5th Grade Math Sample of Proficiency Scales Sample Includes: Grade Level Scales (1 example) Standard-‐by-‐Standard Scales (1 example) Pre-‐Assessment (first 3 pages) Mastery Assessment (first 3 pages) The standards in the Scales Package are based on the work of Marzano Research Laboratory and Re-‐Inventing Schools Coalition to ensure appropriate rigor and depth of understanding. We will go through each part of the scales package, giving a brief explanation of what you would receive and then show an example for 5th Grade Standard: MA.05.MP.RIP.01.01 The student will: use operations to solve problems involving line plots with data in fractions of a unit beyond (1/2, 1/4, 1/8) (5.MD.2) Understanding the Coding for each standard: Example Standard 5th Grade: MA.05.MP.RIP.01.01 Standard Coding Breakdown: MA = Math 05 = 5th Grade MP= Measurement, Data, Statistics, and Probability RIP = Represent and Interpret Data (Labeled from our Digital Platform) 01 = Standard number in learning progression 01 = Standard version for use in refining the learning Grade Level Scales • There is a complete K through 8 scope and sequence of learning for ELA and Math • They are organized in Excel format • The scope and sequence of learning is separated by grade levels • The proficiency scales include learning expectations for score 2, score 3 and score 4 for each standard • Specific common core alignment indicated within the standard descriptions and learning expectations This is a sample of what a Grade Level Scale looks like but it only shows 3 standards. There are a total of 16 standards in 5th Grade Math and you will have access to all of them. MA.05.GE.VO.01.01 = Geometry -‐ Volume MA.05.MP.ME.01.01 = Measurement, Data, Statistics, and Probability -‐ Measurement MA.05.MP.RID.01.01 = Measurement, Data, Statistics, and Probability -‐ Represent and Interpret Data Standard Code (Educate) MA.05.GE.VO.01.01 MA.05.MP.ME.01.01 MA.05.MP.RID.01.01 Standard Description Score 4 Score 3 Score 2 The student will: solve real-‐world and The student will: use the score 3.0 The student will: solve real-‐world and The student will: recognize or recall specific vocabulary, mathematical problems involving volume knowledge to go beyond proficiency mathematical problems involving volume such as: add, attribute, centimeter, count, cube, cubic, (5.MD.5): apply the formula V = l x w x h to expectations. For example, by describing (5.MD.5): apply the formula V = l x w x h to find foot, figure, formula, improvised, inch, measure, overlap, find the volume of right rectangular prisms the relationship between V, l, w, h, and/or the volume of right rectangular prisms part, relationship, right rectangular prism, solid, sum, unit (5.MD.5b) find volumes of solid figures two non-‐overlapping right triangles. (5.MD.5b) find volumes of solid figures cube, volume. The student will perform basic processes, composed of two non-‐overlapping right (Comprehension) composed of two non-‐overlapping right such as: explain that volume is an attribute of solid rectangular prisms by adding the volumes rectangular prisms by adding the volumes of figures (5.MD.3) measure volume by counting unit cubes, of the parts (5.MD.5c) the parts (5.MD.5c) (Retrieval) using cubic centimeters, cubic inches, cubic feet, and improvised units and understand the relationship between the sum of the cubes and the volume formula, V = l x w x h (5.MD.4, 5.MD.5a) (Retrieval) The student will: use conversions to solve The student will: use the score 3.0 The student will: use conversions to solve multistep word problems (5.MD.1) knowledge to go beyond proficiency multistep word problems (5.MD.1) expectations. For example, by analyzing (Comprehension) perspectives on which units of measurement would be most useful within different contexts. (5.MD.1) (Analysis) The student will: recognize or recall specific vocabulary, such as: centimeter, conversion, foot, meter, unit, word problem, yard. The student will perform basic processes, such as: convert among different-‐sized standard measurement units within a given measurement system (e.g., feet to yards, centimeters to meters) (5.MD.1) (Comprehension) The student will: use operations to solve problems involving line plots with data in fractions of a unit beyond (1/2, 1/4, 1/8) (5.MD.2) The student will: recognize or recall specific vocabulary, such as: data, fraction, line plot, operation, unit. The student will perform basic processes, such as: make a line plot of measurement data in fractions of a unit (5.MD.2) (Comprehension) The student will: use the score 3.0 knowledge to go beyond proficiency expectations. For example, by determine which fractional representation is the most suitable to use in certain situations (Knowledge Utilization) The student will: use operations to solve problems involving line plots with data in fractions of a unit beyond(1/2, 1/4, 1/8) (5.MD.2) (Analysis) Standard-‐by-‐Standard Scales • Standards are organized