PSSA Performance Indicator

Transcription

1 GRADE 5 PSSA Performance Indicator Form A Teacher s Guide and Answer Key Mathematics Continental Press

2 Contents Introduction to PSSA Mathematics Performance Indicators Using Your Performance Indicator Directions for Administering Session Directions for Administering Session Directions for Administering Session Answer Key Session Session Session Reproducible Answer Sheet for Multiple-Choice Questions Reproducible Answer Sheet for Multiple-Choice Questions, with Answer Key Scoring Rubric for Open-Ended Items Reproducible Skill Analysis Chart for Sessions Pennsylvania Mathematics Assessment Anchors and Eligible Content, Grade Connecting Assessment to Instruction, Answer Guide Reproducible Cut-Out Tools ISBN K Copyright 2007 The Continental Press, Inc. Excepting the designated reproducible blackline masters, no part of this publication may be reproduced in any form or by any means, electronic, mechanical, photocopying, recording, or otherwise, without the prior written permission of the publisher. All rights reserved. Printed in the United States of America.

3 PSSA Mathematics Performance Indicators The PSSA Mathematics Performance Indicator practice tests are designed to help students prepare for the Pennsylvania System of School Assessment in Mathematics. There are two forms of the Performance Indicators available. They are parallel forms that can be administered before instruction and after, or at any time during the school year. The PSSA Finish Line Mathematics Workbook, Grade 5 provides a complete sequence of instruction in the assessed anchors of the Pennsylvania Mathematics Assessment Anchors and Eligible Content. The workbook includes guided practice and independent practice for each mathematics skill in multiple-choice and open-ended formats. A list of Assessment Anchors and Eligible Content is available at the back of this guide. The PSSA Mathematics Performance Indicators, Grade 5 are divided into three sessions: Session 1, Session 2, and Session 3. The sessions should be administered on two or three consecutive days. All three sessions contain both multiple-choice and open-ended questions. Each multiple-choice question has four answer choices, one of which is the correct answer. Students should circle the best answer. Open-ended questions require students to provide a written response a short statement or a numeric computation, for example. Students should write their response to each open-ended question in the test booklet. This teacher s guide includes suggestions for using these test preparation materials, directions for administering the Performance Indicator, an answer key, correlations to the Pennsylvania Mathematics Assessment Anchors and Eligible Content, scoring guidelines and a rubric, a class skill analysis chart for all question types, and a reproducible page of cut-out tools. The chart below provides a sample timetable for administering the Grade 5 Performance Indicator. Session 1 18 multiple-choice questions 40 minutes, plus an additional Day 1 1 open-ended question 10 minutes for preparation Session 2 18 multiple-choice questions 40 minutes, plus an additional Day 2 1 open-ended question 10 minutes for preparation Session 3 18 multiple-choice questions 40 minutes, plus an additional Day 3 1 open-ended question 10 minutes for preparation PSSA Mathematics Performance Indicator Form 5A 3

4 Session 1 Using Your Performance Indicator Mathematics tests today are usually given in multiple sessions. You will probably want your students to work with the PSSA Mathematics Performance Indicator practice tests in the same way. In addition, schedule review sessions as close as possible to the completion of each part; this will enable you to go over the students answers while the contents are still fresh in their minds. Be sure to consider with the students ways in which their written responses could be improved. Directions for using each booklet begin below. Those that you will read aloud to the class are in boldface type and preceded by the word SAY; those that are not meant to be read aloud are in regular type. The directions that follow instruct the students to write their answers in the test booklets. If you prefer to use a separate answer sheet for the multiple-choice questions, reproduce the answer sheet on page 8 of this guide. Remind students to write their names on the answer sheet. Then instruct them on how to fill in the circles clearly. Like actual tests, the Performance Indicators ask students to use particular mathematical tools, such as rulers. Every student should have his or her own set of these tools. A blackline master for making them appears on page 19 of this guide. Before beginning the practice materials, copy the master for the tools onto heavy cardstock and cut out and distribute a set of tools and an individual storage envelope to each student. These tools are also available in punch-out form from Continental Press. Alternatively, provide students with similar manipulatives and tools to use. At some levels, calculator use is permitted or required. Supply calculators as needed. Allow 40 minutes for this first session. Make sure each student has a Form A booklet, two No. 2 pencils, a set of tools, and an optional answer form, if you are using it. SAY Turn to the inside front cover of the booklet and write your name on the line provided. For Session 1, you will have 40 minutes to answer the 19 questions. Check to be sure students have written their names on the inside front cover of their booklets. Explain to the students that they should read each multiple-choice question and all four answers carefully, before circling the best answer. Then take the time to answer any questions the students may have. SAY Open your booklets to page 3. Read, or have a volunteer read, the directions and go over the sample question together. SAY Read the directions and questions on each page carefully. You may use your tools to help you solve any question on the test. However, you may not use your calculator for questions 1 through 4. Remember that you have 40 minutes to work on Session 1. Continue working until you reach the word Stop on page 8. If you finish early, review your work and just sit quietly until the time is up. Are there any questions? Pause to answer any questions. 4 PSSA Mathematics Performance Indicator Form 5A

5 SAY I am now writing the time on the chalkboard. Turn to page 4 and begin. Check to be sure students have begun working on the booklet correctly. After 30 minutes, alert the students to the time left. SAY There are 10 minutes left for you to complete Session 1. If you finish page 8 before the time is up, be sure to go back and check your answers. When time is up, alert the class. SAY Time s up. Please close your booklets. Collect the booklets. Make sure each booklet has the student s name on it. Thank the class for their cooperation. Session 2 Allow 40 minutes for Session 2. Check that each student has two No. 2 pencils, his or her test booklet, and a set of tools. SAY Now you will begin Session 2. Please turn to page 9 and follow along while I read what is on this page. Read the directions. SAY Read the directions and questions on each page carefully. You may use your tools to help you solve any question on the test. Write all of your answers in the booklet. It is important to show all of your work in addition to your final answers. If you see the words Go On at the bottom of the page, keep on reading and answering the questions. Continue working until you see the word Stop. Does anyone have any questions? Address any questions. Remind the students that you are going to make the session seem as much as possible like the real test they will be taking. SAY You have 40 minutes to work on this session. Continue working until you reach the word Stop on page 14. If you finish early, review your work. Then sit quietly until the time is up. I am now writing the time on the chalkboard. Turn to page 10 and begin. Write the time on the chalkboard. After 30 minutes, alert the students to the time left. SAY There are 10 minutes left for you to complete Session 2. If you finish question 38 before the time is up, be sure to go back and check your answers. When the time is up, get ready to collect the booklets. SAY Time s up. Please close your booklets. Collect the booklets. Thank the class for their cooperation. PSSA Mathematics Performance Indicator Form 5A 5

