Proposed 2016 Mathematics Standards of Learning and Proposed ...
VDOE 2018 Algebra Readiness (AR) Institute October 30, 2018 Fredericksburg October 31, 2018 Williamsburg November 6, 2018 Charlottesville November 7, 2018 - Radford VDOE Team: Tina Mazzacane, Mathematics Coordinator Kristin Hope, Mathematics and Special Education Specialist Michael Traylor, Assessment Specialist Algebra Readiness Committee Representatives: Michele Giglio, Henrico County Public Schools Dr. Brendon Albon, Amherst County Public Schools 1
VDOE AR Session Agenda Welcome and Introductions Introduction to Algebra Readiness Initiative Mathematics Vertical Articulation Activity MVAT and AR Resource Showcase Using Student Score Reports and Data Grade 7 Interpreting Student Score Reports and Data Grade 6 Dynamic MVAT Tool Application/AR Resources Identification Components of Effective AR Programs Mathematics SOL Practice Items and Desmos Reflection and Closure
2 1. Introduction to Algebra Readiness Initiative 3
Algebra Readiness Initiative (ARI) Standards of Quality (Sec. 22.1-253.13:1(D)13) Local school divisions shall provide algebra readiness intervention services to students in grades six through nine who are at risk of failing the Algebra I end-of-course test, as demonstrated by their individual performance on any diagnostic test that has been approved by the Department of Education. Local school divisions shall report the results of the diagnostic tests to the Department of Education on an annual basis, at a time to be determined by the Superintendent of Public Instruction. Each student who receives algebra readiness intervention services will be assessed again at the end of that school year. Funds appropriated for prevention, intervention, and remediation; summer school remediation; atrisk; or algebra readiness intervention services may be used to
meet the requirements of this subdivision. 4 Data Collection: SOQ Compliance School divisions will use the following criteria when providing Algebra Readiness Initiative (ARI) intervention services to individual students: a. Determine the student's knowledge and skills of the Mathematics SOL for grades 3 through 8 and Algebra I. b. Support the following five mathematical process goals for students found in the SOL: 1) Becoming Mathematical Problem Solvers; 2) Communicating Mathematically; 3) Reasoning Mathematically; 4)
Making Mathematical Connections; and 5) Making Mathematical Representations. 5 Data Collection: SOQ Compliance c. Identify mathematics content strengths and challenges, and indicate the level of performance where intervention may be necessary to be successful in each of the following categories: Grades 3 through 8: 1) Number and Number Sense; 2) Computation and Estimation; 3) Measurement and Geometry; 4) Probability and Statistics; and
5) Patterns, Functions, and Algebra Algebra I 1) Expressions and Operations; 2) Equations and Inequalities; 3) Functions; and 4) Statistics. 6 Virginia ARI Annual Report To receive SOL Algebra Readiness Initiative Payments, the school division certifies that it will: Offer an intervention program to targeted students;
Utilize diagnostic methods to assess students at the beginning and at the end of that school year; Submit a report to the Virginia Department of Education by August 1 outlining the methods used for diagnosing individual student mathematics content strengths and challenges, remediation efforts used, the number of students who received ARI services, and the number of students demonstrating improvement during the 20172018 school year; and
Match these funds based on the composite index of local ability-to-pay. 7 Algebra Readiness Initiative Division Contact Name ___________________ Title ___________________ Email ___________________ Who is designated in your school division? 8 ARI Two Major Components
Provides mathematics intervention resources and services to students in grades six through nine who are at risk of failing the Algebra I end-of-course test. 1. Diagnostic assessment designed to guide instructional decisions for students that may need intervention services 2. Targeted intervention services for students Algebra Readiness Initiative (FAQ) #1 9 Identifying At-Risk Students The school division determines which students should be
targeted for diagnostic testing and then subsequently for intervention services. The identified group may include: students in grades 6-9 at risk of failing the Algebra I end-of-course test; students not successful in previous intervention programs; students who performed below average in their previous year's mathematics program; students identified by teachers through formal and informal assessment; and/or students who did not pass their previous mathematics standards of learning assessment. Algebra Readiness Initiative (FAQ) #2 10
