21^st CENTURY

5^th Grade MATH

CONTENT STANDARDS AND OBJECTIVES FOR WEST VIRGINIA SCHOOLS (2520.2)

Janet Benincosa, TI Specialist

The West Virginia Standards for 21st Century Learning include the following components: 21st Century Content Standards and Objectives and 21st Century Learning Skills and Technology Tools. 

All West Virginia teachers are responsible for classroom instruction that integrates learning skills, technology tools and content standards and objectives. 

Fifth Grade

Grade 5		Mathematics
Standard 1		Number and Operations
M.S.5.1		Through communication, representation, reasoning and proof, problem solving, and making connections within and beyond the field of mathematics, students will · demonstrate understanding of numbers, ways of representing numbers, and relationships among numbers and number systems, · demonstrate meanings of operations and how they relate to one another, and · compute fluently and make reasonable estimates.
Performance Descriptors (M.PD.5.1)
Distinguished				Above Mastery			Mastery		Partial Mastery	Novice
Fifth grade students at the distinguished level in mathematics compare and contrast, analyze and summarize properties of whole numbers, fractions, mixed numbers and decimals. They understand place value and estimate, and critique solutions to real-world problems involving whole numbers, decimals, fractions, and percents. They examine, identify and develop the divisibility rules, greatest common factor and lowest common multiple. They construct, design and solve application problems with fractions, mixed numbers and decimals. They select the most efficient strategy to solve multi-digit whole number division problems and justify the strategy used. They demonstrate fluency in addition, subtraction, multiplication and division of whole numbers and relate this fluency to the properties of whole numbers.				Fifth grade students at the above mastery level in mathematics compare and contrast and analyze whole numbers, fractions, mixed numbers and decimals. They understand place value and estimate and formulate solutions to real-world problems involving whole numbers, decimals, fractions, and percents. They examine and identify the divisibility rules, greatest common factor and lowest common multiple. They create and solve application problems with fractions, mixed numbers and decimals. They solve multi-digit whole number division problems using a variety of strategies, including the standard algorithm, make comparisons of strategies used. They demonstrate fluency in addition, subtraction, multiplication and division of whole numbers.			Fifth grade students at the mastery level in mathematics compare whole numbers, fractions, mixed numbers and decimals. They understand place value and estimate solutions to real-world problems involving whole numbers, decimals, fractions, and percents. They identify the divisibility rules, greatest common factor and lowest common multiple. They solve application problems with fractions, mixed numbers and decimals. They solve multi-digit whole number division problems using a variety of strategies, including the standard algorithm and justify the solutions They demonstrate fluency in addition, subtraction, multiplication and division of whole numbers.		Fifth grade students at the partial mastery level in mathematics identify whole numbers, fractions, mixed numbers and decimals. They identify place value and apply solutions to real-world problems involving whole numbers, decimals, fractions, and percents. They explain the divisibility rules, greatest common factor and lowest common multiple. They explain application problems with fractions, mixed numbers and decimals. They solve multi-digit whole number division problems using a variety of strategies, including the standard algorithm They solve addition, subtraction, multiplication and division of whole numbers with accuracy.	Fifth grade students at the novice level in mathematics recognize whole numbers, fractions, mixed numbers and decimals. They confirm place value and recognize solutions to real-world problems involving whole numbers, decimals, fractions, and percents. They state the divisibility rules, greatest common factor and lowest common multiple. They confirm that application problems contain fractions, mixed numbers and decimals. They solve multi-digit whole number division problems They solve addition, subtraction, multiplication and division of whole numbers.
	Objectives	Students will
	M.O.5.1.1	read, write, order and compare all whole numbers, fractions, mixed numbers and decimals using multiple strategies (e.g., symbols, manipulatives, number line).
	M.O.5.1.2	demonstrate an understanding of place value of each digit utilizing standard and expanded form in any whole number using powers of 10 [(3 X 10^5)+ (4 X 10^3) + 7 X 10^2) + (1 X 10^1) + 6].
	M.O.5.1.3	estimate solutions to problems involving whole numbers, decimals, fractions, and percents to determine reasonableness using benchmarks.
	M.O.5.1.4	use inductive reasoning to identify the divisibility rules of 2, 3, 5, 9 and 10 and apply the rules to solve application problems.
	M.O.5.1.5	determine and apply greatest common factor and lowest common multiple to write equivalent fractions and to real-world problem situations.
	M.O.5.1.6	model and write equivalencies of fractions decimals, percents, and ratios.
	M.O.5.1.7	analyze and solve application problems and justify reasonableness of solution in problems involving addition and subtraction of: fractions and mixed numbers decimals.
	M.O.5.1.8	apply the distributive property as it relates to multiplication over addition.
	M.O.5.1.9	solve multi-digit whole number division problems using a variety of strategies, including the standard algorithm and justify the solutions.
	M.O.5.1.10	demonstrate fluency in addition, subtraction, multiplication and division of whole numbers.
