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NO.1.4.1 Recognize equivalent representations for the same whole number and generate them by composing and decomposing numbers Ex. 1,076 = 1,000 + 70 + 6; 500 + 500 + 25 + 25 + 25 + 1; 250 + 250 + 250 + 250 + 75 + 1, etc… AR4M05N0101NXXX-021D 13. Which shows the expanded form of the number below? 656,094 A. 60,000 + 56,000 + 90 + 4 B. 600,000 + 56,000 + 90 + 4 C. 600,000 + 50,000 + 6,000 + 94 * D. 600,000 + 50,000 + 6,000 + 90 + 4 2007 – % ELKINS ELEMENTARY (NEVIN) MATH RELEASED ITEMS – 4TH GRADE UPDATED 7/2008 1 NO.1.4.2 Use the place value structure of the base ten number system and be able to represent and compare whole numbers to millions (using models, illustrations, symbols, expanded notation and problem solving) Ex. 1,246,477___1,244 4. What is the value of the underlined digit below? 218,036,097 A. three thousand * B. thirty thousand C. thirty-six thousand D. three hundred thousand 2006 – % 9. Jean made the chart below to record the number of pencils sold at the school store for the last four months. Pencil Sales Month Number 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. 1,789 < 1,543 B. 1,290 > 1,867 * C. 1,543 > 1,290 D. 1,867 = 1,789 2006 – % ELKINS ELEMENTARY (NEVIN) MATH RELEASED ITEMS – 4TH GRADE UPDATED 7/2008 2 38. The chart below shows the number of calories consumed by a group of students in one week. Student Calorie Chart Number of Student Calories Tony 15,285 James 14,768 Kendra 14,876 Sophia 15,852 Which student consumed the least number of calories? A. Tony * B. James C. Kendra D. Sophia 2006 – % 26. Mrs. Kramer wrote the following number on the board: 9,463,187 What is the value of the 6 in this number? A. 00,006 B. 06,000 * C. 60,000 D. 63,000 2004 – % 14. In the number 652,479,103, in what place value is the underlined digit? A. tens B. ten thousands C. millions * D. ten millions 2003 – % 39. What is the value of 3 in 32.05? * A. 3 tens B. 3 ones C. 3 hundreds D. 3 thousands 2003 – % ELKINS ELEMENTARY (NEVIN) MATH RELEASED ITEMS – 4TH GRADE UPDATED 7/2008 3 A. Rashid and Matthew are playing a math game. There are two stacks of number cards with the digits 0–9 on them. Each player draws 4 cards. • Rashid’s cards: 7 0 3 9 • Matthew’s cards: 0 8 5 2 1. The winner of the first game is the person who can make the largest four- digit number with the numbers drawn. Tell who won the first game. Explain your answer with words and/or numbers. 2. The winner of the second game is the person who can make the smallest four-digit number with the numbers drawn. Tell who won the second game. Explain your answer with words and/or numbers. BE SURE TO LABEL YOUR RESPONSES 1 AND 2. 2003 – /8 SOLUTION Part 1: Rashid won. Work/Explanation: 9,730 > 8,520 OR Rashid has 9,730 and Matthew has 8,520. OR Student states that Rashid’s largest number can have a “9” in the thousands place so it will be greater than Matthew’s largest number, which can only have an “8” in the thousands place. Part 2: Matthew won. Work/Explanation: 2,058 < 3,079 (or 0258 < 0379) OR Matthew has 2,058 and Rashid has 3,079 (or 0258 and 0379). OR Student states that Matthew’s smallest number can have a “2” in the thousands place so it will be less than Rashid’s number since the smallest digit he can have in the thousands place is a “3. Scoring (4 total points possible) Part 1: (2 points possible) • 1 point for correct answer of “Rashid won” with work or explanation containing evidence of some correct procedure using any of the following: Correct comparison of any 4-digit numbers formed using the digits of 7, 0, 3, 9 and 