Approved AR Diagnostic Tests Locally-designed or locally selected diagnostic tests must: a. Assess students knowledge and skills of Mathematics SOL in grades 3-8 and Algebra I b. Support the five mathematics process goals c. Identify content strengths and challenges, and indicate levels of performance where intervention may be necessary in the mathematics content strands of grades 3-8 and Algebra I Algebra Readiness Initiative (FAQ) #3 11
Using SOL Assessments as Diagnostic Tools School divisions also have the option of using student results from Virginia Mathematics Standards of Learning Assessments as a pre-assessment in conjunction with classroom formative assessments to identify areas of individual student focus for remediation. The end-of-year grade level or Algebra I Mathematics Standards of Learning Assessment results can then serve as the post-assessment. Algebra Readiness Initiative (FAQ) #3 12
AR Intervention The school division determines and designs the local intervention service model Intervention Program Requirements: 1. The intervention services should provide 2 hours of instruction per week in addition to regular classroom instruction. 2. The intervention service should be provided on a student/teacher ratio of 10 to 1. 3. A pre- and post-assessment must be administered to students that participate in the intervention program. Algebra Readiness Initiative (FAQ) #4 & 5
13 AR Intervention Intervention Program Requirements (cont.): 4. Local school division determines and designs the local intervention model. 5. Students targeted to participate in the intervention program will include those who did not pass the appropriate diagnostic test. 6. The intervention services can be provided by classroom teachers, paraprofessionals, or parttime tutors who have the appropriate mathematical understanding and pedagogical knowledge to implement an effective remediation
program. Algebra Readiness Initiative (FAQ) #5 14 VDOE Website - ARI Local Funding Amounts 15 Budget Template (ARI ) - Excel Sample Only! 16 ARI Funding - Purchases
1. Intervention and remediation services (teachers, paraprofessionals, tutors) 2. Student transportation to/from services 3. Other costs associated with providing intervention services 4. Salary to employ mathematics teacher specialists (effective 2011) ARI funding carryover is not guaranteed. Algebra Readiness Initiative (FAQ) #7 & 8 17 ARI - Using Multiple Data Points Mathematics
Patterns, Functions, and Algebra Equality/Solving Equations Computation and EstimationPractical Applications Rational numbers and Proportional Reasoning Number and Number Sense Rational Numbers Compare and Order 20 Patterns, Functions, and Algebra Sort Key SOL 1.15 2.17
EQUALITY/SOLVING EQUATIONS demonstrate an understanding of equality through the use of the equal symbol demonstrate an understanding of equality through the use of the equal symbol = and the use of the not equal symbol 3.17 create equations to represent equivalent mathematical relationships 4.16 5.19b 5.19d 6.13 7.12 8.17 A.4a A.4b
A.4c A.4d A.4e AII.3a AII.3b AII.3c AII.3d AII.4 recognize and demonstrate the meaning of equality in an equation write an equation to represent a given mathematical relationship, using a variable create a problem situation based on a given equation, using a single variable solve one-step linear equations in one variable, including practical problems solve two-step linear equations in one variable, including practical problems
solve multistep linear equations in one variable with the variable on one and both sides of the equation, including practical problems solve multistep linear equations in one variable algebraically solve quadratic equations in one variable algebraically solve literal equations for a specified variable solve systems of two linear equations in two variables algebraically and graphically solve practical problems involving equations and systems of equations solve absolute value linear equations solve algebraically and graphically, quadratic equations over the set of complex numbers solve algebraically and graphically, equations containing rational algebraic expressions solve algebraically and graphically, equations containing radical expressions solve systems of linear-quadratic and quadratic-quadratic equations, algebraically and graphically 21
Computation and Estimation Sort Key SOL 3.5 4.5c 4.6b 5.4 Practical Applications Rational Numbers and Proportional Reasoning solve practical problems that involve addition and subtraction with proper fractions having like denominators of 12 or less solve single-step practical problems involving addition and subtraction with fractions and mixed numbers solve single-step and multistep practical problems involving addition and subtraction with decimals create and solve single-step and multistep practical problems involving addition, subtraction, multiplication, and division