6 Session 3 Allow 40 minutes for Session 3. Check that each student has two No. 2 pencils, his or her test booklet, and a set of tools. SAY Now you will begin Session 3. Please turn to page 15 and follow along while I read what is on this page. Read the directions. SAY Read the directions and questions on each page carefully. You may use your tools to help you solve any question on the test. Write all of your answers in the booklet. It is important to show all of your work in addition to your final answers. If you see the words Go On at the bottom of the page, keep on reading and answering the questions. Continue working until you see the word Stop. Does anyone have any questions? Address any questions. Remind the students that you are going to make the session seem as much as possible like the real test they will be taking. SAY You have 40 minutes to work on this session. Continue working until you reach the word Stop on page 22. If you finish early, review your work. Then sit quietly until the time is up. I am now writing the time on the chalkboard. Turn to page 16 and begin. Write the time on the chalkboard. After 30 minutes, alert the students to the time left. SAY There are 10 minutes left for you to complete Session 3. If you finish question 57 before the time is up, be sure to go back and check your answers. When the time is up, get ready to collect the booklets. SAY Time s up. Please close your booklets. You have now completed all the sessions of your Performance Indicator. Collect the students booklets, making sure each student s name is on the inside front cover. Thank the class for their cooperation. After you check the answers for Sessions 1, 2, and 3 using the answer key on page 7 of this guide, review the responses with students. Continue to work with students to improve all aspects of their mathematical skills. 6 PSSA Mathematics Performance Indicator Form 5A

7 Answer Key Session 1 Sample: B [M5.D.1.2.1] 1. A [M5.D.2.1.1] 2. D [M5.A.3.2.1] 3. C [M5.A.2.1.1] 4. B [M5.A.3.1.2] 5. C [M5.A.1.1.1] 6. C [M5.B.2.1.1] 7. B [M5.A.1.5.1] 8. B [M5.A.3.1.1] 9. C [M5.B.1.2.1] 10. A [M5.C.2.1.2] 11. C [M5.B.1.1.1] 12. B [M5.A.1.2.1] 13. B [M5.A.2.1.3] 14. A [M5.E.2.1.2] 15. B [M5.B.2.2.1] 16. D [M5.C.1.2.1] 17. B [M5.A.1.2.2] 18. D [M5.A.1.6.2] 19. Open-ended [M5.A.2.1.1, 3.1.2] A. Explanations may vary but should say something like the following: Randy rounded each score to the nearest hundred: 361 rounds to 400, 246 rounds to 200. Then he added: ,000, which is what he needs to earn the bonus. B. 968 Session B [M5.E.3.1.2] 21. D [M5.A.1.3.1] 22. C [M5.B.1.2.2] 23. C [M5.E.2.1.1] 24. B [M5.B.1.2.1] 25. C [M5.E.1.1.1] 26. A [M5.A.1.5.1] 27. D [M5.B.2.2.2] 28. D [M5.C.1.1.1] 29. B [M5.B.1.1.1] 30. A [M5.C.2.1.1] 31. D [M5.A.1.6.1] 32. C [M5.E.3.1.1] 33. D [M5.A.1.3.2] 34. D [M5.D.1.1.2] 35. A [M5.B.2.2.3] 36. A [M5.B.1.3.2] 37. A [M5.D.2.1.1] 38. Open-ended [M5.C.2.1.1, 2] A. Figure 1 B. C. Session A [M5.A.2.1.2] 40. D [M5.C.1.1.2] 41. A [M5.A.1.3.1] 42. B [M5.D.2.1.2] 43. C [M5.A.1.4.1] 44. D [M5.C.2.1.1] 45. C [M5.A.3.1.2] 46. B [M5.A.1.4.2] 47. D [M5.B.1.3.1] 48. D [M5.E.1.1.1] 49. B [M5.B.2.2.3] 50. C [M5.A.2.1.1] 51. B [M5.D.1.1.1] 52. B [M5.D.1.2.1] 53. A [M5.A.1.3.3] 54. C [M5.D.2.1.2] 55. C [M5.B.1.2.2] 56. B [M5.E.2.1.1] 57. Open-ended [M5.E.1.1.1, 2.1.1] A. 2 B. 16 C. 8; Explanations may vary but should say something like the following: First I put the numbers in order: 2, 4, 5, 8, 12, 12, 18. Then I found the middle number, which represents the median: 8. PSSA Mathematics Performance Indicator Form 5A 7

8 Name Session 1 Answer Sheet 11 a b c d 11 a b c d 12 a b c d 12 a b c d 13 a b c d 13 a b c d 14 a b c d 14 a b c d 15 a b c d 15 a b c d 16 a b c d 16 a b c d 17 a b c d 17 a b c d 18 a b c d 18 a b c d 19 a b c d 19 a b c d 10 a b c d Session 2 Answer Sheet 20 a b c d 30 a b c d 21 a b c d 31 a b c d 22 a b c d 32 a b c d 23 a b c d 33 a b c d 24 a b c d 34 a b c d 25 a b c d 35 a b c d 26 a b c d 36 a b c d 27 a b c d 37 a b c d 28 a b c d 38 a b c d 29 a b c d Session 3 Answer Sheet 39 a b c d 49 a b c d 40 a b c d 50 a b c d 41 a b c d 51 a b c d 42 a b c d 52 a b c d 43 a b c d 53 a b c d 44 a b c d 54 a b c d 45 a b c d 55 a b c d 46 a b c d 56 a b c d 47 a b c d 57 a b c d 48 a b c d Copyright 2007 The Continental Press, Inc. PSSA Mathematics Performance Indicator Duplication permitted Form 5A

