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Mathematics: Fifth GradeIn 5th grade, instructional time will focus on operations with decimals; operations with fractions; conversion of measurement; and classifying 2-dimensional and 3-dimensional shapes. Instruction on decimals will focus on comparing and rounding to the thousandths as well as being able to add, subtract, multiply, and divide decimals to the hundredths. Fraction instruction will involve addition, subtraction, multiplication, and division. The fractions will include like and unlike denominators as well as mixed numbers. Students are expected to simplify their answers. The students will convert length, capacity, and weight measurements within the customary and metric systems. The problems they encounter will involve multistep conversions. Students will classify two-dimensional shapes based on their attributes such as congruent angles, congruent sides, right angles, and parallel lines. They will also identify the properties of three-dimension figures such as faces, edges, and vertices. Course Information:Frequency & Duration: Daily for 60 minutesText: My Math (2013), McGraw Hill00Content: Place Value/Multiplying Whole NumbersDuration: 6 weeks (Aug/Sept)Essential Question:How does the position of a digit in a number relate to its value?What strategies can be used to multiply whole numbers?Skills:Compare and order whole numbers and decimals to the thousandthsRound decimals to the thousandthsUse partial products and distributive property to multiply numbers Use powers to express numbersMultiply mentally using basic facts and powers of 10Develop an understanding that a digit in one place represents 1/10 of what it represents in the place to its left. Read and write decimals to the thousandthsEstimate productsMultiply numbers up to 3-digit factorsAssessment:Pre- and Post-AssessmentsPerformance TasksMid-Chapter (formative)QuizStudents are able to estimate products of whole numbers and decimals to the thousandthsStudents are able to multiply 3-digit numbers by 3-digit numbersRecommended Activity:Problem of the DayFoldablesGamesStandards:CC.2.1.5.B.1 Apply place-value concepts to show an understanding of operations and rounding as they pertain to whole numbers and .2.1.5.B.2 Extend an understanding of operations with whole numbers to perform operations including decimals.Vocabulary:Decimal point; Decimal; Equivalent decimals; Expanded form; Standard formPeriod- each group of three digits on a place value chart; Base-in a power the number used as a factor; Power-a number obtained by raising a base to an exponent; Exponent- in a power, the number of times the base is used as a factor; Compatible numbers-numbers in a problem that are easy to work with mentally; Cubed-a number raised to the third power; Power of 10- a number like 10, 100, 1,000 and so onComments: Content: Divide by a One-Digit DivisorDuration: Oct/Nov (4 weeks)Essential Question:What strategies can be used to divide whole numbers?Skills:Understand how division and multiplication are relatedDivide with two-digit divisorsEstimate quotientsDivide using the distributive property and partial quotients Understand how to place the first digit in a quotientSolve division problems that result in quotients that have zerosInterpret and explain how to interpret the remainder in a division problemIdentify extra information or missing information needed to solve a problemAssessment:Pre- and Post-AssessmentsPerformance TasksMid-Chapter (formative)QuizStudents are able to divide by 2-digit divisorsStudents are able to estimate quotientsStudents are able to interpret remainders when answering word problemsRecommended Activity:FoldablesScoot GameStandards:CC.2.1.5.B.2 – Extend an understanding of operations with whole numbers to perform operations including decimals.Vocabulary:Dividend; Divisor; Fact family; Quotient; RemainderPartial quotient - a method of dividing where you break the dividend into sections that are easy to divide; Unknown - missing value in a number sentence or equation; Variable - a letter or symbol used to represent an unknown quantityComments: Content: Add and Subtract DecimalsDuration: November (2 weeks)Essential Question:How can I use place value and properties to add and subtract decimals?Skills:Round decimalsEstimate sums and differences by roundingSolve problems by using an estimate or an exact answerExplore adding decimals using modelsAdd decimals to the hundredthsSubtract decimals to the hundredthsAssessment:Pre- and Post-AssessmentsPerformance TasksMid-Chapter (formative)Quiz Students are able to add and subtract decimals to the hundredthsStudents are able to estimate sums and differencesStudents are able to determine whether an estimate or exact answer is needed when problem solvingRecommended Activity:FoldablesUse menus from restaurants Standards:CC.2.1.5.B.1 – Apply place value concepts to show an understanding of operations and rounding as they pertain to whole numbers and .2.1.5.B.2 – Extend an understanding of operations with whole numbers to perform operations including decimals.Vocabulary:Continue reviewing and reinforcing previous ments: Content: Multiply and Divide DecimalsDuration: Nov/ December (2 weeks)Essential Question:How is multiplying and dividing decimals similar to multiplying and dividing whole numbers?Skills:Estimate products of whole numbers and decimalsMultiply decimals by whole numbersMultiply decimals by decimalsUse the associative, commutative, and identity properties to multiply mentallyEstimate quotients of decimals and whole numbers Divide decimals by whole numbersDivide decimals by