# Grade 5 Math Expressions 2017-2018 SY

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Grade 5 Math Expressions2017-2018 SYTopicsTotalTeachingDaysDatesBenchmark Cycle 1Benchmark Cycle 2Benchmark Cycle 3Cycle 4September 5 - October 31BM Window Nov 1-17November 2 - January 26BM Window Jan 29-Feb 13January 30 - May 8BM Window May 9-25May 10 - June 12Total Days: 39Including 1 Half DayTotal Days: 50 DaysIncluding 4 Half DaysTotal Days Before PSSA: 50Including 9 Half DaysTotal Days in Cycle: 60Including 13 Half Days;Excluding Week of Math PSSATotal Days: 22Including 1 Half Day1 – Addition and Subtractionwith Fractions2 – Addition and Subtractionwith Decimals3 – Multiplication and Divisionwith Fractions4 – Multiplication with WholeNumbers and Decimals5-1 – 5-5 – Division with WholeNumbers5-6 – 5-11 – Division withWhole Numbers6 – Operations and WordProblems7 – Algebra, Patterns, andCoordinate Graphs8-1 – 8-7 – Measurement andGeometry8-8 – 8-17 – Measurement andGeometryNote: A Benchmark Cycle is defined as the time allotted to teach the content that is on each benchmark, and assumes the benchmark is taken onthe first day of the window. This means that though it is fine to give the test later in the window, you should be moving on to new content as of theabove listed dates, or you will fall behind.THE SCHOOL DISTRICT OF PHILADELPHIA, OFFICE OF CURRICULUM, INSTRUCTION, AND ASSESSMENT, CHRISTOPHER SHAFFER, DEPUTY 2017-20181

Table of ContentsBenchmark Cycle 1 Standards. 3Benchmark Cycle 1 Scope and Sequence . 5Benchmark Cycle 2 Standards. 7Benchmark Cycle 2 Scope and Sequence . 12Benchmark Cycle 3 Standards. 15Benchmark Cycle 3 Scope and Sequence . 21Cycle 4 Standards . 26Cycle 4 Scope and Sequence . 28PA Core Standards and Eligible Content by Cycle . 30Document Information Page . 33THE SCHOOL DISTRICT OF PHILADELPHIA, OFFICE OF CURRICULUM, INSTRUCTION, AND ASSESSMENT, CHRISTOPHER SHAFFER, DEPUTY 2017-20182

CC.2.1.5.B.2 Extend anunderstanding ofoperations with wholenumbers to performoperations includingdecimals.CC.2.4.5.A.1 Solveproblems usingconversions within agiven measurementsystem.CC.2.4.5.A.4 Solveproblems involvingcomputation of fractionsusing informationprovided in a line plot.M05.A-T.1.1.5 Round decimals to any place (limitrounding to ones, tenths, hundredths, or thousandthsplace).M05.A-T.2.1.3 Add, subtract, multiply, and dividedecimals to hundredths (no divisors with decimals).M05.D-M.1.1.1 Convert between different-sizedmeasurement units within a given measurement system.A table of equivalencies will be provided. Example:Convert 5 cm to meters.M05.D-M.2.1.1 Solve problems involving computation offractions by using information presented in line plots.Use place value understanding to round decimals to anyplace.5.NBT.B.7 Add, 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 written methodand explain the reasoning used.5.MD.A.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.5.MD.B.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.THE SCHOOL DISTRICT OF PHILADELPHIA, OFFICE OF CURRICULUM, INSTRUCTION, AND ASSESSMENT, CHRISTOPHER SHAFFER, DEPUTY 2017-20184