9 Session 1 Answer Sheet, Answer Key 11 a b c d 11 a b c d 12 a b c d 12 a b c d 13 a b c d 13 a b c d 14 a b c d 14 a b c d 15 a b c d 15 a b c d 16 a b c d 16 a b c d 17 a b c d 17 a b c d 18 a b c d 18 a b c d 19 a b c d 19 a b c d 10 a b c d Session 2 Answer Sheet, Answer Key 20 a b c d 30 a b c d 21 a b c d 31 a b c d 22 a b c d 32 a b c d 23 a b c d 33 a b c d 24 a b c d 34 a b c d 25 a b c d 35 a b c d 26 a b c d 36 a b c d 27 a b c d 37 a b c d 28 a b c d 38 a b c d 29 a b c d Session 3 Answer Sheet, Answer Key 39 a b c d 49 a b c d 40 a b c d 50 a b c d 41 a b c d 51 a b c d 42 a b c d 52 a b c d 43 a b c d 53 a b c d 44 a b c d 54 a b c d 45 a b c d 55 a b c d 46 a b c d 56 a b c d 47 a b c d 57 a b c d 48 a b c d Copyright 2007 The Continental Press, Inc. PSSA Mathematics Performance Indicator Duplication permitted Form 5A

10 PSSA Mathematics Rubric for Open-Ended Items Rubrics for the PSSA mathematics items are specific to the individual items. The following rubric provides general guidelines for evaluating the open-ended items in the PSSA Mathematics Performance Indicator practice tests. In reviewing student work, tailor the rubric to the assessment anchor(s) covered in the item. Score Description 4 The student response demonstrates an exemplary understanding of the concepts involved in the specific assessment anchor(s). 3 The student response demonstrates a good understanding of the concepts involved in the specific assessment anchor(s). Although there is significant evidence that the student is able to recognize and apply the concepts involved, some aspect of the response is flawed. As a result, the response merits 3 points. 2 The student response demonstrates a fair understanding of the concepts involved in the specific assessment anchor(s). While some aspects of the task are completed correctly, others are not. The mixed evidence provided by the student merits 2 points. 1 The student response demonstrates only a minimal understanding of the concepts involved in the specific assessment anchor(s). 0 The student response contains insufficient evidence of an understanding of the concepts involved in the specific assessment anchor(s) to merit any points. 10 PSSA Mathematics Performance Indicator Form 5A

11 Numbers and Operations #2, 3, 4, 5, 7, 8, 12, 13, 17, 18, 19*, 21, 26, 31, 33, 39, 41, 43, 45, 46, 50, points possible Measurement #6, 9, 11, 15, 22, 24, 27, 29, 35, 36, 47, 49, points possible Geometry #10, 16, 28, 30, 38*, 40, points possible Algebraic Concepts #1, 34, 37, 42, 51, 52, 54 7 points possible Data Analysis and Probability #14, 20, 23, 25, 32, 48, 56, 57* 11 points possible TOTAL SCORE 66 points possible *Open-ended items are worth up to 4 points each. Skill Analysis for Form 5A Sessions 1 3 Student Name PSSA Mathematics Performance Indicator Copyright 2007 The Continental Press, Inc. Class Profile

12 Pennsylvania Mathematics Assessment Anchors and Eligible Content, Grade 5 M5.A Numbers and Operations Assessment Anchor M5.A.1: Demonstrate an understanding of numbers, ways of representing numbers, relationships among numbers, and number systems. M5.A.1.1 Express numbers in equivalent forms. M5.A Use expanded notation to represent whole numbers or decimals (whole numbers less than 10,000,000 and decimals through hundredths). M5.A.1.2 Demonstrate understanding of place value of whole numbers and decimals. M5.A Match the standard form to the word form of decimal numbers through the hundredths. M5.A Identify the place value of a digit (from millions through hundredths). M5.A.1.3 Compare quantities or magnitudes of numbers. M5.A Compare whole numbers through nine digits using the words more, less, equal, least, most, greater than, less than, or the symbols,,. M5.A Compare and/or order decimals through the hundredths. (Limit sets for ordering to no more than four numbers.) M5.A Compare proper fractions through sixteenths with like and unlike denominators. M5.A.1.4 Use simple applications of negative numbers (number line, counting, temperature). M5.A Locate/identify integers on a number line (greater than or equal to -20). M5.A Identify negative temperatures on a thermometer (through -20 C or F). M5.A.1.5 Use or develop models to represent fractions and/or mixed numbers. M5.A Use or develop regions and/or sets (e.g., circle graph, base ten blocks) to model fractions and mixed numbers through hundredths (may include reducing the fractions). M5.A.1.6 Apply number theory concepts (i.e., primes, factors, multiples, composites). M5.A Define/list/identify prime and composite numbers less than or equal to 100. M5.A Define/list/identify factors and/or multiples of a given whole number less than or equal to PSSA Mathematics Performance Indicator Form 5A

