Riverview School District Report Card Benchmarks Math Fifth Grade

Riverview School District Report Card Benchmarks Math Fifth Grade Report Card Expectations Mid-Year Benchmark End-of-year Standard Demonstrates Effort Toward Quality. Understands the concepts and values of decimals and fractions; addition and subtraction of fractions. GLE: 1.1.1, 1.1.2, 1.1.5, 1.1.6, 1.1.7, part of 1.1.8 working to his/her potential using time wisely sustained focus during independent work time taking pride in his/her work working carefully Apply appropriate end-of-year standards from those units on decimals and fractions that were presented to students by the mid-year benchmark working to his/her potential using time wisely sustained focus during independent work time taking pride in his/her work working carefully representing mixed numbers, proper and improper fractions, and decimals using words, pictures, models, and/or numbers making a model when given a symbolic representation or writing a fraction or decimal when given a number line, picture, or model explaining how the value of a fraction changes in relationship to the size of the whole explaining the value for a given digit and/or showing how to read and write decimals to at least the thousandths place representing improper fractions as mixed numbers and mixed numbers as improper fractions ordering decimals, proper and improper fractions, and/or mixed numbers with denominators 2, 3, 4, 5, 6, 10, 12, and/or 15 using symbolic representations, number lines, or pictures identifying and/or explaining the relationship among equivalent decimals and fractions explaining why one fraction or decimal is greater than, less than, or equal to another fraction or decimal showing how factors and multiples can be used to name equivalent fractions representing addition and subtraction of fractions with denominators of 2, 4, 8 or 2, 3, 6, 12 or 2, 5, 10 12/30/06 1 Fifth Grade

Understands the concepts and values of decimals and fractions; addition and subtraction of fractions. (Continued) (continued on next page) representing or explaining addition and subtraction of non-negative decimals through thousandths using words, pictures, models, or numbers explaining a strategy for adding and subtracting fractions selecting and/or using an appropriate operation(s) to show understanding of addition and subtraction of non-negative decimals and/or fractions explaining the relationship between addition and subtraction of non-negative decimals and fractions translating a picture or illustration into an equivalent symbolic representation of addition and subtraction of non-negative fractions and decimals adding and subtracting non-negative decimals and like-denominator fractions with denominators of 2, 3, 4, 5, 6, 8, 10, 12, and/or 15 finding sums or differences of decimals or like-denominator fractions in given situations calculating sums of two numbers with decimals to the thousandths or three numbers with decimals to hundredths calculating difference of numbers with decimals to thousandths selecting and using appropriate tools (e.g., mental computation, estimation, calculators, manipulatives, and paper and pencil) to compute in a given situation explaining why a selected strategy or tool is more efficient or more appropriate than another strategy or tool for a situation describing strategies for mentally adding or subtracting non-negative decimals and/or like-denominator fractions explaining or describing a strategy used for estimation involving addition and subtraction of non-negative decimals and like-denominator fractions 12/30/06 2 Fifth Grade

Applies computation skills using addition, subtraction, multiplication, and division with fluency. adding, subtracting, multiplying, and dividing basic facts quickly and with fluency applying addition, subtraction, multiplication, and division facts when solving for larger amounts adding, subtracting, multiplying, and dividing basic facts quickly and with fluency applying addition, subtraction, multiplication, and division facts when solving for larger amounts Understands and applies appropriate strategies and tools for multiplication and division of larger numbers. GLE: 1.1.3, 1.1.8 using the concepts of odd and even numbers to check for divisibility Illustrating prime or composite numbers by creating a physical model identifying prime or composite numbers between 1 and 100 and explain why a whole number is prime or composite explaining how to find the least common multiple (LCM) and greatest common factor (GCF) of two numbers using factors, multiples, and prime and composite numbers in a variety of situations factoring a number into its prime factorization or into factor pairs explaining or showing whether one number is a factor of another number explaining or demonstrating why a number is prime or composite explaining when an estimation or exact answer is or is not appropriate using a variety of estimation strategies to predict an answer prior to computation using estimation to verify the reasonableness of calculated results computing to check the reasonableness of estimated answers for a given situation explaining an appropriate adjustment when an estimate and a computation do not agree using the concepts of odd and even numbers to check for divisibility Illustrating prime or composite numbers by creating a physical model identifying prime or composite numbers between 1 and 100 and explain why a whole number is prime or composite explaining how to find the least common multiple (LCM) and greatest common factor (GCF) of two numbers using factors, multiples, and prime and composite numbers in a variety of situations factoring a number into its prime factorization or into factor pairs explaining or showing whether one number is a factor of another number explaining or demonstrating why a number is prime or composite explaining when an estimation or exact answer is or is not appropriate using a variety of estimation strategies to predict an answer prior to computation using estimation to verify the reasonableness of calculated results computing to check the reasonableness of estimated answers for a given situation explaining an appropriate adjustment when an estimate and a computation do not agree 12/30/06 3 Fifth Grade