of whole numbers 5.5b create and solve single-step and multistep practical problems involving addition, subtraction, and multiplication of decimals, and create and solve single-step practical problems involving division of decimals 5.6a solve single-step and multistep practical problems involving addition and subtraction with fractions and mixed numbers 5.6b solve single-step practical problems involving multiplication of a whole number, limited to 12 or less, and a proper fraction, with models*
6.5b solve single-step and multistep practical problems involving addition, subtraction, multiplication, and division of fractions and mixed numbers 6.5c 6.6b 7.2 7.3 8.4 solve multistep practical problems involving addition, subtraction, multiplication, and division of decimals solve practical problems involving operations with integers solve practical problems involving operations with rational numbers
solve single-step and multistep practical problems, using proportional reasoning solve practical problems involving consumer applications 22 Number and Number Sense Sort Key SOL K.2a K.2b 1.2b 1.2c 2.1c 2.4c 3.1c
Rational Numbers - Compare and Order given no more than three sets, each set containing 10 or fewer concrete objects, will compare and describe one set as having more, fewer, or the same number of objects as other sets given no more than three sets, each set containing 10 or fewer concrete objects, will compare and order sets from least to greatest compare two numbers between 0 and 100 represented pictorially or with concrete objects, using the words greater than, less than or equal to order three or fewer sets from least to greatest and greatest to least compare and order whole numbers between 0 and 999 compare the unit fractions for halves, fourths, eighths, thirds, and sixths, with models compare and order whole numbers, each 9,999 or less compare fractions having like and unlike denominators, using words and symbols (<, >, =, or
3.2c ), with models 4.1b 4.2a 4.3c 5.2b 6.2b 6.3b 7.1b 7.1c 8.1 compare and order whole numbers expressed through millions compare and order fractions and mixed numbers, with and without models*
compare and order decimals compare and order fractions, mixed numbers, and/or decimals, in a given set, from least to greatest and greatest to least* compare and order positive rational numbers* order and compare integers compare and numbers greater than zero written in scientific notation* compare and order rational numbers* compare and order real numbers 23 Vertical Strand Progression Activity Debrief Purpose of sort activity Importance of vertical alignment and
mapping back 24 3. Mathematics Vertical Articulation Tool (MVAT) Overview 25 Mathematics Vertical Articulation Tool (MVAT) Purpose: provides support in identifying concepts aligned to the 2016 Mathematics Standards of Learning (SOL) that articulate
across mathematics grade levels or courses Possible Uses: Classroom Instructional Planning Individual Student Remediation Planning 26 Mathematics Vertical Articulation Tool (MVAT) Static Formats STATIC = Available in Word and PDF Strand Versions (K Algebra II)
Number and Number Sense Computation and Estimation Measurement and Geometry Probability and Statistics Patterns, Functions, and Algebra Comprehensive Version (K Algebra II) Include all five strands in legal size document
27 Mathematics Vertical Articulation Tool (MVAT) Dynamic Formats DYNAMIC = Customized by inputting student data Dynamic Versions tested grade levels Grade 3 SOL Dynamic MVAT Grade 4 SOL Dynamic MVAT
Algebra I SOL Dynamic MVAT We will review the Dynamic version of MVAT soon! 28 MVAT Strand Versions - Structure Strands (NNS, CE, MG, PS, PFA) Strand Concepts macro concepts of K Algebra II content Standard Descriptors short descriptions of the standards included in each Strand Concept Associated Standards standard numbers that are aligned to each standard descriptor
29 MVAT Strand Versions 30 MVAT Cross-Strand Connections 31 MVAT Comprehensive Version K Algebra II
32 Resources Turn and Talk How might the MVAT support instructional planning in your school division? What steps might be needed to support teachers in using these tools? 33 4. VDOE AR Resource Showcase 34
Data Previously Obtained from Algebra Readiness Diagnostic Test (ARDT) Reported student areas of content strength and weakness based on strand Pinpointed SOL focus content from grades 3 8 Included strand tests to use during remediation 35 Algebra Readiness Curriculum
Companion Targets SOL concepts grades 5 8 Aligned to 2009 SOL Remediation lessons designed for use during ARI Remediation 36 VDOE Remediation Plans MVAT helps to identify unfinished learning L O that will guide the intervention S plan.