13 Assessment Anchor M5.A.2: Understand the meanings of operations, use operations, and understand how they relate to each other. M5.A.2.1 Solve problems involving decimals, fractions, and/or whole numbers (straight computation or word problems). M5.A Solve problems involving addition, subtraction, multiplication, and division of whole numbers (multipliers up to two digits divisors one digit) and decimals including money (answer through hundredths no division with decimals). M5.A Solve problems involving addition and subtraction of fractions (through sixteenths like and unlike denominators for unlike denominators, the LCD must be one of the given denominators). M5.A Choose the correct operation(s) to solve a problem (no more than two operations). Assessment Anchor M5.A.3: Compute accurately and fluently and make reasonable estimates. M5.A.3.1 Apply estimation strategies to a variety of problems. M5.A Round whole numbers through millions and decimals through hundredths. M5.A Use estimation to solve problems involving whole numbers and/or decimals (up to two-digit multipliers, single-digit divisors, or multiples of 10; whole numbers through thousands and decimals through hundredths). M5.A.3.2 Compute accurately without the use of a calculator (straight computation or one operation word problems). M5.A Use addition, subtraction, multiplication, and division to compute accurately without a calculator (multipliers up to two digits, single-digit divisors, or multiples of 10 whole numbers through thousands and decimals through hundredths no division with decimals). M5.B Measurement Assessment Anchor M5.B.1: Demonstrate an understanding of measurable attributes of objects and figures, and the units, systems, and processes of measurement. M5.B.1.1 Select appropriate units (customary or metric) to measure specific attributes of objects. M5.B Select the appropriate unit for measuring weight (mass), capacity, length, perimeter, and area. M5.B.1.2 Solve problems using simple conversions and/or add and subtract measurements. M5.B Convert using linear measurements, capacity, and weight (mass) within the same system to the unit immediately above or below the given unit (using only the units below use a conversion chart or a hint with problems, e.g., hint: 16 oz 1 lb). Metric using mm, cm, m, and km; ml and L; g and kg PSSA Mathematics Performance Indicator Form 5A 13

14 Customary using cup, pint, quart, and gallon; in., ft, and yd; oz and lb M5.B Add or subtract linear measurements (feet and inches), or units of time (hours and minutes), without having to regroup with subtraction (answer should be in simplest form). M5.B.1.3 Estimate and/or compare the perimeters or areas of two figures without computation. M5.B Estimate which polygon (shown on a grid) has a greater perimeter or area (compare either area to area or perimeter to perimeter). M5.B Estimate the area of an irregular figure shown on a grid. Assessment Anchor M5.B.2: Apply appropriate techniques, tools, and formulas to determine measurements. M5.B.2.1 Use appropriate tools to determine measurements. 1 M5.B Use a ruler to measure to the nearest inch or centimeter. 8 M5.B.2.2 Solve problems involving length, time, weight (mass), capacity, temperature, perimeter, and/or area. M5.B Find the perimeter of a figure drawn and labeled (with the same units throughout). M5.B Find the area of a square or rectangle (with the same units throughout whole numbers only). M5.B Solve problems involving weight, time, temperature, length, and capacity (with the same units throughout limited to three digits). M5.C Geometry Assessment Anchor M5.C.1: Analyze characteristics and properties of two- and threedimensional geometric shapes and demonstrate understanding of geometric relationships. M5.C.1.1 Define and/or use basic properties of quadrilaterals (parallelograms, squares, rectangles, trapezoids, rhombi), triangles, circles, pyramids, cubes, and/or prisms. M5.C Identify and/or classify cubes, rectangular prisms, or pyramids using faces, vertices, and edges. M5.C Identify and/or describe properties of all types of quadrilaterals (parallelograms, rectangles, rhombi, squares, trapezoids). M5.C.1.2 Represent and/or use properties of lines, line segments, rays, points, and planes. M5.C Identify, draw, and/or label points, lines, line segments, and rays. Assessment Anchor M5.C.2: Identify and/or apply concepts of transformations or symmetry. M5.C.2.1 Analyze transformations and/or use symmetry to analyze mathematical situations. M5.C Draw or identify a translation (slide), reflection (flip), or rotation (turn) of a two-dimensional shape. 14 PSSA Mathematics Performance Indicator Form 5A

15 M5.C Identify the number of lines of symmetry and/or draw all lines of symmetry in a two-dimensional polygon. M5.D Algebraic Concepts Assessment Anchor M5.D.1: Demonstrate an understanding of patterns, relations, and functions. M5.D.1.1 Create or extend patterns. M5.D Extend or find a missing element in a numerical or simple geometric pattern (,,, or of whole numbers). Pattern must show three repetitions. M5.D Create or replicate a numerical or geometric pattern showing three repetitions of that pattern (,,, or of whole numbers may be used). M5.D.1.2 Analyze patterns. M5.D Form a rule based on a given pattern, or illustrate a pattern based on a given rule (,,, or of whole numbers may be used). Patterns must show three repetitions. Assessment Anchor M5.D.2: Represent and/or analyze mathematical situations using numbers, symbols, words, tables, and graphs. M5.D.2.1 Select and/or use appropriate strategies, including concrete materials, to solve or represent expressions or number sentences. M5.D Solve for a missing number (blank, question mark, variable) in an equation involving a single operation (whole numbers only). M5.D Match a realistic situation to an equation, expression, inequality (,, ), table, or graph (variable must be isolated, e.g., n). M5.E Data Analysis and Probability Assessment Anchor M5.E.1: Formulate or answer questions that can be addressed with data and/or organize, display, interpret, or analyze data. M5.E.1.1 Organize, display, and/or interpret data using pictographs, tallies, tables, charts, line graphs, and bar graphs. M5.E Display and/or interpret data shown in tallies, tables, charts, pictographs, bar graphs, line graphs, and using a title, appropriate scale, and labels. A grid will be provided to display data on bar graphs or line graphs. Assessment Anchor M5.E.2: Select and/or use appropriate statistical methods to analyze data. M5.E.2.1 Describe data sets using mean, median, mode, and/or range. M5.E Determine the mean/average (answer is a whole number), median (answer is a whole number or average of two numbers), and range of data (up to ten numbers). PSSA Mathematics Performance Indicator Form 5A 15

