Summit Public Schools Summit, New Jersey Grade Level 5 .

number by a fractionless than 1 results in aproduct smaller thanthe given number; andrelating the principle offraction equivalencea/b (n a)/(n b)to the effect ofmultiplyinga/b by 1.5.OA.A.1 Useparentheses, brackets,or braces in numericalexpressions, andevaluate expressionswith these symbols.MP 2Title: DividingFractions-Dividing Fractions-Interpret Fractionsas DivisionApproximate number ofinstructional days: tAssessment /aaamath.com/grade4.htm8.12Ch 8DivideFractionsTopic 1111-1,11-9,11-10:DividingFractions5.NF.B.3 Interpret afraction as division ofthe numerator by thedenominator (a/b a b). Solve wordproblems involvingdivision of wholenumbers leading toanswers in the form offractions or mixednumbers, e.g., by usingvisual fraction modelsor equations torepresent the problem.For example, interpret 3/4as the result of dividing 3by 4, noting that 3/4multiplied by 4 equals 3,and that when 3 wholes areshared equally among 4people each person has a

Envision %20Math%20Resources/fifthgrade.htmshare of size 3/4. If 9people want to share a 50pound sack of rice equallyby weight, how manypounds of rice should eachperson get? Between whattwo whole numbers doesyour answer lie?5.NF.B.7 Apply andextend previousunderstandings ofdivision to divide unitfractions by wholenumbers and wholenumbers by unitfractions.15.NF.B.7aInterpret division of aunit fraction by a nonzero whole number,and compute suchquotients. For example,create a story context for(1/3) 4, and use avisual fraction model toshow the quotient. Use therelationship betweenmultiplication and divisionto explain that (1/3) 4 1/12 because (1/12) 4 1/3. 5.NF.B.7bInterpret division of awhole number by aunit fraction, andcompute suchquotients. For example,create a story context for 4 (1/5), and use a visual

fraction model to show thequotient. Use therelationship betweenmultiplication and divisionto explain that 4 (1/5) 20 because 20 (1/5) 4.5.NF.B.7c Solvereal world problemsinvolving division ofunit fractions by nonzero whole numbersand division of wholenumbers by unitfractions, e.g., by usingvisual fraction modelsand equations torepresent the problem.For example, how muchchocolate will each personget if 3 people share 1/2 lbof chocolate equally? Howmany 1/3-cup servings arein 2 cups of raisins?MP 2/MP 3Title: Volume-UnderstandConcepts of VolumeMeasurement-Measuring Volumesby Counting UnitCubes-Finding Volume byApplying Formulas-Solve Real WorldVolume ProblemsApproximate number earnzillion.com/lessons9.8, 9.9,9.10, 11.1Ch 11Geometry andVolumeTopic 12:Volume ofSolids5.MD.C.3 Recognizevolume as an attributeof solid figures andunderstand concepts ofvolumemeasurement.5.MD.C.3a A cube with sidelength 1 unit, called a“unit cube,” is said tohave “one cubic unit”of volume, and can beused to measurevolume. 5.MD.C.3b A

instructional days: 10http://www.brainpop.com/math/Pre-/PostAssessment #9Games:http://www.mrnussbaum.comsolid figure which canbe packed without gapsor overlaps using n unitcubes is said to have avolume of n cubicunits.5.MD.C.4 Measurevolumes by countingunit cubes, using cubiccm, cubic in, cubic ft,and improvised units.5.MD.C.5 Relatevolume to theoperations ofmultiplication andaddition and solve realworld andmathematical problemsinvolving volume.http://aaamath.com/grade4.htmEnvision %20Math%20Resources/fifthgrade.htmMP 3Title: Classifying2-D Figures-Understanding andClassifying 2-DFigures Based d-Exercises.htmlApproximate number ofinstructional days: essment op.com/math/Games:3.7Ch 11Geometry andVolumeTopic 15:ClassifyingPlaneFigures5.G.B.3 Understandthat attributesbelonging to a categoryof two-dimensionalfigures also belong toall subcategories ofthat category. Forexample, all rectangleshave four right anglesand squares arerectangles, so allsquares have four rightangles.5.G.B.4 Classify twodimensional figures ina hierarchy based on

