Everyday Mathematics Pacing Guide

Everyday Mathematics Pacing Guide McDowell County Schools 2006-2007 Grade Level August September October November December January February March April May June Kindergarten 1 2 3 4 5 Pages 10–44 1.1–2.3 Pages 45–65 2.4–3.3 Pages 66–95 3.4–4.1 Pages 96–119 4.2–4.13 Pages 120–152 5.1–5.14 Pages 153–179 6.1–6.13 Pages 180–212 7.1–8.3 Pages 213–262 8.4–9.4 Pages 263–298 9.5–10.7 1.1–2.7 2.8–3.6 3.7–4.7 4.8–5.10 6.1–7.3 7.4–8.5 8.6–9.11 10.1–11.3 11.4–12.8 1.1–2.3 2.4–3.4 3.5–4.10 5.1–5.13 6.1–6.13 7.1–8.2 8.3–9.7 9.8–10.6 10.7–11.10 1.1–2.7 2.8–3.12 4.1–4.11 5.1–5.9 5.10–6.11 7.1–8.2 8.3–9.7 *8.10– 9.11 9.8–10.7 11.1–12.7 1.1–2.6 *2.7–3.8 3.9–5.3 5.4–5.13 *6.1–7.5 7.6–8.9 10.1–11.2 11.3–12.10 *Unit 2 must be completed by October 10th for benchmark testing *Unit 6 Lesson 3 must be completed by January 16th for benchmark testing *Unit 8 must be completed by March 20th for benchmark testing *All Units must by completed by the end of the year. McDowell County Schools Grade 5 Revised May 2006 1 OVERVIEW According to the National Council of Teachers of Mathematics, changes must be made in the kinds of mathematics that are taught and the ways they are taught if we are to expect our children to measure up to the ever-increasing demand for mathematical competence and problem-solving agility. Dr. Steve Paine, WV State Superintendent, states, "Our challenge is to provide instruction that is not only relevant, engaging and meaningful, but that also includes the world-class rigor necessary to prepare our students to be competitive in the 21st century workplace. Students must be able to comprehend, problem solve and communicate solutions if they are expected to compete on a global level." Everyday Mathematics meets these challenges by introducing children to all the major mathematical content domains—number sense; algebra and functions; measurement and geometry; and statistics, data analysis, and probability—beginning in kindergarten. The program directs teachers to move beyond basic arithmetic and to nurture higher-order and critical thinking skills in their students, using everyday, real-world problems and situations, while also building and maintaining basic skills, including automatic fact recall. According to research, if we jump children to the abstract (fact drills), before they concretely understand the concept we can never take them back to the concrete. Therefore, EM waits to start drills until late in the year in 2nd grade. It is imperative that games are played 15 to 20 minutes at least 3 times per week. In order to have successful implementation of the program, the following must happen: The pacing guide and curriculum map must be followed (approximately 4 lessons per week) Establish routines early Follow daily and program routines o Fact practice routines (attained through choral drills, mental math, fact triangles, dominoes, and games on a regular basis) o Routines for fact drills can be found in the following lessons for grades 2-5:  Grade 2 lesson 7.1 and 12.4  Grade 3 Unit 7 (90 second assessment) and Unit 11  Grade 4 Unit 1, Unit 3 (A multiplication routine begins and should be continued throughout the year as needed)  Grade 5 Unit 1 (A multiplication routine begins and should be continued throughout the year as needed) o Essential questions posted (these are provided in the curriculum maps; however teachers may modify them to meet individual needs) o The EM number line must be posted as a line not as a grid; the Ever Day Counts growing number line may be added onto the EM number line to save space. Games are NOT optional (games teach automatic fact recall, as well as other skills) Mandatory record keeping must be maintained and filed o Unit Checking Progress Assessments o Midyear and End-of Year Assessments o Class Check list by Unit (these check lists are an ongoing cumulative record indicating student progress; the end of unit assessment should not be the only indicator of mastery) o Cumulative end-of-year benchmark checklist and county reporting form Follow whole-group, partner, and small group instruction suggestions Third-fifth grade MUST do the one yearlong project o Third Grade: Sunrise/Sunset (begins in Unit 1 Lesson 12) o Fourth Grade: World Tour (begins in Unit 2 Lesson 1) o Fifth Grade: American Tour (begins in Unit 3 Lesson 1) Please review the Management Guide in the Teacher’s Reference Manual for assistance. Remember, Everyday Mathematics is a spiraling curriculum with repeated exposure to objectives throughout the year. If teachers are struggling with the pace, they may be trying to teach to mastery instead of ―trusting the spiral‖. McDowell County Schools Grade 5 Revised May 2006 3 Fifth Grade CSO Prioritization for Mathematics Essential Standards (In order of importance--tested 2-5 times) 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. MA.5.1.12 - Solve grade level appropriate story problems using multiple strategies. MA.5.2.1 - Explore a variety of patterns with missing elements (e.g., square numbers, powers, triangular numbers, arithmetic sequences). MA.5.5.2 - Identify probabilities and solve problems involving the probability of an event by using tree diagrams or by construction of a sample space representing all possible results. MA.5.5.3 - Construct, read, and interpret tables, charts, and graphs to draw reasonable inferences or verify predictions. MA.5.2.2 - Use input/output model with grade level appropriate functions. MA.5.3.2 - Construct a 3-dimensional figure from different views (orthogonal drawings). MA.5.4.8 - Select appropriate customary and metric units and the tools for measuring to desired degree of precision. MA.5.1.4 - Estimate with whole numbers and decimals, including money, to determine reasonableness of an answer. MA.5.1.5 - Identify and use the divisibility rules of 2, 3, 5, 9, and 10. MA.5.1.7 - Model and write equivalencies of fractions, decimals, percents, and ratios. MA.5.1.10 - Model multiplication of decimals and division of decimals by a whole number divisor. MA.5.2.3 - Write an equation using a variable to solve problems. MA.5.3.5 - Recognize the images of figures after reflections, translations, and rotations. MA.5.4.9 - Determine actual measurement from scale drawings. Important Standards (Tested once as constant and/or a released item) 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. MA.5.1.1 - Read, write, order, and compare all whole numbers. MA.5.1.2 - Read, write, order, and compare all decimals. MA.5.1.3 - Identify place value of each digit utilizing standard and expanded form in any whole number. MA.5.1.6 - Compare and order fractions, improper fractions, and mixed numbers with like and unlike denominators (e.g., greatest common factor, lowest common multiple). MA.5.1.8 - Add and subtract fractions and mixed numbers. MA.5.1.9 - Model multiplication and division of fractions to solve the algorithm. MA.5.1.11 - Develop fluency in addition, subtraction, multiplication, and division of whole numbers. MA.5.2.4 - Evaluate an expression given a value for the variable. MA.5.3.1 - Classify and compare polygons. MA.5.3.3 - Measure angles using a protractor. MA.5.3.4 - Draw a design with more than one line of symmetry. MA.5.3.6 - Draw a similar figure using a scale. MA.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. MA.5.4.2 - Determine and compare area of triangles and parallelograms using appropriate formula. MA.5.4.3 - Solve problems using the formulas for determining volume of a rectangular prism. MA.5.4.4 - Understand the relationship between are and perimeter of a plane figure. MA.5.4.5 - Understand appropriate grade level conversions within a system of measure and apply to problem solving situations. MA.5.4.7 - Calculate elapsed time. Compact Standards (Not yet tested at all) 1. 2. 3. 4. MA.5.4.6 - Evaluate and/or measure the weight/mass of real objects in ounces, pounds, toms, grams, and kilograms. MA.5.5.1 - Collect, organize, display, read, and interpret data from a problem-solving situation in a stem and leaf plot. MA.5.5.4 - Carry out experiments to determine probability. MA.5.5.5 - Construct a circle graph. Grade 5 Revised May 2006 McDowell County Schools 4 Fifth Grade Everyday Mathematics Learning Goals--Units 1-12 Learning Goal By Assessment Rubric Indicators Secure Draw arrays to model multiplication Know basic multiplication facts Identify even and odd numbers List the factors of a number Find the sum and difference of multidigit whole numbers and decimals Identify the maximum, minimum, mode and mean for a data set Identify place value in numbers to billions Know properties of polygons Define and create tessellations Know place value to hundredths Find and use data landmarks Convert among fractions, decimals and percents Convert between fractions and mixed or whole numbers Find common denominators Understand the concept of area of a figure Use a formula to find the area of rectangles Use formulas to find the areas of polygons and circles Know the properties of geometric solids Find and identify factors of numbers Find the prime factorizations of numbers Developing/Secure Use a divisibility test to determine if a number is divisible by another number Identify prime and composite numbers Understand how square numbers and their square roots are related Make magnitude estimates Find the product of multidigit whole numbers ands decimals Know place value to billions Estimate the measure of an angle Measure an angle to within 2º Identify types of angles Identify types of triangles Convert between fractions and mixed numbers Find equivalent fractions Convert among fractions, decimals, and percents Understand and apply exponential notation Identify number sentences; tell whether a number sentence is true or false Understand and apply the use of parentheses in number sentences McDowell County Schools Grade 5 Revised May 2006 1 1 1 2 2 2 3 3 3 3 5 5 6 7 7 7 1 1 1 1 2 2 3 3 3 4 6 8 8 8 9 9 11 11 12 12 Unit 5 Order and compare positive and negative numbers Use an algorithm to add mixed numbers Order and compare fractions Plot ordered pairs on a one-quadrant coordinate grid Identify the base and height of triangles and parallelograms Use a formula to find the area of triangles and parallelograms Solve one-step pan-balance problems Interpret mystery line plots ands graphs Use formulas to find the volume of prisms and cylinders Solve ratio and rate number stories 7 8 8 9 9 9 10 10 11 12 Learning Goal By Assessment Rubric Indicators Unit Developing Round numbers to designated places Determine angle measures based on relationships between angles Find the quotient and remainder of a whole number divided by a 1-digit whole number Find the quotient and remainder of a whole number divided by a 2-digit whole number Make magnitude estimates for quotients of whole and decimal numbers divided by whole numbers Interpret the remainder in division number stories Determine the value of a variable; use this value to complete a number sentence Order and compare fractions Convert between fractions