The Pennsylvania System of School Assessment

Transcription

1 The Pennsylvania System of School Assessment Mathematics Item and Scoring Sampler Grade 7 Pennsylvania Department of Education Bureau of Assessment and Accountability

2 TABLE OF CONTENTS Introduction General Description of Mathematics Scoring Guidelines Mathematics Reporting Categories Description of Sample Items Formula Sheet Multiple-Choice Items First Open-Ended Item Item-Specific Scoring Guideline Open-Ended Item Responses Second Open-Ended Item Item-Specific Scoring Guideline Open-Ended Item Responses Third Open-Ended Item Item-Specific Scoring Guideline Open-Ended Item Responses Fourth Open-Ended Item Item-Specific Scoring Guideline Open-Ended Item Responses Grade 7 Mathematics Item Sampler ii i

3 INTRODUCTION General Introduction The Department of Education provides districts and schools with tools to assist in delivering focused instructional programs aligned to the state assessment system. These tools include assessment anchor documents, assessment handbooks, and content-based item and scoring samplers. This Mathematics Item and Scoring Sampler is a useful tool for Pennsylvania educators in the preparation of local instructional programs and the statewide PSSA. What Is Included The Mathematics Item and Scoring Samplers do not contain newly released items. The samplers are a compilation of previously released items. This item and scoring sampler contains mathematics multiple-choice items and open-ended items that have been written to align to the 2008 Assessment Anchor Content Standards (Assessment Anchors). Some of the items are actual items used to assess student performance on the PSSA. They provide an idea of the types of items that will appear on the operational Spring 2009 PSSA. Each item has been through a rigorous review process to ensure alignment with the Assessment Anchors. Purpose and Uses The items in this sampler may be used as examples for creating assessment items at the classroom level, and they may also be copied and used as part of a local instructional program.* Classroom teachers may find it beneficial to have students respond to the open-ended items in this sampler. Educators can then use the sampler as a guide to score the responses either independently or together with colleagues within a school or district. Item Format and Scoring Guidelines The multiple-choice items have four answer choices. Each correct response to a multiple-choice item is worth one point. Each open-ended item is designed to take about ten minutes to complete. During an official testing administration, students are given additional time as necessary to complete the test items. Each open-ended item in mathematics is scored using an item-specific scoring guideline based on a 0 4 point scale. In this sampler, every item-specific scoring guideline is combined with examples of student responses representing each score point to form a practical itemspecific scoring guide. The sampler also includes the General Description of Mathematics Scoring Guidelines used to develop the item-specific guidelines and guides. These General Description Scoring Guidelines should be used if any additional item-specific scoring guidelines are created for use within local instructional programs.* Item Alignment All PSSA items are aligned to statements and specifications included in the Assessment Anchor Content Standards documents. The mathematics content included in the PSSA mathematics multiple-choice items will align with the Assessment Anchors as defined by the Eligible Content statements. The process skills, directives, and action statements will also specifically align with the Assessment Anchors as defined by Eligible Content statements. The mathematics content included in the PSSA mathematics open-ended items will align with content included in Eligible Content statements. The process skills, directives, and action statements included in the performance demands of the PSSA mathematics open-ended items will align with specifications included in the Assessment Anchor statements, the Descriptor statements, and/or the Eligible Content statements. In other words, the verbs or action statements used in the open-ended questions or stems can come from the Eligible Content, Descriptor, or Anchor. * The permission to copy and/or use these materials does not extend to commercial purposes. Grade 7 Mathematics Item Sampler

4 GENERAL DESCRIPTION OF MATHEMATICS SCORING GUIDELINES 4 The response demonstrates a thorough understanding of the mathematical concepts and procedures required by the task. The response provides correct answer(s) with clear and complete mathematical procedures shown and a correct explanation, as required by the task. Response may contain a minor blemish or omission in work or explanation that does not detract from demonstrating a thorough understanding. 3 The response demonstrates a general understanding of the mathematical concepts and procedures required by the task. The response and explanation (as required by the task) are mostly complete and correct. The response may have minor errors or omissions that do not detract from demonstrating a general understanding. 2 The response demonstrates a partial understanding of the mathematical concepts and procedures required by the task. The response is somewhat correct with partial understanding of the required mathematical concepts and/or procedures demonstrated and/or explained. The response may contain some work that is incomplete or unclear. 1 The response demonstrates a minimal understanding of the mathematical concepts and procedures required by the task. 0 The response has no correct answer and insufficient evidence to demonstrate any understanding of the mathematical concepts and procedures required by the task for that grade level. Response may show only information copied from the question. Special Categories within zero reported separately: BLK (blank)...blank, entirely erased, or written refusal to respond OT...Off task IL...Illegible LOE...Response in a language other than English Grade 7 Mathematics Item Sampler

5 MATHEMATICS REPORTING CATEGORIES Mathematics scores are reported in five categories: A Numbers and Operations B Measurement C Geometry D Algebraic Concepts E Data Analysis and Probability Examples of multiple-choice and open-ended items assessing these categories are included in this booklet. DESCRIPTION OF SAMPLE ITEMS The mathematics multiple-choice items begin on page 5. Each item is preceded by the Assessment Anchor and Eligible Content coding. The majority of answer options A D are followed by a brief analysis or rationale. The correct answer is indicated by an asterisk (*). Four open-ended items follow the multiple-choice items. Each of these is displayed with an item-specific scoring guidelines and examples of responses with scores and annotations. A calculator is permitted for use in solving items numbered 7 47 in this sampler. Items numbered 1 6 are to be solved without the use of a calculator. Scratch paper may be used in solving all items. Grade 7 Mathematics Item Sampler