s tic a Remediation plans thatem align with h t a unfinished learning M can be used as a 6 1 0 2
resource. to d e n g i l A 37 VDOE Remediation Plan Structure
Remediation Plan Summary Common Errors and Misconceptions Introductory Activity Plan for Instruction Pulling It All Together (Reflection) Ancillary Activities/Handouts 38
VDOE Formative Assessment Items Assess proficiency related to unfinished L learning after remediation or intervention O S s tic Primarily Target Grades 5maAlgebra I e h t
a areas where additional May be used to target M 6 1 0 remediationomay 2 be needed t d e Can begnused to drive instructional decisions i
Al 39 Sample VDOE AR Resources Remediation Plans: Solving Equations Using Algebra Tiles SOL 6.13 and 7.12 Solving Two-Step and Multi-Step Equations SOL 7.12 and 8.17 Formative Assessments: SOL 7.12 40
5. Student Score Reports and Data 41 Student Score Reports and Data Topics Student Detail by Question Report availability Student performance data contained in the report A closer look at a Student Detail by Question (SDBQ) Report Cautions when using SDBQ data
42 Defining the SDBQ Report Provides a description (item descriptor) of each operational test item, with the SOL identification, level of difficulty, and whether the students response was correct or incorrect. Organized by reporting category according to the test blueprint. Provided at the student level by school. SDBQ is the most granular data available from VDOE on SOL assessments.
43 SDBQ Availability On Demand SDBQ Available for non-writing tests completed online and paper. Updated immediately upon scoring online test attempts (as long as the test is not alerted). Available for print as a PDF by individual student or multiple students. 44
SDBQ Availability Published Reports SDBQ Online and paper test attempts are included. Scheduled refresh cycle All students file - weekly by Monday morning until the administration is closed. All tests completed by 3:00 p.m. the previous Friday. Available as a PDF at the school level. 45 2018 Spring
SDBQ Report Test Scaled Score Performance Level Reporting Categories (RC) RC Scaled Score H, M, L test item difficulty Incorrect/Correct responses Item descriptions 46
SDBQ Report Header - On Demand Report Student Name and Report Title Test Administration Student and Test Specific Information Overall Performance Level and Test Scaled Score 47 SDBQ Report Header - Published Reports Student Specific Information
Report Title Test Administration SDBQ screenshot Test Name, Overall Test Scaled Score, and Performance Level 48 SDBQ Report Grade 7 Math CAT Legend
SDBQ Review Reporting Category Scaled Scores Intended to provide an ESTIMATE of potential strengths and weaknesses related to the SOL assessed within that reporting category. A reporting category score of > 40 may represent a strength while a score of < 30 may suggest an area where additional instruction is needed. May provide an indication of where the student may need additional support. Degree to which reporting category scaled score information is useful differs by student. 51
SDBQ Review Reporting Category Scaled Scores Are more important than a raw score because they provide some indication of proficiency. The scaled score provides an established level of achievement, whereas the raw score provides only a count of correct answers. Reporting category scaled scores are not used to assign passing or failing performance levels for a reporting category. 52
SDBQ Report Grade 7 Math CAT Item Difficulty Level 53 Test Item Difficulty Level Based on actual student performance on the test item Determined using the data from field testing the items Within each level of item difficulty there is a range of items. For example, there are some low level
items that are less difficult than other low level items. 54 SDBQ Report Grade 7 Math CAT Item Descriptors 55 SDBQ Item Descriptors SDBQ item descriptors are:
A brief description of the content being assessed by a test item. A brief description of the skill/process being assessed by a test item, including but not limited to: Justify, Identify, Determine, Interpret, and Construct. For Example: Item descriptor = Solve a linear inequality. Content = Knowledge of linear inequalities Skill/Process = Solve 56
SDBQ Item Descriptors SDBQ item descriptors are NOT: An indicator of item difficulty or rigor. The actual item with the corresponding answer choices in the order they appeared on the SOL assessment. Correlated to a single test item; the same descriptor may be used for different items. 57 SDBQ Report Grade 7 Math CAT Sort order for Item
Descriptors within a Reporting Category: All items answered incorrectly; starting from the highest level of difficulty to the lowest level of difficulty. All items answered correctly; starting from the highest level of difficulty to the lowest level of difficulty.