16 M5.E Identify the mode in a set of data (up to ten numbers). Assessment Anchor M5.E.3: Understand and/or apply basic concepts of probability or outcomes. M5.E.3.1 Predict or determine all possible combinations, outcomes, and/or calculate the probability of a simple event. M5.E Predict or determine whether some outcomes are certain, more likely, less likely, equally likely, or impossible (information could be represented by pictographs, bar graphs, charts, tables, and/or spinners). M5.E Determine the probability of an outcome (e.g., a coin toss, a roll of a number cube) and express as a fraction without reduction. 16 PSSA Mathematics Performance Indicator Form 5A

17 Connecting Assessment to Instruction, Answer Guide PSSA Mathematics Performance Indicator Grade 5, Form A This answer guide will help you connect each PSSA Mathematics Performance Indicator test question directly to the appropriate content lesson in the PSSA Finish Line Mathematics, Grade 5 workbook. The correlation to the anchor and eligible content will assist you in providing more focused instruction in the areas in which students may require additional support. Assessment Anchor PSSA Finish Line Question Answer Standard and Eligible Content Mathematics, Grade 5 1 A G M5.D Unit 9, Lesson 3 2 D H M5.A Unit 4, Lesson 3 3 C B M5.A Unit 4, Lesson 1 Unit 4, Lesson 2 4 B G M5.A Unit 5, Lesson 2 5 C A M5.A Unit 1, Lesson 1 6 C B M5.B Unit 6, Lesson 3 7 B D M5.A Unit 2, Lesson 3 8 B D M5.A Unit 5, Lesson 1 9 C D M5.B Unit 6, Lesson 5 10 A L M5.C Unit 8, Lesson 4 11 C A M5.B Unit 6, Lesson 2 12 B B M5.A Unit 2, Lesson 1 13 B I M5.A Unit 4, Lesson 1 14 A B M5.E Unit 10, Lesson 5 15 B A M5.B Unit 7, Lesson 2 16 D I M5.C Unit 8, Lesson 1 17 B B M5.A Unit 1, Lesson 1 18 D G M5.A Unit 3, Lesson 2 19 Open-ended A M5.A Unit 4, Lesson G M5.A Unit 5, Lesson 2 20 B C M5.E Unit 10, Lesson E 21 D A M5.A Unit 1, Lesson A 22 C E M5.B Unit 7, Lesson 1 23 C B M5.E Unit 10, Lesson 5 24 B D M5.B Unit 6, Lesson 4 25 C E M5.E Unit 10, Lesson 2 26 A D M5.A Unit 2, Lesson 3 27 D A M5.B Unit 7, Lesson 3 PSSA Mathematics Performance Indicator Form 5A 17

18 28 D J M5.C Unit 8, Lesson 3 29 B A M5.B Unit 6, Lesson 1 30 A K M5.C Unit 8, Lesson 5 31 D E M5.A Unit 3, Lesson 1 32 C D M5.E Unit 10, Lesson 6 33 D A M5.A Unit 2, Lesson 2 34 D A M5.D Unit 9, Lesson 1 35 A E M5.B Unit 7, Lesson 1 36 A C M5.B Unit 7, Lesson 3 37 A G M5.D Unit 9, Lesson 3 38 Open-ended K M5.C Unit 8, Lesson L M5.C Unit 8, Lesson 5 39 A C M5.A Unit 4, Lesson 4 40 D B M5.C Unit 8, Lesson 2 41 A A M5.A Unit 1, Lesson A 42 B F M5.D Unit 9, Lesson 2 43 C F M5.A Unit 1, Lesson 3 44 D K M5.C Unit 8, Lesson 5 45 C B M5.A Unit 5, Lesson E 46 B F M5.A Unit 1, Lesson 3 47 D A M5.B Unit 2, Lesson 2 48 D E M5.E Unit 10, Lesson 3 49 B E M5.B Unit 7, Lesson 1 50 C A M5.A Unit 4, Lesson 3 51 B A M5.D Unit 9, Lesson 1 52 B C M5.D Unit 9, Lesson 1 53 A A M5.A Unit 2, Lesson 4 54 C F M5.D Unit 9, Lesson 2 55 C E M5.B Unit 7, Lesson 1 56 B B M5.E Unit 10, Lesson 5 57 Open-ended B M5.E Unit 10, Lesson E M5.E Unit 10, Lesson 5 18 PSSA Mathematics Performance Indicator Form 5A

19 0 0 CUT-OUT TOOLS Protractor Ruler Inches Centimeters Protractor Ruler Inches Centimeters PSSA Mathematics Grade 5 Continental Press

20 Mathematics Grade 5 ISBN K K16587

21 GRADE 5 PSSA Performance Indicator Form B Teacher s Guide and Answer Key Mathematics Continental Press

22 Contents Introduction to PSSA Mathematics Performance Indicators Using Your Performance Indicator Directions for Administering Session Directions for Administering Session Directions for Administering Session Answer Key Session Session Session Reproducible Answer Sheet for Multiple-Choice Questions Reproducible Answer Sheet for Multiple-Choice Questions, with Answer Key Scoring Rubric for Open-Ended Items Reproducible Skill Analysis Chart for Sessions Pennsylvania Mathematics Assessment Anchors and Eligible Content, Grade Connecting Assessment to Instruction, Answer Guide Reproducible Cut-Out Tools ISBN K Copyright 2007 The Continental Press, Inc. Excepting the designated reproducible blackline masters, no part of this publication may be reproduced in any form or by any means, electronic, mechanical, photocopying, recording, or otherwise, without the prior written permission of the publisher. All rights reserved. Printed in the United States of America.