http://www.mrnussbaum.comproperties.5.OA.B.3 Generatetwo numerical patternsusing two given rules.Identify apparentrelationships betweencorresponding terms.Form ordered pairsconsisting ofcorresponding termsfrom the two patterns,and graph the orderedpairs on a coordinateplane. For example, giventhe rule “Add 3” and thestarting number 0, andgiven the rule “Add 6”and the starting number 0,generate terms in theresulting sequences, andobserve that the terms inone sequence are twice thecorresponding terms in theother sequence. Explaininformally why this is so.http://aaamath.com/grade4.htmEnvision %20Math%20Resources/fifthgrade.htmMP 3Title: CoordinatePlane-Understanding andGraphing Points onA Coordinate Planeto Solve Real WorldPlane-Generate andIdentify NumericalPatterns Using ises.htmlhttp://www.mathworksheetsland.com/5/9.1, 9.2,9.3, 10.3,10.4Ch Tables8-8:VariablesandExpression5.G.A.1 Use a pair ofperpendicular numberlines, called axes, todefine a coordinatesystem, with theintersection of the lines(the origin) arranged tocoincide with the 0 oneach line and a givenpoint in the plane

sApproximate number ofinstructional days: nt rnussbaum.comhttp://aaamath.com/grade4.htmEnvision %20Math%20Resources/fifthgrade.htmTopic 14:DataTopic 16:CoordinateGeometrylocated by using anordered pair ofnumbers, called itscoordinates.Understand that thefirst number indicateshow far to travel fromthe origin in thedirection of one axis,and the second numberindicates how far totravel in the directionof the second axis,with the conventionthat the names of thetwo axes and thecoordinatescorrespond (e.g., x-axisand x-coordinate, yaxis and y-coordinate).5.G.A.2 Representreal world andmathematical problemsby graphing points inthe first quadrant ofthe coordinate plane,and interpretcoordinate values ofpoints in the context ofthe situation.5.OA.B.3 Generatetwo numerical patternsusing two given rules.Identify apparentrelationships betweencorresponding terms.Form ordered pairs

consisting ofcorresponding termsfrom the two patterns,and graph the orderedpairs on a coordinateplane. For example, giventhe rule “Add 3” and thestarting number 0, andgiven the rule “Add 6”and the starting number 0,generate terms in theresulting sequences, andobserve that the terms inone sequence are twice thecorresponding terms in theother sequence. Explaininformally why this is so.Unit Description: Marking Period 1StandardsOperations and Algebraic Thinking 5.OANumber and Operations in Base Ten 5.NBTNumber and Operations-Fractions 5NFMeasurement and Data 5MDBig Ideas: Course Objectives / Content Statement(s)Operations and Algebraic Thinking 5.OAWrite and interpret numerical expressions.Number and Operations in Base Ten 5.NBT

Understand the place value system.Perform operations with multi-digit whole numbers and with decimals to hundredths.Number and Operations-Fractions 5.NFApply and extend previous understandings of multiplication and division to multiply and divide fractions.Measurement and Data 5.MDConvert like measurement units within a given measurement system.Geometry 5.GClassify two-dimensional figures into categories based on their properties.Essential QuestionsWhat provocative questions will foster inquiry, understanding,and transfer of learning? What different interpretations can be obtainedfrom a particular pattern or relationship? When are algebraic and numeric expressions used? How would you describe the order of operations? What number or symbol is needed to makenumber sentences true? What is the most appropriate way ofcommunicating a mathematical idea in a particularsituation?Areas of Focus: Proficiencies(Cumulative Progress Indicators)Students will:Operations and Algebraic Thinking 5.OA Write and interpret numerical expressions.5.OA.1Use parentheses, brackets, or braces in numericalexpressions, and evaluate expressions with thesesymbols.Enduring UnderstandingsWhat will students understand about the big ideas?Students will understand that Operations create relationships between numbers. The relationships among the operations and their properties promote computational fluency. There are many ways to represent a number. Doing the opposite operation “undoes” the previous one. Grouping (unitizing) is a way to count, measure, and estimate.Examples, Outcomes, AssessmentsInstructional Focus: Write number models for rectangular arrays. Explore the relationship between multiplication and division. Find factors of a number. Use divisibility rules to solve problems.

