Grade5 ScopeSequence Math

7/27/2019 Grade5 ScopeSequence Math

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5th Grade Mathematics-Quarter 1Focus Clusters:5.NBT Understand the place value system.

5.NBT Perform operations with multi-digit whole numbers with decimals to hundredthsFoundational:4.NBT Generalize place value understanding for multi-digit whole numbers.

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. For example, recognize that 700 70 = 10 by applying concepts of place value and division. 2. Read andwrite 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 of comparisons.3. Use place value understanding to round multi-digit whole numbers to any place.4. Fluently add and subtract multi-digit whole numbers using the standard algorithm.5. Multiply a whole number of up to four digits by a one-digit whole number, and multiply two two-digit numbers, using strategies based on place value and the properties of operations. Illustrate and explain the calculation by usingequations, rectangular arrays, and/or area models.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. Illustrateand explain the calculation by using equations, re ctangular arrays, and/or area models.

4.OA Use the four operations with whole numbers to solve problems.3. Solve multistep word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with aletter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies i ncluding rounding.

Unit CCSSM Learning Targets(KDEandNC Unpacked Standards)

SMP emphasized(NC Unpacked Standards)

Corresponding SPIs(NotAddressed by CCSSM) Corresponding EPASStandards

OperationswithWholeN

umbers(6weeks)

5.NBT.1 Recognize that in a multi-digitnumber, a digit in one place represents 10times as much as it represents in the placeto its right and 1/10 of what it represents inthe place to its left.

Represent powers of 10 usingwhole number exponents

Fluently translate between powersof ten written as ten raised to awhole number exponent, theexpanded form, and standardnotation (103 = 10 x 10 x 10 =1000)

SMP7 and 8 Students lookfor structure in place valueand use that structure tomake generalizations abouthow multiplying or dividingby 10 affects a numbersplace value.

SPI 0506.2.1 Read and writenumbers from millions tomillionths in variouscontexts.

Identify a digits place value Exhibit knowledge of

elementary numberconcepts includingrounding, the ordering ofdecimals, patternidentification, absolutevalue, primes, and greatestcommon factor

5.NBT.2 Explain patterns in the number ofzeros of the product when multiplying anumber by powers of 10, and explainpatterns in the placement of the decimalpoint when a decimal is multiplied ordivided by a power of 10. Use whole-number exponents to denote powers of10.

Explain the patterns in the numberof zeros of the product whenmultiplying a number by powers of10.

Compare whole numbers inmultiple forms using anunderstanding of equivalency.

5.NBT.5 Fluently multiply multi-digit wholenumbers using the standard algorithm.

Recall multiplication facts up to atleast 9s

Execute and explain a multi-digitmultiplication algorithm

SMP6 Students attend toprecision in theircalculations, ensuringcorrect place value andpositioning of digits.

Perform one-operationcomputation with wholenumbers and decimals.
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5.NBT.6 Find whole-number quotients ofwhole numbers with up to four-digitdividends and two-digit divisors, usingstrategies based on place value, theproperties of operations, and/or therelationship between multiplication anddivision. Illustrate and explain the

calculation by using equations, rectangulararrays, and/or area models.

Find whole-number quotients ofwhole numbers with up to four-digitdividends and two- digit divisors

Use strategies based on placevalue, the properties of operations,and/or the relationship betweenmultiplication and division to solve

division problems. Illustrate and explain division

calculations by using equations,rectangular arrays, and/or areamodels.

SMP2 Students model realworld division problems withmathematics,decontextualizing andrecontextualizinginformation, selectingappropriate expressions and

equations to represent theirwork.

Solve problems in one ortwo steps using wholenumbers.



Corresponding SPIs(NotAddressed by CCSSM)

Corresponding EPASStandards

Decimals(3weeks)

5.NBT.2 Explain patterns in the number ofzeros of the product when multiplying anumber by powers of 10, and explainpatterns in the placement of the decimalpoint when a decimal is multiplied ordivided by a power of 10. Use whole-number exponents to denote powers of10.