by grade level and by strand for both ELA and Math • Each standard is presented in two separate documents, PDF and Excel format • PDF for printing and incorporating into documents • Excel for adding to or modifying to fit your personal needs • Each level of learning for the standard is given a taxonomy level for better alignment in the instruction and assessment • Assessment items are given to show the level of learning in the standard • Specific common core alignment indicated within the standard description and the score 2, score 3, and score 4 expectations Example of 5th Grade Standard-‐by-‐Standard below: Content Area: Math Measurement Topic: Represent and Interpret Data Scope Level: 05 Learning Target: MA.05.MP.RID.01.01 Proficiency Level Proficiency Level Description Taxonomy Level Assessment Items 4.0 The student will: use the score 3.0 knowledge to go beyond proficiency expectations. Using Knowledge By determine which fractional representation is the most suitable to use in certain situations Measure 10 different shoes using a ruler to the nearest 1/4 inch. Record the data in a table Display the data on a line plot. 3.0 The student will: • use operations to solve problems involving line plots with data in fractions of a unit beyond (1/2, 1/4, 1/8) (5.MD.2) Analysis Draw a horizontal line and figure out your scale. Plot your data by placing an X over the correct number for each object you measured. Label the horizontal axis and record the title of the line plot. What is the combined length of all of objects you measured? Show your work. What is the difference between the longest and shortest show you measured? Show your work. 2.0 1.0 The student will recognize or recall specific vocabulary, such as: • data, fraction, line plot, operation, unit The student will perform basic processes, such as: • make a line plot of measurement data in fractions of a unit (5.MD.2) (5.MD.2) A student measured the length of 10 bugs to the nearest 1/8 of an inch and recorded the following data: Comprehension Bug Lengths: 12/8 in., 23/8 in., 3½ in., 41 in., 56/8 in., 62/8 in., 7½ in., 83/8 in., 91/8 in.,107/8 in. Display the data on a line plot. What was the difference in length between the longest and shortest bug? Explain your answer. Pre-‐Assessment • Pre-‐assessments can be used to determine student readiness level before instruction • There are pre-‐assessment questions for all standards in Grades K through 6 for score 3 & score 2. • We are currently making the 7th and 8th grade pre-‐ assessments and incorporating the score 4 into all of the grade level pre-‐assessments. We will be finished soon and you will be given the most updates pre-‐assessment version when available • Pre-‐assessments are presented in PDF and Word format Example of the first three pages of the 5th Grade Pre-‐ Assessment below: GRADE 5 PRE-‐ASSESSMENTS MATH MA.05.NQ.PV.01.01 Number and Quantity: Place Value The student will: • (5.NBT.3b) compare two decimals to thousandths • (5.NBT.4) round decimals to any place Score 3/ (Analysis): Using the symbols <, =, or >, describe the relationship between the pairs of numbers below: 5.6 _____5.599 3.781 ____ 4.0 3.99 ____3. 785 2.9 ____ 2.900 Which of the following have been rounded correctly? 3.891 rounded to the nearest tenths is 3.9 correct incorrect 2.586 rounded to the nearest hundredths is 2.6 correct incorrect 3.359 rounded to the nearest whole number is 3 correct incorrect Score 2/ (Retrieval): The student will recognize or recall specific vocabulary, such as base-‐ten numeral, decimal, decimal point, digit, divide, expanded form, multi-‐digit number, multiply, number name, pattern, place, round, thousandth, value, whole number The student will perform basic processes, such as read and write decimals to thousandths using base-‐ ten numerals, number names, and expanded form (5.NBT.3a) Read the following decimal numbers out loud: 3.45 6.2 122.673 Write the following as numbers: one hundred ten and thirty-‐one hundredths eight and five hundred twenty-‐one thousandths three tenths seventy-‐eight hundredths Re-‐Inventing Schools Coalition 2013 Grade 5– Math Pre Assessment MA.05.NQ.PV.02.01 Number and Quantity: Place Value The student will: • (5.NBT.2) use whole number exponents to denote powers of 10 Score 3/ (Comprehension): Fill in the blank with the exponent that will produce the answer. 