5.OA.2 Use exponential notation to name square numbers, and explore the relationship betweenWrite simple expressions that record calculations withsquare numbers and square roots.numbers, and interpret numerical expressions without Rename numbers as factor strings or products of exponents.evaluating them. Convert between inches, feet, and miles. Write whole numbers and decimals in expanded notation.Number and Operations in Base Ten 5.NBT Use line plots to organize reaction-time data. Understand the place value system. Read, write, and order decimals to the hundredths place.5.NBT.1Recognize that in a multi-digit whole number, a digit Compare order of magnitude for large numbers.in one place represents ten times what it represents in Use magnitude estimates to place the decimal point in products.the place to its right and 1/10th of what it represents Solve whole number and decimal problems using the partial-products algorithm.in the place at the left. Explore angle types and relationships. Determine angle measures.5.NBT.2 Classify triangles as isosceles, equilateral, or scalene.Explain patterns in the number of zeros of the Describe, identify and draw properties of regular polygons.product when multiplying a number by powers of 10, Make reasonable estimates for whole number and decimal multiplication problems.and explain patterns in the placement of the decimal Express probability as a percent, decimal, or fraction.point when a decimal is multiplied or divided by apower of 10. Use whole-number exponents to denote Define and classify angles according topowers of 10.Sample Assessments:5.NBT.3 Game Record SheetsRead, write, and compare decimals to thousandths.o Make a factor rainbow.a. Read and write decimals to thousandths using baseo Play Factor Bingoten numerals, number names, and expanded form.o High Number Tossb. Compare two decimals to thousandths based ono Triangle Sortmeanings of the digits in each place, using , , ando Polygon Capture symbols to record the results of comparisons. Exit Slipso What number is 10 times as large as 37,900?5.NBT.4

Use place value understanding to round decimals toany place. Perform operations with multi-digit whole numbersand with decimals to hundredths.5.NBT.6Find whole-number quotients of whole numbers withup to four-digit dividends and two-digit divisors,using strategies based on place value, the propertiesof operations, and/or the relationship betweenmultiplication and division. Illustrate and explain thecalculation by using equations, rectangular arrays,and/or area models.5.NBT.7Add, subtract, multiply, and divide decimals tohundredths, using concrete models or drawings andstrategies based on place value, properties ofoperations, and/or the relationship between additionand subtraction: relate the strategy to a writtenmethod and explain the reasoning used.Numbers and Operations –Fractions 5.NF Apply and extend previous understandings ofmultiplication and division to multiply and dividefractions.5.NF.5aInterpret multiplication as scaling (resizing) bycomparing the size of one factor on the basis of theo Round 0.551674 to the thousandths place.o What is the nearest multiple of a power of 10 for: 76; 220; 4,892?o Draw and identify 3 different triangles. Student Self Assessment Writing Promptso Explain to a friend the relationship between the dimensions of a rectangle andthe factors of a number.o How does knowing how to round decimal numbers helpful?o William had 3.55. Sinbad had 4.55. Sinbad said he had 10 times more moneythan William. Tell why you agree or disagree.o Explain the meaning of a magnitude 6.5 earthquake.o How do we estimate the reasonableness of an answer when we add, subtract,multiply or divide decimals? Progress Check Written Assessment Teacher Observationo Assign each student a fraction amount and arrange themselves to form a“human” line plot.o Students should signal “thumbs up or thumbs down” whether 676.8 is areasonable product for 9.4 x 7.2 Class Checklists Beginning, Middle, End-of-Year Assessments Math Journals/Interactive Student Notebookso Draw a picture that could be used to help solve this problem: What polygons aremade by the diagonals in a hexagon?o Draw a picture that could be used to help solve this problem: How are atrapezoid and a parallelogram alike?

size of the other factor, without performing theindicated multiplication.Interdisciplinary Connections Reading/Writing Word Problems Math Literature ListMeasurement and Data 5.MDo The Adventures of Penrose, the Mathematical Cat by Theoni Pappas Convert like measurement units within a given I Hate Mathematics by Marilyn Burns and Martha Westonmeasurement system. Suggested Projects: Create a 10-page, How-To book to help students learn one topic from math class.5.MD.1 Design a menu for a themed restaurant. Include criteria for how many of eachConvert among different-sized standard measurementtype of item (appetizers, beverages, main dishes, etc.). Write word problems usingunits within a given measurement system and usetheir menu.these conversions in solving multi-step, real world Students can construct a maze by drawing a diagonal from each vertex of aproblems.regular pentagon or hexagon. Write an operation and quantity on each line Represent and interpret data.segment. Students should try to find the path that results in the highest andlowest values. A start number may also be included as a target value. An example5.MD.2can be found in activity 3 this site:Make a line plot to display a data set of tail.aspx?id L252xin fractions of a unit (1/2,1/4, 1/8). Technology Integrationo Visit the Challenges index - http://www.figurethis.org/challengesGeometry 5Go Visit related topics - http://www.ixl.com/math/grade-6 Classify two-dimensional figures into categories based ono Students can explore the math inherent in a chosen career path their l world Google Earth activities - http://www.realworldmath.org/conceptUnderstand that attributes belonging to a category oflessons.htmltwo-dimensional figures also belong to allsubcategories of that category. Global Perspectives5.G.4o The Inch Boy adapted from Japanese fairy tale.Classify two-dimensional figures

Adding and Subtracting Fractions Topic 10: Adding and Subtracting Mixed Numbers Topic 13: Units of Measure 5.NF.A.1 subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For