6 FORMULA SHEET Formulas that you may need to work questions are found below. You may use calculator Õ or the number Grade 7 s A s s h V lwh s l w w P 2l + 2w A lw l h V r 2 h r h A bh b a h V 1 (Area of the base) h 3 h A 1 h(a b) 2 base b Customary Conversions : c h d P b c d A 1 2 bh 1yard(yd)=3feet(ft) 1 foot = 12 inches (in.) 1 pound (lb) = 16 ounces (oz.) b 1 gallon (gal) = 4 quarts (qt) 1 quart = 2 pints (pt) 1pint=2cups(c) 1 cup = 8 fluid ounces r C 2 r A r 2 1 day = 24 hours (hr) 1 hour = 60 minutes (min) 1 minute = 60 seconds (sec) Metric Conversions : s s s V s s s 1 kilometer = 1000 meters 1 hectometer = 100 meters 1 dekameter = 10 meters 1meter 1 decimeter = 0.1 meter 1 centimeter = 0.01 meter 1 millimeter = meter Grade 7 Mathematics Item Sampler

7 MULTIPLE-CHOICE ITEMS During an assessment, students would not be permitted to use a calculator on items 1 4. A Jordan answered 80% of the questions on a test correctly. What fraction of the questions did Jordan answer correctly? A B C D 1 } 80 2 } 25 3 } 4 4 } 5 80 as denominator 8/100 = 2/25 3 } = 75%; rounded up 4 * A Which is the closest estimate of ? A 10 * B ; decimal point moved left C 45 close to 45.23, D 100 decimal point moved right A A Liz had } 7 of a puzzle finished. What 8 percent did she have finished? A 70% based on numerator B 87.5% * 4. Multiply: A decimal point 1 place to left B 21.6 zero in tens place dropped C in ones place dropped D * C 114.3% approximately 8 7 D 875% decimal placement error Grade 7 Mathematics Item Sampler

8 During an assessment, students would not be permitted to use a calculator on items 5 and 6. A Solve: A Solve: A 17 } } } 3 17 } 9 3 } 7 56 ( 42) A B B 1 1 } 3 C 6 2 } 9 D 9 13 } 27 * added multiplied C D 98 * Grade 7 Mathematics Item Sampler

9 A Use the numbers below to answer question } } } 5 7. What is the order of the numbers from least to greatest? A 4 1 } 4 1 } 4 2 } mixed numbers ordered by denominators, then decimals B } 4 1 } 4 2 } decimals ordered, then mixed numbers ordered by denominators A Point M is graphed on the number line below. 1 2 M 3 4 What is the location of point M? A 2 } 3 B 1 5 } 9 C 2 2 } 3 point M between 2 and 3 point M on the 5th of 9 tick marks after 1 * C 4 1 } } } 5 ordered by denominator and decimal values D 3 1 } 3 point M 1 } 3 from 3 D } 3 * 4 2 } } 2 A Simplify: (10 + 4) A 4 7 } 8 B 6 1 } 2 left to right; using 8 for 2 3 left to right; 2 3 as 6 C 11 * D 12 1 } as 6 Grade 7 Mathematics Item Sampler

10 A Michael bought a 4-pound package of ground beef for $ What is the cost per pound of the ground beef? A Use the map below to answer question 12. Ridgeway A $ , rounded B $ 2.89 * C $ Clarion DuBois A D $ Carlos bought 3 gallons of ice cream for $9.50. Which proportion can be used to find the cost of 7 gallons of ice cream? A B C D 3 } 7 = } x } 9.5 = x } 7 7 } 9.5 = } x } 3 = x } 7 * 12. The distance from Clarion to DuBois is 2 1 } inches on the map. The actual distance 2 is 40 miles. The distance from Dubois to Ridgeway is 1 1 } inches on the map. What is 2 the actual distance, in miles, from DuBois to Ridgeway? A 10 2 } 3 B 24 * } } 2 2 C } 2 D 66 2 } } } 2 2 B Doreen had 15 yards (yd) of string. She used 11 feet (ft) of string to tie some boxes together. What is the total length of string that Doreen has left? A 14 yd 1 ft 1 yard regrouped as 12 feet B 11 yd 1 ft * C 9 yd 1 ft 6 yards regrouped as 12 feet D 4 yd 15yd 11yd Grade 7 Mathematics Item Sampler

11 B Mia put 2 1 } gallons of milk in the 2 refrigerator. How many pints of milk are equal to 2 1 } 2 gallons? A 8 } 1 2 pints 8 quarts = 2 gallons; plus 1 } 2 B Tamiko made a paper decoration as shown below. Each side of the square is 12 inches. Each triangle has a height of 12 inches. 12 in. 12 in. B 10 pints in quarts C pints = 2 gallons; } 2 pints plus 1 } 2 D 20 pints * What is the total area of the decoration? A 144 sq in. area of square B The figure below shows two equilateral triangles that share one side. B 288 sq in. area of square + 2 triangles C 432 sq in. * D 720 sq in. area of square + 4(bh) B cm 17. The radius of Hattie s circular mirror is 5 } 1 inches. What is the approximate 4 circumference of her mirror? A 8.24 inches r What is the perimeter of the figure? A 60 cm 20 3 B 80 cm * B inches r 3.14 C inches * D inches r C 100 cm 20 5 D 120 cm 20 6 Grade 7 Mathematics Item Sampler