Unit 2: Addition and Subtraction with Decimals10/6-10/121 Day Per Lesson 2 DaysSuggestedDatesUnitLessonLesson TitleLesson ObjectiveEligible ContentBIG IDEA 1: Read and Write Whole Numbers and Decimals2-12-22-3Decimals as EqualDivisionsThousands toThousandthsEquate and CompareThousandthsLearn about decimals as equal divisions of a whole.Understand decimals to 4Compare decimal numbers through thousandths.10/24-10/311 Day Per Lesson 2.5 Days10/13-10/231 Day Per Lesson 3DaysBIG IDEA 2: Addition and Subtraction2-42-52-62-72-82-92-10Adding and SubtractingDecimalsAdd Whole Numbersand DecimalsSubtract Whole andDecimal NumbersProperties andStrategiesRound and Estimatewith DecimalsGraph with DecimalNumbersFocus on MathematicalPracticesUse models to add and subtract decimals.Add decimals by aligning their place values.Subtract whole and decimal numbers to hundredths.M05.A-T.2.1.3M05.D-M.1.1.1Use the Commutative, Associative and Distributive Properties tocompute mentally.BIG IDEA 3: Round and Estimate with DecimalsEstimate decimal sums and differences.Interpret and construct bar graphs that involve decimal ve real world problems with decimals.Benchmark 1 Window: 11/1 – 11/17THE SCHOOL DISTRICT OF PHILADELPHIA, OFFICE OF CURRICULUM, INSTRUCTION, AND ASSESSMENT, CHRISTOPHER SHAFFER, DEPUTY 2017-20186

CC.2.1.5.C.2 Apply andextend previousunderstandings ofmultiplication anddivision to multiply anddivide fractions.M05.A-F.2.1.2 Multiply a fraction (including mixednumbers) by a fraction.M05.A-F.2.1.3 Demonstrate an understanding ofmultiplication as scaling (resizing). Example 1: Comparingthe size of a product to the size of one factor on the basisof the size of the other factor without performing theindicated multiplication. Example 2: Explaining whymultiplying a given number by a fraction greater than 1results in a product greater than the given number(recognizing multiplication by whole numbers greaterthan 1 as a familiar case); explaining why multiplying agiven number by a fraction less than 1 results in a productsmaller than the given number.5.NF.B.4 Apply and extend previous understandings ofmultiplication to multiply a fraction or whole numberby a fraction.a. Interpret the product (a/b) q as a parts of apartition of q into b equal parts; equivalently, as theresult of a sequence of operations a q b. Forexample, use a visual fraction model to show (2/3) 4 8/3, and create a story context for this equation (Ingeneral, (a/b) (c/d) (ac)/(bd).5.NF.B.4 Apply and extend previous understandings ofmultiplication to multiply a fraction or whole numberby a fraction.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 sidelengths. Multiply fractional side lengths to find areas ofrectangles, and represent fraction products asrectangular areas.5.NF.B.6 Solve real world problems involvingmultiplication of fractions and mixed numbers, e.g., byusing visual fraction models or equations to representthe problem.5.NF.B.5 Interpret multiplication as scaling (resizing),by:a. Comparing the size of a product to the size of onefactor on the basis of the size of the other factor,without performing the indicated multiplication.THE SCHOOL DISTRICT OF PHILADELPHIA, OFFICE OF CURRICULUM, INSTRUCTION, AND ASSESSMENT, CHRISTOPHER SHAFFER, DEPUTY 2017-20188

CC.2.1.5.C.2 Apply andextend previousunderstandings ofmultiplication anddivision to multiply anddivide fractions.M05.A-F.2.1.4 Divide unit fractions by whole numbers andwhole numbers by unit fractions.5.NF.B.5 Interpret multiplication as scaling (resizing) by:b. Explaining why multiplying a given number by afraction greater than 1 results in a product greater thanthe given number (recognizing multiplication by wholenumbers greater than 1 as a familiar case); explainingwhy multiplying a given number by a fraction less than1 results in a product smaller than the given number;and relating the principle of fraction equivalence a/b (n a)/(n b) to the effect of multiplying a/b by 1.5.NF.B.7 Apply and extend previous understandings ofdivision to divide unit fractions by whole numbers andwhole 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) 4, and use avisual fraction model to show the quotient. Use therelationship between multiplication and division toexplain that (1/3) 4 1/12 because (1/12) 4 1/3.5.NF.B.7 Apply and extend previous understandings ofdivision to divide unit fractions by whole numbers andwhole numbers by unit fractions.b. Interpret division of a whole number by a unitfraction, and compute such quotients. For example,create a story context for 4 (1/5), and use a visualfraction model to show the quotient. Use therelationship between multiplication and division toexplain that 4 (1/5) 20 because 20 (1/5) 4.THE SCHOOL DISTRICT OF PHILADELPHIA, OFFICE OF CURRICULUM, INSTRUCTION, AND ASSESSMENT, CHRISTOPHER SHAFFER, DEPUTY 2017-20189