and percents Draw a circle graph for a set of data Measure pieces of a circle graph; interpret a circle graph Add and subtract fractions with common denominators Add and subtract fractions with unlike denominators Understand how sample size affects results Find a common denominator Understand and apply powers of 10 Understand and apply order of operations to evaluate expressions and sole number sentences Add and subtract positive and negative numbers Use an algorithm to multiply fractions Use an algorithm to subtract mixed numbers with like denominators Find a percent of a number Plot ordered pairs on a four-quadrant coordinate grid Understand the concept of volume of a figure Use a formula to find the volume of prisms Write algebraic expressions to describe situations Represent rate problems as formulas, graphs, and tables Use formulas to find circumference and area of a circle Distinguish between circumference and area of circle problems Find the greatest common factor of two numbers Find the least common multiple of two numbers Beginning/Developing Rename numbers written in exponential notation McDowell County Schools Grade 5 Revised May 2006 1 2 3 4 4 4 4 4 5 5 5 5 6 6 6 6 7 7 7 8 8 8 9 9 9 10 10 10 10 12 12 6 Add fractions with like denominators Construct stem-and-leaf plots Read and interpret stem-and-leaf plots Understand and apply scientific notation Use the Multiplication Counting Principle to find the total number of possible outcomes of a sequence of choices Beginning Find the prime factorization of numbers Write and solve open sentences for number stories Divide decimal numbers by whole numbers with no remainders Write and solve number sentences with variables for division number stories Use an algorithm to multiply mixed numbers Solve two-step pan-balance problems Understand the relationship between the volume of pyramids and prisms, and the volume of cones and cylinders Find the surface area of prisms Understand how to find the surface area of cylinders Understand the concept of capacity and how to calculate it Use tree diagrams to find all possible ways a sequence of choices can be made Compute the probability of outcomes when choices are equally likely 5 6 6 7 12 1 2 4 4 8 10 11 11 11 11 12 12 McDowell County Schools Grade 5 Revised May 2006 7 Name: Aug./Sept. (see pacing) Topic: Unit 1 – Number Theory Grade: ____5______ Instructional Key Learning Goals: Tools/Reminders: a. b. c. d. e. f. g. h. i. B Find the prime factorizations of numbers. (5.1.6) B Rename numbers written in exponential notation. (5.2.1) D/S Use a divisibility test to determine if a number is divisible by another number. (5.1.5, 5.1.11) D/S Identify prime and composite numbers. (5.1.1) D/S Understand how square numbers and their square roots are related. (5.1.1, 5.2.1) S Draw arrays to model multiplication. S Know multiplication facts. (5.1.11) S Identify even and odd numbers. (5.1.5, 5.1.6) S Find the factors of numbers. (5.1.6) Unit Essential Question(s) How can I use Number Theory to become stronger in math? Rectangular array Number model Turn-around rule Factor Product Divisibility Composite number Prime number Square number Name collection box Exponent GAMES: Baseball Multiplication Beat the Calculator Multiplication Top-It Factor Captor Factor Top-It Factor Bingo Name That Number Concept: Kinds and Classifications of Numbers Lesson Essential Questions & Vocabulary: 1.3 How do I determine all factor pairs for a number? Factor Product Factor pair 1.4 How can I relate factors and divisibility? Even numbers Odd numbers Divisibility 1.6 How can I classify whole numbers as prime and composite? Composite number Prime number 1.9 How do I represent numbers as products of factors and prime factors? Name collection boxes Factor strings Prime factorization Concept: Math Tools Lesson Essential Questions & Vocabulary: 1.1 How do I use the student reference book? Glossary Index Table of contents 1.2 How do I use multiplication number models to represent arrays? Rectangular array Number model Turn-around rule 1.5 How can I use a calculator to test for divisibility? Divisible Quotient Divisibility test Factor rainbow Concepts: Squaring and Unsquaring a Number Lesson Essential Questions & Vocabulary: 1.7 How can I write square numbers using exponents? Square number Exponential notation Exponent 1.8 How can I find the square root of a square number? Unsquaring a number Square root Square root key Concept: Review and Assessment Lesson Essential Questions & Vocabulary: 1.10 How did I progress on my learning goals? CSO/Unit Correlation CSO Description Level of Importance I I I E I WESTEST Thinking Skill 1 1 1 1 2 Read, write, order, and compare all whole numbers. Read, write, order, and compare all decimals. 5.1.2 Identify place value of each digit utilizing 5.1.3 standard and expanded form in any whole number. *5.1.5 Identify and use the divisibility rules of 2, 3, 5, 9, and 10. Compare and order fractions, improper 5.1.6 fractions, and mixed numbers with like and unlike denominators (eg: greatest common factor, least common multiple) *5.1.7 Model and write equivalencies of fractions, decimals, percents, and ratios *5.1.10 Model multiplication of decimals and division of decimals by a whole number division. *5.1.11 Develop fluency in addition, subtraction, multiplication, and division. *5.2.1 Explore a variety of patterns with missing elements (eg: square numbers, powers, triangular numbers, arithmetic sequences) Evaluate and expression given a value for a 5.2.4 variable. *5.3.1 Classify and compare polygons. *5.4.7 Calculate elapsed time. *5.5.2 Determine probability and solve problems using tree diagrams. 5.1.1 E E E E* C E E E* 1 1 1 1 1 1 2 2 CSO: Star (*) = 80% constant on WESTEST Italicized = Constructed Response Item on WESTEST Bold = Formerly released item from WESTEST Level of Importance: E: Essential (*: assessed 3 or more times on WESTEST) I: Important C: Compact Unit 1 Constructed Response Items CSO ma5.1.1; ma5.1.6 List all factors of 88: Write a related number sentence using the factors and the number: ______________________________________________________ On the lines below explain why the number is prime or composite. __________________________________________________________________________ __________________________________________________________________________ __________________________________________________________________________ McDowell County Schools Grade 5 Revised May 2006 10 Scoring Rubric: 3 points: Demonstrates all of the following elements: 2 correct answers correct explanation 2 points: 2 of 3 elements correct incorrect explanation 1 point: 1 of 3 element correct 0 points: incorrect, no attempt made, or irrelevant response McDowell County Schools Grade 5 Revised May 2006 11 Name: September/October (see pacing) Topic: Unit 2-Estimation and Computation Grade: 5 Key Learning Goals: a. B Write and solve open sentences for number stories. (5.1.12, 5.2.3) b. D Round numbers to designated places. (5.1.4) c. D/S Make magnitude estimates. (5.1.4, 5.4.1, 5.4.7) d. D/S Find the product of multidigit whole numbers and decimals. (5.1.10, 5.1.11) e. S Find the sum and difference of multidigit whole numbers and decimals. (5.1.11) f. S Identify the maximum, minimum, median, mode, and mean for a data set. (5.5.1) Unit Essential Question(s) How can I use estimation and computation to improve my math skills? Instructional Tools/Reminders: Algorithms for addition, subtraction, and multiplication Geometry templates, polygon manipulatives, Probability Meter Poster GAMES: Baseball Multiplication, Getting to One, Addition Top-It, Subtraction Target Practice, High Number Toss, Multiplication Bull’s Eye, Multiplication Wrestling, Number Top-It Concept: Estimation and Data Landmarks Lesson Essential Questions & Vocabulary: 2.1 How can I devise an estimation strategy to solve a problem? 2.5 How do I use sets of data to estimate reaction times? Mean Stimulus Reaction time Minimum Maximum Range Mode Median 2.6 How do I estimate the probability of an event? Impossible Certain Probability Meter Poster (very, extremely) likely 50-50 chance (very, extremely) unlikely 2.7 How do I determine magnitude estimates for products of multi-digit numbers? Magnitude Estimate Concept: Computation of whole numbers and decimals Lesson Essential Questions & Vocabulary: 2.2 How can I add whole numbers and decimals using the partialsums and column-addition methods? Value Digit Place Place value Algorithm Partial-sums method Column-addition method 2.3 How can I subtract whole numbers and decimals using the trade-first and partial-differences algorithm? Trade-first method Partial differences method 2.8 How can I use the partialproducts method to multiply whole numbers? Partial-products method 2.9 How do I use the lattice method for multiplication? Lattice method Lattice Concepts: Number Sentences Lesson Essential Questions & Vocabulary: Concept: Place Value and Review Lesson Essential Questions & Vocabulary: 2.4 How do I use open sentences to solve number stories? Number sentence True number sentence False number sentence Relation symbol Operation symbol Variable Open sentence Solution 2.10 How do I know the relative sizes of one million, one billion, and one trillion? Sample 2.11 Review and Assessment: How did I progress on my learning goals? CSO/Unit Correlation CSO Description Level of Importance I I I E E I E E E E E C E E I E E C E E I WESTEST Thinking Skill 1 1 1 2 1 2 1 1 1 2 2 1 1 1 2 2 2 3 2 2 3 Read, write, order, and compare all whole numbers. Read, write, order, and compare all decimals. 5.1.2 Identify place value of each digit utilizing 5.1.3 standard and expanded form in any whole number. *5.1.4 Estimate with whole numbers and decimals, including money. *5.1.5 Identify and use the divisibility rules of 2, 3, 5, 9, and 10 *5.1.6 Compare and order fractions (e.g. greatest common factor, lowest common multiple) *5.1.10 Model multiplication of decimals and division of decimals by a whole number divisor *5.1.11 Develop fluency in addition, subtraction, multiplication and division of whole numbers. *5.1.12 Solve story problems using multiple strategies. *5.2.1 Explore a variety of patterns with missing elements. *5.2.3 Write an equation using a variable to solve problems Evaluate an expression given a value for the 5.2.4 variable. *5.3.1 Classify and compare polygons. *5.3.3 Measure angles using a protractor. Estimate, measure, compare, order, and draw 5.4.1 lengths of real objects in parts of an inch up to 1/8 of an inch and millimeters. *5.4.7 Calculate elapsed time. *5.4.8 Select appropriate customary and metric units. Collect, organize, display, read and interpret 5.5.1 data from a problem-solving situation in a stem and leaf plot. *5.5.2 Determine probability and solve problems by using tree diagrams. *5.5.3 Construct, read, and interpret tables, charts, and graphs. Carry out experiments to determine 5.5.4 probability. 