12 B The radius of a circle is 8 centimeters (cm). What is the approximate circumference of the circle? (Use π = 3.14.) A 16 cm 8 2 B 25 cm rounded C 50 cm * D 201 cm rounded C The diameter of a circular plate is 11.5 inches. What is the radius of the plate in inches? A 5.75 * B 11.5 diameter C D (estimate of π) C Oscar wants to draw a chord on the circle shown below. A D B Where should he draw the line segment? C A from point A to point C * B C D from point B to point D from point A to point B from point D to point C Grade 7 Mathematics Item Sampler

13 B The radius of a circle is 8 centimeters (cm). What is the approximate circumference of the circle? (Use π = 3.14.) A 16 cm 8 2 B 25 cm rounded C 50 cm * D 201 cm rounded C The diameter of a circular plate is 11.5 inches. What is the radius of the plate in inches? A 5.75 * B 11.5 diameter C D (estimate of π) C Oscar wants to draw a chord on the circle shown below. * A B D C Where should he draw the line segment? A from point A to point each C * length + 2cm B from point B to point D C D from point A to point B from point D to point C each length + 1cm (or more) measures are close to those in nghj Grade 7 Mathematics Item Sampler

14 C Use the triangle below to answer question Which triangle is similar to triangle GHJ? A G 2 cm 3 cm 4 cm 6 cm J 3.4 cm H 6.8 cm B 4 cm 5 cm 5.4 cm C 3 cm 4 cm 5 cm D 3 cm 3 cm 2.5 cm Grade 7 Mathematics Item Sampler

15 C Mr. Chang made 2 similar rectangular window frames. One frame was 12 feet wide and 16 feet long. What could be the dimensions of the other frame? A 2 feet wide and 6 feet long B 6 feet wide and 8 feet long * C 16 feet wide and 20 feet long C Trapezoid QRST is congruent to trapezoid WXYZ. Which side corresponds to } TQ? A B C D } XY } YZ } ZW * } WX D 24 feet wide and 48 feet long C C Quadrilateral EFGH is similar to quadrilateral WXYZ, as shown below. 25. Four points are graphed on the coordinate grid below. y E Y X F H G Z Which segment corresponds to } FG? W K G H J x A } WX corresponds to } EF B C D } WZ corresponds to } EH } YZ corresponds to } GH } XY * Which point represents the ordered pair (0, 2)? A point G * B point H (2, 0) C point J (0, {2) D point K ( {2, 0) Grade 7 Mathematics Item Sampler

16 C Use the coordinate plane below to answer question 26. y D Students give 6 speeches. The lengths of the first four speeches are shown in the table below. Length of Speeches Speech Length of Speech (in minutes) 2 1 } } 2 10 K x The length of each speech continues to increase by the same amount. What is the length of the 6th speech? A 2 1 } minutes rate of increase 2 B 12 minutes In which quadrant is point K located? A quadrant I B quadrant II C 12 1 } 2 minutes } (5th speech) 2 D 15 minutes * C quadrant III D quadrant IV * Grade 7 Mathematics Item Sampler

17 D Devonne created the following pattern ? The pattern continues. What is the next number in the pattern? A 16.2 wrong sign B 10.8 multiply by 2 C 10.8 multiply by 2 D 16.2 * D Use the expression below to answer question 30. x y (10 + 3) 30. What is the value of the expression when x = 4 and y = 8? A B C 56 * D D Dave uses the equation 15m = 165 to calculate the amount of money (m) he earned during each hour of work. Which step should Dave use to solve the equation for m? A B add 15 to both sides subtract 15 from both sides C multiply both sides by 15 D divide both sides by 15 * D The formula below is used to convert Fahrenheit (8 F) temperatures to Celsius. 8C = 10(8F 32) 4 18 The temperature outside is 418F. What is this temperature in degrees Celsius (8C)? A 5 * B 21 ( ) 4 18 C 50 decimal point error D 56 ( ) 18, rounded Grade 7 Mathematics Item Sampler

18 D Kevin heard that the overnight temperature (t) would not rise above 32 F. Which statement represents the overnight temperature in F? D A t # 32 * B t < 32 C t = 32 D t $ The amount of money Margaret has is twice the amount Emily has plus $5. The amount of money Emily has is e. Which expression describes Margaret s amount of money? A B e } 2 5 e } C 2e 5 D Li can type 170 words every 2 minutes. How many words should Li be able to type in 5 minutes? D A 34 B 85 C 425 * 170 } } 2 D A radio station plays 15 songs each hour. At this rate, how many hours will it take the radio station to play 75 songs? A 5 * B ] 15 C D 1, D 2e + 5 * Grade 7 Mathematics Item Sampler

19 D Use the line graph below to answer question 36. Amount of Tip ($) Dining Tips Amount of Check ($) 36. Jacob went out to eat at many restaurants. He graphed the total cost of each meal and the amount of money he gave for a tip. Which describes the rate at which the amount of the tip changed? A B C It increased $1 for every $1 increase in the amount of the check. interval change on x-axis as 1 It increased $4 for every $1 increase in the amount of the check. greatest y value It increased $1 for every $5 increase in the amount of the check. * E The rainfall for 3 cities is graphed below. At what time was the total of the rainfall for the 3 cities approximately 4 inches? Rainfall (in.) x 11:00 1:00 3:00 5:00 7:00 Time Key City A City B City C A 1:00 * B 3:00 C 5:00 D 7:00 Rainfall for 3 Cities x x x x x D It increased $5 for every $1 increase in the amount of the check. reversed variables Grade 7 Mathematics Item Sampler