23 PSSA Mathematics Performance Indicators The PSSA Mathematics Performance Indicator practice tests are designed to help students prepare for the Pennsylvania System of School Assessment in Mathematics. There are two forms of the Performance Indicators available. They are parallel forms that can be administered before instruction and after, or at any time during the school year. The PSSA Finish Line Mathematics Workbook, Grade 5 provides a complete sequence of instruction in the assessed anchors of the Pennsylvania Mathematics Assessment Anchors and Eligible Content. The workbook includes guided practice and independent practice for each mathematics skill in multiple-choice and open-ended formats. A list of Assessment Anchors and Eligible Content is available at the back of this guide. The PSSA Mathematics Performance Indicators, Grade 5 are divided into three sessions: Session 1, Session 2, and Session 3. The sessions should be administered on two or three consecutive days. All three sessions contain both multiple-choice and open-ended questions. Each multiple-choice question has four answer choices, one of which is the correct answer. Students should circle the best answer. Open-ended questions require students to provide a written response a short statement or a numeric computation, for example. Students should write their response to each open-ended question in the test booklet. This teacher s guide includes suggestions for using these test preparation materials, directions for administering the Performance Indicator, an answer key, correlations to the Pennsylvania Mathematics Assessment Anchors and Eligible Content, scoring guidelines and a rubric, a class skill analysis chart for all question types, and a reproducible page of cut-out tools. The chart below provides a sample timetable for administering the Grade 5 Performance Indicator. Session 1 18 multiple-choice questions 40 minutes, plus an additional Day 1 1 open-ended question 10 minutes for preparation Session 2 18 multiple-choice questions 40 minutes, plus an additional Day 2 1 open-ended question 10 minutes for preparation Session 3 18 multiple-choice questions 40 minutes, plus an additional Day 3 1 open-ended question 10 minutes for preparation PSSA Mathematics Performance Indicator Form 5B 3

24 Session 1 Using Your Performance Indicator Mathematics tests today are usually given in multiple sessions. You will probably want your students to work with the PSSA Mathematics Performance Indicator practice tests in the same way. In addition, schedule review sessions as close as possible to the completion of each part; this will enable you to go over the students answers while the contents are still fresh in their minds. Be sure to consider with the students ways in which their written responses could be improved. Directions for using each booklet begin below. Those that you will read aloud to the class are in boldface type and preceded by the word SAY; those that are not meant to be read aloud are in regular type. The directions that follow instruct the students to write their answers in the test booklets. If you prefer to use a separate answer sheet for the multiple-choice questions, reproduce the answer sheet on page 8 of this guide. Remind students to write their names on the answer sheet. Then instruct them on how to fill in the circles clearly. Like actual tests, the Performance Indicators ask students to use particular mathematical tools, such as rulers. Every student should have his or her own set of these tools. A blackline master for making them appears on page 19 of this guide. Before beginning the practice materials, copy the master for the tools onto heavy cardstock and cut out and distribute a set of tools and an individual storage envelope to each student. These tools are also available in punch-out form from Continental Press. Alternatively, provide students with similar manipulatives and tools to use. At some levels, calculator use is permitted or required. Supply calculators as needed. Allow 40 minutes for this first session. Make sure each student has a Form B booklet, two No. 2 pencils, a set of tools, and an optional answer form, if you are using it. SAY Turn to the inside front cover of the booklet and write your name on the line provided. For Session 1, you will have 40 minutes to answer the 19 questions. Check to be sure students have written their names on the inside front cover of their booklets. Explain to the students that they should read each multiple-choice question and all four answers carefully, before circling the best answer. Then take the time to answer any questions the students may have. SAY Open your booklets to page 3. Read, or have a volunteer read, the directions and go over the sample question together. SAY Read the directions and questions on each page carefully. You may use your tools to help you solve any question on the test. However, you may not use your calculator for questions 1 through 4. Remember that you have 40 minutes to work on Session 1. Continue working until you reach the word Stop on page 8. If you finish early, review your work and just sit quietly until the time is up. Are there any questions? Pause to answer any questions. 4 PSSA Mathematics Performance Indicator Form 5B

25 SAY I am now writing the time on the chalkboard. Turn to page 4 and begin. Check to be sure students have begun working on the booklet correctly. After 30 minutes, alert the students to the time left. SAY There are 10 minutes left for you to complete Session 1. If you finish page 8 before the time is up, be sure to go back and check your answers. When time is up, alert the class. SAY Time s up. Please close your booklets. Collect the booklets. Make sure each booklet has the student s name on it. Thank the class for their cooperation. Session 2 Allow 40 minutes for Session 2. Check that each student has two No. 2 pencils, his or her test booklet, and a set of tools. SAY Now you will begin Session 2. Please turn to page 9 and follow along while I read what is on this page. Read the directions. SAY Read the directions and questions on each page carefully. You may use your tools to help you solve any question on the test. Write all of your answers in the booklet. It is important to show all of your work in addition to your final answers. If you see the words Go On at the bottom of the page, keep on reading and answering the questions. Continue working until you see the word Stop. Does anyone have any questions? Address any questions. Remind the students that you are going to make the session seem as much as possible like the real test they will be taking. SAY You have 40 minutes to work on this session. Continue working until you reach the word Stop on page 16. If you finish early, review your work. Then sit quietly until the time is up. I am now writing the time on the chalkboard. Turn to page 10 and begin. Write the time on the chalkboard. After 30 minutes, alert the students to the time left. SAY There are 10 minutes left for you to complete Session 2. If you finish question 38 before the time is up, be sure to go back and check your answers. When the time is up, get ready to collect the booklets. SAY Time s up. Please close your booklets. Collect the booklets. Thank the class for their cooperation. PSSA Mathematics Performance Indicator Form 5B 5

26 Session 3 Allow 40 minutes for Session 3. Check that each student has two No. 2 pencils, his or her test booklet, and a set of tools. SAY Now you will begin Session 3. Please turn to page 17 and follow along while I read what is on this page. Read the directions. SAY Read the directions and questions on each page carefully. You may use your tools to help you solve any question on the test. Write all of your answers in the booklet. It is important to show all of your work in addition to your final answers. If you see the words Go On at the bottom of the page, keep on reading and answering the questions. Continue working until you see the word Stop. Does anyone have any questions? Address any questions. Remind the students that you are going to make the session seem as much as possible like the real test they will be taking. SAY You have 40 minutes to work on this session. Continue working until you reach the word Stop on page 23. If you finish early, review your work. Then sit quietly until the time is up. I am now writing the time on the chalkboard. Turn to page 18 and begin. Write the time on the chalkboard. After 30 minutes, alert the students to the time left. SAY There are 10 minutes left for you to complete Session 3. If you finish question 57 before the time is up, be sure to go back and check your answers. When the time is up, get ready to collect the booklets. SAY Time s up. Please close your booklets. You have now completed all the sessions of your Performance Indicator. Collect the students booklets, making sure each student s name is on the inside front cover. Thank the class for their cooperation. After you check the answers for Sessions 1, 2, and 3 using the answer key on page 7 of this guide, review the responses with students. Continue to work with students to improve all aspects of their mathematical skills. 6 PSSA Mathematics Performance Indicator Form 5B