CC.2.1.5.C.2 Apply andextend previousunderstandings ofmultiplication anddivision to multiply anddivide fractions.CC.2.4.5.A.1 Solveproblems usingconversions within agiven measurementsystem.CC.2.4.5.A.4 Solveproblems involvingcomputation of fractionsusing informationprovided in a line plot.M05.D-M.1.1.1 Convert between different-sizedmeasurement units within a given measurement system.A table of equivalencies will be provided. Example:Convert 5 cm to meters.CC.2.1.5.B.1 Apply place‐value concepts to showan understanding ofoperations and roundingas they pertain to wholenumbers and decimals.M05.A-T.1.1.1 Demonstrate an understanding that in amulti-digit number, a digit in one place represents 1/10 ofwhat it represents in the place to its left. Example:Recognize that in the number 770, the 7 in the tens placeis 1/10 the 7 in the hundreds place.M05.A-T.1.1.2 Explain patterns in the number of zeros ofthe product when multiplying a number by powers of 10and explain patterns in the placement of the decimalpoint when a decimal is multiplied or divided by a powerof 10. Use whole-number exponents to denote powers ofM05.D-M.2.1.1 Solve problems involving computation offractions by using information presented in line plots.5.NF.B.7 Apply and extend previous understandings ofdivision to divide unit fractions by whole numbers andwhole numbers by unit fractions.c. 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 theproblem. For example, how much chocolate will eachperson get if 3 people share 1/2 lb of chocolate equally?How many 1/3-cup servings are in 2 cups of raisins?5.MD.A.1 Convert among different-sized standardmeasurement units within a given measurementsystem (e.g., convert 5 cm to 0.05 m), and use theseconversions in solving multi-step, real world problems.5.MD.B.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 beakerswere redistributed equally.5.NBT.A.1 Recognize that in a multi-digit number, adigit in one place represents 10 times as much as itrepresents in the place to its right and 1/10 of what itrepresents in the place to its left.5.NBT.A.2 Explain patterns in the number of zeros ofthe product when multiplying a number by powers of10, and explain patterns in the placement of thedecimal point when a decimal is multiplied or dividedby a power of 10. Use whole-number exponents todenote powers of 10.THE SCHOOL DISTRICT OF PHILADELPHIA, OFFICE OF CURRICULUM, INSTRUCTION, AND ASSESSMENT, CHRISTOPHER SHAFFER, DEPUTY 2017-201810

CC.2.1.5.B.1 Apply place‐value concepts to showan understanding ofoperations and roundingas they pertain to wholenumbers and decimals.CC.2.1.5.B.2 Extend anunderstanding ofoperations with wholenumbers to performoperations includingdecimals.10. Example 1: 4 102 400 Example 2: 0.05 103 0.00005M05.A-T.1.1.3 Read and write decimals to thousandthsusing base-ten numerals, word form, and expanded form.Example: 347.392 300 40 7 0.3 0.09 0.002 3 100 4 10 7 1 3 (0.1) 9 (0.01) 2 (0.001)5.NBT.A.3 Read, write, and compare decimals tothousandths.a. Read and write decimals to thousandths using baseten 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).M05.A-T.1.1.4 Compare two decimals to thousandthsbased on meanings of the digits in each place using , ,and symbols.5.NBT.A.3 Read, write, and compare decimals tothousandths.b. Compare two decimals to thousandths based onmeanings of the digits in each place, using , , and symbols to record the results of comparisons.M05.A-T.1.1.5 Round decimals to any place (limitrounding to ones, tenths, hundredths, or thousandthsplace).M05.A-T.2.1.1 Multiply multi-digit whole numbers (not toexceed three-digit by three-digit).M05.A-T.2.1.2 Find whole-number quotients of wholenumbers with up to four-digit dividends and two-digitdivisors.5.NBT.4 Use place value understanding to rounddecimals to any place.5.NBT.B.5 Fluently multiply multi-digit whole numbersusing the standard algorithm.5.NBT.B.6 Find whole-number quotients of wholenumbers with up to four-digit dividends and two-digitdivisors, using strategies based on place value, theproperties of operations, and/or the relationshipbetween multiplication and division. Illustrate andexplain the calculation by using equations, rectangulararrays, and/or area models.M05.A-T.2.1.3 Add, subtract, multiply, and divide decimals 5.NBT.B.7 Add, subtract, multiply, and divide decimalsto hundredths (no divisors with decimals).to hundredths, 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.THE SCHOOL DISTRICT OF PHILADELPHIA, OFFICE OF CURRICULUM, INSTRUCTION, AND ASSESSMENT, CHRISTOPHER SHAFFER, DEPUTY 2017-201811