	M.O.5.1.11	solve real-world problems involving whole numbers, decimals and fractions using multiple strategies and justify the reasonableness by estimation.
	Grade 5	Mathematics
	Standard 2	Algebra
	M.S.5.2	Through communication, representation, reasoning and proof, problem solving, and making connections within and beyond the field of mathematics, students will demonstrate understanding of patterns, relations and functions, represent and analyze mathematical situations and structures using algebraic symbols, use mathematical models to represent and understand quantitative relationships, and analyze change in various contexts.
Performance Descriptors (M.PD.5.2)
Distinguished				Above Mastery	Mastery			Partial Mastery		Novice
Fifth grade students at the distinguished level in mathematics use inductive reasoning to find missing elements in patterns, analyze results and construct their own patterns. They develop and determine rules from an input/output model as well as from an abstract model and identify and analyze square, prime and composite numbers.				Fifth grade students at the above mastery level in mathematics use inductive reasoning to find missing elements in patterns and analyze results. They develop and determine rules from an input/output model, identify, and describe square, prime and composite numbers.	Fifth grade students at the mastery level in mathematics use inductive reasoning to find missing elements in patterns. They infer rules from an input/output model, identify, and describe square, prime and composite numbers.			Fifth grade students at the partial mastery level in mathematics use inductive reasoning to confirm missing elements in patterns. They determine rules from an input/output model and recognize square, prime and composite numbers.		Fifth grade students at the novice level in mathematics use inductive reasoning models to label missing elements in patterns. They name rules from an input/output model and verify square, prime and composite numbers.
	Objectives	Students will
	M.O.5.2.1	use inductive reasoning to find missing elements in a variety of patterns (e.g., square numbers, arithmetic sequences).
	M.O.5.2.2	given an input/output model using two operations, determine the rule, output or input.
	M.O.5.2.3	solve simple equations and inequalities using patterns and models of real-world situations, create graphs of the equations and interpret the results.
	M.O.5.2.4	model identify and describe square, prime and composite numbers.
	Grade 5	Mathematics
	Standard 3	Geometry
	M.S.5.3	Through communication, representation, reasoning and proof, problem solving, and making connections within and beyond the field of mathematics, students will · analyze characteristics and properties of two- and three-dimensional geometric shapes and develop mathematical arguments about geometric relationships, · specify locations and describe spatial relationships using coordinate geometry and other representational systems, · apply transformations and use symmetry to analyze mathematical situations, and · solve problems using visualization, spatial reasoning, and geometric modeling.
Performance Descriptors (M.PD.5.3)
Distinguished			Above Mastery		Mastery			Partial Mastery		Novice
Fifth grade students at the distinguished level in mathematics classify, compare, develop and critique the properties of triangles and construct and compare 3 dimensional shapes. They construct, analyze and compare designs with symmetry and construct circles. They draw and construct similar figures using a scale that involves reducing or enlarging by fractional units.			Fifth grade students at the above mastery level in mathematics classify, compare and determine the properties of triangles and construct 3 dimensional shapes. They create and analyze designs with symmetry and construct circles. They draw similar figures using a scale that involves reducing.		Fifth grade students at the mastery level in mathematics classify and compare triangles and construct 3 dimensional shapes. They create designs with symmetry and construct circles. They draw similar figures using a scale.			Fifth grade students at the partial mastery level in mathematics model triangles and describe 3 dimensional shapes. They identify designs with symmetry and draw circles. They identify similar figures using a scale.		Fifth grade students at the novice level in mathematics recognize triangles and identify 3 dimensional shapes. They recognize designs with symmetry and circles. They recognize similar figures using a scale.
	Objectives	Students will
	M.O.5.3.1	classify and compare triangles by sides and angles; measure the angles of a triangle using a protractor.
	M.O.5.3.2	construct and analyze three-dimensional shapes using properties (i.e. edges, faces or vertices).
	M.O.5.3.3	create a design with more than one line of symmetry.
	M.O.5.3.4	construct a circle with a given radius or diameter.
	M.O.5.3.5	draw a similar figure using a scale, given a real-world situation.
	Grade 5	Mathematics
	Standard 4	Measurement
	M.S.5.4	Through communication, representation, reasoning and proof, problem solving, and making connections within and beyond the field of mathematics, students will demonstrate understanding of measurable attributes of objects and the units, systems, and processes of measurement, and apply appropriate techniques, tools and formulas to determine measurements.
Performance Descriptors (M.PD.5.4)
Distinguished				Above Mastery		Mastery		Partial Mastery		Novice
