web viewstudents will practice word problems involving addition, subtraction, multiplication and...

Pine Island Public SchoolsC u r r i c u l u m P o w e r S t a n d a r d s

Course: 5th grade Math Textbook: Macmillon McGraw-Hill Math Connects Date: Updated October 2014

Power Standard: I can solve real-world and mathematical problems requiring addition, subtraction, multiplication and division of multi-digit whole numbers.

5.1.1.4

Key Vocabulary Learning Targets Assessment TextbookTest Specifications:Vocabulary from previous grades

Additional Textbook Vocab:Chapter 2 (none that apply to this power standard)Chapter 3 (factor and product)Chapter 4 (quotient, dividend, divisor)

Supplement Vocab:division, remainder, divisible

Students will practice word problems involving addition, subtraction, multiplication and division Students will learn a variety of problem-solving strategies such as (but not limited to):

- Act it out- Draw a picture- Find a pattern- Create an equation- Delete extra information- Identify missing information

Students will participate in real-world situations involving the computation of addition, subtraction, multiplication, division and combinations of the four Students will continue to practice basic computation of addition, subtraction, multiplication and division in a NON-WORD PROBLEM format Student “I can” statements:

- I can divide multi-digit numbers- I can solve real-world problems

using addition- I can solve real-world problems

using subtraction- I can solve real-world problems

using multiplication- I can solve real-world problems

using division

Formative:Daily homework assignments from workbookQuizzes in chapter 2, 3 and 4

OR supplement curriculum in replacement of Chapter 3 (depending on the assessment of prior knowledge from the group of students)

Hands-on learning day reflectionsAdditional Supplements

Summative:Chapter 2 test (addition and subtraction)Chapter 3 test (multiplication)Chapter 4 test (division)

Chapter 2Chapter 3Chapter 4

Additional Supplements:Problem Solving Techniques and Stations

Multiplication Review Packet

Lattice Multiplication

Multiplication Stations

Draw a picture (multiplication)

Base-ten division

Partial Quotient Division

Interpreting the remainder practice



Power Standard: I can read, write, model, represent, compare and order fractions and decimals by locating these numbers on a number line. (Millions to Millionths; Denominators limited to 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20)

5.1.2.15.1.2.3

Key Vocabulary Learning Targets Assessment TextbookTest Specifications:Place Value

Additional Textbook Vocab:Chapter 1 (decimal, equations, expanded form, inequality, place value, standard form, value)Chapter 8 (denominator, fractions, improper fractions, mixed number, numerator)Chapter 9 (factor, multiple, common factors/multiples, prime/composite, prime factorization, GCF, LCM, common denominator)

Students will learn the names of the place values Students will be able to read numbers out loud using the word AND for the decimal point and correctly identifying decimals in their given place value Students can place decimals and fractions on a number line to assist when comparing and ordering Students can model and represent decimals and fractions as part of a whole Students will be able compare decimals with fractions, improper fractions and mixed numbers (by using conversion skills) Students will be able to order a set of numbers that include decimals, fractions, improper fractions and mixed numbers (by using conversion skills) Student “I can” statements:

- I can name the place values- I can read and write decimals

according to which place value they are in

- I can order decimals- I can order fractions

Formative:Daily homework assignments from workbookHands-on learning day reflectionsAdditional SupplementsPlace Value Name QuizQuizzes in Chapter 1, 8 and 9 quizzesVideotaping students individually reading and writing numbers

Summative:Chapter 1 test (names of place value, reading and writing decimals according to their place value, comparing and ordering decimals, locating decimals on a number line)

Chapter 8 test (basic fraction knowledge – reading and writing, modeling and representing fractions, locating fractions on a number line)Chapter 9 test (comparing and ordering fractions by creating common denominators)

Converting Decimals to Fractions, Comparing and Ordering Decimals with Fractions, Improper Fractions and Mixed Numbers Supplement Unit Test


Additional Supplements:Decimal representation with base-ten blocks (tenths, hundredths and thousandths)

Silent Decimal Line-up

Fraction Modeling with foam fractions

Comparing and Ordering fractions by finding a common denominator (using the LCM)