27 Answer Key Session 1 Sample: B [M5.D.1.2.1] 1. C [M5.D.2.1.1] 2. A [M5.A.3.2.1] 3. A [M5.A.2.1.1] 4. C [M5.A.3.1.2] 5. C [M5.A.1.1.1] 6. B [M5.B.2.1.1] 7. D [M5.A.1.5.1] 8. A [M5.A.3.1.1] 9. A [M5.B.1.2.1] 10. C [M5.C.2.1.2] 11. D [M5.B.1.1.1] 12. A [M5.A.1.2.1] 13. C [M5.A.2.1.3] 14. D [M5.E.2.1.2] 15. D [M5.B.2.2.1] 16. A [M5.C.1.2.1] 17. D [M5.A.1.2.2] 18. A [M5.A.1.6.2] 19. Open-ended [M5.A.2.1.1, 3.1.2] A. $13.20 B. Explanations may vary but should say something like the following: Rounding to smaller place values gives amounts that are closer to the actual costs. So the estimate found by rounding to the nearest ten cents is more accurate than an estimate found by rounding to the nearest dollar. C. $6.88 Session C [M5.E.3.1.2] 21. C [M5.A.1.3.1] 22. B [M5.B.1.2.2] 23. B [M5.E.2.1.1] 24. D [M5.B.1.2.1] 25. A [M5.E.1.1.1] 26. C [M5.A.1.5.1] 27. C [M5.B.2.2.2] 28. C [M5.C.1.1.1] 29. B [M5.B.1.1.1] 30. C [M5.C.2.1.1] 31. A [M5.A.1.6.1] 32. C [M5.E.3.1.1] 33. B [M5.A.1.3.2] 34. C [M5.D.1.1.2] 35. A [M5.B.2.2.3] 36. C [M5.B.1.3.2] 37. B [M5.D.2.1.1] 38. Open-ended [M5.C.2.1.1, 2] A. 0; Explanations may vary but should say something like the following: There is no way to draw a line through the S that will create two mirror images. B. C. Session D [M5.A.2.1.2] 40. A [M5.C.1.1.2] 41. C [M5.A.1.3.1] 42. B [M5.D.2.1.2] 43. C [M5.A.1.4.1] 44. C [M5.C.2.1.1] 45. B [M5.A.3.1.2] 46. C [M5.A.1.4.2] 47. A [M5.B.1.3.1] 48. C [M5.E.1.1.1] 49. C [M5.B.2.2.3] 50. D [M5.A.2.1.1] 51. C [M5.D.1.1.1] 52. C [M5.D.1.2.1] 53. C [M5.A.1.3.3] 54. C [M5.D.2.1.2] 55. C [M5.B.1.2.2] 56. C [M5.E.2.1.1] 57. Open-ended [M5.E.1.1.1, 2.1.1] A. Minutes Monday MINUTES DOING HOMEWORK Tuesday Wednesday Thursday Day Friday B. 30 C. 35; Explanations may vary but should say something like the following: First I added the number of minutes for each day: Then I divided by the total number of days, 5, to find the average: PSSA Mathematics Performance Indicator Form 5B 7

28 Name Session 1 Answer Sheet 11 a b c d 11 a b c d 12 a b c d 12 a b c d 13 a b c d 13 a b c d 14 a b c d 14 a b c d 15 a b c d 15 a b c d 16 a b c d 16 a b c d 17 a b c d 17 a b c d 18 a b c d 18 a b c d 19 a b c d 19 a b c d 10 a b c d Session 2 Answer Sheet 20 a b c d 30 a b c d 21 a b c d 31 a b c d 22 a b c d 32 a b c d 23 a b c d 33 a b c d 24 a b c d 34 a b c d 25 a b c d 35 a b c d 26 a b c d 36 a b c d 27 a b c d 37 a b c d 28 a b c d 38 a b c d 29 a b c d Session 3 Answer Sheet 39 a b c d 49 a b c d 40 a b c d 50 a b c d 41 a b c d 51 a b c d 42 a b c d 52 a b c d 43 a b c d 53 a b c d 44 a b c d 54 a b c d 45 a b c d 55 a b c d 46 a b c d 56 a b c d 47 a b c d 57 a b c d 48 a b c d Copyright 2007 The Continental Press, Inc. PSSA Mathematics Performance Indicator Duplication permitted Form 5B

29 Session 1 Answer Sheet, Answer Key 11 a b c d 11 a b c d 12 a b c d 12 a b c d 13 a b c d 13 a b c d 14 a b c d 14 a b c d 15 a b c d 15 a b c d 16 a b c d 16 a b c d 17 a b c d 17 a b c d 18 a b c d 18 a b c d 19 a b c d 19 a b c d 10 a b c d Session 2 Answer Sheet, Answer Key 20 a b c d 30 a b c d 21 a b c d 31 a b c d 22 a b c d 32 a b c d 23 a b c d 33 a b c d 24 a b c d 34 a b c d 25 a b c d 35 a b c d 26 a b c d 36 a b c d 27 a b c d 37 a b c d 28 a b c d 38 a b c d 29 a b c d Session 3 Answer Sheet, Answer Key 39 a b c d 49 a b c d 40 a b c d 50 a b c d 41 a b c d 51 a b c d 42 a b c d 52 a b c d 43 a b c d 53 a b c d 44 a b c d 54 a b c d 45 a b c d 55 a b c d 46 a b c d 56 a b c d 47 a b c d 57 a b c d 48 a b c d Copyright 2007 The Continental Press, Inc. PSSA Mathematics Performance Indicator Duplication permitted Form 5B