0, 8, 5, 2, or Some correct explanation regarding place value (ex. 9 is the biggest number), or 4-digit number formed with 9 in the thousands place using 7, 0, 3, 9 (ex. 9037). OR • ½ point for correct answer of “Rashid won” with no work or explanation containing any of the above support. OR • 0 points for answer of “Rashid won” with evidence of incorrect procedure: Adding digits (7 + 0 + 3 + 9 = 19 and 0 + 8 + 5 + 2 = 15) and comparing ELKINS ELEMENTARY (NEVIN) MATH RELEASED ITEMS – 4TH GRADE UPDATED 7/2008 4 numbers: 19 > 15, or Comparing first digits listed (7 > 0). Work/Explanation: • 1 point for either of the following: 2 correct numbers (9,730 and 8,520), or Correct and complete explanation regarding place value (ex. 9 > 8, etc.). OR • ½ point for either of the following: 1 correct number (9,730 or 8,520), or Partial explanation regarding place value (ex. 9 is the largest number). Part 2: (2 points possible) • 1 point for correct answer of “Matthew won” with work or explanation containing evidence of some correct procedure using any of the following: Correct comparison of any 4-digit numbers formed using the digits of 7, 0, 3, 9 and 0, 8, 5, 2, or Some correct explanation regarding place value (ex. 2 is the smallest number), or 4-digit number formed with 2 in the thousands place using 0, 8, 5, 2 (ex. 2,508) (or 2 in the hundreds place and 0 in the thousands place – ex. 0285). OR • ½ point for correct answer of “Matthew won” with no work or explanation containing any of the above support. OR • 0 points for correct answer of “Matthew won” with evidence of incorrect procedure: Adding digits (7 + 0 + 3 + 9 = 19 and 0 + 8 + 5 + 2 = 15) and comparing numbers: 15 < 19, or Same numbers in Part 1 are compared. Work/Explanation: • 1 point for either of the following: 2 correct numbers (2,058 and 3,079 or 258 and 379), or Correct and complete explanation regarding place value (ex. 2 < 3, etc.) OR • ½ point for either of the following: 1 correct number (258; 2,058; 379; or 3,079), or Partial explanation regarding place value (ex. 2 is the smallest number). ELKINS ELEMENTARY (NEVIN) MATH RELEASED ITEMS – 4TH GRADE UPDATED 7/2008 5 NO.1.4.3 Use mathematical language and symbols to compare and order any whole numbers with and without appropriate technology (<, >, =) 17. Sean has 36 baseball cards. Tom has 25 baseball cards. Which of the following is a true statement about their baseball card collections? A. 25 > 36 B. 25 × 36 * C. 36 > 25 D. 36 = 25 2006 – % 29. What symbol can replace the in the number sentence below to make it true? 1,840 1,804 * A. > B. = C. < D. + 2006 – % ELKINS ELEMENTARY (NEVIN) MATH RELEASED ITEMS – 4TH GRADE UPDATED 7/2008 6 NO.1.4.4 Write a fraction to name part of a whole, part of a set, a location on a number line, and the division of whole numbers, using models up to 12/12 Ex. 1 4 1 = 4 1 =I * I I 4 1 1 0 1 4 2 1 = One cookie shared by 4 children 4 29. What fractional part is shown on the geoboard below? 1 * A. 4 3 B. 4 C. 1 D. 4 2007 – % ELKINS ELEMENTARY (NEVIN) MATH RELEASED ITEMS – 4TH GRADE UPDATED 7/2008 7 33. Toby has a candy bar that is divided into 12 squares, as shown below. He gave Shelly 2 pieces and Ron 3 pieces. What portion of the candy bar does Toby have left for himself? 5 A. 12 7 * B. 12 5 C. 7 7 D. 5 2007 – % 40. Which of the following fractions identifies the part of the dozen eggs shown below that has been used? 1 A. 8 1 B. 4 4 C. 12 ELKINS ELEMENTARY (NEVIN) MATH RELEASED ITEMS – 4TH GRADE UPDATED 7/2008 8 8 * D. 12 2006 – % Use the figures below to answer question 14. 