Understands and applies concepts and procedures in measurement (angle, capacity, weight, area, time, perimeter, polygons, metric system). (Continued) GLE: 1.2 Apply appropriate end-of-year standards from those units on measurement that were presented to students by the midyear benchmark identifying or describing angles in pictures, diagrams, illustrations and in the environment sorting, classifying, and labeling angles as equal to, less than, or greater than 90 describing angles in shapes and figures as equal to, less than, or greater than 90 explaining and providing examples of how angles are formed explaining how degrees are used as measures of angles describing an angle in relation to a 90 angle sorting, classifying, and labeling angles as approximately 30, 45, 60, 90, or 180 drawing angles with approximate measures of 30, 45, 60, 90, and 180 identifying or describing angles with approximate measures of 30, 45, 60, 90, or 180 with or without a protractor explaining and citing examples of the metric system units for capacity, mass, and length explaining or showing the relationship between units in the metric system for capacity, mass, or length converting between units in the metric system: Length millimeter, centimeter, meter, kilometer Capacity milliliter, liter Mass gram, kilogram using a systematic procedure to measure and describe the area of rectangles or triangles selecting and describing the appropriate units and/or tools for measuring length, perimeter, and/or area demonstrating a procedure for measuring the area of a rectangle or right triangle. using procedures to measure length, perimeter, and/or area measuring the area in figures composed of rectangles and triangles 12/30/06 4 Fifth Grade

Understands and applies concepts and procedures in measurement (Continued) (continued on next page) determining whether an area measurement has been done correctly explaining how to find the perimeter or area of any rectangle using a rule explaining and using formulas to calculate the perimeter or area of a rectangle and labels units explaining and using a formula to determine or calculate the area of a right triangle and labels units determining and labeling right triangles and all rectangles with whole number dimensions and a given perimeter or area explaining why formulas are used to find area and/or perimeter describing situations in which estimated measurements are appropriate estimating and labeling areas of rectangles and right triangles explaining an appropriate process for estimating perimeter or area of a rectangle or right triangle or an angle measurement using estimation to determine reasonableness of an angle or area measurement determining whether an angle is closest to 30, 45, 60, 90, or 180 drawing angles with measurements that are approximately 30, 45, 60, 90, or 180 12/30/06 5 Fifth Grade