Benchmark Cycle 2 Scope and SequenceUnit 3: Multiplication and Division with Fractions11/2-11/161 Day Per Lesson 3 DaysSuggestedDates3-13-23-33-43-53-611/17-11/281 Day Per Lesson 3 Half Days11/29-12/111 Day Per Lesson 3.5 DaysUnitLesson3-73-83-93-103-113-123-133-14Lesson TitleLesson ObjectiveBIG IDEA 1: Multiplication with FractionsConnect multiplying by 1/n to dividing by n, and extend thisBasic Multiplication Conceptsunderstanding to make multiplicative comparisons.Multiplication with Non-UnitInterpret a/b times a quantity as a of b equal parts of thatFractionsquantity.Multiplication with FractionalMultiply a whole number by a fraction when the product is aSolutionsfraction.Multiply a Fraction by a FractionMultiply any two fractions.Multiplication StrategiesLearn strategies to simplify multiplication of fractions.Multiply Mixed NumbersMultiply with mixed numbers.BIG IDEA 2: Multiplication LinksRelate the operations with fractions to operations withRelate Fraction Operationswhole numbers.Add, subtract, multiply, and compare fractions to solve wordSolve Real-World Problemsproblems.Predict how the size of a fractional factor will affect the sizeMake Generalizationsof the product relative to the other factor.BIG IDEA 3: Division with FractionsLearn how division by a unit fraction or a whole numberWhen Dividing Is Also Multiplyingrelates to multiplication.Use diagrams to analyze division problems and learn to solveSolve Division Problemsthem.Distinguish Multiplication fromDiscern whether word problems should be solved byDivisionmultiplication or division equations.Analyze and solve a variety of problems involving fractionsReview Operations with Fractionsand all the operations.Focus on Mathematical PracticesSolve real-world problems involving division with fractions.Eligible THE SCHOOL DISTRICT OF PHILADELPHIA, OFFICE OF CURRICULUM, INSTRUCTION, AND ASSESSMENT, CHRISTOPHER SHAFFER, DEPUTY 2017-201812

Unit 4: Multiplication with Whole Numbers and Decimals12/12-12/221 Day Per Lesson 4 DaysSuggestedDatesUnitLesson4-1Lesson ObjectiveEligible ContentBIG IDEA 1: Multiplication with Whole NumbersLearn how the digits of a number shift their place valueShift Patterns in Multiplicationpositions when multiplied by powers of 10.4-2Patterns with Fives and ZerosLearn how multiples of 5 affect the zeros pattern.4-3Sharing Methods forMultiplication4-4Multiply Two-Digit NumbersUse place value models to help solve multi-digitmultiplication problems.Learn new methods, new Group Below Method, Place ValueRows Method, and Short Cut Method, to multiply multi-digitnumbers.4-5Practice Multiplication4-61/3-1/181 Day Per Lesson 4 DaysLesson T.2.1.3Develop fluency multiplying multi-digit numbers.BIG IDEA 2: Multiplication with Decimal NumbersMultiply Decimals by WholeSolve multiplication problems in which one factor is aNumbersdecimal number.4-7Multiply by DecimalsMultiply a whole or decimal number by a decimal number.4-8Multiply with Decimals GreaterThan 1Multiply with decimal numbers greater than 1.4-9Compare Shift Patterns4-10Estimate Products4-11Multiplication Practice4-12Focus on Mathematical PracticesCompare shift patterns when multiplying by whole numbersand when multiplying by decimals.Round whole numbers and decimal numbers to estimate aproduct.Solve a variety of problems that involve multiplying decimalnumbers.Solve real world problems using multiplication of multi-digitdecimal 05.A-T.2.1.3THE SCHOOL DISTRICT OF PHILADELPHIA, OFFICE OF CURRICULUM, INSTRUCTION, AND ASSESSMENT, CHRISTOPHER SHAFFER, DEPUTY 2017-201813