14. Stanley’s mom made 2 sandwiches for his lunch. She cut each into 4 pieces. Stanley ate only the shaded portions. What fraction of the sandwiches did he eat? 3 A. 5 3 B. 4 1 * C. 1 4 1 D. 1 3 2005 – % ELKINS ELEMENTARY (NEVIN) MATH RELEASED ITEMS – 4TH GRADE UPDATED 7/2008 9 NO.1.4.5 Utilize models, benchmarks, and equivalent forms to recognize that the size of the whole determines the size of the fraction ELKINS ELEMENTARY (NEVIN) MATH RELEASED ITEMS – 4TH GRADE UPDATED 7/2008 10 NO.1.4.6 Use the place value structure of the base ten number system and be able to represent and compare decimals to hundredths (using models, illustrations, symbols, expanded notation and problem solving) Ex. 3.87___3.78 ELKINS ELEMENTARY (NEVIN) MATH RELEASED ITEMS – 4TH GRADE UPDATED 7/2008 11 NO.1.4.7 Write an equivalent decimal for a given fraction relating to money Ex. 1/10 = $0.10 1/4 = $0.25 18. Which amount equals ¼ of $1.00? A. $0.04 * B. $0.25 C. $0.40 D. $0.50 2007 – % 1 3. Bill’s mom gives him of a dollar for taking out the trash. Which decimal 4 represents the amount of money Bill receives? A. 0.04 B. 0.14 C. 0.20 * D. 0.25 2003 – % ELKINS ELEMENTARY (NEVIN) MATH RELEASED ITEMS – 4TH GRADE UPDATED 7/2008 12 NO.1.4.8 Write a fraction that is equivalent to a given fraction with the use of models 1 2 4 Ex. = = 3 6 12 ELKINS ELEMENTARY (NEVIN) MATH RELEASED ITEMS – 4TH GRADE UPDATED 7/2008 13 NO.2.4.1 Develop an understanding of the associative and zero properties of multiplication using objects ELKINS ELEMENTARY (NEVIN) MATH RELEASED ITEMS – 4TH GRADE UPDATED 7/2008 14 NO.2.4.2 Apply number theory determine if any number is even or odd use the terms multiple, factor, and divisible by in an appropriate context generate and use divisibility rules for 2, 5, and 10 demonstrate various multiplication & division relationships 35. Mr. Booth put the two groups of numbers below on the board. What is the rule he used when forming the two groups? A. Group X: Multiples of 5 Group Y: Even Numbers * B. Group X: Odd Numbers Group Y: Even Numbers C. Group X: Odd Numbers Group Y: Multiples of 3 D. Group X: Odd Numbers Group Y: Multiples of 6 2006 – % ELKINS ELEMENTARY (NEVIN) MATH RELEASED ITEMS – 4TH GRADE UPDATED 7/2008 15 AR4M02N107Y130-130R E. Jake used the 100’s chart above to solve a mystery number puzzle with the following clues: ● It is a two-digit number greater than 23, but less than 50. ● It is an even number. ● Two, four, and twelve are some of its factors. ● The sum of its digits is a two-digit number. What is the mystery number? Use words, pictures, and/or numbers to explain your answer. 2004 – /8 SOLUTION AND SCORING Answer: The mystery number is 48. Explanations may be: ● Numerical – Clue 1: All numbers from 24 to 49 (or 23 to 50) are listed. Clue 2: All odd numbers are eliminated: 24, 26, 28, 30, 32, 34, 36, 38, 40, 42, 44, 46, 48 remain. Clue 3: All numbers that do not have two, four and twelve as factors are eliminated: 24, 36 and 48 remain. Clue 4: All numbers whose digit sum is not a two-digit number are eliminated: only 48 remains. Note: Some students perform Clue 4 before Clue 3 (after Clues 1 and 2). ♦ Example: 28, 38, 46 and 48 remain since the digit sum is a 2-digit number. Then, the only number remaining with factors of 2, 4 and 12 is 48. OR ● A chart – The numbers are listed and eliminated clue by clue. The clues are differentiated in some way. ELKINS ELEMENTARY (NEVIN) MATH RELEASED ITEMS – 4TH GRADE UPDATED 7/2008 16 OR ● Verbal – The response contains a correct and complete verbal explanation of the procedure using elimination clue by clue, with at least 24, 36, and 48 mentioned (or 28, 38, 46, and 48 if Clue 4 is performed before Clue 3). Example: “First, I omitted all of the numbers that were not greater than 23 or less than 50. Then I omitted all of the odd numbers, since it said the number was even. Then I crossed out all of the numbers that 2, 4, and 12 did not go into, leaving 24, 36 and 48. Then I saw which of these numbers had a 2-digit sum and it was 48.” 