Student Responses If a student does not answer an item, the respective item descriptor will be marked incorrect. 58 SDBQ Review Reporting Category Scaled Score Lets take a closer look at this Gr 7 Mathematics CAT example for MATH WIZARD
Grade 7 Mathematics (2009 SOL) CAT 59 SDBQ Analysis In the next few slides, we will analyze an example of SDBQ for Gr 7 Mathematics CAT. When analyzing this data, we will focus on two major areas: o Content o Skill/Process 60
2018 Spring SDBQ Report Content Concerns Volume/surface area (7.4 A, B) Similarity (7.5) Properties of quads (7.6 A) Transformations (7.7) 61 SDBQ Analysis Skill/Process Concerns
Measurement and Geometry Skill/Process Concerns Apply = 2 of 3 incorrect Classify/Compare/Contrast = 2 of 3 incorrect Describe = 1 of 1 incorrect Determine = 1 of 2 incorrect Solve = 1 of 2 incorrect 62 SDBQ Analysis Measurement and Geometry Content and Skill/Process Concerns Content Concerns
Skill/Process Concerns Volume/Surface Area (7.4 A, B) Describe and Solve Similarity (7.5) Determine and Identify Properties of quads (7.6 A)
SDBQ Analysis Content Concerns Patterns, Functions, and Algebra Content Concerns Two-step linear equations (7.12) Algebraic expressions (7.11) One- and two-step inequalities (7.13) 65 SDBQ Analysis Skill/Process Concerns
Patterns, Functions, and Algebra (PFA) Skill/Process Concerns Apply = 0 of 1 incorrect Identify = 1 of 3 incorrect Represent/Determine = 1 of 4 incorrect Evaluate = 2 of 2 incorrect Inference/Compare = 0 of 2 incorrect Solve = 3 of 5 incorrect Analyze = 1 of 1 incorrect Graph = 1 of 1 incorrect 66
SDBQ Analysis PFA Content and Skill/Process Concerns Content Concerns Skill/Process Concerns Two-step linear equations (7.12) Solve Algebraic expressions (7.11) Evaluate and Identify
One- and two-step inequalities (7.13) Graph and Solve 67 2016 Curriculum Framework Limit the number of replacements to no more than three per expression. Other parameters include
exponents, bases, and grouping symbols used. 68 SDBQ Analysis Reporting Category Reporting Categories are consistent across different forms of the same test. Refer back to standards and curriculum framework for details to apply to on-going and SOL test remediation. How was the content taught prior to the SOL assessment?
How will the content be taught during remediation? 69 SDBQ Analysis Content Concerns Gr 7 Mathematics CAT This students performance on items with identical item descriptors is inconsistent. Why might this occur? Level of item difficulty
Higher order thinking skills Multistep vs. single-step Language load Visuals (graphs, pictures) 70 5. Networking with Padlet 71 6. Unfinished Learning/ Grade 6 Score Report 72
Grade 6 Sample Score Report Analyze the overall score report Review the scaled scores for each reporting category What observations can you make about the data represented in the report? What inferences can be made, if any? 73 SDBQ Review Reporting Category Scaled Score Lets take a closer look at this Gr 6 Mathematics CAT
example 74 TASK What areas of content and what skills should the focus of support be for this student? 75 SDBQ Analysis Content Concerns
Number and Number Sense Content Concerns Equivalent relationships fractions, decimals, percents (2 of 2 incorrect) Ratios (2 of 2 incorrect) Integers Compare and Order; Absolute Value (2 of 2
incorrect) 76 SDBQ Analysis Skill/Process Concerns Number and Number Sense Skill/Process Concerns Represent = 3 of 5 incorrect Determine = 1 of 1 incorrect Identify and Describe = 1 of 1 incorrect Compare and Order =
1 of 2 incorrect 77 SDBQ Analysis Number and Number Sense Content and Skill/Process Concerns Content Concerns Skill/Process Concerns Equivalent relationships fractions, decimals, percents Represent
Ratios Determine Integers Identify and describe 78 SDBQ Analysis Content Concerns Probability, Statistics, and Patterns, Functions, and Algebra Content Concerns
Balance Point = 2 of 2 incorrect Independent and Dependent Events = 2 of 3 incorrect Arithmetic and Geometric Sequences = 2 of 2 incorrect Representations of Data in Graphs = 3 of 3 incorrect Linear Equations = 2 out of 3 incorrect Linear Inequalities = 2 out of 2 incorrect Properties = 1 out of 2 incorrect 79 SDBQ Analysis Skill/Process Concerns Probability,
Statistics, and Patterns, Functions, and Algebra 80 SDBQ Analysis Probability, Statistics, and Patterns, Functions and Algebra Content and Skill/Process Concerns Content Concerns Skill/Process Concerns Linear Equations Solve