Converting Decimals to Fractions, Comparing and Ordering Decimals with Fractions, Improper Fractions and Mixed Numbers Supplement Unit



Power Standard: I can use my knowledge of place value to round and estimate whole numbers, fractions, mixed numbers and decimals to come up with a reasonable answer. (Denominators limited to 2, 3, 4, 5, 6, 8, 10, 12)

5.1.1.35.1.2.55.1.3.3


Additional Textbook Vocab:Chapter 2 (round, estimate, compatible numbers, compensation)Chapter 3 (factor and product)Chapter 4 (quotient, dividend, divisor)Chapter 8 (denominator, fractions, improper fractions, mixed number, numerator)Chapter 10 (GCF, unlike fractions, whole number)

Students will be able to round decimals to nearest tenth, hundredth and thousandth Students will be able to round fractions and mixed numbers (as well as improper fractions converted to mixed numbers) Students will estimate mathematical problems (addition, subtraction, multiplication, division, sums/differences of decimals and fractions) to come up with a reasonable answer Students will give answers to estimations problems using the word “about” Student “I can” statements:- I can estimate numbers to come up with a reasonable answer- I can round numbers to the nearest tenth, hundredth, and thousandth- I can round fractions- I can estimate the sums and differences of decimals- I can estimate the sums and differences of fractions

Formative:Daily homework assignments from workbookQuizzes in chapter 2, 3, 4, 8 and 10Rounding Steps QuizHands-on learning day reflectionsAdditional Supplements

Summative:Chapter 2 test (rounding decimals, estimating addition and subtraction problems, estimating sums/differences of decimals)

Chapter 3 test (estimating products)

Chapter 4 test (estimating quotients)

Chapter 8 (rounding fractions)

Chapter 10 (estimating sums/differences of fractions by using rounding skills from chapter 8 in addition to adding and subtracting fraction knowledge from chapter 10)

Chapter 2Chapter 3Chapter 4Chapter 8Chapter 10

Additional Supplements:Rounding Process

Rounding and Estimating by Ordering Pizza

Rounding fractions using foam fractions

Power Standard: I can recognize and write equivalent fractions and decimals. (Denominators 5.1.2.4



limited to 2, 3, 4, 5, 6, 8, 10, 15, 16, 20, 25, 50, 100)Key Vocabulary Learning Targets Assessment TextbookTest Specifications:Place Value

Additional Textbook Vocab:Chapter 1 (decimals, equivalent decimals)Chapter 9 (equivalent fractions, simplest form)

Students will recognize what equivalent decimals are by modeling these numbers using base-ten representation Students will recognize a pattern in creating equivalent decimals Students will be able to generate and identify equivalent decimals Students will recognize what equivalent fractions are by modeling these numbers with fraction pieces Students will recognize a pattern in creating equivalent fractions Students will be able to generate and identify equivalent fractions Students will relate giving a fraction in simplest form/lowest terms with equivalent fractions Student “I can” statements:

- I know what equivalent decimals are and can create them- I know what equivalent fractions are and can create them

Formative:Daily homework assignments from workbookQuizzes in chapter 1 and 9Hands-on learning day reflectionsAdditional Supplements

Summative:Chapter 1 test (equivalent decimals)

Chapter 9 test (equivalent fractions)

Chapter 1Chapter 9

Additional Supplements:Decimal representation with base-ten blocks (tenths, hundredths and thousandths)

Fraction Modeling with foam fractions

Equivalent Fractions with egg cartons

Equivalent Fraction Match/Memory Game



Power Standard: I can divide a multi-digit number creating and converting its remainder as both a fraction and decimal.