5.1.1 CSO: Star (*) = 80% constant on WESTEST Italicized = Constructed Response Item on WESTEST Bold = Formerly released item from WESTEST Level of Importance: E: Essential (*: assessed 3 or more times on WESTEST) I: Important C: Compact Unit 2 Constructed Response Items CSO ma5.1.11 Danny sold red and yellow balloons at the school carnival. He sold 142 red balloons out of a total of 325 balloons. Danny tried to calculate the number of yellow balloons he sold, as shown below. 325 balloons 142 red balloons 173 yellow balloons On the lines below, explain the error Danny made in his calculation. _________________________________________________________________________ _________________________________________________________________________ _________________________________________________________________________ How many more yellow balloons than red balloons did Danny sell? In the box below, show your work and write your answer on the line. Answer ________________ yellow balloons McDowell County Schools Grade 5 Revised May 2006 14 Scoring Rubric: 3 points: Demonstrates all of the following elements: Correct answer Correct operation used Clear explanation 2 points: 2 of 3 elements correct Wrong answer but correct operation used Fairly clear explanation 1 point: 1 of 3 elements correct Attempted to work problem Unclear explanation Incorrect answer 0 points: incorrect, no attempt made, or irrelevant response McDowell County Schools Grade 5 Revised May 2006 15 Name: October/November (see pacing) Topic: Unit 3-Geometry Explorations and the American Tour Grade: 5 Key Learning Goals: Tools/Reminders: angle measures based on a. D Determine b. c. d. e. f. g. relationships between angles. (5.3.3) D/S Estimate the measure of an angle. (5.3.3) D/S Measure an angle to within 2 degrees. (5.3.3, 5.4.8) D/S Identify types of angles. (5.3.3) S Identify types of triangles. (5.3.1) S Identify place value in numbers to billions. (5.1.3) S Know properties of polygons. (5.3.1) Unit Essential Question(s) How can I use math tools to examine the properties of basic plane figures? Instructional Meter, Geometry Template, polygon shapes, types of triangles, regular polygons Games: Angle Tangle Polygon Capture Pr obability Concept: American Tour Lesson Essential Questions & Vocabulary: 3.1 How can I use the probability meter to analyze data? Census 3.2 How do I interpret a table of population estimates? Concept: Tools for Measuring and Drawing Lesson Essential Questions & Vocabulary: 3.3 How can I find the degree measures of angles? 3.4 How can I measure and draw angles using a protractor? Acute angle Obtuse angle Right angle Straight angle Reflex angle Geometry Template 3.5 How can I use a compass to draw a circle and measure and investigate angles? Radius Center Diameter Vertical (or opposite)angles Adjacent angles 3.6 How do I define equilateral, isosceles, scalene, and congruent triangles? Equilateral triangle Isosceles triangle Scalene triangle Congruent 3.10 How do I use the Geometry Template for problem solving? Parallel Unit Perimeter Parallelogram Pentagon Kite Concepts: Polygons Lesson Essential Questions & Vocabulary: 3.7 How can I classify and sort geometric shapes? 3.9 How can I calculate the sum of the measures of the angles of any polygon? Concept: Tessellations and Review Lesson Essential Questions & Vocabulary: 3.8 How can I determine which polygons tessellate and which do not? Regular polygon Tessellation Regular tessellation Tessellate 3.11 How did I progress on my learning goals? CSO/Unit Correlation CSO Description Level of Importance I I I E* E E E* E* E* C E E E WESTEST Thinking Skill 1 1 1 2 1 1 1 2 2 1 1 1 1 Read, write, order and compare all whole numbers. Read, write, order and compare all decimals. 5.1.2 Identify place value of each digit utilizing 5.1.3 standard and expanded form in any whole number. *5.1.4 Estimate with whole numbers and decimals, including money, to determine reasonableness of an answer. *5.1.5 Identify and use the divisibility rules of 2,3, 5, 9 and 10. *5.1.11 Develop fluency in addition, subtraction, multiplication, and division of whole numbers. *5.1.12 Solve grade level appropriate story problems using multiple strategies. *5.2.1 Explore a variety of patterns with missing elements (e.g., square numbers, powers, triangular numbers, arithmetic sequences). *5.2.2 Use input/output model with grade appropriate functions. Evaluate an expression given a value for the 5.2.4 variable. *5.3.1 Classify and compare polygons. *5.3.3 Measure angles using a protractor. *5.3.5 Recognize the images of figures after reflections, translations, and rotations. 5.1.1 CSO: Star (*) = 80% constant on WESTEST Italicized = Constructed Response Item on WESTEST Bold = Formerly released item from WESTEST Level of Importance: E: Essential (*: assessed 3 or more times on WESTEST) I: Important C: Compact Unit 3 Constructed Response Items CSO ma5.3.1 Sort the triangles into 2 sections. Explain why you placed them in the sections you chose. ______________________________________________________________________________ McDowell County Schools Grade 5 Revised May 2006 18 Scoring Rubric: 3 points: Shows clear understanding two distinct groups clear, logical explanation 2 points: two groups reasonable explanation 1 point: two groups reason unclear 0 points: unclear groups no reason no attempt McDowell County Schools Grade 5 Revised May 2006 19 Name: a. b. c. d. e. f. g. h. November (see pacing) Topic: Unit 4 – Division Grade: 5 Key Learning Goals: Unit Essential Question(s) How can I use division of whole and decimal numbers in problem solving? Instructional Tools/Reminders: Partial quotient Map scale Games: Division Dash First to 100 Algebra Election B Divide decimal numbers by whole numbers with no remainders.(5.1.10, 5.1.11) B/D Write and solve number sentences with variables for division number stories. (5.2.3, 5.1.12) D Find the quotient and remainder of a whole number divided by a 1-digit whole number. (5.1.10, 5.1.11) D Find the quotient and remainder of a whole number divided by a 2-digit whole number. (5.1.10, 5.1.11) D Make magnitude estimates for quotients of whole and decimal numbers divided by whole numbers. (5.1.4) D Interpret the remainder in division number stories. (5.2.3) D Determine the place value of a variable; use this va;ie valuevalue to complete a number sentence. (5.2.3) S Know place value to hundredths. (5.1.3) Concept: Division Lesson Essential Questions & Vocabulary: 4.1 How do I mentally divide 2-digit numbers by 1-digit numbers? Divisor Dividend Quotient Remainder 4.2 How can I use the partialquotients division algorithm for dividing whole numbers? Dividend Divisor Partial quotient Quotient Remainder 4.4 How can I use the partialquotients division algorithm to divide decimals by whole numbers? Magnitude estimate 4.5 How can I solve division number stories and interpret remainders? Concept: American Tour Lesson Essential Questions & Vocabulary: 4.3 How do I estimate distances using a map scale? Map legend or map key Direction symbol Map scale Concepts: Skills Review Lesson Essential Questions & Vocabulary: 4.6 How can I use a variable to represent a range of values? Variable Open number sentence Concept: Review Lesson Essential Questions & Vocabulary: 4.7 How did I progress on my learning goals? CSO/Unit Correlation CSO Description Level of Importance I I I E* E I WESTEST Thinking Skill 1 1 1 2 1 2 Read, write, order and compare all whole numbers. Read, write, order and compare all decimals. 5.1.2 Identify place value of each digit utilizing 5.1.3 standard and expanded form in any whole number. *5.1.4 Estimate with whole numbers and decimals, including money, to determine reasonableness of an answer. *5.1.5 Identify and use the divisibility rules of 2, 3, 5, 9, and 10. Compare and order fractions, improper 5.1.6 fractions and mixed numbers with like and unlike denominators (e.g., greatest common factor, lowest common multiple). *5.1.7 Model and write equivalencies of fractions, decimals, percents, and ratios. *5.1.9 Model multiplication and division of fractions to solve the algorithm. *5.1.10 Model multiplication of decimals and division of decimals by a whole number divisor. *5.1.11 Develop fluency in addition, subtraction, multiplication, and division of whole numbers. *5.1.12 Solve grade level appropriate story problems using multiple strategies. *5.2.3 Use input/output model with grade appropriate functions. Evaluate an expression given a value for the 5.2.4 variable. *5.3.1 Classify and compare polygons. *5.3.3 Measure angles using a protractor. Estimate, measure, compare, order and draw 5.4.1 lengths of real objects in parts of an inch up to 1/8 of an inch and millimeters. *5.4.5 Understand appropriate grade level conversions within a system of measure and apply to problem solving. *5.4.9 Determine actual measurement from scale drawings. 5.1.1 E E E E E* E C E E I E E 1 3 1 1 2 2 1 1 1 2 2 2 CSO: Star (*) = 80% constant on WESTEST Italicized = Constructed Response Item on WESTEST Bold = Formerly released item from WESTEST Level of Importance: E: Essential (*: assessed 3 or more times on WESTEST) I: Important C: Compact Unit 4 Constructed Response Items CSO ma5.1.12 On the lines below, write a division word problem. The answer to the problem must be ―12 pencils‖. ______________________________________________________________________________ ______________________________________________________________________________ ______________________________________________________________________________ In the box below, show how to solve your problem using a number sentence. McDowell County Schools Grade 5 Revised May 2006 22 Scoring Rubric: 3 points: Clearly demonstrates math understanding. Clearly written word problem Correct problem/solution (12 pencils) Correct number sentence 2 points: partial understanding 2 of the 3 elements correct minor misunderstandings 1 point: incomplete understanding 1 of the 3 elements correct faulty or incomplete 0 points: 0 correct responses no attempt made McDowell County Schools Grade 5 Revised May 2006 23 CSO ma5.3.6 McDowell County Schools Grade 5 Revised May 2006 24 Grade 5 Mathematics Scoring Rubrics – Constructed Response Item 10 McDowell County Schools Grade 5 Revised May 2006 25 McDowell County Schools Grade 5 Revised May 2006 26 McDowell County Schools Grade 5 Revised May 2006 27 Name: Nov./Dec. (see pacing) Topic: Unit 5 - Fractions, Decimals, and Percents Grade: 5 Instructional Tools/Reminders: Fraction stick Percent circle Games: Factor Captor Multiplication Bull’s Eye Estimation Squeeze Frac-Tac-Toe Fraction Percent Concentration Key Learning Goals: a. b. c. d. e. f. g. B/D Add fractions with like denominators. (5.1.8) D Order and compare fractions. (5.1.6) D Convert between fractions and percents. (5.1.7) D Draw a circle graph for a set of data.