Understands and applies concepts and procedures in geometric sense (angles; parallel, perpendicular, symmetric lines; congruence; slides, flips; coordinate grids). GLE: 1.3 Apply appropriate end-of-year standards from those units on geometric sense that were presented to students by the midyear benchmark explaining the difference between a regular and irregular polygon describing a 2-dimensional shape and/or figure using properties including number of sides, number of vertices, and types of angles drawing a simple 2-dimensional shape and/or figure having given characteristics including number of sides, number of vertices, types of angle(s), and/or congruence using and/or explaining mathematical conventions used to label vertices, line segments, and angles describing parallel and perpendicular lines and/or lines of symmetry drawing, describing, and/or labeling a figure or design that includes a given set of properties including parallel or perpendicular lines and/or line of symmetry drawing, describing, and/or labeling angles, quadrilaterals, parallel and/or perpendicular lines, lines of symmetry, and congruent 2-dimensional shapes or figures sorting, classifying, and labeling shapes and figures using the properties of parallel lines, perpendicular lines, and lines of symmetry completing a picture or design using a line of symmetry completing pictures or designs from a variety of cultures that incorporate parallel line(s), perpendicular line(s), and/or a line(s) of symmetry plotting points with positive coordinates on a number line describing the relative position of fractions and/or decimals on a positive number line drawing a translation or reflection of a given figure on a grid using translations or reflections to describe patterns in art, architecture, or nature describing whether a figure has been translated or reflected creating designs using translations and/or reflections identifying a picture or diagram of a particular translation or reflection 12/30/06 6 Fifth Grade

Understands and applies concepts and procedures in probability and statistics (likelihood of events; chance; question, data, table/charts/graphs/line plot/pictographs; mode/median/range/mean; interpret results). GLE: 1.4 Apply appropriate end-of-year standards from those units on probability and statistics that were presented to students by the mid-year benchmark predicting and testing how likely it is that a certain outcome will occur given a fair game, creating an advantage for one of the players explaining whether a game for two people is fair creating a spinner, game, or situation that would produce a fair outcome or make it more or less likely for an event to happen explaining why some outcomes are equally likely or more or less likely to happen than others determining whether a real-life event has zero probability, 50% probability, or 100% probability of occurring listing and/or counting possible outcomes of simple experiments using strategies, including pictures, lists, and tree diagrams, to show the possible outcomes of a simple experiment writing questions needed to obtain data about a specific topic explaining how different data collection methods, including phone survey, internet search, and person-to-person survey, affect the data set for a given question. describing an appropriate sample for a given question or population explaining how different samples, populations, or questions can affect the data explaining how to determine the mean of a set of data and explain the significance of the mean determining the mean of a given set of data using objects or pictures determining and explaining whether mean, median, or mode is the most appropriate measure of central tendency in a given situation explaining why the mean, median, or mode may be greater than or less than the other measures for a given set of data determining the mean for two samples from the same population and explain why they may not be the same reading and interpreting data from text and circle graphs in terms of patterns explaining the completeness and accuracy of data presented in circle graphs explaining whether line plots, pictographs, tables, charts, bar or circle graphs are more appropriate for a given set of data, particular situation, or purpose, or answers a question most effectively summarizing data given in a circle graph or text describing trends or patterns in data 12/30/06 7 Fifth Grade