5.1.1.15.1.1.2

Key Vocabulary Learning Targets Assessment TextbookTest Specifications:Remainder

Additional Textbook Vocab:Chapter 1 (decimal, place value)Chapter 4 (quotient, dividend, divisor)Chapter 8 (fraction, numerator, denominator)Chapter 9 (none that apply to this power standard)

Supplement Vocab:division, remainder, divisible

Students will learn what division is (separating a number into groups) Students will learn how to divide multi-digit numbers the involve a remainder Students will be able to write remainders as both decimals and as fractions Students will be able to divide multi-digit numbers and determine the best way to give its remainder (as a remainder, decimal or fraction) Students will be able to convert between decimals and fractions Student “I can” statements:

- I can divide a number and find an answer with a remainder- I can divide a number and put it in fraction form

Formative:Daily homework assignments from workbookDaily homework from Conversion (Decimals, Fractions, Percentages) Supplement UnitQuizzes in chapter 1, 4, 8 and 9Hands-on learning day reflectionsAdditional Supplements

Summative:Chapter 1 test (one introductory lesson on converting fractions to decimals)

Chapter 4 test (division with a remainder, interpreting the remainder)

Chapter 8 test (comparing fractions with division, writing the remainder of a division problem as a fraction)

Chapter 9 (one introductory lesson on converting decimals to fractions)

Converting Decimals to Fractions, Comparing and Ordering Decimals with Fractions, Improper Fractions and Mixed Numbers Supplement Unit Test

Chapter 1Chapter 4Chapter 8Chapter 9

Additional Supplements:Dividing and interpreting the remainder with base-ten units

Interpreting the remainder story problems (through acting, base-10, pictures, etc)

Converting Decimals to Fractions, Comparing and Ordering Decimals with Fractions, Improper Fractions and Mixed Numbers Supplement Unit



Power Standard: I can add and subtract real-world and mathematical problems using fractions, mixed numbers and decimals. (Denominators limited to 2, 3, 4, 5, 6, 8, 10, 12)

5.1.2.25.1.3.4


Additional Textbook Vocab:Chapter 2 (addend, compatible numbers, compensation, difference, sum)Chapter 8 (denominator, fraction, improper fraction, mixed number, numerator)Chapter 9 (greatest common factor, multiple, simplest form)Chapter 10 (unlike fractions)

Students will be able to add and subtract numbers that include decimals, fractions and/or mixed numbers (common and uncommon denominators) Students will be able to add and subtract decimals, fractions and/or mixed numbers that appear in word problems and real-world situations (common and uncommon denominators) Students will be able to add or subtract improper fractions and give the answer as a mixed number. Students will know be able to find common denominators so that addition and subtraction can occur in fractions and mixed numbers. Student “I can” statements:

- I can add decimals- I can subtract decimals- I can distinguish the difference between mixed numbers and improper fractions- I can add fractions- I can subtract fractions- I can solve real-world problems by adding decimals- I can solve real-world problems by subtracting decimals- I can solve real-world problems by adding fractions- I can solve real-world problems by subtracting fractions

Formative:Daily homework assignments from workbookQuizzes in chapter 2, 8, 9 and 10Hands-on learning day reflectionsAdditional Supplements

Summative:Chapter 2 test (addition and subtraction of decimals)

Chapter 8 test (writing improper fractions as mixed numbers)

Chapter 9 test (finding common denominators)

Chapter 10 test (adding and subtraction fractions and mixed numbers; both with common and uncommon denominators)

Chapter 2Chapter 8Chapter 9Chapter 10

Additional Supplements:Math Store – adding/subtracting decimals

Adding/Subtracting Fractions with foam fractions

Yummy Math – adding/subtracting fractions

Prime and Composite Number Hands-on

Equivalent Fraction Egg Cartons



Power Standard: I can apply the commutative, associative and distributive properties along with order of operations to solve numerical expressions.

5.2.2.1

Key Vocabulary Learning Targets Assessment TextbookTest Specifications:Expression

Additional Textbook Vocab:Chapter 2 (Associative and Commutative Properties)Chapter 3 (Distributive Property)Chapter 5 (order of operations)

Students will apply the commutative and associative properties with addition. Example:

4 + 5 = 9; 5 + 4 = 9 (2+3)+5 = 5+ 5 = 10; 2+(3+5) = 2 + 8 = 10 Students will apply the commutative, associative and distributive properties with multiplication.

