems.New York State Next Generation Mathematics Learning StandardsGrade 5 CrosswalkGeometryNYS P-12 CCLSNYS Next Generation Learning Standard5.G.1 Use a pair of perpendicular number lines, calledaxes, to define a coordinate system, with the intersectionof the lines (the origin) arranged to coincide with the 0on each line and a given point in the plane located byusing an ordered pair of numbers, called its coordinates.Understand that the first number indicates how far totravel from the origin in the direction of one axis, and thesecond number indicates how far to travel in thedirection of the second axis, with the convention that thenames of the two axes and the coordinates correspond(e.g., x-axis and x-coordinate, y-axis and y-coordinate).NY-5.G.1 Use a pair of perpendicular number lines, called axes, todefine a coordinate system, with the intersection of the lines (theorigin) arranged to coincide with the 0 on each line and a given point inthe plane located by using an ordered pair of numbers, called itscoordinates.Understand that the first number indicates how far to travel from theorigin in the direction of one axis, and the second number indicateshow far to travel in the direction of the second axis, with theconvention that the names of the two axes and the coordinatescorrespond.e.g., x-axis and x-coordinate, y-axis and y-coordinate.Classify two-dimensionalfigures into categoriesbased on theirproperties.5.G.2 Represent real world and mathematical problemsby graphing points in the first quadrant of the coordinateplane, and interpret coordinate values of points in thecontext of the situation.5.G.3 Understand that attributes belonging to a categoryof two-dimensional figures also belong to allsubcategories of that category. For example, allrectangles have four right angles and squares arerectangles, so all squares have four right angles.5.G.4 Classify two-dimensional figures in a hierarchybased on properties.NYSED Grade 5 Draft Updated June 2019NY-5.G.2 Represent real world and mathematical problems bygraphing points in the first quadrant of the coordinate plane, andinterpret coordinate values of points in the context of the situation.NY-5.G.3 Understand that attributes belonging to a category of twodimensional figures also belong to all subcategories of that category.e.g., All rectangles have four right angles and squares are rectangles, soall squares have four right angles.Note: The inclusive definition of a trapezoid will be utilized, whichdefines a trapezoid as “A quadrilateral with at least one pair ofparallel sides.”NY-5.G.4 Classify two-dimensional figures in a hierarchy based onproperties.

Grade 5 Crosswalk Number and Operations in Base Ten Cluster NYS P-12 CCLS NYS Next Generation Learning Standard . Perform operations with multi-digit whole numbers and with decimals to hundredths. 5.NBT.5. Fluently multipl

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