Understands and applies concepts in algebraic sense (number patterns, develop rules using patterns, understand inequality, write/solve equations using symbols). GLE: 1.5 extending, describing, or creating patterns of numbers using division based on a single operation between terms extending, describing, or creating patterns of shapes or objects extending and representing patterns using words, tables, numbers, models, and pictures extending a pattern by supplying missing elements in the beginning, middle, and/or end of the pattern generating a rule for a pattern to extend or fill in parts of the pattern determining a rule for a pattern of alternating operations and explains the rule identifying a rule for a pattern with two operations between terms explaining why a given rule with a single operation fits a given pattern describing or writing a rule for a pattern based on a single operation explaining why a given rule fits a pattern based on a single arithmetic operation in the rule expressing relationships between like denominator fractions and decimal quantities using <, >, =, or describing a situation represented by an equation or inequality involving like denominator fractions and/or decimals writing a simple equation or inequality using non-negative decimals or like-denominator fractions to represent a given situation reading expressions and equations involving variables writing an expression or equation using a variable to represent a given situation. describing a situation that represents a given expression or equation that includes a variable explaining the meaning of a variable in a formula, expression, or equation writing or illustrating expressions or equations using manipulatives, models, pictures, and symbols for given situations showing and/or explaining how to substitute a numeric value for a symbol in an expression determining the value of simple expressions or formulas involving addition and subtraction of non-negative decimals and like denominator fractions and/or multiplication and division of whole numbers given the values of the variables writing an expression with a variable to represent a situation and determine the value of the expression given a value for the variable solving a one-step equation involving multiplication or division using manipulatives, pictures, and/or symbols writing and solving an equation in a given situation explaining or showing the meaning of the solution to an equation represented in a line plot or pictograph extending, describing, or creating patterns of numbers using division based on a single operation between terms extending, describing, or creating patterns of shapes or objects extending and representing patterns using words, tables, numbers, models, and pictures extending a pattern by supplying missing elements in the beginning, middle, and/or end of the pattern generating a rule for a pattern to extend or fill in parts of the pattern determining a rule for a pattern of alternating operations and explains the rule identifying a rule for a pattern with two operations between terms explaining why a given rule with a single operation fits a given pattern describing or writing a rule for a pattern based on a single operation explaining why a given rule fits a pattern based on a single arithmetic operation in the rule expressing relationships between like denominator fractions and decimal quantities using <, >, =, or describing a situation represented by an equation or inequality involving like denominator fractions and/or decimals writing a simple equation or inequality using non-negative decimals or like-denominator fractions to represent a given situation reading expressions and equations involving variables writing an expression or equation using a variable to represent a given situation. describing a situation that represents a given expression or equation that includes a variable explaining the meaning of a variable in a formula, expression, or equation writing or illustrating expressions or equations using manipulatives, models, pictures, and symbols for given situations showing and/or explaining how to substitute a numeric value for a symbol in an expression determining the value of simple expressions or formulas involving addition and subtraction of non-negative decimals and like denominator fractions and/or multiplication and division of whole numbers given the values of the variables writing an expression with a variable to represent a situation and determine the value of the expression given a value for the variable solving a one-step equation involving multiplication or division using manipulatives, pictures, and/or symbols writing and solving an equation in a given situation explaining or showing the meaning of the solution 12/30/06 8 Fifth Grade

Solves problems (define the problem, create a plan, use appropriate strategies and tools to find a solution). EALR: 2 Define Problems investigating a situation and determines if there is a problem to solve defining or clarifying the question the problem presents generating questions that would need to be answered in order to solve the problem determining what missing information is needed to solve the problem differentiating between information that is necessary or extraneous determining what data, numbers, and information are known and unknown Construct solutions selecting and using relevant data or information from the problem determining whether a given solution shows the use of relevant information selecting and using appropriate concepts and procedures to construct a solution determining whether a given solution shows use of concepts and procedures that are appropriate selecting and using tools such as rulers, manipulatives, calculators, and technology to construct a solution selecting and applying a variety of strategies and approaches to construct a solution determining when an approach is unproductive and modify or try a new approach determining whether a given solution shows the application of strategies that are appropriate checking work for mathematical accuracy determining whether the solution is reasonable for the situation checking the solution with an estimate or results from an alternate approach checking to be certain the solution answers the question to an equation Define Problems investigating a situation and determines if there is a problem to solve defining or clarifying the question the problem presents generating questions that would need to be answered in order to solve the problem determining what missing information is needed to solve the problem differentiating between information that is necessary or extraneous determining what data, numbers, and information are known and unknown Construct solutions selecting and using relevant data or information from the problem determining whether a given solution shows the use of relevant information selecting and using appropriate concepts and procedures to construct a solution determining whether a given solution shows use of concepts and procedures that are appropriate selecting and using tools such as rulers, manipulatives, calculators, and technology to construct a solution selecting and applying a variety of strategies and approaches to construct a solution determining when an approach is unproductive and modify or try a new approach determining whether a given solution shows the application of strategies that are appropriate checking work for mathematical accuracy determining whether the solution is reasonable for the situation checking the solution with an estimate or results from an alternate approach checking to be certain the solution answers the question 12/30/06 9 Fifth Grade