19. Mrs. Teasley’s fourth-grade class divided into teams of 4 for field day races. There were 3 students left over after all of the teams were formed. Which could be the total number of students that are in Mrs. Teasley’s class? A. 24 B. 26 * C. 27 D. 28 2003 – % ELKINS ELEMENTARY (NEVIN) MATH RELEASED ITEMS – 4TH GRADE UPDATED 7/2008 17 NO.2.4.3 Use conventional mathematical symbols to write equations for contextual problems involving multiplication See Appendix for examples 1. Michael bought 5 cases of juice for the soccer team. Each case cost $6. Which equation (number sentence) describes how much money Michael paid in all? A $6 x 1 = 6 B 5 + 1 = $6 C 5 + $6 = $11 * D 5 x $6 = $30 2008 - ELKINS ELEMENTARY (NEVIN) MATH RELEASED ITEMS – 4TH GRADE UPDATED 7/2008 18 NO.2.4.4 Represent and explain division as measurement and partitive division including equal groups, related rates, price, rectangular arrays (area model), combinations and multiplicative comparison See Appendix for more details Ex. translate contextual situations involving division into conventional mathematical symbols explain how a remainder may impact an answer in a real world situation 20. Ms. Summers has 41 pencils for 9 students. If they all receive the same number of pencils, what is the greatest number each student can receive? * A. 4 B. 5 C. 32 D. 50 2007 – % 6. Mrs. Smith and Mr. Jones are taking their classes on a field trip. Each school van holds 8 people. If there are 48 people going on the trip, how many vans do they need? A. 5 * B. 6 C. 40 D. 56 2006 – % 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? * A. 7 B. 8 C. 780 D. 800 2006 – % ELKINS ELEMENTARY (NEVIN) MATH RELEASED ITEMS – 4TH GRADE UPDATED 7/2008 19 31. The fourth-grade classes at Valley Elementary are going on a field trip. There are 392 students. Each bus holds 56 students. How many buses will they need? A. 6 * B. 7 C. 8 D. 9 2005 – % 11. Marty is about to begin reading the 250-page book she just checked out from the library. She plans to read 25 pages per night. At this rate, how many nights will it take her to finish her book? A. 1 B. 5 * C. 10 D. 20 2004 – % 25. Lark Creek Elementary School had 4 fifth-grade classrooms and a total of 96 fifth-grade students. If each classroom has exactly the same number of students, which number sentence could be used to calculate the number of students in each classroom? A. 96 + 4 = B. 96 − 4 = C. 96 × 4 = * D. 96 ÷ 4 = 2003 – % ELKINS ELEMENTARY (NEVIN) MATH RELEASED ITEMS – 4TH GRADE UPDATED 7/2008 20 NO.3.4.1 Demonstrate, with and without appropriate technology, computational fluency in multi-digit addition and subtraction in contextual problems 11. The table below shows how many students are in each fourth-grade class at Birchwood School. Fourth-Grade Students at Birchwood School Class Number of Students Mrs. Adams 25 Mr. Thompson 28 Ms. Sanchez 29 Mr. Jones 27 1. The cafeteria can seat as many as 83 students. Name three classes that could sit in the cafeteria at the same time. Explain your answer using words and/or numbers. 2. The school auditorium seats 500 people. After all four fourth-grade classes are seated in the auditorium, how many seats are left empty? Explain your answer using words and/or numbers. BE SURE TO LABEL YOUR RESPONSES 1 AND 2. 