Explain the relationship of theplacement of the decimal pointwhen a decimal is multiplied ordivided by a power of 10.

SMP7 and 8 Students lookfor structure in place valueand use that structure tomake generalizations abouthow multiplying or dividingby 10 affects a numbersplace value and to assistthem in rounding to a certainplace.

Exhibit knowledge ofelementary numberconcepts includingrounding, the ordering of

decimals, patternidentification, absolutevalue, primes, and greatestcommon factor

5.NBT.3 Read, write, and comparedecimals to thousandths:a. Read and write decimals to thousandthsusing base-ten numerals, number names,and expanded form,e.g., 347.392 = 3 100 + 4 10 + 7 1 +3 (1/10) + 9 (1/100) + 2 (1/1000).b. Compare two decimals to thousandthsbased on meanings of the digits in eachplace, using >, =, and < symbols to recordthe results of comparisons.

Read and write decimal tothousandths using base-tennumerals, number names, andexpanded form.

Use >, =, and < symbols to recordthe results of comparisonsbetween decimals

Compare two decimals to thethousandths based on the placevalue of each digit.

SMP2 Students reasonabstractly and quantitativelywhen interpret a context anddecontextualize decimalamounts, solving comparingand rounding decimals, thenexplaining their reasoning;recontextualizing the decimalamount.

SPI 0506.2.1 Read and writenumbers from millions tomillionths in various contexts.SPI 0506.2.9 Compare wholenumbers, decimals andfractions using the symbols , and =.

Identify a digits place value

5.NBT.4 Use place value understanding toround decimals to any place.

Use knowledge of base ten andplace value to round decimals toany place.

Exhibit knowledge ofelementary numberconcepts includingrounding, the ordering ofdecimals, patternidentification, absolutevalue, primes, and greatestcommon factor
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5.NBT.7 Add, subtract, multiply, and dividedecimals to hundredths, using concretemodels or drawings and strategies basedon place value, properties of operations,and/or the relationship between additionand subtraction; relate the strategy to awritten method and explain the reasoning

used.

Add, subtract, multiply, and dividedecimals to hundredths usingconcrete models or drawings andstrategies based on place value,properties of operations, and/or therelationship between addition andsubtraction.

Relate the strategy to a writtenmethod and explain the reasoningused to solve decimal operationcalculations.

SMP1 Students will makesense of word problems andpersevere in solving them.Students interpret wordproblems, consideranalogous problems, and tryspecial cases and simpler

forms of the original problemin order to gain insight intoits solution, (CCSSM)

SPI 0506.2.5 Solve additionand subtraction problemsinvolving both fractions anddecimals.

Perform one-operationcomputation with wholenumbers and decimals.

Solve problems in one ortwo steps using wholenumbers.

Instructional Notes: Operations with whole numbers includes word problems with an emphasis on understanding and interpreting the remainder.Example division task. Example DecimalOperations Task

When working with decimals and place value the meaning of the equal sign should be emphasized. Understanding place value is more than simply naming places and identifying digits. Studentsshould be flexible in grouping and regrouping, decomposing and recomposing numbers. For example, students could interpret the number 124 as 12 tens and 4 ones or 11 tens and 14 ones. Thishelps build flexibility and fluency with operations.

Due to time constraints standard 5.NBT.7, should be limited to addition and subtraction of decimals. Teachers should be mindful of the language they use to describe mathematics. For example the

phrases borrowing or carrying should be avoided and instead regrouping should be used. This emphasizes equality and the relationship between the digits place value. Standard 5.NBT.2requires students to explain patterns in the number of zeros of the product when multiplying a number by powers of 10. Teachers should be careful about the language they use to describe thispattern. The phrase add a zero can be misinterpreted since actually adding zero to a number results in the same value. Instead the phrase tack-on a zero helps students recognize that when azero is tacked on the result is a new number. When teaching decimal place value and operations, it is important to draw the connection to fractions as decimals are base-ten fractions, when written inexpanded form.