10? = 1000 _______ 10? = 1,000,000 _________ 10? = 100 __________ 10? = 10 __________ Score 2/ (Retrieval): The student will recognize or recall specific vocabulary, such as base-‐ten numeral, decimal, decimal point, digit, divide, exponent, multi-‐digit number, multiply, number name, pattern, place, powers of 10, thousandth, value, whole number The student will perform basic processes, such as describe the value of digits in a multi-‐digit number (e.g., a digit in one place represents 10 times as much as it represents in the place to its right and 1/10 of what it represents in the place to its left) (5.NBT.1), explain patterns in the number of zeroes and the decimal point when multiplying or dividing by powers of 10 (5.NBT.2), read and write decimals to thousandths using base-‐ten numerals, number names, and expanded form (5.NBT.3a) For the number 3,542: *state the place value of each number: ex. 3 is at the thousandth place 5 is at the ____________ place 4 is at the ___________ place 2 is at the __________ place How much greater is the thousandths place than the hundredths place? How much less is the tenths place than the hundredths place? MA.05.NQ.AF.01.01 Adding and Subtracting Fractions Re-‐Inventing Schools Coalition 2013 Grade 5-‐ Math Pre Assessment The student will: • (5.NF.2) solve word problems involving the addition and subtraction of fractions referring to the same whole, including cases of unlike denominators • (5.NF.2) use benchmark fractions to estimate answers and check for reasonableness Score 3/ (Analysis): • James was helping his dad paint his bedroom. They started with 4 5/8 gallons of paint. When they finished, they had 1 2/3 gallons remaining. How many gallons of paint did they use? Defend your answer by illustrating your work on a number line. Score 2/ (Retrieval): The student will recognize or recall specific vocabulary, such as add, addition, benchmark fraction, denominator, estimate, fraction, mixed number, reasonableness, refer, subtract, subtraction, unlike, whole, word problem The student will perform basic processes, such as add and subtract fractions with unlike denominators, including mixed numbers (5.NF.1) • Solve the following problems: 3/8 + 1/4 = 2/3 + 5/6 = 1 2/3 + 3 1/4 = 2 2/7 + 1/3 = MA.05.NQ.MF.01.01 Multiplying and Dividing Fractions The student will: • solve real-‐world problems involving multiplication of fractions and mixed numbers (5.NF.6) • solve real-‐world problems involving division of unit fractions by non-‐zero whole numbers and division of whole numbers by unit fractions (5.NF.7c) • Re-‐Inventing Schools Coalition 2013 Grade 5– Math Pre Assessment Mastery Assessment • The mastery assessment developed and aligned with each individual ELA and Math standard may be used to validate proficiency for a standard(s). • Mastery assessment will ensures inter-‐related reliability and consistency of expectations within an organization. • Each ELA and Math standard has score 2 and score 3 assessment items • Each assessment item is followed by the correct answers, as needed with open ended responses and other specific questions a rational to support the correct answer is provided • Assessment items are organized by measurement topic and grade level • The mastery assessment items are presented in PDF format • Grade 7 and 8 will be completed and available soon and will be sent to you when ready. Example of the first three pages of the 5th Grade mastery assessment below: 5th Grade Summative Assessment MATH-‐ MP MA.05.MP.ME.01.01 (5.MD.1): The student will use conversions to solve multistep word problems Score 3.0/(Comprehension): Jessica's bedroom is 800 centimeters long and 5 meters wide. How many more millimeters is the length of the room than the width? Kelly has a 2.3 meter long piece of wood. He wants to cut it into 4 equal lengths. How long should each piece be in millimeters? Correct Answer : 3000 millimeters 575 millimeters Stanley ran 4 miles a day. How many feet does he run in three days? Buster goes to the auto parts store and is looking at a battery. It has a mass of 14.5 kilograms. 7000 grams of that mass is water. What is the mass of the rest of the battery in kilograms? Correct Answer : 63,360 feet in 3 days 7.5 kilograms MA.05.MP.RID.01.01 (5.MD.2): The student will use operations to solve problems involving line plots with data in fractions of a unit beyond (1/2, 1/4, 1/8)(5.MD.2) Score 3.0/(Analysis): Measure 10 objects in your desk using a ruler to the nearest ½ inch. Record the data in a table Object Length 1 2 3 4 5 6 7 8 9 10 Display the data on a line plot. Re-‐Inventing Schools Coalition 2013 5-‐MP Math Summative Draw a horizontal line and figure out your scale. Plot your data by placing an X over the correct number for each object you measured. Label the horizontal axis and record the title of the line plot. What is the combined length of all of objects you measured? Show your work. Correct Answer : Answer may vary depending on objects measured. Measure 10 used pencils using a ruler to the nearest 1/4 inch. Record the data in a table Pencil Length 1 2 3 4 5 6 7 8 9 10 Display the data on a line plot. Draw a horizontal line and figure out your scale. Plot your data by placing an X over the correct number for each object you measured. Label the horizontal axis and record the title of the line plot. What is the difference between the longest and shortest pencil you measured? Show your work. Correct Answer : Answer may vary depending on objects measured. Re-‐Inventing Schools Coalition 2013 5-‐MP Math Summative