2008 - ELKINS ELEMENTARY (NEVIN) MATH RELEASED ITEMS – 4TH GRADE UPDATED 7/2008 21 ELKINS ELEMENTARY (NEVIN) MATH RELEASED ITEMS – 4TH GRADE UPDATED 7/2008 22 NO.3.4.2 Demonstrate fluency with combinations for multiplication and division facts (12 x 12) and use these combinations to mentally compute related problems (30 x 50) ELKINS ELEMENTARY (NEVIN) MATH RELEASED ITEMS – 4TH GRADE UPDATED 7/2008 23 NO.3.4.3 Attain, with and without appropriate technology, computational fluency in multiplication and division using contextual problems using two-digit by two-digit multiplication (larger numbers with technology), up to three-digit by two-digit division (larger numbers with technology), strategies for multiplication and dividing numbers, performance of operations in more than one way, estimation of products and quotients in appropriate situations, and relationships between operations E. Jansen is helping to prepare for a bicycle race. His job is to set up tables with cups of water along the course. There will be 10 tables with 24 paper cups of water on each table. 1. How many paper cups will Jansen need in all? Explain your answer using words and/or numbers. 2. The paper cups come in packages of 48. Based on your answer in Part 1, how many packages of cups will Jansen need? Explain your answer using words and/or numbers. BE SURE TO LABEL YOUR RESPONSES 1 AND 2 2007 – /8 SOLUTION AND SCORING PART 1 2 points possible 1 point: Correct answer: 240 (cups). AND 1 point: Correct and complete procedure shown and/or explained. Work may contain a calculation or copy error. Give credit for the following or equivalent: • 10 × 24 = # cups, or • Student adds 24 ten times, or • “I multiplied 10 by 24 to get my answer.” PART 2 2 points possible 1 point: Correct answer: 5 (packages), or correct answer based on calculation error in Part 1. Note: Answer may be a mixed # or rounded up to the next whole #. AND 1 point: Correct and complete procedure shown and/or explained. Work may contain a calculation, copy, or counting error or may be based on an incorrect answer in Part 1. Give credit for the following or equivalent: • 240 ÷ 48 = # packages, or • “I divided 240 by 48 to get the # of packages,” or • (# of cups from Part 1) ÷ 48 = # of packages, or • “Since 24 + 24 = 48, 2 tables will use 1 package. There are 10 tables, so they will need 10/2 = 5 packs,” or ELKINS ELEMENTARY (NEVIN) MATH RELEASED ITEMS – 4TH GRADE UPDATED 7/2008 24 • 5 x 48 = 240 (guess and check), or • 48 + 48 + 48 + 48 + 48 = 240 (guess and check). Note: Do not give credit for incomplete or vague procedure. 7. Ashley has a 43-page sticker album. Each page will hold about 20 stickers. About how many stickers can she place in the album? A. 2 B. 20 C. 60 * D. 800 2006 – % 01/ C. Mrs. Grey wrote the following two numbers on the board. 12 4 1. 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. 2. If 12 is the dividend and 4 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 1 AND 2. 2006 – /8 SOLUTION AND SCORING PART 1 2 points possible 1 point: Correct answer: 16 (sum). Note: Do not give credit if incorrect procedure is used: Ex: 4 x 4 = 16 AND 1 point: Correct equation given. Work may contain a calculation error. Give credit for the following: • 12 + 4 = # or • 4 + 12 = # Give credit for the following only with an answer of 16: • 16 – 4 = 12 (Guess & Check) • 16 – 12 = 4 (Guess & Check) Note: Do not give procedure credit for work that is not in the form of an equation: Ex: 12 or +4 16 Ex: “I added 12 and 4 and got…” PART 2 ELKINS