(5.5.5) D Measure pieces of a circle graph; interpret a circle graph. (5.5.5) D/S Convert between fractions and mixed numbers. (5.1.6, 5.1.8) D/S Find equivalent fractions. (5.1.7) Unit Essential Question(s) How can I use fractions, decimals, and percents to solve problems in everyday life? Concept: Rational Numbers and Their Notations Lesson Essential Questions & Vocabulary: 5.1 How can I find fractional parts of large whole numbers? Whole (or ONE or unit) Denominator Numerator Unit fraction 5.2 How do I convert between mixed numbers and ―improper‖ fractions? Improper fraction Mixed number 5.3 How do I compare and order fractions? Equivalent fractions Fraction stick 5.4 How can I use fraction sticks to find equivalent fractions? Equivalent fractions Concept: Equivalence and Conversions among Fractions, Decimals, and Percents Lesson Essential Questions & Vocabulary: Concepts: Circle Graph and Percent Circle Concept: American Tour and Review Lesson Essential Questions & Vocabulary: 5.5 How can I rename simple 5.9 How do I construct and fractions as decimals? label bar graphs? Round down Bar graph Round up Circle (or pie graph) Round to the nearest… 5.10 How can I use the 5.6 How do I use a FractionPercent Circle to find Stick Chart to find the percents of circle decimal equivalents for graphs? fractions? 5.11 How do I construct 5.7 How do I use a calculator circle graphs with the to convert fractions to Percent Circle? decimals and decimals to percents? Repeating decimal 5.8 How do I use a calculator to convert fractions to decimals and decimals to percents? percent Lesson Essential Questions & Vocabulary: 5.12. How can I interpret information and solve related historical problems? 5.13 How did I progress on my learning goals? CSO/Unit Correlation CSO Description Level of Importance I I I WESTEST Thinking Skill 1 1 2 Read, write, order and compare all whole numbers. Read, write, order and compare all decimals. 5.1.2 Compare and order fractions, improper 5.1.6 fractions and mixed numbers with like and unlike denominators (e.g., greatest common factor, lowest common multiple). *5.1.7 Model and write equivalencies of fractions, decimals, percents, and ratios. *5.1.8 Add and subtract fractions and mixed numbers. *5.1.11 Develop fluency in addition, subtraction, multiplication, and division of whole numbers. *5.1.12 Solve grade level appropriate story problems using multiple strategies. *5.2.1 Explore a variety of patterns with missing elements (e.g., square numbers, powers, triangular numbers, arithmetic sequences). *5.2.2 Use input/output model with grade appropriate functions. *5.2.3 Write an equation using a variable to solve problems. Evaluate an expression given a value for the 5.2.4 variable. *5.3.1 Classify and compare polygons. Estimate, measure, compare, order, and draw 5.4.1 lengths of real objects in parts of an inch up to 1/8 of an inch and millimeters. *5.4.5 Understand appropriate grade level conversions within a system of measure and apply to problem solving situations. Construct, read, and interpret tables, charts, 5.5.3 and graphs to draw reasonable inferences or verify predictions. Carry out experiments to determine 5.5.4 probability. Construct a circle graph. 5.5.5 5.1.1 E E E E* E* E* E C E I E E I 1 2 1 1 2 2 2 1 1 2 2 1 3 CSO: Star (*) = 80% constant on WESTEST Italicized = Constructed Response Item on WESTEST Bold = Formerly released item from WESTEST C 2 Level of Importance: E: Essential (*: assessed 3 or more times on WESTEST) I: Important C: Compact Unit 5 Constructed Response Items CSO ma5.5.5 Richard asked several students to name their favorite lunch. The results of the survey were as follows: 25% - Hot Dogs 35% - Pizza 25% - Hamburgers 15% - Tacos Make a circle graph for this data on the circle below. Use your Percent Circle. 1. If 100 students answered the survey, how many of them chose pizza? ________ 2. If 50 students answered the survey, about how many of them chose hot dogs? _____ McDowell County Schools Grade 5 Revised May 2006 30 Scoring Rubric: 3 points: demonstrates a clear understanding 2 correct response show data clearly and correctly on the circle graph 2 points: demonstrates some understanding 1 correct response the circle graph has minor errors 1 point: demonstrates some misunderstanding work is partially correct selects and uses some information attempts to complete the circle graph 0 points: incorrect response no attempt to complete the circle graph McDowell County Schools Grade 5 Revised May 2006 31 Name: January (see pacing) Key Learning Goals: B/D Construct stem-and-leaf plots. (5.5.1) B/D Read and interpret stem-and-leaf plots.(5.5.1) c. D Add and subtract fractions with like denominators.(5.1.8) d. D Add and subtract fractions with unlike denominators.(5.1.8) e. D Understand how sample size affects results.(5.5.2) f. D Find common denominators.(5.1.6) g. D/S Convert between fractions, decimals, and percents.(5.1.7) h. S Identify and use data landmarks. h. S Identify and use data landmarks. (5.5.1) a. b. Topic: Unit 6 – Using Data, Addition and Subtraction of Fractions Grade: 5 Unit Essential Question(s) Instructional Tools/Reminders: How can I display and use data? How can I add and subtract fractions? Landmark minimum maximum range Mode Median Mean Line Plot Span Stem-and-Leaf Plot Survey Sample Contour map Map legend Slide rule Common Denominator GAMES: First to 21 Frac-Tac-Toe Angle Tangle Fraction Capture Concept: Landmarks in Data Sets; ―Natural‖ Measures versus Standardized Measures Lesson Essential Questions & Vocabulary: 6.1 How would I describe the prominent features of a data set? Organizing data Landmark Minimum Maximum Range Mode Median Mean (average) Line plot 6.2 How do I use metric and U.S. customary units of length? Span Cubit Fathom Fair game 6.3 How do I use stem-and-leaf plots? Span Normal span Great span Stem Leaf Stem-and-leaf plot Angle of separation Concept: ―Mystery Plots‖Establishing a New Routine; Survey Design, Implementation, and Data Analysis Lesson Essential Questions & Vocabulary: 6.4 How can I interpret data in line plots and stem-and-leaf plots? 6.5 How can I interpret the relationship between sample size and reliability of predictions? Sample 6.6 How can I display and analyze data from a repeated experiment? Survey Decennial Population Sample Frequency table Concepts: A Slide Rule for Adding and Subtracting Fractions; Common Denominator Uses and Misconceptions Lesson Essential Questions & Vocabulary: 6.7 How can I add and subtract fractions using a slide rule? 6.8 How can I use a clock face to add and subtract fractions? Common denominator Unlike denominators 6.9 How can I find common denominators quickly? Quick common denominator Simplest form Concept: Contour Maps: Showing a Third Dimension on a 2-D Map (American Tour); Review and Assessment Lesson Essential Questions & Vocabulary: 6.8 How do I read and use contour maps? Contour map Climate Precipitation Map legend (map key) Contour line 6.11 How did I progress on my learning goals? CSO/Unit Correlation CSO Description Level of WESTEST Importance Thinking Skill I I I E* E I E E E E E* E* E E E I I E E* E C E* E* 1 1 1 2 1 2 1 2 1 1 1 2 1 1 1 2 1 2 2 2 2 2 1 5.1.1 5.1.2 5.1.3 *5.1.4 *5.1.5 5.1.6 *5.1.7 *5.1.8 *5.1.10 *5.1.11 *5.1.12 *5.2.1 *5.3.1 *5.3.3 *5.3.5 5.4.1 5.4.2 *5.4.5 *5.4.8 *5.4.9 5.5.1 *5.5.2 *5.5.3 5.5.4 5.5.5 CSO: Star (*) = 80% constant on WESTEST Italicized = Constructed Response Item on WESTEST Bold = Formerly released item from WESTEST Read, write, order and compare all whole numbers. Read, write, order and compare all decimals. Identify place value of each digit utilizing standard and expanded form in any whole number. Estimate with whole numbers and decimals, including money, to determine reasonableness of an answer. Identify and use the divisibility rules of 2, 3, 5, 9, and 10. Compare and order fractions, decimals, percents, and ratios. Model and write equivalencies of fractions, decimals, percents, and ratios. Add and subtract fractions and mixed numbers. Model multiplication of decimals and division of decimals by a whole number divisor. Develop fluency in addition, subtraction, multiplication, and division of whole numbers. Solve grade level appropriate story problems using multiple strategies. Explore a variety of patterns with missing elements (e.g., square numbers, powers, triangular numbers, arithmetic sequences). Classify and compare polygons. Measure angles using a protractor. Recognize the images of figures after reflections, translations, and rotations. Estimate, measure, compare, order, and draw lengths of real objects in parts of an inch up to 1/8 of an inch and millimeters Determine and compare area of triangles and parallelograms using appropriate formula. Understand appropriate grade level conversions within a system of measure and apply to problem solving situations. Select appropriate customary and metric units and the tools for measuring to desired degree of precision. Determine actual measurement from scale drawings. Collect, organize, display, read and interpret data from a problem-solving situation in a stem and leaf plot. Identify probabilities and solve problems involving the probability of an event by using tree diagrams or by construction of a sample space representing all possible results. Construct, read, and interpret tables, charts, and graphs to draw reasonable inferences or verify predictions. Carry out experiments to determine probability. Construct a circle graph. I 3 C 2 Level of Importance: E: Essential (*: assessed 3 or more times on WESTEST) I: Important C: Compact Unit 6 Constructed Response Items CSO ma5.5.1 Use the following data to complete the exercises: 13, 63, 53, 59, 33, 18, 67, 8, 55, 33, 43, 22, 69, 61, 33 1. Make a stem-and-leaf plot of the data: 2. What is the range of the data? ________________ 3. How many numbers are in the fifties? ________________ 4. How does this stem-and-leaf plot make it easy to tell which values occurred most frequently? ______________________________________________________________________________ ______________________________________________________________________________ ______________________________________________________________________________ McDowell County Schools Grade 5 Revised May 2006 34 Scoring Rubric: 3 points: demonstrates clear understanding correctly plots numbers correctly answers both questions writes a correct, clear explanation 2 points: demonstrates some understanding correctly plots numbers answers at least one question correctly writes a partially correct explanation 1 point: demonstrates some misunderstandings incorrectly plots numbers explanation is unclear, or incomplete 0 points: incorrectly plots numbers makes no attempt to write an explanation McDowell County Schools Grade 5 Revised May 2006 35 Name: Jan./Feb. (see pacing) Key Learning Goals: Topic: Unit 7 – Exponents and Negative Numbers Grade: 5 Unit Essential Question(s) How can I use exponents and negative numbers to prepare for algebra? Instructional Tools/Reminders: Exponential notation Standard notation Powers key GAMES: Exponent Ball High-Number Toss First to 100 Broken Calculator Scientific-Notation Toss Name That Number 500 and Top-It Advanced Credits/Debits Game a. b. c. d. e. f. g. h. B/D Understand and apply scientific notation. (5.2.1) D Understand and apply powers of 10. (5.2.1) D Understand and apply order of operations to evaluate expressions and solve number sentences. (5.2.1, 5.2.3) D Add and subtract integers. (5.2.4) D/S Understand and apply exponential notation. (5.2.1) D/S Determine whether number sentences are true or false. (5.2.2, 5.2.3, 5.2.4) D/S Understand the function and placement of parentheses in number sentences. (5.2.1) D/S Compare and order integers. (5.1.1, 5.1.2) Concept: Exponential and Scientific Notation Lesson Essential Questions & Vocabulary: 7.1 How can I rename numbers written in exponential notation? Exponential notation Exponent Base Factor Standard notation Powers key Power 7.2 How do I use standard notation, exponential notation and powers of 10 to represent large numbers? Number-and-word notation Power of 10 7.3 How can I translate numbers written in Scientific Notation? Scientific notation Concept: Parentheses and Order of Operations Lesson Essential Questions & Vocabulary: 7.4 How can I use parentheses in number sentences to make the expression correct? Ambiguous Nested parentheses 7.5 What are the rules for using order of operations? Order of operations Concepts: Using Negative Numbers Lesson Essential Questions & Vocabulary: 7.6 How can I compare and order positive and negative numbers? Negative number Opposite 7.7 What rule is used for adding positive and negative numbers? Account balance In the black In the red 7.8 What rule is used for subtracting positive and negative numbers? 