20 E The monthly rents for 10 units of an apartment building are shown in the table below. Monthly Rents Apartment Number Rent ($) ,900 E A bowl contains 13 cards numbered 1 to 13. Josh randomly selects 1 card from the bowl. What is the probability the card has an even number on it? A B C D 6 } 13 1 } 2 7 } 13 6 } 7 * 1 } 2 even, 1 } 2 odd probability odd even to odd What is the mode of the rents at the apartment building? A * B median C mean D range Grade 7 Mathematics Item Sampler

21 E A restaurant display case has the following tea bag selections. Flavor Number black tea 15 cinnamon 10 green tea 15 lemon 4 raspberry 6 Tea Bags What is the probability that a tea bag randomly selected from the case will be cinnamon? A B C D 1 } 50 1 } 10 1 } 5 1 } 4 1 bag in 50 1 of 10 cinnamon * 10 cinnamon/40 others Grade 7 Mathematics Item Sampler

22 E Use the spinner below to answer question 41. green green green red 41. The arrow on the spinner is spun once. What is the probability the arrow on the spinner does not stop on green? A B C D 1 } 4 1 } 3 2 } 3 3 } 4 * 1 red and 3 green opposite of option B probability of green Grade 7 Mathematics Item Sampler

23 FIRST OPEN-ENDED ITEM A.3 MATHEMATICS 45. A total of 8,000 runners started a long distance race. The results of the race are listed below. 3 } of the runners finished the race in less than 4 hours of the runners finished the race in 4 or more hours. The rest of the runners did not finish the race. A. Calculate the number of runners who finished the race in less than 4 hours. Show all your work. GO TO THE NEXT PAGE TO FINISH THE QUESTION. Grade 7 Mathematics Item Sampler

24 45. Continued. Please refer to the previous page for task explanation. B. Calculate the number of runners who did not finish the race. Show all your work. Explain why you did each step. Grade 7 Mathematics Item Sampler

25 ITEM-SPECIFIC SCORING GUIDELINE Item #45 This item will be reported under Category A, Numbers and Operations. Assessment Anchor: A.3 Compute accurately and fluently and make reasonable estimates. Specific Eligible Content addressed by this item: Scoring Guide: A Solve problems involving operations (+, ],, 4) of whole numbers, decimals, fractions, or mixed numbers (straight computation or word problems). Score Nonscorable In response to this item, the student demonstrates a thorough understanding of how to solve problems involving operations (+, ],, 4) of whole numbers, decimals, or fractions (straight computation or word problems) by correctly solving problems and clearly explaining procedures. demonstrates a general understanding of how to solve problems involving operations (+, ],, 4) of whole numbers, decimals, or fractions (straight computation or word problems) by correctly solving problems and clearly explaining procedures with only minor errors or omissions. demonstrates a partial understanding of how to solve problems involving operations (+, ],, 4) of whole numbers, decimals, or fractions (straight computation or word problems) by correctly performing a significant portion of the required task. demonstrates minimal understanding of how to solve problems involving operations (+, ],, 4) of whole numbers, decimals, or fractions (straight computation or word problems). The response has no correct answer and insufficient evidence to demonstrate any understanding of the mathematical concepts and procedures as required by the task. Response may show only information copied from the question. BLK (blank)... Blank, entirely erased, or written refusal to respond OT... Off task IL... Illegible LOE... Response in a language other than English Grade 7 Mathematics Item Sampler

26 Item #45 Top Scoring Response: Part A Answer Support 1,500 (runners) } 3 8,000 = 1, OR equivalent (1.5 score points) 0.5 point for correct answer 1 point for correct work Part B Answer 1,300 (runners) ,000 = 5,200 1, ,200 = 6,700 8,000 6,700 = 1,300 Support AND Sample Explanation: I needed to find the total number of runners who finished the race. From part A, 1,500 runners finished in less than 4 hours. Of the 8,000 runners, 0.65 of them finished in 4 or more hours. So I multiplied 8,000 by 0.65 and got 5,200. Then I added 1,500 and 5,200 to get 6,700 who finished the race. I subtracted 6,700 from 8,000 to get 1,300. This is the number of runners who did not finish the race. OR equivalent (2.5 score points) 0.5 point for correct answer 1 point for correct work 1 point for complete explanation Grade 7 Mathematics Item Sampler

27 OPEN-ENDED ITEM RESPONSES A.3 Response Score: 4 MATHEMATICS 45. A total of 8,000 runners started a long distance race. The results of the race are listed below. 3 } of the runners finished the race in less than 4 hours of the runners finished the race in 4 or more hours. The rest of the runners did not finish the race. A. Calculate the number of runners who finished the race in less than 4 hours. Show all your work. The student has given a correct answer. The student has shown correct work. GO TO THE NEXT PAGE TO FINISH THE QUESTION. Grade 7 Mathematics Item Sampler