decimalsAssessment:Pre- and Post-AssessmentsPerformance TasksMid-Chapter (formative)QuizStudents are able to multiply decimals to the hundredthsStudents are able to divide decimals to the hundredths (no divisors with decimals) Students are able to estimate products and quotientsRecommended Activity:Problem of the DayScoot ReviewStandards:CC.2.1.5.B.2 – Extend an understanding of operations with whole numbers to perform operations including decimals.Vocabulary:Continue reviewing and reinforcing previous ments: Content: Expressions and PatternsDuration: December (2 weeks)Essential Question:How are patterns used to solve problems?Skills:Write and evaluate numerical expressionsUse the order of operations to evaluate expressionsUse numbers and operation symbols to write verbal phrases as numerical expressionsSolve problems by working backwardsGenerate numerical patterns and identify pattern relationships between corresponding terms of 2 patternsIdentify and extend patterns and sequencesPlot points on a grid to solve real-world problemsGraph ordered pairs on a coordinate planeAssessment:Pre- and Post-AssessmentsPerformance TasksMid-Chapter (formative)QuizStudents are able to evaluate numerical expressions containing exponents, parentheses, and bracketsStudents are able to generate numerical patterns and identify the relationship between corresponding terms in two different patternsStudents are able to graph an ordered pair in the first quadrant on a coordinate plane. Recommended Activity:Students create their own patternsMystery picture (plot points to reveal picture)Standards:CC.2.2.5.A.1 – Interpret and evaluate numerical expressions using order of .2.2.5.A.4 – Analyze patterns and relationships using two .2.3.5.A.1 – Graph points in the first quadrant on the coordinate plane and interpret these points when solving real world and mathematical problems.Vocabulary:Coordinate plane - a plane that is formed when two number lines intersect; Evaluate - to find the value of an expression by replacing variables by numbers; Numerical expression - combination of numbers and operations; Ordered pair - a pair of numbers that is used to name a point on a coordinate grid order of operations; Origin - the point (0,0) on a coordinate plane where the vertical axis meets the horizontal axis; Sequence - a list of numbers that follow a specific pattern; Term - a number in a patternComments: Content: Fractions and DecimalsDuration: January (2 weeks)Essential Question:How are factors and multiples helpful in solving problems?Skills:Determine the common factors and the greatest common factor of a set of numbersGenerate equivalent fractions by writing a fraction in simplest formGuess, check, and revise to solve word problemsDetermine the least common multiples of a set of numbersCompare fractions by using the least common denominatorsUse fraction equivalence to write fractions as decimalsAssessment:Pre- and Post-AssessmentsPerformance TasksMid-Chapter (formative)QuizStudents are able to generate equivalent fractions using the greatest common factorStudents are able to compare fractions by using least common denominatorsRecommended Activity:Factor TreesProvide students with a fraction card; then have students find their equivalent fractionStandards:CC.2.1.5.C.1 – Use the understanding of equivalency to add and subtract .2.1.5.C.2 – Apply and extend previous understandings of multiplication and division to multiply and divide .2.1.5.B.2 – Extend an understanding of operations with whole numbers to perform operations including decimals.Vocabulary:Common factor; Common multiple; Denominator; Equivalent fractions; Fraction; Greatest common factor; Least common multiple; Least common denominatorComments: Content: Add and Subtract FractionsDuration: Jan/February (4 weeks)Essential Question:How can equivalent fractions help me add and subtract fractions?Skills:Add like fractions including mixed numbersSubtract like fractions including mixed numbersUse models to add unlike fractions including mixed numbersAdd unlike fractions including mixed numbersSubtract unlike fractions including mixed numbersSolve problems by determining reasonable answersAssessment:Pre- and Post-AssessmentsPerformance TasksMid-Chapter (formative)QuizStudents will be able to add and subtract like fractions including mixed numbers. Students will be able to add and subtract unlike fractions including mixed numbers. Recommended Activity:Use models to add and subtract fractionStandards:CC.2.1.5.C.1 – Use the understanding of equivalency to add and subtract .2.2.5.A.1 – Interpret and evaluate numerical expressions using order of operations.Vocabulary:Like fractions; Unlike fractionsComments: Content: Multiply and Divide FractionDuration: February/March (3 weeks)Essential Question:What strategies can be used to multiply and divide fractions?Skills:Estimate products of fractionsMultiply whole numbers and fractionsMultiply fraction by a fractionsMultiply mixed numbersMultiplication as scalingDivide whole number by fractionDivided fractions by a whole numberAssessment:Pre- and Post-AssessmentsPerformance TasksMid-Chapter (formative)QuizStudents are able to multiply whole numbers, fractions, and mixed numbersStudents are able to divide whole numbers and fractions using modelsRecommended Activity:Create foldable math skills practice sheetCompare fractions and decimals using a Venn DiagramStandards:CC.2.1.5.C.2 – Apply and extend previous understandings of multiplication and division to multiply and divide fractionsVocabulary:Unit fractionScaling - the process of resizing a number when it is multiplied by a fraction that is greater than or