7.9 How can I use a slide rule to add and subtract positive and negative numbers? Slide rule Holder Slider 7.10How can I use a calculator to add and subtract positive and negative numbers? Change of sign or OPP key Concept: Review and Assessment Lesson Essential Questions & Vocabulary: 7.11 How did I progress on my learning goals? CSO/Unit Correlation CSO Description Level of Importance I I I E E E E E E* E* E C I I E C WESTEST Thinking Skill 1 1 1 1 1 2 1 2 1 2 2 1 1 2 2 2 Read, write, order and compare all whole numbers. Read, write, order and compare all decimals. 5.1.2 Identify place value of each digit utilizing 5.1.3 standard and expanded form in any whole number. *5.1.5 Identify and use the divisibility rules of 2, 3, 5, 9 and 10. *5.1.7 Model and write equivalencies of fractions, decimals percents, and ratios. *5.1.8 Add and subtract fractions and mixed numbers. *5.1.11 Develop fluency in addition, subtraction, multiplication, and division of whole numbers. *5.1.12 Solve grade level appropriate story problems using multiple strategies. *5.2.1 Explore a variety of patterns with missing elements (e.g., square numbers, powers, triangular numbers, arithmetic sequences) *5.2.2 Use input/output model with grade appropriate functions. *5.2.3 Write an equation using a variable to solve problems. Evaluate an expression given a value for the 5.2.4 variable. Determine and compare area of triangles and 5.4.2 parallelograms using appropriate formula. Understand the relationship between area and 5.4.4 perimeter of a plane figure. *5.4.7 Calculate elapsed time. Collect, organize, display, read, and interpret 5.5.2 data from a problem-solving situation in a stem and leaf plot. 5.1.1 CSO: Star (*) = 80% constant on WESTEST Italicized = Constructed Response Item on WESTEST Bold = Formerly released item from WESTEST Level of Importance: E: Essential (*: assessed 3 or more times on WESTEST) I: Important C: Compact Unit 7 Constructed Response Items CSO ma5.2.1, ma5.2.3 Place 1 pair of parentheses in the number sentence below to make it true. 4 x 2 + 8 = 40 In the box below, show that your answer is correct. McDowell County Schools Grade 5 Revised May 2006 38 Scoring Rubric: 2 points: demonstrates clear understanding correctly places parentheses in number sentence correctly shows work in the box 1 point: demonstrates partial understanding correctly places parentheses incorrectly show work 0 points: no correct response no attempt McDowell County Schools Grade 5 Revised May 2006 39 Name: a. b. c. d. e. f. g. h. i. Feb./Mar. (see pacing) B Use an algorithm to multiply mixed numbers. (5.1.9) D Use an algorithm to multiply fractions. (5.1.9) D Use an algorithm to subtract mixed numbers with like denominators. (5.1.8) D Find a percent of a number. (5.1.7) D/S Use an algorithm to add mixed numbers. (5.1.8) D/S Order and compare fractions (5.1.6) S Convert among fractions, decimals, and percents. (5.1.7) S Convert between fractions and mixed or whole numbers. (5.1.7) S Find common denominators. (5.1.6) Topic: Unit 8 – Fractions and Ratios Grade: 5 Key Learning Goals: Unit Essential Question(s) How can I use fractions to become stronger in math? Instructional Tools/Reminders: Quick Common Denominator Unit Fraction Unit Percent GAMES: Build It Fraction Capture Mixed Number Spin Fraction Action, Fraction Friction Fraction Spin Frac-Tac-Toe Fraction Multiplication Top It Fraction/Whole Number Multiplication Top It; Name That Number Concept: Comparing, Adding, Subtracting, and Dividing Fractions and Mixed Numbers Lesson Essential Questions & Vocabulary: 8.1 How do I rename fractions as equivalent fractions and compare fractions by using a common denominator? Quick Common Denominator (QCD) 8.2 How do I add fractions and mixed fractions? 8.3 How can I subtract mixed numbers with like denominators? 8.4 How can I use a calculator to solve fraction problems? Unit fraction 8.12 How do I divide fractions using the common denominator method? Concept: “Many of” and “Part of” as Indicators of Multiplication Lesson Essential Questions & Vocabulary: 8.5 How do I fold paper to find a fraction of a fraction? Horizontal Vertical 8.6 How can I develop a fraction multiplication algorithm using an area model? Area model 8.7 How do I find the product of a whole number and a fraction? 8.8 How do I use two algorithms for multiplication with mixed numbers? Concepts: Unit Rate, Unit Fraction, Unit Percent Strategies Lesson Essential Questions & Vocabulary: 8.9 Using fractions and decimals, how can I estimate and calculate the percent of a number and discounts? Discount 8.10 How do I find the whole if I’m given a fraction or a percent of the whole? Unit fraction Concept: American Tour: Rural and Urban; Review and Assessment Lesson Essential Questions & Vocabulary: 8.11 How can I estimate rural and urban populations using percents? majority 8.13 How did I progress on my learning goals? Unit percent CSO/Unit Correlation CSO Description Level of Importance I I E* E I E E E E E E E* E* C E E I I WESTEST Thinking Skill 1 1 2 1 2 1 2 3 1 1 2 1 1 1 1 1 3 1 read, write, order and compare all whole numbers. Read, write, order and compare all decimals. 5.1.2 *5.1.4 Estimate with whole numbers and decimals, including money, to determine reasonableness of an answer. *5.1.5 Identify and use the divisibility rules of 2, 3, 5, 9, and 10 Compare and order fractions, decimals, 5.1.6 percents, and ratios. *5.1.7 Model and write equivalencies of fractions, decimals, percents, and ratios. *5.1.8 Add and subtract fractions and mixed numbers. *5.1.9 Model multiplication and division of fractions to solve the algorithm. *5.1.10 Model multiplication of decimals and division of decimals by a whole number divisor. *5.1.11 Develop fluency in addition, subtraction, multiplication, and division of whole numbers. *5.1.12 Solve grade level appropriate story problems using multiple strategies. *5.2.1 Explore a variety of patterns with missing elements (e.g., square numbers, powers, triangular numbers, arithmetic sequences). *5.2.2 Use input/output model with grade appropriate functions. Evaluate an expression given a value for the 5.2.4 variable. *5.3.1 Classify and compare polygons. *5.3.3 Measure angles using a protractor. Draw a design with more than one line of 5.3.4 symmetry. Determine and compare area of triangles and 5.4.2 parallelograms using appropriate formula. 5.1.1 CSO: Star (*) = 80% constant on WESTEST Italicized = Constructed Response Item on WESTEST Bold = Formerly released item from WESTEST Level of Importance: E: Essential (*: assessed 3 or more times on WESTEST) I: Important C: Compact Unit 8 Constructed Response Items CSO ma5.3.4 McDowell County Schools Grade 5 Revised May 2006 42 Grade 5 Mathematics Scoring Rubrics – Constructed Response Item 10 Exemplary Response: Part A Part B McDowell County Schools Grade 5 Revised May 2006 43 Name: Mar. (see pacing) Key Learning Goals: a. b. c. d. e. f. g. h. B Plot ordered pairs on a four-quadrant coordinate grid. (5.5.3) D/S Understand the concept of volume of a figure. (5.4.3) D Use a formula to find the volume of prisms. (5.4.3) S Plot ordered pairs on a one-quadrant coordinate grid. (5.5.3) D/S Identifying the base and height of triangles and parallelograms. (5.4.2) D/S Use a formula to find the area of triangles and parallelograms. (5.4.2) S Understand the concept of area of a figure. (5.3.6, 5.4.2) S Use a formula to find the area of rectangles.(5.4.2) Topic: Unit 9 - Coordinates, Area, Volume, Capacity Grade: 5 Unit Essential Question(s) Instructional Tools/Reminders: How can I graph points on a coordinate grid? Coordinate grid Order number pair Axis transformation Perpendicular Volume Cubic unit Prism Capacity GAMES: Hidden Treasure Advanced Hidden Treasure Frac-Tac-Toe Fraction Spin Concept: Coordinate Grids Lesson Essential Questions & Vocabulary: 9.1 How can I find ordered number pairs and coordinates on a coordinate grid? Coordinate grid Ordered number pair Coordinate Axis 9.2 How can I plot number pairs that form a given figure? Coordinate grid Ordered number pair Coordinate Transformation 9.3 How do I identify transformations of number pairs that change the figure? Opposite of a number Concept: Formulas for Area Area Explorations Lesson Essential Questions & Vocabulary: 9.4 How can I identify and apply the formula for the area of a rectangle? Area Square units Base Height Formula Variable 9.5 How can I use the rectangle method to find the area of triangles and parallelograms? Personal references Rectangle method 9.6 How can I use formulas for the area of a triangle and the area of a parallelogram? Base Height (altitude) Perpendicular 9.7 How can I use sampling to estimate the percent of Earth’s surface covered by water? Concepts: Volume and Capacity Lesson Essential Questions & Vocabulary: 9.8 How do I develop and use a formula to find the volume of a rectangle prism? Volume Cubic unit Rectangular prism Face Base (of a rectangular prism) Height (of a rectangular prism) 9.9 How can I calculate the volume of any prism by multiplying the area of its base by its height? Prism Face 9.10 What are the relationships among the liter, milliliters, and cubic centimeter? Capacity Liter (L) Quart (qt) Cup (c) Milliliter (mL) Cubic centimeter (cm cubed) Concept: Review and Assessment Lesson Essential Questions & Vocabulary: 9.11 How did I progress toward my learning goals? Latitude Longitude CSO/Unit Correlation CSO 5.1.1 5.1.2 5.1.3 *5.1.4 5.1.6 *5.1.7 *5.1.8 *5.1.9 *5.1.10 *5.1.11 *5.1.12 *5.2.1 *5.2.2 5.2.4 *5.3.1 *5.3.2 *5.3.5 