Sample Tasks for each CCSSM can be found on the following sites:

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

http://www.turnonccmath.net/?p=map

http://www.illustrativemathematics.org/illustrations/330

http://www.parcconline.org/samples/item-task-prototypes

http://www.smarterbalanced.org/sample-items-and-performance-tasks/

http://www.turnonccmath.net/?p=mapSample Tasks for TCAP can be found at:http://www.tn.gov/education/assessment/ach_samplers.shtml
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5th Grade Mathematics-Quarter 2

Focus Clusters:5.NF Use equivalent fractions as a strategy to add and subtract fractions. 5.NF Apply and extend previous understandings of multiplication and division to multiply and divide fractions.

Foundational: 4.NF Extend understanding of fraction equivalence and ordering. 1. Explain why a fraction a/b is equivalent to a fraction (n a)/(n b)by using visual fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Use this principle torecognize and generate equivalent fractions.2. Compare two fractions with different numerators and different denominators, e.g., by creating common denominators or numerators, or by comparing to a benchmark fraction such as 1/2. Recognize that comparisons are valid only when the twofractions refer to the same whole. Record the results of comparisons with symbols >, =, or 1 as a sum of fractions 1/b.4. Apply and extend previous understandings of multiplication to multiply a fraction by a whole number.Understand decimal notation for fractions, and compare decimal fractions.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 100.4 For example, express 3/10 as 30/100, and add 3/10 + 4/100 = 34/100.6. 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.



CorrespondingSPIs(NotAddressed by

CCSSM)


EquivalentRep

resentations(4weeks)

5.NF.3 Interpret a fraction as division of thenumerator by the denominator (a/b = a b). Solveword problems involving division of wholenumbers leading to answers in the form offractions or mixed numbers, e.g., by using visualfraction models or equations to represent theproblem. For example, interpret 3/4 as the resultof dividing 3 by 4, noting that 3/4 multiplied by 4equals 3, and that when 3 wholes are sharedequally among 4 people each person has a shareof size 3/4. If 9 people want to share a 50-poundsack of rice equally by weight, how many poundsof rice should each person get? Between what

two whole numbers does your answer lie?

Interpret a fraction as division of the numerator bythe denominator (a/b = a b).

Solve word problems involving division of wholenumbers leading to answers in the form of fractionsor mixed numbers. (e.g. using visual fractionmodels or equations to represent the problem.)

Interpret the remainder as a fractional part of theproblem.

Write decimals as simplified fractions. Compare fractions and decimals. Explain decimals as fractions over powers of t en.

SMP1 and 2 Students will reasonabstractly and quantitatively aboutfractions as they solve wordproblems and model the problemswith mathematics and visual fractionmodels (number lines, area models,etc.) Students consider theiranswer and judge thereasonableness in terms of thecontext. Students also reasonquantitatively as they comparefractions and decimals.

SMP5 Students select appropriaterepresentations and use them astools to make meaning of thesituation. For example, a studentmay use a number line to comparetwo decimals but use a bar model tocompare two fractions.

SPI0506.2.7Recognizeequivalentrepresentations forthe same number.

0SPI506.2.8 Writeterminatingdecimals in theform of fractions ormixed numbers.

Order fractions Recognize equivalent

fractions and fractions inlowest terms



CorrespondingSPIs(NotAddressed byCCSSM)

Corresponding EPASStandards\
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FractionOper

ations(6Weeks)

5.NF.1 Add and subtract fractions with unlikedenominators (including mixed numbers) byreplacing given fractions in such a way as toproduce an equivalent sum or difference offractions with like denominators. For example, 2/3+ 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b +c/d = (ad + bc)/bd)

Generate equivalent fractions to find the likedenominator

Solve addition and subtraction problemsinvolving fractions (including mixed numbers)with like and unlike denominators using anequivalent fraction strategy.

