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PART II Released Mathematics Items – 2006 Benchmark Grade CALCULATOR NOT PERMITTED — ITEMS 1–8 AR4M04A0403Y166-166D What is the missing operation in the pattern below? Input n 10 11 12 13 14 15 Output ? A add B add 10 C subtract * D subtract AR4M04M1311Y052-052C Jamie built a block structure with a volume of cubic units Which of the structures below did he build? A Figure B Figure * C Figure D Figure 21 PART II Released Mathematics Items – 2006 Benchmark Grade AR4M02M1309NXXX-114C AR4M02N0204NXXX-015B How many yards of fencing would it Mrs Smith and Mr Jones are taking their classes on a field trip Each school van holds people If there are 48 people going on the trip, how many vans they need? take to surround a dog’s play area that is a square measuring yards per side? A 16 yards B 16 yards * C 18 yards D 25 yards A * B C 40 D 56 Ashley has a 43-page sticker album Each page will hold about 20 stickers About how many stickers can she place in the album? What is the value of the underlined digit below? 218,036,097 A B 20 A three thousand C 60 * B thirty thousand * D 800 C thirty-six thousand D three hundred thousand Based on the data collection below, how many more fourth-grade students preferred chocolate chip than preferred vanilla? Zach created the secret code below to write messages to his friends My Secret Code 1=B 2=C 3=D 4=E etc What numbers will Zach write to represent the word “HE”? A 4, * B 7, C 4, D 8, 22 A B * C 19 D 27 PART II Released Mathematics Items – 2006 Benchmark Grade CALCULATOR PERMITTED — ITEMS 9–40 AR4M04N0102NXXX-178C AR4M04N0305NXXX-017D Jean made the chart below to record the number of pencils sold at the school store for the last four months 12 Randy has bags of marbles Each bag has 86 marbles About how many marbles does Randy have in all? Pencil Sales Month # of Pencils Sold September 1,543 October 1,867 November 1,290 December 1,789 Which of the following is a true statement about the number of pencils sold? A 83 B 89 C 240 * D 270 13 What is the rule for the number pattern below? 1,125 225 45 A 1,789 < 1,543 B 1,290 > 1,867 A add 900 * C 1,543 > 1,290 B divide by D 1,867 = 1,789 * C divide by D 10 Mr Carter’s class has 30 students Which mathematical sentence shows how many 5-player basketball teams the class will be able to make at recess? subtract 900 14 Joey covered a hexagon pattern block using triangles and other shape What is the other shape? You may use your pattern blocks to help you * A 30 ÷ = n B 30 × = n A square C 30 – = n B triangle D 30 + = n C rhombus * D trapezoid 11 Felton weighed apples and found that they weighed pounds Approximately how much does apple weigh? A oz * B oz C 16 oz D 32 oz 23 PART II Released Mathematics Items – 2006 Benchmark Grade AR4M04G1102Y047-047C 15 How many triangle pattern blocks are needed to cover the figure below? You may use your pattern blocks to help you A B * C 12 D 13 AR4M04D1702NXXX-136B AR4M02N0103NXXX-084C 16 Carl has a bag of fruit-flavored candy that contains the following pieces: 17 Sean has 36 baseball cards Tom has 25 baseball cards Which of the following is a true statement about their baseball card collections? • • • • grape strawberry cherry watermelon Carl pulls a piece of candy from the bag without looking What is the probability that he picks a watermelon-flavored piece? A out of 11 * B out of 11 C out of 11 D out of 11 24 A 25 > 36 B 25 × 36 * C 36 > 25 D 36 = 25 PART II Released Mathematics Items – 2006 Benchmark Grade AR4M04D1702Y122-122D AR4M04D1501Y139-139D 18 Patty is playing a shape game with the spinner below 21 Jim and his friends made the table below to show how many seashells they have in their collections What is the probability that the pointer will land on a hexagon on her next spin? A out of 10 B out of 10 C out of 10 * D out of 10 How many seashells they have in all? 19 Mrs Rodriguez will use 54 square feet of tile to cover her bathroom floor What are the dimensions of her bathroom? * A ft by ft B ft by ft C ft by ft D ft by ft soda can B stop sign C cereal box D front door of a house 13 B 14 C 52 * D 54 2 22 Sheila is making beaded necklaces that are 10 inches long She has a piece of string that is 78 inches long How many necklaces can she make from the string? 