less than one; Fair share - an amount divided equallyComments: Content: MeasurementDuration: March (2 weeks)Essential Question:How can I use measurement conversions to solve real-world problems?Skills:Convert measurements of length within the customary systemConvert measurement of weight within the customary systemEstimate and measure the capacity of liquidsConvert measurements of capacity within the customary systemDisplay measurement data in fractions of a unit on a line plot and solve real-world problemsConvert measurements of length within the metric systemConvert measurement of mass within the metric systemConvert measurement of capacity within the metric systemAssessment:Pre- and Post-AssessmentsPerformance TasksMid-Chapter (formative)QuizStudents will be able to compute multi-step conversions within the same measurement systemStudents will be able to display fractional data on a line plot and determine the fair shareRecommended Activity:Have students stand and use hand motions showing large to small means multiply. Graph measurement data on a line plot. Standards:CC.2.4.5.A.1 – Solve problems using conversions within a given measurement .2.4.5.A.4 – Solve problems involving computation of fractions using information provided in a line plot.Vocabulary:Capacity; Centimeter; Convert; Cup; Customary system; Fair share; Fluid ounces; Foot; Gallon; Gram; Inch; Kilogram; Kilometer; Length; Liter; Mass; Meter; Metric system; Mile; Milligram; Milliliter; Ounce; Pint; Pound; Quart; Ton; Weight; YardComments: Content: PolygonsDuration: April (4 weeks)Essential Question:How does geometry help me solve problems in everyday life?Skills:Classify two-dimensional figures based on propertiesClassify triangles based on attributesMeasure the sides and angles of quadrilateralsClassify quadrilaterals based on attributes, such as congruent sides, parallel sides, and right anglesBuild nets and explore properties of three-dimensional figuresDescribe properties of three-dimensional figuresUse volume formulas to find the volume of rectangular prismsAssessment:Pre- and Post-AssessmentsPerformance TasksMid-Chapter (formative)Quiz Students are able to classify polygons according to their attributesStudents are able to use volume formulas to calculate volume of rectangular prisms and composite figuresRecommended Activity:Quadrilateral sortCut out and build netsStandards:CC.2.3.5.A.2 – Classify two-dimensional figures into categories based on an understanding of their .2.4.5.A.6 – Apply concepts of volume to solve problems and relate volume to multiplication and to addition.Vocabulary:Congruent angles; Congruent figures; Congruent sides; Hexagon; Octagon; Parallelogram; Polygon; Prism; Rectangle; Regular polygon; Rhombus; Square; TrapezoidAttribute- the characteristic of a figure; Base - any side of a parallelogram; Composite figure - a figure made up of 2 or more 3 dimensional figure; Cube - a rectangular prism with 6 faces that are congruent squares; Cubic unit - a unit of measuring volume; Edge - line segment where 2 faces of a 3 dimension figure meet; Face - a flat surface; Net - a two dimensional pattern of a 3 dimensional figure; Three-dimensional figure - a figure that has length, width, and height; Triangular prism - a prism that has triangular bases; Unit cube - a cube with a side length of 1 unit; Vertex - the point where two rays meet in an angle where three or more faces meet on a 3-D figure; Volume - the amount of space inside a 3-D figureComments: Content: Prime FactorizationDuration: May (1 week)Essential Question:What strategies can be used to multiply whole numbers?Skills:Identify and explore patterns in prime factorizationAssessment:Pre- and Post-AssessmentsPerformance TasksQuizStudents will be able to break down a number into its prime factorizationRecommended Activity:Develop factor treesStandards:There is no PA common core standard aligned to this content.Vocabulary:Prime factorization - a way of expressing a composite number as a product of its prime factorsComments: Content: Adding and Subtracting Fractions (with renaming)Duration: May (1 week)Essential Question:How can equivalent fractions help me add and subtract fractions?Skills:Adding mixed numbers with renamingSubtract mixed numbers with renamingAssessment:Pre- and Post-AssessmentsPerformance TasksMid-Chapter (formative)Quiz Students are able to add and subtract mixed numbers with renamingRecommended Activity:Use fractions bars to demonstrate renamingStandards:CC.2.1.5.C.1 – Use the understanding of equivalency to add and subtract fractions.Vocabulary:Continue reviewing and reinforcing previous vocabularyComments: Content: PolygonsDuration: May/June (2 weeks)Essential Question:How does geometry help me solve problems in everyday life?Skills:Measure the sides and angles of trianglesMeasure sides and angles of quadrilateralsAssessment:Pre- and Post-AssessmentsPerformance TasksMid-Chapter (formative)QuizStudents are able to classify triangles based on their angles and length of sidesRecommended Activity:Measure lengths of sides and measure angles of trianglesStandards:CC.2.1.5.C.2 – Apply and extend previous understandings of multiplication and division to multiply and divide fractions.Vocabulary:Acute triangle- a triangle with three acute angles; Obtuse triangle- a triangle with one obtuse angle; Equilateral triangle- a triangle with three congruent sides; Isosceles triangle- a triangle with at least 2 sides the same length; Scalene triangle- a triangle with no congruent sides; Right triangle- a triangle with one right anglesComments: ................
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