5.3.6 5.4.1 5.4.2 5.4.3 *5.4.9 *5.5.3 Description Read, write, order and compare all whole numbers. Read, write, order and compare all decimals. Identify place value of each digit utilizing standard and expanded form in any whole number. Estimate with whole numbers and decimals, including money, to determine reasonableness of an answer. Compare and order fractions, improper fractions and mixed numbers with like and unlike denominators (e.g., greatest common factor, lowest common multiple). Model and write equivalencies of fractions, decimals, percents, and ratios. Add and subtract fractions and mixed numbers. Model multiplication and division of fractions to solve the algorithm. Model multiplication of decimals and division of decimals by a whole number divisor. Develop fluency in addition, subtraction, multiplication, and division of whole numbers. Solve grade level appropriate story problems using multiple strategies. Explore a variety of patterns with missing elements (e.g., square numbers, powers, triangular numbers, arithmetic sequences). Use input/output model with grade appropriate functions. Evaluate an expression given a value for the variable. Classify and compare polygons. Construct a 3-dimensional figure from different views (orthogonal drawings) Recognize the images of figures after reflections, translations, and rotations. Draw a similar figure using a scale. Estimate, measure, compare, order, and draw lengths of real objects in parts of an inch up to 1/8 of an inch and millimeters. Determine and compare area of triangles and parallelograms using appropriate formula. Solve problems using the formulas for determining volume of a rectangular prism. Determine actual measurement from scale drawings. Construct, read, and interpret tables, charts, and graphs to draw reasonable inferences or verify predictions. Construct a circle graph. Level of Importance I I I E* I E E E E E E* E* E* C E E E I I I I E E* WESTEST Thinking Skill 1 1 1 2 2 1 2 3 1 1 1 2 1 1 1 2 1 3 2 1 2 2 1 5.5.5 CSO: Star (*) = 80% constant on WESTEST Italicized = Constructed Response Item on WESTEST Bold = Formerly released item from WESTEST C 3 Level of Importance: E: Essential (*: assessed 3 or more times on WESTEST) I: Important C: Compact Unit 9 Constructed Response Items CSO ma5.4.2 Alex is planning a rectangular garden. The garden will be 9 feet wide and 15 feet long. What will be the area of the garden? What will be the perimeter of the garden? In the box below, show your work and write your answer on the line. Answer: A = ___________ square feet, P = ________________ feet McDowell County Schools Grade 5 Revised May 2006 46 Scoring Rubric: 2 points: clear understanding correct responses work shown correctly 1 point: correct responses work shown reasonably 0 points: no attempt made McDowell County Schools Grade 5 Revised May 2006 47 Name: a. April (see pacing) B Understand the relationship between the volume of pyramids and prisms, and the volume of cones and cylinders. (5.4.3) B Find the surface area of prisms. (5.4.4) B Understand how to find the surface area of cylinders. (5.4.4) B Understand the concept of capacity and how to calculate it. (5.4.6) D/S Use formulas to find the volume of prisms and cylinders. (5.4.3) S Use formulas to find the area of polygons and circles. (5.4.5) S Know the properties of geometric solids. (5.3.2) Topic: Unit10-Algebra Concepts and Skills Grade: 5 Key Learning Goals: Unit Essential Question(s) How can I use a pan-balance approach to solve simple equations? Instructional Tools/Reminders: Algebraic expression Rate Rate of speed Formula GAMES: First to 100 Mixed Number Spin Fraction Spin b. c. d. e. f. g. Concept: Pan-Balance Equations; Algebraic Expressions Lesson Essential Questions & Vocabulary: 10.1 How can I use a panbalance approach to solve simple equations? 10.2 How can I solve panbalance problems that model sets of two equations in two unknowns? 10.3 How do I translate word descriptions into algebraic expressions? Algebraic equations Concepts: Rules, Tables, and Graphs; Math Modeling with Data, Formulas, Rules, Tables, and Graphs Lesson Essential Questions & Vocabulary: 10.4 How do I represent rates with formulas, tables, and graphs? Rate Rate of speed Formula Variable Line graph 10.6 How can I use a table and graph to solve and interpret a problem based on a real-world situation? Ordered number pairs Coordinate 10.7 How can I interpret line graphs? Mystery graph 10.5 How can I use a formula to predict the time of Old Faithful’s next eruption? Concept: Circumference and Area of Circles Concept: Review and Assessment Lesson Essential Questions & Vocabulary: 10.8 How can I relate circumference to the diameter of a circle? 10.9 How can I measure the area of a circle? Lesson Essential Questions & Vocabulary: 10.10 How did I progress on my learning goals? Geyser Predict CSO/Unit Correlation CSO Description Level of Importance I I E E E E E E* E* E* E C E I I I C E* WESTEST Thinking Skill 1 2 1 2 3 1 1 2 1 1 2 1 1 2 1 2 2 1 Read, write, order and compare all decimals. Compare and order fractions, improper fractions and mixed numbers with like and unlike denominators (e.g., greatest common factor, lowest common multiple). *5.1.7 Model and write equivalencies of fractions, decimals, percents, and ratios. *5.1.8 Add and subtract fractions and mixed numbers. *5.1.9 Model multiplication and division of fractions to solve the algorithm. *5.1.10 Model multiplication of decimals and division of decimals by a whole number divisor. *5.1.11 Develop fluency in addition, subtraction, multiplication and division of whole numbers. *5.1.12 Solve grade level appropriate story problems using multiple strategies. *5.2.1 Explore a variety of patterns with missing elements (e.g., square numbers, powers, triangular numbers, arithmetic sequences). *5.2.2 Use input/output model with grade appropriate functions. *5.2.3 Write an equation using a variable to solve problems. Evaluate an expression given a value for the variable. 5.2.4 *5.3.1 Classify and compare polygons. Estimate, measure, compare, order, and draw lengths of 5.4.1 real objects in parts of an inch up to 1/8 inch and millimeters. Determine and compare area of triangles and 5.4.2 parallelograms using appropriate formula. *5.4.4 Understand the relationship between area and perimeter of a plane figure. *5.4.6 Evaluate and/or measure the weight/mass of real objects in ounces, pounds, tons, grams, and kilograms. *5.5.3 Construct, read, and interpret tables, charts, and graphs to draw reasonable inferences or verify predictions. Construct a circle graph 5.5.5 5.1.2 5.1.6 CSO: Star (*) = 80% constant on WESTEST Italicized = Constructed Response Item on WESTEST Bold = Formerly released item from WESTEST C 3 Level of Importance: E: Essential (*: assessed 3 or more times on WESTEST) I: Important C: Compact Unit 10 Constructed Response Item CSO ma5.5.3 Mrs. Jones surveyed her class. Use the line pot below to answer the questions. X X X X X X Alternative X X X Rock X X X R&B X Classical X X X X X Country 1. If the entire class responded to the survey, how many students are in the class? _________ 2. What information was collected about music? ____________________________________ ___________________________________________________________________________ 3. Which type of CD’s did students buy most often? _______________________________ 4. Write a survey question that might gather the following information: In one school there are 6 sets of twins, 2 sets of triplets, and 1 set of quadruplets. _________________________________________________________________________ _________________________________________________________________________ _________________________________________________________________________ McDowell County Schools Grade 5 Revised May 2006 50 Scoring Rubric: 4 points: demonstrates clear understanding 3 correct response correct explanation (survey question) 3 points: demonstrates good understanding 2 of 3 correct responses explanation mostly correct 2 points: demonstrates some understanding 1 of 3 correct responses attempts explanation, but not clear 1 point: demonstrates little understanding work has major errors explanation attempted, does not make sense 0 points: no attempt made irrelevant responses McDowell County Schools Grade 5 Revised May 2006 51 Name: a. April/May (see pacing) B Understand the relationship between the volume of pyramids and prisms, and the volume of cones and cylinders. (5.4.3) B Find the surface area of prisms. (5.4.4) B Understand how to find the surface area of cylinders. (5.4.4) B Understand the concept of capacity and how to calculate it. (5.4.6) D/S Use formulas to find the volume of prisms and cylinders. (5.4.3) S Use formulas to find the area of polygons and circles. (5.4.5) S Know the properties of geometric solids. (5.3.2) Topic: Unit 11-Volume Grade: 5 Key Learning Goals: Unit Essential Question(s) How can I use volume to understand the relationship between pyramids and prisms to cones and cylinders? Instructional Tools/Reminder Geometric solid prism pyramid cylinder Cone sphere edge vertex face Polyhedron cube base apex Surface are Games: 3D Shape Sort Polygon Capture Name That Number b. c. d. e. f. g. Concept: Geometric Solids; Hands on Exploration of Volume of Pyramids, Cylinders, and Cones Lesson Essential Questions & Vocabulary 11.1 What are the names and properties of geometric solids? Geometric solid Prism Pyramid Cylinder Cone Sphere Edge Vertex (vertices or vertexes) Flat surface Curved surface Face Polyhedron Cube 11.2 How can I compare the properties of prisms, pyramids, cylinders, and cones? Base Apex 11.3 How do I solve volume problems for prisms and cylinders? 11.4 How do I determine the relationship between the volume of prisms and pyramids, and the volume of cylinders and cones? Concept: Links of Volume to Density and Displacement; Relationships Among Units of Capacity, Volume, and Weight Lesson Essential Questions & Vocabulary: 11.5 How do I use the displacement method to determine the volume of an irregular object? Displacement Calibrate 11.6 How can I convert measurements among units of weight, capacity, and volume in cubic units? Concepts: Surface Area Concept: Review and Assessment Lesson Essential Questions & Vocabulary: 11.7 How do I calculate the surface area of prisms, cylinders, and pyramids? Surface area Lesson Essential Questions & Vocabulary: 11.8 How have I progressed towards my learning goals? CSO/Unit Correlation CSO Description Level of Importance I E E E E E E E* E* E* E C E E I I I E C WESTEST Thinking Skill 1 1 1 2 3 1 1 1 2 1 2 1 1 2 2 1 2 2 2 Read, write order and compare all decimals. Identify and use the divisibility rules of 2, 3, 5, 9 and 10. *5.1.7 Model and write equivalencies of fractions, decimals, percents, and ratios. *5.1.8 Add and subtract fractions and mixed numbers. *5.1.9 Model multiplication and division of fractions to solve the algorithm. *5.1.10 Model multiplication of decimals and division of decimals by a whole number divisor. *5.1.11 Develop fluency in addition, subtraction, multiplication, and division of whole numbers. *5.1.12 Solve grade level appropriate story problems using multiple strategies. *5.2.1 Explore a variety of patterns with missing elements (e.g., square numbers, powers, triangular numbers, arithmetic sequences). *5.2.2 Use input/output model with grade appropriate functions. *5.2.3 Write an equation using a variable to solve problems. Evaluate an expression given a value for the 5.2.4 variable. *5.3.1 Classify and compare polygons. *5.3.2 Construct a 3-dimensional figure from different views (orthogonal drawings). Estimate, measure, compare, order, and draw 5.4.1 lengths of real objects in parts of an inch up to 1/8 of an inch and millimeters. Determine and compare area of triangles and 5.4.2 parallelograms using appropriate formula. Solve problems using the formulas for 5.4.3 determining volume of a rectangular prism. *5.4.5 Understand appropriate grade level conversions within a a system of measure and apply to problem solving situations. Evaluate and/or measure the weight/mass of 5.4.6 real objects in ounces, pounds, tons, grams, and kilograms. 