Linear Inequalities Translate Representations of Data Compare and contrast 81 2016 Curriculum Framework 82
Crosswalked 2009 to 2016 SOL 2009 2016 6.15a 6.11a 6.16a None 6.16b
None 6.17 None 6.14a 6.10a 6.14c 6.10c
6.14c 6.10c 6.15a 6.11a 6.17 None 86
Grade 6 Sample Score Report Crosswalking 2009 to 2016 SOL Crosswalk the remaining Prob/Stat and PFA Reporting Category When finished compare your standards with those provided on the annotated score report 87 Grade 6 Sample Score Report Cross-walked 2009 to 2016 SOL 88
SDBQ Analysis Reporting Category Refer back to standards and curriculum framework for details to apply to on-going and SOL test remediation. How was the content taught prior to the SOL assessment? How will the content be taught during remediation? 89 Analysis:
90 8. MVAT Tool Application/ AR Resource Identification 91 2016 TASK For the Number and Number Sense and Patterns, Functions, and Algebra strands, list student areas of strength and unfinished learning? 92
Planning for Remediation VDOE Resources Use either the strand or comprehensive MVAT to map backward to find possible areas of unfinished learning for the following two item descriptors: 93 Planning for Remediation VDOE Resources 94
Planning for Remediation VDOE Resources What AR Remediation Plans and Formative Assessment Items would you recommend be utilized with this student? 95 MVAT Tool Dynamic Version 1. Go to the ARCC website (ARCC) 2. Select Resources, and check Other and click Filter Resources.
96 Student Strengths - Report 97 Student Unfinished Learning Report 98 9. AR Program Structures 99
Brainstorm Structures of Effective AR School Programs 1. 2. 3. 4. 5. How are students identified? When is intervention provided? How is student progress measured? Who provides intervention services? What instructional resources are used during intervention?
6. How is the intervention time structured? 100 Effective ARI Program Components How are students identified? When is intervention provided?
Multiple measures are used (screeners, benchmark assessments, classroom assessments, previous SOL data) Time is built into the regular school day schedule Afterschool tutoring with transportation (and snacks ) How is student progress measured?
Formative assessment results are tracked regularly Pre- and post-assessment results 101 ARI Program Exemplars Who provides intervention services?
What instructional resources are used during intervention? Mathematics teachers at the school Retired mathematics teachers Instruction that promotes student discourse and problem solving
Mathematics SOL aligned activities that engage learners How is the intervention time structured? Remediation bells/blocks that parallel daily instruction 102 Padlet - Large Group Share-Out What challenges could limit the effectiveness of the AR program? What are some solutions to those
challenges? What strategies might be used to motivate students? How can parents/community be involved in Algebra Readiness Initiative? 103 10. TestNav Practice Items and Desmos 104 Desmos Online Calculators
Spring 2019 Mathematics Standards of Learning tests (assessing the 2016 Mathematics SOL) administered online will include access to an online calculator from Desmos within TestNav 8 Students may use Desmos and one of the hand-held calculators on the List of Approved Calculators 2018-2019 School Year Transition period for school division staff and students to become more familiar with Desmos 105
Desmos Online Calculators 2019-2020 School Year Students taking the Mathematics SOL tests administered online expected to use only the Virginia Desmos online calculator Mathematics Practice Items in TestNav 2016 items include Virginia Desmos online calculator where applicable Superintendents Memo 144-18
Student Classroom Hub Desmos Art 108 Reflection/Closure 109
Reflection ARI Institute Take-Aways What am I taking back to my division? What additional support is needed? 110 Thank you!!!!!! Algebra Readiness Development Committee Brendon Albon, Amherst County Public Schools Michele Giglio, Henrico County Public Schools Mary Hardesty, Virginia Beach City Public Schools
Alfreda Jernigan, Norfolk City Public Schools Amy Jones, Hanover County Public Schools Jennifer Mason, Henrico County Public Schools Kelly Pocta, Hanover County Public Schools Ashley Rea, Fredericksburg City Public Schools Kathleen Stoebe, Stafford County Public Schools Elaine Smetts, Stafford County Public Schools Carol Walsh, Middlesex County Public Schools 111 Questions?? [email protected]
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