28 45. Continued. Please refer to the previous page for task explanation. B. Calculate the number of runners who did not finish the race. Show all your work. Explain why you did each step. The student has given a correct answer. The student has shown correct work. The student has given a complete explanation. Grade 7 Mathematics Item Sampler

29 A.3 Response Score: A total of 8,000 runners started a long distance race. The results of the race are listed below. 3 } of the runners finished the race in less than 4 hours of the runners finished the race in 4 or more hours. The rest of the runners did not finish the race. A. Calculate the number of runners who finished the race in less than 4 hours. Show all your work. The student has given a correct answer. The student has shown correct work. GO TO THE NEXT PAGE TO FINISH THE QUESTION. Grade 7 Mathematics Item Sampler

30 45. Continued. Please refer to the previous page for task explanation. B. Calculate the number of runners who did not finish the race. Show all your work. Explain why you did each step. The student has given a correct answer. The student has shown all correct work. The student did not give a complete explanation. Grade 7 Mathematics Item Sampler

31 A.3 Response Score: A total of 8,000 runners started a long distance race. The results of the race are listed below. 3 } of the runners finished the race in less than 4 hours of the runners finished the race in 4 or more hours. The rest of the runners did not finish the race. A. Calculate the number of runners who finished the race in less than 4 hours. Show all your work. The student has given a correct answer. The student has shown correct work. GO TO THE NEXT PAGE TO FINISH THE QUESTION. Grade 7 Mathematics Item Sampler

32 45. Continued. Please refer to the previous page for task explanation. B. Calculate the number of runners who did not finish the race. Show all your work. Explain why you did each step. The student has given a correct answer. The student has shown all correct work. The student did not give an explanation. Grade 7 Mathematics Item Sampler

33 A.3 Response Score: A total of 8,000 runners started a long distance race. The results of the race are listed below. 3 } of the runners finished the race in less than 4 hours of the runners finished the race in 4 or more hours. The rest of the runners did not finish the race. A. Calculate the number of runners who finished the race in less than 4 hours. Show all your work. The student has given a correct answer. The student has shown correct work. GO TO THE NEXT PAGE TO FINISH THE QUESTION. Grade 7 Mathematics Item Sampler

34 45. Continued. Please refer to the previous page for task explanation. B. Calculate the number of runners who did not finish the race. Show all your work. Explain why you did each step. The student has given an incorrect answer. The student has shown incomplete work. The student has given an incomplete explanation. Grade 7 Mathematics Item Sampler

35 A.3 Response Score: A total of 8,000 runners started a long distance race. The results of the race are listed below. 3 } of the runners finished the race in less than 4 hours of the runners finished the race in 4 or more hours. The rest of the runners did not finish the race. A. Calculate the number of runners who finished the race in less than 4 hours. Show all your work. The student has given a correct answer. The student has shown correct work. GO TO THE NEXT PAGE TO FINISH THE QUESTION. Grade 7 Mathematics Item Sampler

36 45. Continued. Please refer to the previous page for task explanation. B. Calculate the number of runners who did not finish the race. Show all your work. Explain why you did each step. The student has given an incorrect answer. The student has shown incomplete work. The student has given an incomplete explanation. Grade 7 Mathematics Item Sampler

37 A.3 Response Score: A total of 8,000 runners started a long distance race. The results of the race are listed below. 3 } of the runners finished the race in less than 4 hours of the runners finished the race in 4 or more hours. The rest of the runners did not finish the race. A. Calculate the number of runners who finished the race in less than 4 hours. Show all your work. The student has given a correct answer. The student has shown correct work. GO TO THE NEXT PAGE TO FINISH THE QUESTION. Grade 7 Mathematics Item Sampler

38 45. Continued. Please refer to the previous page for task explanation. B. Calculate the number of runners who did not finish the race. Show all your work. Explain why you did each step. The student has given an incorrect answer. The student has shown incorrect work. The student has given an incorrect explanation. Grade 7 Mathematics Item Sampler

39 A.3 Response Score: A total of 8,000 runners started a long distance race. The results of the race are listed below. 3 } of the runners finished the race in less than 4 hours of the runners finished the race in 4 or more hours. The rest of the runners did not finish the race. A. Calculate the number of runners who finished the race in less than 4 hours. Show all your work. The student has given a correct answer. The student has shown incomplete work. GO TO THE NEXT PAGE TO FINISH THE QUESTION. Grade 7 Mathematics Item Sampler

40 45. Continued. Please refer to the previous page for task explanation. B. Calculate the number of runners who did not finish the race. Show all your work. Explain why you did each step. The student has given an incorrect answer. The student has shown incomplete work. The student has given an incomplete explanation. Grade 7 Mathematics Item Sampler

41 A.3 Response Score: A total of 8,000 runners started a long distance race. The results of the race are listed below. 3 } of the runners finished the race in less than 4 hours of the runners finished the race in 4 or more hours. The rest of the runners did not finish the race. A. Calculate the number of runners who finished the race in less than 4 hours. Show all your work. The student has given an incorrect answer. The student has shown incorrect work. GO TO THE NEXT PAGE TO FINISH THE QUESTION. Grade 7 Mathematics Item Sampler

42 45. Continued. Please refer to the previous page for task explanation. B. Calculate the number of runners who did not finish the race. Show all your work. Explain why you did each step. The student has given an incorrect answer. The student has shown incorrect work. The student has given an incorrect explanation. Grade 7 Mathematics Item Sampler