20 Which of the following is most like a cylinder? * A A 25 * A B C 780 D 800 PART II Released Mathematics Items – 2006 Benchmark Grade AR4M04D1702Y121-121C AR4M03G1102Y081-081D 23 On the cube below, the shapes on the faces not showing are triangles Use the shapes below to answer question 25 25 When the shapes above are combined with no empty spaces left over, what new shape is formed? (You may use your pattern blocks to help you.) What are the chances the cube will land on a triangle when rolled? A out of B out of * C out of D out of * 24 How many more vertices does a cube have than a triangular prism? * A B C D 14 26 It is 150 miles between Little Rock and Ashdown Driving at 50 miles per hour, how many hours will the trip take? 26 * A B C D 2 PART II Released Mathematics Items – 2006 Benchmark Grade AR4M04M1308Y098-098A 27 Which length, rounded to the nearest inch, best describes the toy cheetah below? Use your ruler to help you * A B inches C D inches inches inches AR4M04M1307Y094-094C 28 What is the length, measured to the nearest A B inches * C D inch, of the plastic fork below? Use your ruler to help you inches inches inches 27 PART II Released Mathematics Items – 2006 Benchmark Grade AR4M02N0103NXXX-010A AR4M04A0403NXXX-163A 29 What symbol can replace the in the number sentence below to make it true? 31 When Ashley says “13,” the answer is 113 When she says “36,” the answer is 136 When she says “94,” the answer is 194 What is the rule for Ashley’s pattern? 1,840 1,804 * A > * A add 100 B = B add 117 C < C divide by 100 D + D divide by 117 AR4M02D1701Y078-078C AR4M04M1307Y091-091A 30 There are 124 jelly beans in a bag The table below lists the colors and number of jelly beans Which fraction represents Katie’s chances of picking out a pink jelly bean on her first try? 32 Jacob drew the map below to show the distance he drives from his house to the mall Jelly beans in the Bag Color Number black 16 orange 17 pink 24 purple 12 red 14 yellow 24 white 17 A 16 124 B Based on Jacob’s scale, what is the distance? Use your ruler to help you * A miles 12 124 B miles C miles * C 24 124 D miles D 124 24 28 PART II Released Mathematics Items – 2006 Benchmark Grade AR4M04D1401Y123-123B 33 Toshio asked 55 fourth-grade students about their favorite after-school activity He created the graph below to display the results of his survey How many students chose riding their bike as their favorite activity? A 15 * B 25 C 30 D 55 AR4M04D1702Y125-125B 34 Brad has a bag containing the shapes below Which statement best describes the outcome if Brad chooses a shape from the bag without looking? A He is most likely to choose a triangle * B He is most likely to choose a rectangle C He is least likely to choose a rectangle D He is equally likely to choose triangles and circles 29 PART II Released Mathematics Items – 2006 Benchmark Grade AR4M04N0202Y167-167B AR4M02G0802NXXX-005C 35 Mr Booth put the two groups of numbers below on the board 37 I am a polygon I have sides What is my name? A square B octagon * C hexagon D quadrilateral AR4M02N0102Y036-036B 38 The chart below shows the number of calories consumed by a group of students in one week What is the rule he used when forming the two groups? Student Calorie Chart Student Number of Calories Tony James Kendra Sophia 15,285 14,768 14,876 15,852 A Group X: Multiples of Group Y: Even Numbers * B Group X: Odd Numbers Group Y: Even Numbers C Group X: Odd Numbers Group Y: Multiples of Which student consumed the least number of calories? D Group X: Odd Numbers Group Y: Multiples of A * B AR4M04M1203NXXX-084B 36 Mrs Berini used 18 yards of fabric to make her living room curtains and 16 yards to make her bedroom curtains How much more fabric did she use in the living room than in the bedroom? Tony James C Kendra D Sophia AR4M04M1203NXXX-089D 39 Craig’s little brother weighed pounds and ounces when he was born How many ounces did he weigh? A feet * B feet A 40 C 34 feet B 44 D 72 feet C 80 * D 88 30 PART II Released Mathematics Items – 2006 Benchmark Grade AR4M02N0104Y037-037D 40 Which of the following fractions identifies the part of the dozen eggs shown below that has been used? A B C 12 * D 12 31 PART II Released Mathematics Items – 2006 Benchmark Grade MATHEMATICS OPEN-RESPONSE ITEM A AR4M04M1310Y100-100CR A Cameron drew the rectangle below The length of Cameron’s rectangle is times