SMP1 and 2 Students will need tointerpret given contexts anddetermine the appropriate symbolicnotation that describes the si tuation.Students will make sense of divisionproblems and persevere in solvingthem by creating their own andrelating division of fractions to their

understanding of multiplication anddivision.

SMP4 and 6 Students will modelequivalent representations withmathematics, using visual models torepresent fractions and decimalsand providing written explanations.Students also model fractionmultiplication with area models.Students also choose models anduse them as tools to solveproblems.

SMP7 and 8 Students look forstructure when comparing repeatedaddition to multiplication of fractionsby whole numbers. After repeatedlycalculating they generalize that (a/b) (c/d) = ac/bd.)

Solve routine one-steparithmetic problems(using whole numbers,fractions, and decimals)such as single steppercent

Recognize equivalentfractions and fractions in

lowest terms Find and use the least

common multipleRecognize one-digitfactors of a number

5.NF.2 Solve word problems involving addition

and subtraction of fractions referring to the samewhole, including cases of unlike denominators,e.g. by using visual fraction models or equationsto represent the problem. Use benchmarkfractions and number sense of fractions toestimate mentally and assess the reasonablenessof answers. For example, recognize an incorrectresult 2/5 + 1/2 = 3/7, by observing that 3/7


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5.NF.5 Interpret multiplication as scaling(resizing), by:a. Comparing the size of a product to the size ofone factor on the basis of the size of the otherfactor, without performing the indicatedmultiplication.

b. Explaining why multiplying a given number by a

fraction greater than 1 results in a product greaterthan the given number (recognizing multiplicationby whole numbers greater than 1 as a familiarcase); explaining why multiplying a given numberby a fraction less than 1 results in a productsmaller than the given number; and relating theprinciple of fraction equivalence a/b = (n a)/(n b) to the effect of multiplying a/b by 1.

Know that scaling (resizing) involves multiplication. Compare the size of a product to the size of one

factor on the basis of the size of the other factor,without performing the indicated multiplication. Forexample, a 2x3 rectangle would have an area twicethe length of 3.

Know that multiplying whole numbers and fractionsresult in products greater than or less than one

depending upon the factors. Draw a conclusion multiplying a fraction greater

than one will result in a product greater than thegiven number.

Draw a conclusion that when you multiply a fractionby one (which can be written as various fractions,ex 2/2, 3/3, etc.) the resulting fraction is equivalent.

Draw a conclusion that when you multiply a fractionby a fraction, the product will be smaller than thegiven number.

5.NF.6 Solve real world problems involvingmultiplication of fractions and mixed numbers,e.g., by using visual fraction models or equationsto represent the problem.

Represent word problems involving multiplication offractions and mixed numbers( e.g., by using visualfraction models or equations to represent theproblem.)

Solve real world problems involving multiplication offractions and mixed numbers.


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5.NF.7 Apply and extend previous understandingsof division to divide unit fractions by wholenumbers and whole numbers by unit fractions.a. Interpret division of a unit fraction by a non-zerowhole number, and compute such quotients. Forexample, create a story context for (1/3) dividedby 4, and use a visual fraction model to show thequotient. Use relationships between multiplication

and division to explain that (1/3) 4 = 1/12because (1/12) x 4 = 1/3.b. Interpret division of a whole number by a unitfraction, and compute such quotients. Forexample, create a story context for 4 (1/5), anduse a visual fraction model to show the quotient.Use the relationship between multiplication anddivision to explain that 4 (1/5) = 20 because 20x (1/5) = 4.c. Solve real world problems involving division ofunit fractions by non-zero whole numbers anddivision of whole numbers by unit fractions, e.g.,by using visual fraction models and equations torepresent the problem. For example, how muchchocolate will each person get if 3 people share1/2 lb. of chocolate equally? How many 1/3 cupservings are in 2 cups of raisins?

Know the relationship between multiplication anddivision

Interpret division of a unit fraction by a wholenumber and justify your answer using therelationship between multiplication and division,and by creating story problems, using visualmodels, and relationship to multiplication, etc.