Fifth grade students at the distinguished level in mathematics estimate and measure, compare, order and construct lengths up to 1/8 of an inch. They find, develop and analyze strategies to determine volume of a rectangular prism. They construct and solve real-world problems requiring conversion within a system of measurement and interpret the relationship between conversions. They estimate and measure weight/mass of real objects in ounces, pounds, grams and kilograms and compare properties of each unit. They estimate and calculate elapsed time from real-world settings, create real-world problems and analyze the solution. They design a scale drawing and determine the actual measurements of a figure from a scale drawing.				Fifth grade students at the above mastery level in mathematics estimate and measure, compare, and order lengths up to 1/8 of an inch. They find and develop strategies to determine volume of a rectangular prism. They construct and solve real-world problems requiring conversion within a system of measurement. They estimate and measure weight/mass of real objects in ounces, pounds, grams and kilograms and compare properties of each unit. They estimate and calculate elapsed time from real-world settings and create in context problems. They create a scale drawing and determine the actual measurements of a figure from a scale drawing.		Fifth grade students at the mastery level in mathematics estimate and measure lengths up to 1/8 of an inch. They find strategies to determine volume of a rectangular prism. They solve real-world problems requiring conversion within a system of measurement. They estimate and measure weight/mass of real objects in ounces, pounds, grams and kilograms. They estimate and calculate elapsed time from real-world settings and determine the actual measurements of a figure from a scale drawing.		Fifth grade students at the partial mastery level in mathematics identify estimate and measure lengths up to 1/8 of an inch. They determine volume of a rectangular prism, given a strategy. They identify real-world problems requiring conversion within a system of measurement. They measure weight/mass of real objects in ounces, pounds, grams and kilograms. They estimate elapsed time if given choices from real-world settings and determines the actual measurements of a figure from a scale drawing.		Fifth grade students at the novice level in mathematics identify lengths up to 1/4 of an inch. They replicate how to find volume of a rectangular prism. They recognize real-world problems requiring conversion within a system of measurement. They recognize that weight/mass of real objects is in ounces, pounds, grams or kilograms. They recognize time has elapsed in real-world settings and recognizes measurements of a figure from a scale drawing are different.
	Objectives	Students will
	M.O.5.4.1	estimate, measure, compare, order and draw lengths of real objects in parts of an inch up to 1/8 of an inch and millimeters.
	M.O.5.4.2	model, calculate and compare area of triangles and parallelograms using multiples strategies (including, but not limited to, formulas).
	M.O.5.4.3	develop strategies (i.e. finding number of same sized units of volume)to determine the volume of a rectangular prism; solve application problems involving estimating or measuring volume of rectangular prisms.
	M.O.5.4.4	describe the effects on the measurements of a two-dimensional shape (such as its perimeter and area) when the shape is changed in some way, justify changes.
	M.O.5.4.5	solve real-world problems requiring conversions within a system of measurement.
	M.O.5.4.6	estimate and/or measure the weight/mass of real objects in ounces, pounds, grams, and kilograms.
	M.O.5.4.7	collect, record, estimate and calculate elapsed times from real-world situations (with and without technology)
	M.O.5.4.8	determine the actual measurements of a figure from a scale drawing, using multiple strategies.
	Grade 5	Mathematics
	Standard 5	Data Analysis and Probability
	M.S.5.5	Through communication, representation, reasoning and proof, problem solving, and making connections within and beyond the field of mathematics, students will formulate questions that can be addressed with data and collect, organize, and display relevant data to answer them, select and use appropriate statistical methods to analyze data, develop and evaluate inferences and predictions that are based on models, and apply and demonstrate an understanding of basic concepts of probability.
Performance Descriptors (M.PD.5.5)
Distinguished			Above Mastery		Mastery			Partial Mastery		Novice
Fifth grade students at the distinguished level in mathematics design experiments or surveys to collect, interpret and analyze data from a problem-solving situation. They design, construct and manipulate sample spaces to predict the probability of a real-world simulation. They collect and organize data into a circle graph, draw conclusions, interpret results and summarize findings from similar data sets.			Fifth grade students at the above mastery level in mathematics collect, interpret and analyze data from a problem-solving situation. They design and construct sample spaces to predict the probability of a real-world simulation. They collect and organize data into a circle graph, draw conclusions and interpret results.		Fifth grade students at the mastery level in mathematics collect and interpret data from a problem-solving situation. They construct sample spaces to predict the probability of a real-world simulation. They organize data into a circle graph and draw conclusions.			Fifth grade students at the partial mastery level in mathematics collect data from a problem-solving situation. They use existing sample spaces to predict the probability of a real-world simulation. They organize data into a circle graph.		Fifth grade students at the novice level in mathematics display data from a problem-solving situation. They identify existing sample spaces to recognize a real-world simulation. They identify data.
	Objectives	Students will
	M.O.5.5.1	construct a sample space to predict the probability of a real-world simulation and test the prediction with experimentation.
	M.O.5.5.2	construct, read, and interpret tables, charts, and graphs including stem and leaf plots to draw reasonable inferences or verify predictions.
	M.O.5.5.3	collect and organize real-world data to construct a circle graph (with and without technology), present data and draw conclusions.