its width What is the length of Cameron’s rectangle? Explain your answer using words, numbers, and/or pictures What is the area of Cameron’s rectangle? Explain your answer using words, numbers, and/or pictures BE SURE TO LABEL YOUR RESPONSES AND RUBRIC FOR MATHEMATICS OPEN-RESPONSE ITEM A SCORE B DESCRIPTION The student earns points Correct units of “cm” in Part Correct units of “Sq cm.” in Part The response contains no incorrect work The student earns points The student earns points The student earns point Some minimal understanding is shown: Ex Student uses formula for area in Part AND perimeter in Part with all calculations correct The student earns points No understanding is shown Blank – No Response A score of “B” will be reported as “NA.” (No attempt to answer the item Score of “0” assigned for the item.) 32 PART II Released Mathematics Items – 2006 Benchmark Grade Solution and Scoring Part Points points possible point: Correct answer: (cm) Note: Do not give credit for answer if incorrect procedure is evident AND point: Correct procedure shown and/or explained Work may contain a calculation error Give credit for the following or equivalent: • x = L (uses fact that length is times the width and w = cm.) • “If the width is 3, just multiply that by 3.” or • + + + = 24 (Finds length based on perimeter, uses Guess & Check) or • + = 6, 24 – = 18, 18 ÷ = L Note: Do not give credit for incomplete procedure: Ex: L = because 24 – = 18 points possible point: Correct answer: 27 (square cm) or correct answer based on incorrect answer to Part AND point: Correct procedure shown and/or explained Work may contain a calculation error and/or may be based on an incorrect answer given in Part Give credit for the following or equivalent: • “3 x = Area.” or • “I multiplied the width of by the length of 9.” or • “I multiplied the length times the width, and the length is and the width is 3.” or • Drawing of a x rectangle that is divided into 27 squares Note: Do not give credit for only repeating the formula LW = Area only 33 PART II Released Mathematics Items – 2006 Benchmark Grade MATHEMATICS OPEN-RESPONSE ITEM B AR4M03A0402Y003-003R B Karen wants to make a bookmark out of leather She is planning the design above on paper before she starts cutting the leather Using Karen’s pattern, complete the design for the bookmark How many of each shape will she need to cut out to make her bookmark? Use the same number of squares, circles, and rhombuses to design a new bookmark that follows a regular pattern BE SURE TO LABEL YOUR RESPONSES 1, 2, AND RUBRIC FOR MATHEMATICS OPEN-RESPONSE ITEM B SCORE DESCRIPTION The student earns points The response contains no incorrect work The student earns points The student earns points The student earns point Some minimal understanding is shown: Ex Part 1: row is completed correctly with no other credit The student earns points No understanding is shown Blank – No Response A score of “B” will be reported as “NA.” (No attempt to answer the item Score of “0” assigned for the item.) B 34 PART II Released Mathematics Items – 2006 Benchmark Grade Solution and Scoring Part Points point possible point: The last top and bottom sections of the bookmark (positions 7-10) are correctly completed, as shown in the diagram below: Note: Top and bottom row not have to be aligned point possible point: Correct number of shapes: 10 squares, rhombuses, circles (shapes may be named or drawn) Or Correct # of squares, rhombuses and circles based on Part answer points possible Note: Design may be in a single row or a continuous pattern Note: If design is in a double row, both rows must have a repeating pattern the 2nd row is a repeat of the 1st row Note: Design must be different from the original bookmark points: Or point: or Correct and complete design that contains all of the following: • 10 squares, rhombuses, circles OR Equal #’s of each shape • The pattern is repeating horizontally, repeats at least once and has no errors Partially correct design: • Design uses 10 Squares, rhombuses, circles or equal #’s of each (Repeats correctly at least once, proceeds with something incorrect.) or • The #’s of squares, rhombuses and circles ≠10, 5, and/or 5, and there are not equal #’s of each shape, but the design repeats correctly at least once 35 PART II Released Mathematics Items – 2006 