Interpret division of a whole number by a unitfraction and justify your answer using therelationship between multiplication and division,and by representing the quotient with a visualfraction model.

Solve real world problems involving division of unitfractions by whole numbers other than 0 anddivision of whole numbers by unit fractions usingstrategies such as visual fractions models andequations.

Instructional Notes: Operations with Fractions provides the richest examples of common core instruction. Formative assessment will play an important role in your unit planning as you craft instruction that embedsreview and teaches new skills and concepts. Where are the Cookies, Pizza with Friends, andRepresenting Fractions on the Number lineare formative assessment lessons that promote grade level content as well asreview of foundational content. The frequent use of open-ended tasks is vital. Students need much practice explaining fractional amounts in terms of a context. Example Task 1. Example Task 2Example Task 3ExampleTask 4Students frequently struggle with fractions because of the many equivalent forms in which they can be represented.



http://www.turnonccmath.net/?p=maphttp://www.illustrativemathematics.org/illustrations/330



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5th Grade Mathematics- Quarter 3

Focus Clusters:5.NBT Perform operations with multi-digit whole numbers with decimals to hundredths.

Foundational:4.OA Generate and analyze patterns.5. Generate a number or shape pattern that follows a given rule. Identify apparent features of the pattern that were not explicit in the rule itself. For example, given the rule Add 3 and the starting number 1, generate terms in the resulting sequenceand observe that the terms appear to alternate between odd and even numbers. Explain informally why the numbers will continue to alternate in this way.





ExpressionsandEquations(4weeks)

Balance equalities, i.e. 11 = 8+_____

Use strategies to solve single stepequations involving fractions anddecimals for an unknown.

Create a story problem thatdemonstrates an understanding ofa variable

Students reason quantitativelyto determine if their answersmake sense.

SPI 3.3 Find the unknown insingle-step equations involvingfractions and mixed numbers.

Solve equations in the form x + a =b, where a and b are wholenumbers or decimals

Solve one-step equations havinginteger or decimal answers

5.0A.1 Use parentheses,brackets, or braces innumerical expressions, andevaluate expressions with

these symbols.

Use order of operations includingparenthesis, brackets, or braces.

Evaluate expressions using theorder of operations (including usingparenthesis, brackets, or braces.)

Students will attend toprecision as they show eachstep of the order of operationswhile evaluating expressions.

SPI 3.2 Evaluate multi-stepnumerical expressions involvingfractions using order ofoperations.

5.OA.2 Write simpleexpressions that recordcalculations with numbers,

and interpret numericalexpressions withoutevaluating them. Forexample, express thecalculation add 8 and 7,then multiply by 2 as 2 x(8+7). Recognize that 3 x(18932 + 921) is three timesas large as 18932 + 921,without having to calculatethe indicated sum of product.

Write numerical expressions forgiven numbers with operationwords.

Write operation words to describea given numerical expression. Interpret numerical expressions

without evaluating them.

Students will be able to reasonquantitatively to interpret thevalue of numerical expressions

prior to their evaluation andabstractly as theydecontextualize orcontextualize numericalexpressions into numbers orwords.

Exhibit knowledge of basicexpressions (e.g., identify anexpression for a total as b + g)
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Patterns&Graphs(4weeks)

5.OA.3 Generate twonumerical patterns using twogiven rules. Identify apparentrelationships betweencorresponding terms. Formordered pairs consisting ofcorresponding terms for two

patterns, and graph theordered pairs on acoordinate plane. Forexample, given the rule Add3 and the starting number 0,and the given rule Add 6and the starting number 0,generate the terms in theresulting sequences, andobserve that the terms inone sequence are twice thecorresponding terms in the

other sequence. Explaininformally why this is so.

Generate two numerical patternsusing two given rules.

Form ordered pairs consisting ofcorresponding terms for the twopatterns

Graph generated ordered pairs ona coordinate plane

Analyze and explain therelationships betweencorresponding terms in the twonumerical patterns

Students look for and makeuse of pattern structures tomake predictions and analyzerelationships.