43 SECOND OPEN-ENDED ITEM B An architect made a scale drawing on a grid of the front of an arch for a public park. Scale height 1 = 4 } 2 feet width A. What will be the actual width and height, in feet, of the arch? Show or explain all your work. GO TO THE NEXT PAGE TO FINISH THE QUESTION. Grade 7 Mathematics Item Sampler

44 46. Continued. Please refer to the previous page for task explanation. B. The architect wanted to make another scale drawing of the arch based on its actual height and width. The drawing of the arch had to measure 4 inches by 3 inches to fit on a card. What scale should the architect use for this drawing? Show or explain all your work. C. The architect planned to enlarge the arch for a project in another city. The larger arch was to be 1 1 } the size of the original. What will be the width and height, in feet, of 4 the larger arch? Show or explain all your work. Grade 7 Mathematics Item Sampler

45 ITEM-SPECIFIC SCORING GUIDELINE Item #46 This item will be reported under Category B, Measurement. Assessment Anchor: B.2 Apply appropriate techniques, tools, and formulas to determine measurements. Specific Eligible Content addressed by this item: B Interpret and/or apply scales shown on maps, blueprints, models, etc. B Determine and/or apply an appropriate scale for reduction or enlargement. Scoring Guide: Score Nonscorable In response to this item, the student demonstrates a thorough understanding of interpreting, applying, and determining scales based on a model for reduction or enlargement by correctly solving problems and clearly explaining procedures. demonstrates a general understanding of interpreting, applying, and determining scales based on a model for reduction or enlargement with only minor errors or omissions. demonstrates a partial understanding of interpreting, applying, and determining scales based on a model for reduction or enlargement by correctly performing a significant portion of the required task. demonstrates minimal understanding of interpreting, applying, and determining scales based on a model for reduction or enlargement. The response has given no correct answer and insufficient evidence to demonstrate any understanding of the mathematical concepts and procedures as required by the task. Response may show only information copied from the question. BLK (blank)... Blank, entirely erased, or written refusal to respond OT... Off task IL... Illegible LOE... Response in a language other than English Grade 7 Mathematics Item Sampler

46 Item #46 Top Scoring Response: Part A Answer 72 ft high; 54 ft wide Support 16 4 } 1 2 = } 2 = 54 (2 score points) 1 point for correct answers 1 point for complete support Part B Answer 1 inch = 18 feet OR equivalent Support 72 4 = = 18 (1 score point) 0.5 point for correct answer 0.5 point for complete support Part C Answer 90 ft high; 67.5 ft wide Support 5 } 72 = } 54 = (1 score point) 0.5 point for correct answers 0.5 point for complete support Grade 7 Mathematics Item Sampler

47 OPEN-ENDED ITEM RESPONSES B.2 Response Score: An architect made a scale drawing on a grid of the front of an arch for a public park. Scale height 1 = 4 } 2 feet width A. What will be the actual width and height, in feet, of the arch? Show or explain all your work. The student has given correct answers. The student has shown complete support. GO TO THE NEXT PAGE TO FINISH THE QUESTION. Grade 7 Mathematics Item Sampler

48 46. Continued. Please refer to the previous page for task explanation. B. The architect wanted to make another scale drawing of the arch based on its actual height and width. The drawing of the arch had to measure 4 inches by 3 inches to fit on a card. What scale should the architect use for this drawing? Show or explain all your work. The student has given a correct answer. The student has shown complete support. C. The architect planned to enlarge the arch for a project in another city. The larger arch was to be 1 1 } the size of the original. What will be the width and height, in feet, of 4 the larger arch? Show or explain all your work. The student has given correct answers. The student has shown complete support. Grade 7 Mathematics Item Sampler

49 B.2 Response Score: An architect made a scale drawing on a grid of the front of an arch for a public park. Scale height 1 = 4 } 2 feet width A. What will be the actual width and height, in feet, of the arch? Show or explain all your work. The student has given correct answers. The student has shown complete support. GO TO THE NEXT PAGE TO FINISH THE QUESTION. Grade 7 Mathematics Item Sampler

50 46. Continued. Please refer to the previous page for task explanation. B. The architect wanted to make another scale drawing of the arch based on its actual height and width. The drawing of the arch had to measure 4 inches by 3 inches to fit on a card. What scale should the architect use for this drawing? Show or explain all your work. The student has given a correct answer. The student has shown complete support. C. The architect planned to enlarge the arch for a project in another city. The larger arch was to be 1 1 } the size of the original. What will be the width and height, in feet, of 4 the larger arch? Show or explain all your work. The student has given an incorrect width. The student has shown complete support. Based on PSSA scoring rules, 3½ becomes 3. Grade 7 Mathematics Item Sampler

51 B.2 Response Score: An architect made a scale drawing on a grid of the front of an arch for a public park. Scale height 1 = 4 } 2 feet width A. What will be the actual width and height, in feet, of the arch? Show or explain all your work. The student has given correct answers. The student has shown complete support. GO TO THE NEXT PAGE TO FINISH THE QUESTION. Grade 7 Mathematics Item Sampler

52 46. Continued. Please refer to the previous page for task explanation. B. The architect wanted to make another scale drawing of the arch based on its actual height and width. The drawing of the arch had to measure 4 inches by 3 inches to fit on a card. What scale should the architect use for this drawing? Show or explain all your work. The student has given an incorrect answer. The student has shown incorrect support. C. The architect planned to enlarge the arch for a project in another city. The larger arch was to be 1 1 } the size of the original. What will be the width and height, in feet, of 4 the larger arch? Show or explain all your work. The student has given correct answers. The student has shown complete support. Grade 7 Mathematics Item Sampler