Benchmark Grade MATHEMATICS OPEN-RESPONSE ITEM C AR4M04N0303NXXX-032CR C Mrs Grey wrote the following two numbers on the board 12 What is the sum of the two numbers that Mrs Grey wrote on the board? Write a number sentence using Mrs Grey’s numbers and your sum If 12 is the dividend and is the quotient, what is the divisor? Write a number sentence using Mrs Grey’s numbers and your divisor BE SURE TO LABEL YOUR RESPONSES AND RUBRIC FOR MATHEMATICS OPEN-RESPONSE ITEM C SCORE DESCRIPTION The student earns points The response contains no incorrect work The student earns points The student earns points The student earns point Some minimal understanding is shown: Ex x = 12 with no other credit The student earns points No understanding is shown Blank – No Response A score of “B” will be reported as “NA.” (No attempt to answer the item Score of “0” assigned for the item.) B 36 PART II Released Mathematics Items – 2006 Benchmark Grade Solution and Scoring Part Points points possible point: Correct answer: 16 (sum) Note: Do not give credit if incorrect procedure is used: Ex: x = 16 AND point: Correct equation given Work may contain a calculation error Give credit for the following: • 12 + = # or • + 12 = # Give credit for the following only with an answer of 16: • 16 – = 12 (Guess & Check) • 16 – 12 = (Guess & Check) Note: Do not give procedure credit for work that is not in the form of an equation: Ex: 12 or + 16 Ex: “I added 12 and and got…” points possible point: Correct answer: (divisor) Give credit if the answer is stated “The divisor is 3.” or if is shown as the divisor in a division operation: Ex: 12 Note: Do not give credit if incorrect procedure is used: Ex: ÷ 12 = AND point: Correct equation given (Divisor may be incorrect.) Give credit for the following: • 12 ÷ = or • 12 ÷ (divisor) = or Give credit for the following only with an answer of 3: • x = 12 (Guess & Check) • x = 12 (Guess & Check) • 12 ÷ = (Give credit except at “4” level) Note: Do not give procedure credit for work that is not in the form of an equation: Ex: Shows short division: 12 Ex: “I divided 12 by and got…” 37 or PART II Released Mathematics Items – 2006 Benchmark Grade MATHEMATICS OPEN-RESPONSE ITEM D AR4M04G1102Y070-070CR D Casey used four pattern blocks to create the design below Name the four pattern blocks Casey used You may use your pattern blocks to help you find the answer What is another way that Casey’s design could have been created if he had used more than four blocks? Explain your answer using words, numbers, and/or pictures BE SURE TO LABEL YOUR RESPONSES AND RUBRIC FOR MATHEMATICS OPEN-RESPONSE ITEM D SCORE DESCRIPTION The student earns points The response contains no incorrect work The student earns points The student earns points The student earns point Some minimal understanding is shown: Ex Part 1: correct names and #’s, 3rd name incorrect (with no drawing) (Square, Trapezoid, Octagons) Ex Part 1: correct drawings of Hexagon, Trapezoid, and Square The student earns points No understanding is shown Ex different polygons named – Octagon, Hexagon, Square, Trapezoid Ex Part 1: Octagons, Square, and Quadrilateral Blank – No Response A score of “B” will be reported as “NA.” (No attempt to answer the item Score of “0” assigned for the item.) B 38 PART II Released Mathematics Items – 2006 Benchmark Grade Solution and Scoring Part Points points possible points: Answer is correct and complete: Hexagons, Trapezoid and Square (Shapes are correctly named with correct # of each.) Note: Rhombus, rectangle, parallelogram or quadrilateral may be used for the square Quadrilateral may be used for trapezoid But not give credit if quadrilateral is used for both the trapezoid & square Or point: Partially correct answer Give credit for the following: • Hexagon, Trapezoid and Square (correct shapes, no #’s) Or • names & #’s are correct, 3rd has correct drawing of remaining shape, but name may be incorrect or missing points possible points: Correct and complete answer Give credit for the following: Note: If incorrect name(s) are given in Part 1, not penalize again Credit can be given if answer is “correct” based on Pt answer • Correct shapes and # of shapes (> 4) needed to make new design with support explaining or showing why they will work: Ex: hexagon, trapezoids and square with given diagram