SPI 5.1 Depict data using variousrepresentations, including decimaland/or fractional data.

Locate points on the number lineand in the first quadrant


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5.G.1 Use a pair ofperpendicular number lines,called axes, to define acoordinate system, with theintersection of the lines (theorigin) arranged to coincidewith the 0 on each line and a

given point in the planelocated by using an orderedpair of numbers, called itscoordinates. Understand thatthe first number indicateshow far to travel from theorigin in the direction of oneaxis, and the second numberindicates how far to travel inthe direction of the secondaxis, with the convention thatthe names of the two axes

and the coordinatescorrespond (e.g., x-axis andx-coordinate, y-axis and y-coordinate).

Define the coordinate system Identify the x- and y-axis Locate the origin on the coordinate

system

Identify coordinates of a point on acoordinate system

Recognize and describe theconnection between the orderedpair and the x- and y- axis (fromthe origin)

Locate points on the number lineand in the first quadrant

5.G.2 Represent real worldand mathematical problemsby graphing points in the firstquadrant of the coordinateplane, and interpretcoordinate values of pointsin the context of thesituation.

Graph points in the first quadrant Represent real world and

mathematical problems bygraphing points in the first quadrant

Interpret coordinate values ofpoints in real world context andmathematical problems

Students will make sense ofproblems involving fractionalmeasurements and perseverein solving them, ready todefend their claims withevidence.

SPI 4.5 Find the length of verticalor horizontal line segments in thefirst quadrant of the coordinateplans, including problems thatrequire the use of fractions anddecimals.


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5.MD.2 Make a line plot todisplay a data set ofmeasurements in fractions ofa unit.

Identify benchmark fractions (1/2,1/4, 1/8)

Make a line plot to display a dataset of measurements in fractions ofa unit (1/2, 1/4, 1/8).

Solve problems involvinginformation presented in line plots

which use fractions of a unit (1/2,1/4, 1/8) by adding, subtracting,multiplying, and dividing fractions.

Represent data in tables, circlegraphs, bar graphs, line graphs

Identify and interpret scale whenusing graphs

Students will attend toprecision as they interpret andrecord fractional data.

SPI 5.1 Depict data using variousrepresentations, including decimaland/or fractional data.

Read tables and graphs Translate from one representation

of data to another (e.g., a bargraph to a circle graph)

5.MD.1 Convert amongdifferent-sized standardmeasurement units within agiven measurement system(e.g., convert 5 cm to 0.05

m), and use theseconversions in solving multi-step, real world problems.

Recognize units of measurementwithin the same system

Divide and multiply to change units Convert units of measurement

within the same system

Solve multi-step, real worldproblems that involve convertingunits

Students will attend toprecision, noting theimportance of units andunderstanding the relativemeaning of different units.

2DSh

apes(2weeks)

5.G.3 Understand thatattributes belonging to acategory of two-dimensionalfigures also belong to allsubcategories of thatcategory. For example, allrectangles have four rightangles and squares are

rectangles, so all squareshave four right angles.

Recognize that some two-dimensional shapes can beclassified into more than onecategory based on their attributes.

Recognize if a two-dimensionalshape is classified into a category,that it belongs to all subcategoriesof that category.

Students will look for structurein the attributes of 2D shapesand use it to help themcategorize shapes.

Properties of Plane FiguresCluster


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5.G.4 Classify two-dimensional figures in ahierarchy based onproperties.

Recognize the hierarchy of two-dimensional shapes based on theirattributes.

Analyze properties of two-dimensional figures in order toplace into a hierarchy.

Classify two-dimensional figuresinto categories and/or sub-categories based on theirattributes.