30 PSSA Mathematics Rubric for Open-Ended Items Rubrics for the PSSA mathematics items are specific to the individual items. The following rubric provides general guidelines for evaluating the open-ended items in the PSSA Mathematics Performance Indicator practice tests. In reviewing student work, tailor the rubric to the assessment anchor(s) covered in the item. Score Description 4 The student response demonstrates an exemplary understanding of the concepts involved in the specific assessment anchor(s). 3 The student response demonstrates a good understanding of the concepts involved in the specific assessment anchor(s). Although there is significant evidence that the student is able to recognize and apply the concepts involved, some aspect of the response is flawed. As a result, the response merits 3 points. 2 The student response demonstrates a fair understanding of the concepts involved in the specific assessment anchor(s). While some aspects of the task are completed correctly, others are not. The mixed evidence provided by the student merits 2 points. 1 The student response demonstrates only a minimal understanding of the concepts involved in the specific assessment anchor(s). 0 The student response contains insufficient evidence of an understanding of the concepts involved in the specific assessment anchor(s) to merit any points. 10 PSSA Mathematics Performance Indicator Form 5B

31 Numbers and Operations #2, 3, 4, 5, 7, 8, 12, 13, 17, 18, 19*, 21, 26, 31, 33, 39, 41, 43, 45, 46, 50, points possible Measurement #6, 9, 11, 15, 22, 24, 27, 29, 35, 36, 47, 49, points possible Geometry #10, 16, 28, 30, 38*, 40, points possible Algebraic Concepts #1, 34, 37, 42, 51, 52, 54 7 points possible Data Analysis and Probability #14, 20, 23, 25, 32, 48, 56, 57* 11 points possible TOTAL SCORE 66 points possible *Open-ended items are worth up to 4 points each. Skill Analysis for Form 5B Sessions 1 3 Student Name PSSA Mathematics Performance Indicator Copyright 2007 The Continental Press, Inc. Class Profile

32 Pennsylvania Mathematics Assessment Anchors and Eligible Content, Grade 5 M5.A Numbers and Operations Assessment Anchor M5.A.1: Demonstrate an understanding of numbers, ways of representing numbers, relationships among numbers, and number systems. M5.A.1.1 Express numbers in equivalent forms. M5.A Use expanded notation to represent whole numbers or decimals (whole numbers less than 10,000,000 and decimals through hundredths). M5.A.1.2 Demonstrate understanding of place value of whole numbers and decimals. M5.A Match the standard form to the word form of decimal numbers through the hundredths. M5.A Identify the place value of a digit (from millions through hundredths). M5.A.1.3 Compare quantities or magnitudes of numbers. M5.A Compare whole numbers through nine digits using the words more, less, equal, least, most, greater than, less than, or the symbols,,. M5.A Compare and/or order decimals through the hundredths. (Limit sets for ordering to no more than four numbers.) M5.A Compare proper fractions through sixteenths with like and unlike denominators. M5.A.1.4 Use simple applications of negative numbers (number line, counting, temperature). M5.A Locate/identify integers on a number line (greater than or equal to -20). M5.A Identify negative temperatures on a thermometer (through -20 C or F). M5.A.1.5 Use or develop models to represent fractions and/or mixed numbers. M5.A Use or develop regions and/or sets (e.g., circle graph, base ten blocks) to model fractions and mixed numbers through hundredths (may include reducing the fractions). M5.A.1.6 Apply number theory concepts (i.e., primes, factors, multiples, composites). M5.A Define/list/identify prime and composite numbers less than or equal to 100. M5.A Define/list/identify factors and/or multiples of a given whole number less than or equal to PSSA Mathematics Performance Indicator Form 5B

33 Assessment Anchor M5.A.2: Understand the meanings of operations, use operations, and understand how they relate to each other. M5.A.2.1 Solve problems involving decimals, fractions, and/or whole numbers (straight computation or word problems). M5.A Solve problems involving addition, subtraction, multiplication, and division of whole numbers (multipliers up to two digits divisors one digit) and decimals including money (answer through hundredths no division with decimals). M5.A Solve problems involving addition and subtraction of fractions (through sixteenths like and unlike denominators for unlike denominators, the LCD must be one of the given denominators). M5.A Choose the correct operation(s) to solve a problem (no more than two operations). Assessment Anchor M5.A.3: Compute accurately and fluently and make reasonable estimates. M5.A.3.1 Apply estimation strategies to a variety of problems. M5.A Round whole numbers through millions and decimals through hundredths. M5.A Use estimation to solve problems involving whole numbers and/or decimals (up to two-digit multipliers, single-digit divisors, or multiples of 10; whole numbers through thousands and decimals through hundredths). M5.A.3.2 Compute accurately without the use of a calculator (straight computation or one operation word problems). M5.A Use addition, subtraction, multiplication, and division to compute accurately without a calculator (multipliers up to two digits, single-digit divisors, or multiples of 10 whole numbers through thousands and decimals through hundredths no division with decimals). M5.B Measurement Assessment Anchor M5.B.1: Demonstrate an understanding of measurable attributes of objects and figures, and the units, systems, and processes of measurement. M5.B.1.1 Select appropriate units (customary or metric) to measure specific attributes of objects. M5.B Select the appropriate unit for measuring weight (mass), capacity, length, perimeter, and area. M5.B.1.2 Solve problems using simple conversions and/or add and subtract measurements. M5.B Convert using linear measurements, capacity, and weight (mass) within the same system to the unit immediately above or below the given unit (using only the units below use a conversion chart or a hint with problems, e.g., hint: 16 oz 1 lb). Metric using mm, cm, m, and km; ml and L; g and kg PSSA Mathematics Performance Indicator Form 5B 13