correctly divided Ex: “4 trapezoids, triangles and one square because trapezoids could make up each hexagon and triangles could make up one trapezoid.” Ex: “2 hexagons, square, triangle, rhombus since a trapezoid can be made up of triangle and rhombus.” Ex: trapezoids and square with given diagram correctly divided Ex: “15 triangles and square because triangles make up hexagon and triangles make up trapezoid so + + = 15 triangles, + square.” Or • Correct and complete drawing of given design divided up into more than pattern blocks Or point: Partially correct answer Give credit for the following: • Correct shapes and #’s of each shape needed to make new design with missing, incomplete or contradicting support or • Correct and complete new drawing with contradicting support or • Description of how to divide one of the figures in the given drawing, but no reference is made to the rest of the given figure 39 PART II Released Mathematics Items – 2006 Benchmark Grade MATHEMATICS OPEN-RESPONSE ITEM E AR4M04D1501Y148-148CR E Joseph made the pictogram below to show the number of hits he had in his last four baseball games How many hits did Joseph have in Game 2? Explain your answer using words and/or numbers How many more hits did Joseph have in Game than in Game 3? Explain your answer using words and/or numbers BE SURE TO LABEL YOUR RESPONSES AND RUBRIC FOR MATHEMATICS OPEN-RESPONSE ITEM E SCORE DESCRIPTION The student earns points The response contains no incorrect work The student earns points The student earns points The student earns point Some minimal understanding is shown: Ex Part 2: minus any # (≠ 3) = answer with no credit in any other part Ex Part 2: # (≠ 9) – = answer with no credit in any other part Ex Part 2: correct # of hits (identified) in Game and/or The student earns points No understanding is shown Blank – No Response A score of “B” will be reported as “NA.” (No attempt to answer the item Score of “0” assigned for the item.) B 40 PART II Released Mathematics Items – 2006 Benchmark Grade Solution and Scoring Part Points points possible point: Correct answer: (hits) Note: Do not give credit if incorrect procedure is evident AND point: Correct and complete procedure shown and/or explained Work may contain a calculation error Give credit for the following or equivalent: • x = # of hits or • “I multiplied and 2.” or • + + + = # of hits or • + = # of hits or • “I skip counted by four times.” or • Draws four baseballs and accumulates hits With the correct answer of 8, give credit for the following: • “I counted (skip counted) by 2’s.” points possible point: Correct answer: (more hits) Note: Do not give credit if incorrect procedure is evident Ex: 10 – = AND point: Correct procedure shown and/or explained Work may contain a calculation error Give credit for the following or equivalent: • Game 4: (2 x 4) + = Game 3: + = 9–3=6 • “He has hits in game and hits in game so minused from 9.” or • 9–3=# or • 4½ – 1½ = baseballs, x = # or • “I subtracted from 9.” or “I subtracted and 3.” Note: Do not give credit for incomplete procedure: Ex: “He had hits in Game and hits in game 3.” and stops Note: Do not give credit for vague procedure or procedure stated incorrectly: Ex: “I subtracted and 9.” (order implies is subtracted from 3) Ex: “I subtracted from 3.” (incorrectly stated) 41 PART II Released Mathematics Items – 2006 Benchmark Grade Mathematics Reference Sheet Grade Use the information below, as needed, to answer questions on the Mathematics test foot = 12 inches cup = ounces (oz) kilogram = 1000 grams yard = feet pint = cups liter = 1000 milliliters quart = pints gallon = quarts pound (lb) = 16 ounces (oz) 42 ... 2 006 Benchmark Grade AR4M04G1102Y 047 - 047 C 15 How many triangle pattern blocks are needed to cover the figure below? You may use your pattern blocks to help you A B * C 12 D 13 AR4M04D1702NXXX-136B... says “ 94, ” the answer is 1 94 What is the rule for Ashley’s pattern? 1, 840 1,8 04 * A > * A add 100 B = B add 117 C < C divide by 100 D + D divide by 117 AR4M02D1701Y07 8-0 78C AR4M04M1307Y09 1-0 91A... miles D 1 24 24 28 PART II Released Mathematics Items – 2 006 Benchmark Grade AR4M04D 140 1Y12 3-1 23B 33 Toshio asked 55 fourth -grade students about their favorite after-school activity He created the
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