Instructional Notes: With Algebra and Measurement, fractions and decimals must be present to match TCAP level of rigor. Patterns and equalities, although not on TCAP, are a large part of theMAP Assessments.






http://www.smarterbalanced.org/sample-items-and-performance-tasks/http://www.turnonccmath.net/?p=mapSample Tasks for TCAP can be found at:http://www.tn.gov/education/assessment/ach_samplers.shtml
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5th Grade Mathematics-Quarter 4Focus Clusters:5.MD Geometric measurement: understand concepts of volume and relate volume to multiplication and to addition.

Foundational: 4.MD Solve problems involving measurement and conversion of measurements f rom a larger unit to a smaller unit.1. Use the four operations to solve word problems involving distances, intervals of time, liquid volumes, masses of objects, and money, including problems involving simple fractions or decimals, and problems that require expressing measurementsgiven in a larger unit in terms of a smaller unit. Represent measurement quantities using diagrams such as number line diagrams that feature a measurement scale.2. Apply the area and perimeter formulas for rectangles in real world and mathematical problems. For example, find the width of a rectangular room given the area of the flooring and the length, by viewing the area formula as a multiplication equationwith an unknown factor.





Volume(4weeks)

5.MD.3 Recognize volume asan attribute of solid figures andunderstands concepts ofvolume measurement.a. A cube with side length 1

unit, called a unit cube, issaid to have one cubicunit of volume, and canbe used to measurevolume.

b. A solid figure which can bepacked without gaps oroverlaps using n unitcubes is said to have avolume ofn cubic units.

Recognize that volume is themeasurement of the space inside asolid three-dimensional figure.

Recognize a unit cube has 1 cubic unitof volume and is used to measure

volume of three- dimensional shapes. Recognize any solid figure packed

without gaps or overlaps and filled with(n) unit cubes indicates the total cubicunits or volume.

SPI 4.4 Solve problems involvingsurface area and volume ofrectangular prisms and polyhedralsolids.

Use geometric formulas when allnecessary information is given

Compute the area of triangles andrectangles when one or moreadditional simple steps are required

5.MD.4 Measure volumes bycounting unit cubes, using cubiccm, cubic in., cubic ft., andimprovised units.

Measure volume by counting unitcubes, cubic cm, cubic in., cubic ft.,and improvised units.

Students will use measurementtools appropriately, like unit cubes,to measure volume.
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5.MD.5 Relate volume to theoperations of multiplication andaddition and solve real worldand mathematical problemsinvolving volume.a. Find the volume of a rightrectangular prism with whole-number side lengths by packing

it with unit cubes, and show thatthe volume is the same aswould be found by multiplyingthe edge lengths, equivalentlyby multiplying the height by thearea of the base. Representthreefold whole-numberprocedures as volumes, e.g., torepresent the associativeproperty of multiplication.b. Apply the formulas V=l x w xh and V=B x h for rectangularprisms to find volumes of rightrectangular prisms with whole-

number lengths in the context ofsolving real world andmathematical problems.c. Recognize volume asadditive. Find volumes of solidfigures composed of two non-overlapping right rectangularprisms by adding the volumes ofthe non-overlapping parts,applying this technique to solvereal world problems.

Identify a right rectangular prism. Multiply the three dimensions in any

order to calculate volume(Commutative and associativeproperties)

Develop volume formula for arectangle prism by comparing volumewhen filled with cubes to volume by

multiplying the height by the area ofthe base, or when multiplying the edgelengths (LxWxH)

Find the volume of a right rectangularprism with whole number side lengthsby packing it with unit cubes.

Know that B is the area ofthe base Apply the following formulas to right

rectangular prisms having wholenumber edge lengths in the context ofreal world mathematical problems:Volume = length x width x heightVolume = area of base x height

Recognize volume as additive. Solve real world problems by

decomposing a solid figure into twonon-overlapping right rectangularprisms and adding their volumes.

SMP8 Students will look forregularity in repeated calculationsof volume to develop a formula forfinding volume of a rectangularprisms.

Instructional Notes: It is likely that students will need significant review in measurement and calculation of area and perimeter, and may need a better conceptualunderstanding of the two concepts. This can be addressed at the beginning of this quarter or the end of the previous one.







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