53 B.2 Response Score: An architect made a scale drawing on a grid of the front of an arch for a public park. Scale height 1 = 4 } 2 feet width A. What will be the actual width and height, in feet, of the arch? Show or explain all your work. The student has given incorrect height and width. The student has shown complete support. GO TO THE NEXT PAGE TO FINISH THE QUESTION. Grade 7 Mathematics Item Sampler

54 46. Continued. Please refer to the previous page for task explanation. B. The architect wanted to make another scale drawing of the arch based on its actual height and width. The drawing of the arch had to measure 4 inches by 3 inches to fit on a card. What scale should the architect use for this drawing? Show or explain all your work. The student has given a correct answer (based on carry-through error). The student has shown complete support. C. The architect planned to enlarge the arch for a project in another city. The larger arch was to be 1 1 } the size of the original. What will be the width and height, in feet, of 4 the larger arch? Show or explain all your work. The student has given correct answers (based on carry-through error). The student has shown no support. Based on PSSA scoring rules, 2½ becomes 2. Grade 7 Mathematics Item Sampler

55 B.2 Response Score: An architect made a scale drawing on a grid of the front of an arch for a public park. Scale height 1 = 4 } 2 feet width A. What will be the actual width and height, in feet, of the arch? Show or explain all your work. The student has given correct answers. The student has shown no support. GO TO THE NEXT PAGE TO FINISH THE QUESTION. Grade 7 Mathematics Item Sampler

56 46. Continued. Please refer to the previous page for task explanation. B. The architect wanted to make another scale drawing of the arch based on its actual height and width. The drawing of the arch had to measure 4 inches by 3 inches to fit on a card. What scale should the architect use for this drawing? Show or explain all your work. The student has given an incorrect answer. The student has shown incomplete support. C. The architect planned to enlarge the arch for a project in another city. The larger arch was to be 1 1 } the size of the original. What will be the width and height, in feet, of 4 the larger arch? Show or explain all your work. The student has given correct answers. The student has shown complete support. Grade 7 Mathematics Item Sampler

57 B.2 Response Score: An architect made a scale drawing on a grid of the front of an arch for a public park. Scale height 1 = 4 } 2 feet width A. What will be the actual width and height, in feet, of the arch? Show or explain all your work. The student has given incorrect answers. The student has shown no support. GO TO THE NEXT PAGE TO FINISH THE QUESTION. Grade 7 Mathematics Item Sampler

58 46. Continued. Please refer to the previous page for task explanation. B. The architect wanted to make another scale drawing of the arch based on its actual height and width. The drawing of the arch had to measure 4 inches by 3 inches to fit on a card. What scale should the architect use for this drawing? Show or explain all your work. The student has given a correct answer (based on carrythrough error). The student has shown complete support. C. The architect planned to enlarge the arch for a project in another city. The larger arch was to be 1 1 } the size of the original. What will be the width and height, in feet, of 4 the larger arch? Show or explain all your work. The student has given no answers. The student has shown incorrect support. Grade 7 Mathematics Item Sampler

59 B.2 Response Score: An architect made a scale drawing on a grid of the front of an arch for a public park. Scale height 1 = 4 } 2 feet width A. What will be the actual width and height, in feet, of the arch? Show or explain all your work. The student has given incorrect answers. The student has shown no support. GO TO THE NEXT PAGE TO FINISH THE QUESTION. Grade 7 Mathematics Item Sampler

60 46. Continued. Please refer to the previous page for task explanation. B. The architect wanted to make another scale drawing of the arch based on its actual height and width. The drawing of the arch had to measure 4 inches by 3 inches to fit on a card. What scale should the architect use for this drawing? Show or explain all your work. The student has given an incorrect answer. The student has shown no support. C. The architect planned to enlarge the arch for a project in another city. The larger arch was to be 1 1 } the size of the original. What will be the width and height, in feet, of 4 the larger arch? Show or explain all your work. The student has given correct answers (based on carry-through errors). The student has shown complete support. Grade 7 Mathematics Item Sampler

61 B.2 Response Score: An architect made a scale drawing on a grid of the front of an arch for a public park. Scale height 1 = 4 } 2 feet width A. What will be the actual width and height, in feet, of the arch? Show or explain all your work. The student has given incorrect answers. The student has shown no support. GO TO THE NEXT PAGE TO FINISH THE QUESTION. Grade 7 Mathematics Item Sampler

62 46. Continued. Please refer to the previous page for task explanation. B. The architect wanted to make another scale drawing of the arch based on its actual height and width. The drawing of the arch had to measure 4 inches by 3 inches to fit on a card. What scale should the architect use for this drawing? Show or explain all your work. The student has given no answer. The student has shown incorrect support. C. The architect planned to enlarge the arch for a project in another city. The larger arch was to be 1 1 } the size of the original. What will be the width and height, in feet, of 4 the larger arch? Show or explain all your work. The student has given incorrect answers. The student has shown incorrect support. Grade 7 Mathematics Item Sampler