5.1.2 *5.1.5 CSO: Star (*) = 80% constant on WESTEST Italicized = Constructed Response Item on WESTEST Bold = Formerly released item from WESTEST Level of Importance: E: Essential (*: assessed 3 or more times on WESTEST) I: Important C: Compact Unit 11 Constructed Response Items CSO ma5.4.4 Find the surface area of a prism where the height is 8 inches, the width is 10 inches, and the depth is 4 inches. Explain how you found your answer: _________________________________________________________________________ _________________________________________________________________________ _________________________________________________________________________ _________________________________________________________________________ McDowell County Schools Grade 5 Revised May 2006 54 Scoring Rubric: 3 points: correct response clear explanation 2 points: incorrect response due to calculation error correct explanation 1 point: incorrect response unclear or incorrect explanation 0 points: incorrect response no attempt made for explanation McDowell County Schools Grade 5 Revised May 2006 55 Name: a. b. c. May/June (see pacing) B Understand and use tree diagrams to solve problems. (5.5.2) B Compute the probability of outcomes when choices are equally likely. (5.4.2) B/D Use the Multiplication Counting Principle to find the total number of possible outcomes of sequence of numbers. (5.5.2) D Find the greatest common factor of two numbers. (5.1.6) D Find the least common multiple of two numbers. (5.1.6) D/S Solve ratio and rate number stories. (5.1.7) S Find the factors of numbers. (5.1.6) S Find the prime factorizations of numbers.(5.1.6) Topic: Unit 12-Probability, Ratio, and Rates Grade: 5 Key Learning Goals: Unit Essential Question(s) How can I use probability, ratio, and rates to improve my math? Instructional Tools/Reminders: Factor tree prime factorization Common factor Least common multiple Probability Tree diagram ratio Multiplication Counting Principle GAMES: Frac-Tac-Toe Name That Number Spoon Scramble d. e. f. g. h. Concept: Factor Trees; Choices, Tree Diagrams, and Probability Lesson Essential Questions & Vocabulary: 12.1 How do I use a factor tree to find the prime factors, greatest common factors, and least common multiples of numbers? Factor tree Prime factorization Common factor Greatest common factor Least common multiple 12.2 How can I use tree diagrams, choices, and probability to find the number of ways a sequence of choices can be made? Probability Multiplication counting principle Tree diagram Equally likely Concept: Ratios Concepts: Heart Rate and Exercise Project Lesson Essential Questions & Vocabulary: 12.6 How can I find my heart rate? Heart rate Pulse Pulse rate 12.7 How can I find my heart rate and graph personal and heart rate data? Rate Profile Target heart rate 12.8 How can I calculate and compare cardiac output data before and after excercising? Oxygen Nutrients Carbon dioxide Cardiac output Lesson Essential Questions & Vocabulary: 12.3 How do I use and express ratios? Ratio Ratio comparison Magnitude 12.4 How can I solve problems involving ratios of part of a set to the whole set? 12.5 How can I write and solve number models for ratio number stories? Concept: American Tour-End of Year Project; End of Unit Assessment Lesson Essential Questions & Vocabulary: 12.9 How can I plan and complete a mathematical project based on data in the American Tour? 12.10 How did I progress toward my learning goals? CSO/Unit Correlation CSO Description Level of Importance I I I E I E E E E E E* E* E* E C I E* WESTEST Thinking Skill 1 1 1 1 2 1 2 3 1 1 1 2 2 2 1 1 2 Read, write, order and compare all whole numbers. Read, write, order and compare all decimals. Identify place value of each digit utilizing standard and expanded form in any whole number. *5.1.5 Identify and use the divisibility rules of 2, 3, 5, 9 and 10. Compare and order fractions, improper fractions and 5.1.6 mixed numbers with like and unlike denominators(e.g., greatest common factor, lowest common multiple). *5.1.7 Model and write equivalencies of fractions, decimals, percents, and ratios. *5.1.8 Add and subtract fractions and mixed numbers. *5.1.9 Model multiplication and division of fractions to solve the algorithm. *5.1.10 Model multiplication of decimals and division of decimals by a whole number divisor. *5.1.11 Develop fluency in addition, subtraction, multiplication, and division of whole numbers. *5.1.12 Solve grade level appropriate story problems using multiple strategies. *5.2.1 Explore a variety of patterns with missing elements (e.g., square numbers, powers, triangular numbers, arithmetic sequences). *5.2.2 Use input/output modle with grade appropriate functions. *5.2.3 Write an equation using a variable to solve problems. Evaluate an expression given a value for the variable. 5.2.4 Determine and compare area of triangles and 5.4.2 parallelograms using appropriate formula. *5.5.2 Identify probabilities and solve problems involving the probability of an event by using tree diagrams or by construction of a sample space representing all possible results. *5.5.3 Construct, read, and interpret tables, charts, and graphs to draw reasonable inferences or verify predictions. 5.1.1 5.1.2 5.1.3 E* 2 CSO: Star (*) = 80% constant on WESTEST Italicized = Constructed Response Item on WESTEST Bold = Formerly released item from WESTEST Level of Importance: E: Essential (*: assessed 3 or more times on WESTEST) I: Important C: Compact Unit 12 Constructed Response Items CSO ma5.5.2 Janice, Kayle, and Mary are running for class president. Andrew, Jason, and Mike are running for vice-president. Each student has an equal chance of being elected. 1. Create a tree diagram to find all the possible outcomes. 2. How many possible outcomes are there? ____________ McDowell County Schools Grade 5 Revised May 2006 58 Scoring Rubric: 2 points: correct tree diagram correct answer 1 point: partially correct tree diagram answer correct according to student’s diagram 0 points no attempt made McDowell County Schools Grade 5 Revised May 2006 59 APPENDIX McDowell County Schools Grade 5 Revised May 2006 60 WESTEST Mathematics Rubric Grades 3-8 3-Point Rubric for Constructed-Response Items This rubric is used to score students’ responses to constructed-response items. 3 Points A three-point response clearly communicates the student’s mathematical understanding of the task. The response demonstrates a thorough understanding of the mathematical concepts and/or procedures embodied in the task. The student completes the task correctly, using mathematically sound procedures. The response contains clear, complete explanations and/or accurate work when required. 2 Points A two-point response demonstrates a partial understanding of the task. The response demonstrates adequate understanding of the mathematical concepts and/or procedures embodied in the task. The response addresses most aspects of the task, using mathematically sound procedures. It may contain an incorrect solution but applies a mathematically appropriate process with valid reasoning and/or explanation. The response may contain a correct solution but provides faulty or incomplete procedures, reasoning, and/or explanations. The response may contain a correct solution but lacks work when required. The response may reflect some misunderstanding of the underlying mathematical concepts and/or procedures. Minor omissions may exist, but do not detract from the correctness of the response. 1 Point A one-point response is incomplete and exhibits many flaws but is not completely incorrect. The response demonstrates only a limited understanding of the mathematical concepts and/or procedures embodied in the task. The response may address some elements of the task correctly but reaches an inadequate solution and/or provides reasoning that is faulty or incomplete. The response exhibits multiple flaws related to a misunderstanding of important aspects of the task, misuse of mathematical procedures, or faulty mathematical reasoning. The response reflects a lack of essential understanding of the underlying mathematical concepts. 0 Points A zero-point response lacks any evidence of mathematical knowledge that is appropriate to the intent of the task. Also, the response may be inaccurate or lack relevancy or the student failed to respond to the task. McDowell County Schools Grade 5 Revised May 2006 61 Crosswalk between Blooms Taxonomy and WESTEST Thinking Skills WESTEST Thinking Skills Knowledge • observation and recall of information • knowledge of dates, events, places • knowledge of major ideas • mastery of subject matter Question Cues: list, define, tell, describe, identify, show, label, collect, examine, tabulate, quote, name, who, when, where, etc. Comprehension • understanding information • grasp meaning • translate knowledge into new context • interpret facts, compare, contrast • order, group, infer causes • predict consequences Question Cues: summarize, describe, interpret, contrast, predict, associate, distinguish, estimate, differentiate, discuss, extend Application • use information • use methods, concepts, theories in new situations • solve problems using required skills or knowledge Questions Cues: apply, demonstrate, calculate, complete, illustrate, show, solve, examine, modify, relate, change, classify, experiment Analysis • seeing patterns • organization of parts • recognition of hidden meanings • identification of components Question Cues: analyze, separate, order, explain, connect, classify, arrange, divide, compare, select, explain, infer Level 1 Knowledge/Recall/Recognition: • recall of material learned • knowledge of major ideas • observation of information Sample item: Who was the first president of the United States? Level 2 Comprehension/Application/ Conceptual Thinking: • understanding the meaning of material or information • using learned information