Reasons mathematically (make predictions and estimations based on information and prior knowledge, draw conclusions and justify results by using evidence). EALR: 3, 5 Apply appropriate end-of-year standards from those units that were presented to students by the mid-year benchmark where mathematical reason was assessed Analyze information analyzing mathematical information or results represented in tables, charts, graphs, text, diagrams, figures, or pictures comparing mathematical information represented in tables, charts, graphs, text, diagrams, figures, or pictures identifying agreements and/or differences between mathematical information, diagrams, and/or pictorial representations differentiating between valid and invalid analysis of mathematical information or results Conclude drawing a conclusion from a given situation and support the conclusion with appropriate numerical, measurement, geometric, and/or statistical data or facts using data or examples as evidence to support or contradict a given conclusion identifying a valid conclusion based on given information checking the viability and appropriate use of selected procedures in a given situation evaluating procedures and/or results based on a given situation Verify results justifying results using evidence and information from the problem situation and/or known facts, patterns, and relationships checking for reasonableness of results in a given situation explaining and supporting thinking about mathematical ideas using models, facts, patterns, or relationships (continued on next page) 12/30/06 10 Fifth Grade

Reasons mathematically (make predictions and estimations based on information and prior knowledge, draw conclusions and justify results by using evidence). (Continued) Relate concepts and procedures within mathematics, other disciplines and the real world using concepts and procedures from two or more content strands in a given problem or situation identifying mathematical models or representations that are equivalent to a given model or representation. explaining how two or more different models represent the same mathematical idea creating a model or representation that is equivalent to a given graphical, numerical, pictorial, geometric, and/or written model or representation giving examples of mathematical patterns and ideas in other disciplines using mathematical concepts and procedures in other disciplines describing a contribution to the development of mathematics generating examples and explain how mathematics is used in everyday life describing situations in which mathematics can be used to solve problems in the real-world describing specific examples of mathematics associated with a given career and/or used by workers in a specific job describing the mathematical requirements to enter a given career 12/30/06 11 Fifth Grade

Communicates mathematically (gather and organize information, represent using charts/graphs/summary, share using mathematical language and notation). EALR: 4 Gather information determining appropriate mathematical information needed for a specific purpose or audience developing a plan, not a survey, for collecting mathematical information, including what information is needed and where and how to find the information listing or describing the general procedure or order of steps of a plan to gather exactly the mathematical information sought with no irrelevant information following a plan, not a survey, to collect mathematical information for a given audience and purpose extracting and using mathematical information from various sources such as pictures, symbols, text, tables, charts, bar graphs, line plots, pictographs, circle graphs, and/or models for a purpose writing questions to be answered using data sources such as magazines, newspapers, menus, sales or travel brochures, TV or bus schedules, and/or sales receipts selecting a useful format and organizing mathematical information for a given purpose Organize, represent, and share information representing mathematical information using tables, charts, pictographs, bar graphs, line plots, circle graphs, pictures, drawings, or other forms including titles, labels, appropriate and consistent scales, and accurate display of data using both everyday and mathematical language and notation to explain, defend, or present mathematical ideas, facts, procedures or strategies appropriate for a given audience or purpose Gather information determining appropriate mathematical information needed for a specific purpose or audience developing a plan, not a survey, for collecting mathematical information, including what information is needed and where and how to find the information listing or describing the general procedure or order of steps of a plan to gather exactly the mathematical information sought with no irrelevant information following a plan, not a survey, to collect mathematical information for a given audience and purpose extracting and using mathematical information from various sources such as pictures, symbols, text, tables, charts, bar graphs, line plots, pictographs, circle graphs, and/or models for a purpose writing questions to be answered using data sources such as magazines, newspapers, menus, sales or travel brochures, TV or bus schedules, and/or sales receipts selecting a useful format and organizing mathematical information for a given purpose Organize, represent, and share information representing mathematical information using tables, charts, pictographs, bar graphs, line plots, circle graphs, pictures, drawings, or other forms including titles, labels, appropriate and consistent scales, and accurate display of data using both everyday and mathematical language and notation to explain, defend, or present mathematical ideas, facts, procedures or strategies appropriate for a given audience or purpose 12/30/06 12 Fifth Grade