Example: 8 x 2 = 16; 2 x 8 = 16 (4x5)x2= 20x2= 40; 4x(5x2)= 4 x 10= 40 2 x (7+3) = (2x7) + (2x3) = 14+6 = 20 OR 2 x (7+3) = 2 x 10 = 20 Students will know the order of operations and apply them when solving numerical expressions. Student “I can” statements:

- I know what the commutative property is- I can use the associative property- I can use the distributive property

Formative:Daily homework assignments from workbookQuizzes in chapter 2, 3 and 5Hands-on learning day reflectionsAdditional Supplements

Summative:Chapter 2 Test (Addition Properties)

Chapter 3 Test (Multiplication Properties)

Chapter 5 Test (Order of Operations)


Additional Supplements:Property Index Card Game – additional properties

Distributive Property Supplement materials – multiplication stations

Distributive Property additional teaching

Order of Operation Supplement materials



Power Standard: I can understand and interpret real-world and mathematical equations and inequalities involving variables and whole numbers.

5.2.3.15.2.3.25.2.3.3

Key Vocabulary Learning Targets Assessment TextbookTest Specifications:InequalityExpression

Additional Textbook Vocab:Chapter 5 (evaluate, expression, variable)Chapter 6 (defining the variable, equation, solution)

Students will learn what a variable is. Students will solve inequalities using variables and whole numbers. Students will be able to solve simple algebraic equations that use variables and whole numbers. Students will be able to solve simple algebraic word problems and real-world situations using variables and whole numbers. Student “I can” statements:- I can solve equations and inequalities using variables

Formative:Daily homework assignments from workbookDaily homework assignments from Hands-on Algebra UnitQuizzes in chapter 5 and 6Hands-on learning day reflectionsAdditional Supplements

Summative:Chapter 5 Test (Addition expressions, multiplication, expressions, more algebraic expressions)

Chapter 6 Test (addition and subtraction equations, inequalities, multiplication equations)

Hands-on Algebra Test

Chapter 5Chapter 6

Additional Supplements:Hands-on Algebra Unit

Power Standard: I can use a coordinate plane to graph ordered pairs. 5.2.1.2Key Vocabulary Learning Targets Assessment TextbookTest Specifications:Ordered PairGraph

Additional Textbook Vocab:Chapter 6 (coordinate grid, graph, ordered pair, x-coordinate, y-coordinate)

Students will be able to graph ordered pairs on a coordinate plane. Students will be able to locate points on a coordinate plane by giving its ordered pair. Student “I can” statements:

- I can graph ordered pairs

Formative:Daily homework assignments from workbookQuizzes in chapter 6Hands-on learning day reflectionsAdditional Supplements

Summative:Chapter 6 Test (ordered pairs, graphing function)

Chapter 6

Additional Supplements:Mystery Graphing Picture



Power Standard: I can describe, classify and draw 3-D figure based on the faces, edges and vertices it has. (Cube, cone, cylinder, prism and pyramids – limited to triangular, rectangular, pentagonal, hexagonal and octagonal)

5.3.1.1

Key Vocabulary Learning Targets Assessment TextbookTest Specifications:CubePrismPyramidConeCylinderEdgeFaceBaseThree-dimensionalTriangularRectangular

Additional Textbook Vocab:Chapter 14 (base, cone, cylinder, polyhedron, prism, rectangular prism, three-dimensional figure)

Students will able to identify and name a variety of 3-D objects. Students will know the differences and be able to locate faces, edges and vertices on a variety of 3-D objects. Students will make their best effort at drawing a variety of 3-D objects. Student “I can” statements:

- I can describe 3-D figures by how many edges, faces and vertices they have- I can name and draw 3-D figures


Summative:Chapter 14 Test (three-dimensional figures)

Chapter 14

Additional Supplements:3-D figure Stations



Power Standard: I can determine the area of triangles, quadrilaterals and other closed figures that can be broken down into triangular and quadrilateral pieces.