Unit 5: Division with Whole Numbers and Decimals1/19-1/261 Day Per Lesson 1 DaySuggestedDatesUnitLessonLesson TitleLesson ObjectiveEligible ContentBIG IDEA 1: Division with Whole Numbers5-4Divide Whole Numbers by OneDigitExplore Dividing by Two-DigitWhole NumbersToo large, Too Small, or JustRight?Interpret Remainders5-5Division Practice5-15-25-3Divide multi-digit numbers by single-digit divisors.Divide when the divisor has two digits.Adjust estimated digits that are too high or too low andrecognize how to handle each case.Interpret remainders for a variety of problem types.Increase competency in division of whole numbers byproviding numerical and word problems.M05.A-T.2.1.2Benchmark 2 Window: 1/29 – 2/13THE SCHOOL DISTRICT OF PHILADELPHIA, OFFICE OF CURRICULUM, INSTRUCTION, AND ASSESSMENT, CHRISTOPHER SHAFFER, DEPUTY 2017-201814

Benchmark Cycle 3 StandardsPA Common CoreStandardCC.2.1.5.B.1 Apply place‐value concepts to showan understanding ofoperations and roundingas they pertain to wholenumbers and decimals.CC.2.1.5.B.2 Extend anunderstanding ofoperations with wholenumbers to performoperations includingdecimals.PA Eligible ContentCommon Core State StandardM05.A-T.1.1.2 Explain patterns in the number of zeros ofthe product when multiplying a number by powers of 10and explain patterns in the placement of the decimalpoint when a decimal is multiplied or divided by a powerof 10. Use whole-number exponents to denote powers of10. Example 1: 4 102 400 Example 2: 0.05 103 0.00005M05.A-T.1.1.4 Compare two decimals to thousandthsbased on meanings of the digits in each place using , ,and symbols.5.NBT.A.2 Explain patterns in the number of zeros ofthe product when multiplying a number by powers of10, and explain patterns in the placement of thedecimal point when a decimal is multiplied or dividedby a power of 10. Use whole-number exponents todenote powers of 10.M05.A-T.1.1.5 Round decimals to any place (limitrounding to ones, tenths, hundredths, or thousandthsplace).M05.A-T.2.1.1 Multiply multi-digit whole numbers (not toexceed three-digit by three-digit).M05.A-T.2.1.2 Find whole-number quotients of wholenumbers with up to four-digit dividends and two-digitdivisors.5.NBT.4 Use place value understanding to rounddecimals to any place.5.NBT.A.3 Read, write, and compare decimals tothousandths.b. Compare two decimals to thousandths based onmeanings of the digits in each place, using , , and symbols to record the results of comparisons.5.NBT.B.5 Fluently multiply multi-digit whole numbersusing the standard algorithm.5.NBT.B.6 Find whole-number quotients of wholenumbers with up to four-digit dividends and two-digitdivisors, using strategies based on place value, theproperties of operations, and/or the relationshipbetween multiplication and division. Illustrate andexplain the calculation by using equations, rectangulararrays, and/or area models.M05.A-T.2.1.3 Add, subtract, multiply, and divide decimals 5.NBT.B.7 Add, subtract, multiply, and divide decimalsto hundredths (no divisors with decimals).to hundredths, using concrete models or drawings andstrategies based on place value, properties ofoperations, and/or the relationship between additionTHE SCHOOL DISTRICT OF PHILADELPHIA, OFFICE OF CURRICULUM, INSTRUCTION, AND ASSESSMENT, CHRISTOPHER SHAFFER, DEPUTY 2017-201815

CC.2.1.5.C.1 Use theunderstanding ofequivalency to add andsubtract fractions.M05.A-F.1.1.1 Add and subtract fractions (including mixednumbers) with unlike denominators. (May includemultiple methods and representations.) Exampl

Oct 05, 2017 · Understand decimals to thousandths. 2-3 Equate and Compare Thousandths Compare decimal numbers through thousandths. 3-3 ays BIG IDEA 2: Addition and Subtraction 2-4 Adding and Subtracting Decimals Use models to add and subtract decimals. M05.A-T.2.1.3 M05.D-M.1.1.1 2-5 Add Whole Numbers and Decimals Add decimals by aligning their place values. 2-6

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