63 THIRD OPEN-ENDED ITEM E Mr. Oakley s class surveyed 200 students about their favorite type of pie. The double bar graph below shows the results of the survey. Number of Students apple Favorite Type of Pie cherry peach strawberry Type of Pie Key Girls Boys A. What is the difference in the total number of students who chose peach pie as their favorite type of pie and the total number of students who chose apple pie? Show all your work. Explain why you did each step. GO TO THE NEXT PAGE TO FINISH THE QUESTION. Grade 7 Mathematics Item Sampler

64 47. Continued. Please refer to the previous page for task explanation. B. What fraction of the boys surveyed chose cherry pie as their favorite type of pie? Show all your work. Explain why you did each step. Grade 7 Mathematics Item Sampler

65 ITEM-SPECIFIC SCORING GUIDELINE Item #47 This item will be reported under Category E, Data Analysis and Probability. Assessment Anchor: E.1 Formulate or answer questions that can be addressed with data and/or organize, display, interpret or analyze data. Specific Eligible Content addressed by this item: Scoring Guide: E Analyze data and/or answer questions pertaining to data represented in histograms, double bar graphs, multiple line graphs or stem-and-leaf plots. Score Nonscorable In response to this item, the student demonstrates a thorough understanding of how to analyze data and/or answer questions pertaining to data represented in double bar graphs by correctly solving problems and clearly explaining procedures. demonstrates a general understanding of how to analyze data and/or answer questions pertaining to data represented in double bar graphs by correctly solving problems and clearly explaining procedures with only minor errors or omissions. demonstrates a partial understanding of how to analyze data and/or answer questions pertaining to data represented in double bar graphs by correctly performing a significant portion of the required task. demonstrates minimal understanding of how to analyze data and/or answer questions pertaining to data represented in double bar graphs. The response has no correct answer and insufficient evidence to demonstrate any understanding of the mathematical concepts and procedures as required by the task. Response may show only information copied from the question. BLK (blank)... Blank, entirely erased, or written refusal to respond OT... Off task IL... Illegible LOE... Response in a language other than English Grade 7 Mathematics Item Sampler

66 Item #47 Top Scoring Response: Part A Answer = = = 10 Support AND Sample Explanation: To find out the total number of students who chose peach pie, I read the bar heights for girls and boys for peach pie and added them together (the number of girls, 40, plus the number of boys, 15, which is 55). Then, I did the same for apple pie (the number of girls, 20, plus the number of boys, 25, which is 45). To find the difference in the total number of students who chose each pie, I subtracted the 45 from the 55 to come up with 10. OR equivalent (2 score points) 0.5 point for correct answer 1.5 points for complete support Part B Answer 30 } 100 or } = } 100 AND Support (2 score points) 0.5 point for correct answer 1.5 points for complete support Sample Explanation: To find what part the boys who chose cherry are of all the boys, I first read the bar height for boys cherry pie which was 30. Then I found the total number of boys surveyed by looking at the bar heights for each type of pie. There were 25 boys for apple pie, 30 for cherry pie, 15 for peach pie, and 30 for strawberry pie. I added those together to get 100 which is the total number of boys. I then wrote a fraction of the part to the whole with 30 as the numerator and 100 as the denominator, which is } OR equivalent Grade 7 Mathematics Item Sampler

67 OPEN-ENDED ITEM RESPONSES E.1 Response Score: 4 MATHEMATICS 47. Mr. Oakley s class surveyed 200 students about their favorite type of pie. The double bar graph below shows the results of the survey. Number of Students apple Favorite Type of Pie cherry peach strawberry Type of Pie Key Girls Boys A. What is the difference in the total number of students who chose peach pie as their favorite type of pie and the total number of students who chose apple pie? Show all your work. Explain why you did each step. The student has given a correct answer. The student has shown complete support. GO TO THE NEXT PAGE TO FINISH THE QUESTION. Grade 7 Mathematics Item Sampler

68 47. Continued. Please refer to the previous page for task explanation. B. What fraction of the boys surveyed chose cherry pie as their favorite type of pie? Show all your work. Explain why you did each step. The student has given a correct answer. The student has shown complete support. Grade 7 Mathematics Item Sampler

69 E.1 Response Score: Mr. Oakley s class surveyed 200 students about their favorite type of pie. The double bar graph below shows the results of the survey. Number of Students apple Favorite Type of Pie cherry peach strawberry Type of Pie Key Girls Boys A. What is the difference in the total number of students who chose peach pie as their favorite type of pie and the total number of students who chose apple pie? Show all your work. Explain why you did each step. The student has given a correct answer. The student has shown complete work. The student has given no explanation. GO TO THE NEXT PAGE TO FINISH THE QUESTION. Grade 7 Mathematics Item Sampler

70 47. Continued. Please refer to the previous page for task explanation. B. What fraction of the boys surveyed chose cherry pie as their favorite type of pie? Show all your work. Explain why you did each step. The student has given a correct answer. The student has shown complete support. Grade 7 Mathematics Item Sampler

71 E.1 Response Score: Mr. Oakley s class surveyed 200 students about their favorite type of pie. The double bar graph below shows the results of the survey. Number of Students apple Favorite Type of Pie cherry peach strawberry Type of Pie Key Girls Boys A. What is the difference in the total number of students who chose peach pie as their favorite type of pie and the total number of students who chose apple pie? Show all your work. Explain why you did each step. The student has given a correct answer. The student has shown complete work. The student has given no explanation. GO TO THE NEXT PAGE TO FINISH THE QUESTION. Grade 7 Mathematics Item Sampler