5.3.2.1

Key Vocabulary Learning Targets Assessment TextbookTest Specifications:Formula

Additional Textbook Vocab:Chapter 14 (area, polygon)

Students will know that area is counting the number of square units within a closed figure. Students will learn and use the area formula to find the area of a rectangle. Students will learn that triangles are simply half of a rectangle, therefore understanding the formula for the area of triangles. Students will learn and use the area formula for triangles or closed figures that can be broken down into rectangles and triangles. Student “I can” statements:

- I can find the area of triangles- I can find the area of other objects using the area of triangles


Summative:Chapter 14 Test (area or rectangles, squares and parallelograms)

Chapter 14

Additional Supplements:Area of Triangles – cutting out graph paper rectangles and slicing them in half then creating a triangle

Area of Polygons



Power Standard: I can determine the surface area and volume of rectangular prisms. 5.3.1.25.3.2.25.3.2.35.3.2.4

Key Vocabulary Learning Targets Assessment TextbookTest Specifications:NetCylinderCubePrismPyramidEdgeFaceBaseThree-dimensionalTriangularRectangularSurface AreaVolumeHeight

Additional Textbook Vocab:Chapter 14 (area, base, cylinder, polyhedron, prism, rectangular prism, surface area, three-dimensional figure, volume)

Students will learn that surface area is simply adding up the area of each side to find the area of the entire surface. Students will learn and use the formula for surface area of rectangular prisms. Students will know that surface area is measure in square units. Students will learn that volume is the amount of cubic units that can fit inside of a 3-D object. Students will learn and use the formula for volume of rectangular prisms. Student “I can” statements:

- I can find the volume of a rectangular prism- I can find the surface area of a rectangular prism


Summative:Chapter 14 Test (volumes of prisms, surface area of prisms)

Chapter 14

Additional Supplements:Surface Area Project – various rectangular prisms

Volume representation through layered base-ten blocks to emphasize the necessity of the three parts of the formula (length, width, height)



Power Standard: I know and can use the definitions of mean, median and range to apply to a set of data.

5.4.1.1

Key Vocabulary Learning Targets Assessment TextbookTest Specifications:MeanMedianRangeMinimumMaximum

Additional Textbook Vocab:Chapter 7 (data, mean, median, mode, range)

Students will be able to take a set of data and organize it so that they will be able find its mean, median and range. Students will know to first organize the data from least to greatest. Students will learn and use strategies when finding the:

- mean (add up all of the data points, divide by how many data points there are)

- median (find the middle number after organizing the data. If there are an even amount of data points, find the middle number between to the two middle data points)

- range (take the largest data point and subtract the smallest data point)

Student “I can” statements:- I can define mean, median and range, and can use these with data


Summative:Chapter 7 Test (mean, median, mode)

Chapter 7

Additional Supplements:Science variables unit – collecting, organizing, graphing and analyzing data from in-class FOSS experiments (flippers and swingers) as well as at home science fair project



Power Standard: I can create and analyze patterns, rules, tables and graphs (bar and line) by applying understanding of whole numbers, fractions and decimals.

5.2.1.15.4.1.2

Key Vocabulary Learning Targets Assessment TextbookTest Specifications:Double-bar graphLine Graph

Additional Textbook Vocab:Chapter 5 (function table, input, output)Chapter 7 (bar graph, data, frequency table, line graph, line plot, pictograph)

Students will relate algebra and their knowledge of variables to creating function tables. Students will be able to take an input number, apply a rule, and find an output number. Students should be able to work this in reverse order as well. Students will be able to create a variety of graphs based on the data provided. Students will be able to analyze data and decide which graph is the best for representing that data. Student “I can” statements:- I can make an input/output table- I can create and read bar graphs- I can create and read line graphs

Formative:Daily homework assignments from workbookQuizzes in chapter 5 and 7Hands-on learning day reflectionsAdditional Supplements

Summative:Chapter 5 Test (function tables, functions representing change)

Chapter 7 Test (line plots, frequency tables, scales and intervals, bar graphs/double bar graphs, line graphs/double line graphs, using the appropriate graph)

Chapter 5 and 7

Additional Supplements:Creating Function Machines – to create and apply function rules

Science variables unit – collecting, organizing, graphing and analyzing data from in-class FOSS experiments (flippers and swingers) as well as at home science fair project

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