in new, different situations and problems Sample: If Bill had 49 cents, how many 10 cent balloons could he buy? Level 3 Analysis/Strategic Thinking: • identifying parts of new material, • analyzing the relationships • seeing principles involved Sample: What evidence can you find to support the principle that air expands when heated? McDowell County Schools Grade 5 Revised May 2006 62 Fifth Grade Performance Descriptors Performance Descriptors: Number and Operations (MA.PD.5.1) ■ Distinguished The student demonstrates exceptional and exemplary performance with distinctive and sophisticated application of knowledge and skills that exceeds the standard in number and operations. The student multiplies and divides fractions and decimals without models. The student uses clear mathematical language to explain answers in oral and written form. ■ Above Mastery The student demonstrates competent and proficient performance and shows a thorough and effective application of knowledge and skills that exceeds the standard in number and operations. The student is proficient in comparing and ordering fractions and decimals. The student applies estimation strategies to determine reasonableness of answers and solves grade level appropriate story problems using multiple strategies. ■ Mastery The student demonstrates fundamental course or grade level knowledge and skills by showing consistent and accurate academic performance that meets the standard in number and operations. The student is fluent in place value and operations with whole numbers. The student is proficient in adding and subtracting fractions and mixed numbers and models multiplication and division of fractions and decimals. The student demonstrates an understanding of equivalence of fractions, decimals, percents, and ratios with models. ■ Partial Mastery The student demonstrates basic but inconsistent performance of fundamental knowledge and skills characterized by errors and/or omissions in number and operations. Performance needs further development. The student is developing fluency in whole number operations and place value. The student is not consistently able to accurately add and subtract fractions. ■ Novice The student demonstrates substantial need for the development of fundamental knowledge and skills, characterized by fragmented and incomplete performance in number and operations. Performance needs considerable development in place value and some operations with whole numbers. Performance Descriptors: Algebra (MA.PD.5.2) ■ Distinguished The student demonstrates exceptional and exemplary performance with distinctive and sophisticated application of knowledge and skills that exceeds the standard in algebra. The student generates a variety of patterns with missing elements. The student translates a word problem into an equation using a variable, solves the problem, and justifies the solution in oral or written form. ■ Above Mastery The student demonstrates competent and proficient performance and shows a thorough and effective application of knowledge and skills that exceeds the standard in algebra. The student explores a variety of patterns with missing elements with square numbers, powers, and triangular numbers. Given a table of outputs, the student identifies the rule and gives the input with grade-level appropriate functions. The student translates a word problem into an equation using a variable and solves the problem. ■ Mastery The student demonstrates fundamental course or grade level knowledge and skills by showing consistent and accurate academic performance that meets the standard in algebra. The student explores a variety of patterns with missing elements with arithmetic sequences. Given the input and the output, the student identifies the rule with grade-level appropriate functions. The student evaluates an expression given a value for the variable. The student translates a word problem into an equation using a variable. ■ Partial Mastery The student demonstrates basic but inconsistent performance of fundamental knowledge and skills characterized by errors and/or omissions in algebra. Performance needs further development. The student continues a pattern with missing elements when given the rule. Given the input and the rule, the student identifies the output with grade-level appropriate functions. The student solves an equation with a variable. McDowell County Schools Grade 5 Revised May 2006 63 ■ Novice The student demonstrates substantial need for the development of fundamental knowledge and skills, characterized by fragmented and incomplete performance in algebra. Performance needs considerable development in using patterns, functions, expressions, and equations with variables. Performance Descriptors: Geometry (MA.PD.5.3) ■ Distinguished The student demonstrates exceptional and exemplary performance with distinctive and sophisticated application of knowledge and skills that exceeds the standard in geometry. The student uses clear mathematical language and more than one characteristic to compare polygons in oral or written form. The student describes a series of motions of a figure that has been transformed. ■ Above Mastery The student demonstrates competent and proficient performance and shows a thorough and effective application of knowledge and skills that exceeds the standard in geometry. The student constructs a threedimensional figure from orthogonal drawings. The student draws a similar figure using a scale. ■ Mastery The student demonstrates fundamental course or grade level knowledge and skills by showing consistent and accurate academic performance that meets the standard in geometry. The student classifies and compares polygons. The student measures angles using a protractor and draws a design with more than one line of symmetry. The student recognizes the images of figures after reflections, translations, and rotations. ■ Partial Mastery The student demonstrates basic but inconsistent performance of fundamental knowledge and skills characterized by errors and/or omissions in geometry. Performance needs further development. The student identifies and classifies polygons and identifies lines of symmetry in a design. The student identifies a figure that is drawn to scale. ■ Novice The student demonstrates substantial need for the development of fundamental knowledge and skills, characterized by fragmented and incomplete performance in geometry. Performance needs considerable development in classifying polygons, constructing three-dimensional figures, and recognizing transformations. Performance Descriptors: Measurement (MA.PD.5.4) ■ Distinguished The student demonstrates exceptional and exemplary performance with distinctive and sophisticated application of knowledge and skills that exceeds the standard in measurement. The student models, applies, and explains the formulas for area of triangles and parallelograms. The student solves a wide variety of problems involving measurement and explains solutions in oral and written form. ■ Above Mastery The student demonstrates competent and proficient performance and shows a thorough and effective application of knowledge and skills that exceeds the standard in measurement. The student models and applies the formulas for area of triangles and parallelograms and volume of a rectangular prism. The student applies knowledge of measurement tools, units, and conversions in problem-solving situations. ■ Mastery The student demonstrates fundamental course or grade level knowledge and skills by showing consistent and accurate academic performance that meets the standard in measurement. The student demonstrates understanding of the relationship between area and perimeter of plane figures. The student applies the formulas for finding the area of triangles and parallelograms and the volume of rectangular prism. The student selects appropriate tools, formulas, and/or units of measure of mass/weight and uses appropriate conversions within the metric and customary systems. The student calculates elapsed time involving more than a 24-hour span. ■ Partial Mastery The student demonstrates basic but inconsistent performance of fundamental knowledge and skills characterized by errors and/or omissions in measurement. Performance needs further development. The student calculates elapsed time within a 24-hour span. The student is developing proficiency in conversion of units of measurement and the use of formulas. McDowell County Schools Grade 5 Revised May 2006 64 ■ Novice The student demonstrates substantial need for the development of fundamental knowledge and skills, characterized by fragmented and incomplete performance in measurement. Performance needs considerable development in using measurement tools, units, and conversions. Performance Descriptors: Data Analysis (MA.PD.5.5) ■ Distinguished The student demonstrates exceptional and exemplary performance with distinctive and sophisticated application of knowledge and skills that exceeds the standard in data analysis and probability. The student chooses the most appropriate statistical method, collects, organizes and displays data, analyzes the data, and formulates questions based on the data. The student explains the relationship between the theoretical and experimental probability of an event in oral and/or written form. ■ Above Mastery The student demonstrates competent and proficient performance and shows a thorough and effective application of knowledge and skills that exceeds the standard in data analysis and probability. The student interprets data displayed in a chart, table, graph, and/or stem and leaf plot. The student constructs a sample space and/or uses a tree diagram to represent the probability of an event. ■ Mastery The student demonstrates fundamental course or grade level knowledge and skills by showing consistent and accurate academic performance that meets the standard in data analysis and probability. The student collects, organizes, displays, and reads data in a chart, table, graph, and/or stem and leaf plot. The student constructs, reads, or interprets tables, charts, and graphs to draw reasonable inferences or verify predictions. The student constructs a circle graph. The student carries out experiments to determine probabilities and interprets the results. ■ Partial Mastery The student demonstrates basic but inconsistent performance of fundamental knowledge and skills characterized by errors and/or omissions in data analysis and probability. Performance needs further development. The student reads data in a chart, table, graph, and stem and leaf plot. The student carries out experiments to determine probabilities. ■ Novice The student demonstrates substantial need for the development of fundamental knowledge and skills, characterized by fragmented and incomplete performance in data analysis and probability. Performance needs considerable development in using appropriate statistical methods to analyze data. The student carries out probability experiment McDowell County Schools Grade 5 Revised May 2006 65