ELEMENTARY (NEVIN) MATH RELEASED ITEMS – 4TH GRADE UPDATED 7/2008 25 2 points possible 1 point: Correct answer: 3 (divisor). Give credit if the answer is stated “The divisor is 3.” or if 3 is shown as the 4 divisor in a division operation: Ex: 3 12 Note: Do not give credit if incorrect procedure is used: Ex: 4 ÷ 12 = 3. AND 1 point: Correct equation given. (Divisor may be incorrect.) Give credit for the following: • 12 ÷ 3 = 4 or • 12 ÷ (divisor) = 4. or Give credit for the following only with an answer of 3: • 3 x 4 = 12 (Guess & Check) • 4 x 3 = 12 (Guess & Check) • 12 ÷ 4 = 3 (Give credit except at “4” level). Note: Do not give procedure credit for work that is not in the form of an equation: 4 Ex: Shows short division: 3 12 or Ex: “I divided 12 by 3 and got…” 34. The fourth grade had a pizza party. There are 86 children in the fourth grade. If each child ate 3 slices, how many total slices were eaten? A. 83 B. 89 C. 256 * D. 258 2005 – % ELKINS ELEMENTARY (NEVIN) MATH RELEASED ITEMS – 4TH GRADE UPDATED 7/2008 26 NO.3.4.4 Solve simple problems using operations involving addition, subtraction, and multiplication using a variety of methods and tools (e.g., objects, mental computation, paper and pencil and with and without appropriate technology) 7. Beth had 9 groups of pencils with 4 in each group. She skip-counted by 4 to find the total number of pencils. What are the last 3 numbers she said? A. 14 23 32 B. 20 24 28 * C. 28 32 36 D. 32 36 48 2007 – % 24. Larissa needs to bake 120 cookies. If there are 30 cookies in a batch, how many batches does she need to bake? A. 3 * B. 4 C. 90 D. 150 2005 – % Use the table below to answer question 40. Money Lisa Earned Last Week AJob Baby-Sitting Raking Leaves Mowing Lawn Hourly Rate $2.25 $1.50 $3.00 Number of 7 3 2 Hours Worked 40. How much money did Lisa earn baby-sitting last week? A. $ 9.25 B. $15.25 C. $15.65 * D. $15.75 2005 – % ELKINS ELEMENTARY (NEVIN) MATH RELEASED ITEMS – 4TH GRADE UPDATED 7/2008 27 School Store Item Amount Pencils $1.25 Pen $1.75 Paper $2.25 Ruler $1.75 Eraser $0.10 Notebook $3.50 D. Anthony needs to buy school supplies. 1. Anthony plans to buy one pack of pencils, paper, a ruler, and a notebook at the school store. What will be the total cost for all of Anthony’s supplies? Explain your answer using words and/or numbers. 2. Anthony has $10.00. Will this be enough money for all of the supplies Anthony plans to buy? Explain your answer using words and/or numbers. BE SURE TO LABEL YOUR RESPONSES 1 AND 2. 2005 – /8 SOLUTION AND SCORING Part 1: (2 points possible) Answer: 1 point for correct answer of ($)8.75. AND Work: 1 point for correct and complete procedure shown and/or explained. Work may contain a calculation or copy error. ● Give credit for the following explanations or equivalent: $1.25 + $2.25 + $1.75 + $3.50 = Total Cost, or “I added 1.25, 2.25, 1.75 and 3.50 to get the cost of the supplies.” Note: Do not give credit for vague or incomplete explanations. ● Example: “I added his supplies.” Part 2: (2 points possible) Answer: 2 points for correct answer and explanation based on total in Part 1. ● Give credit for the following or equivalent: “Yes, because he only spent (8.75 or Total Cost in Part 1 ≤ 10.00), and he has 10.00” (both 10.00 and Total Cost from Part 1 are mentioned), or “Yes, since 8.75 < 10.00,” or “Yes, because 10.00 – 8.75 = 1.25,” or “No, because he spent (Total Cost in Part 1 > 10.00) and he only has 10.00” (both 10.00 and Total Cost from Part 1 are mentioned). OR 1 point for correct “Yes, No” response based on answer in Part 1. Explanation is partial, vague, or work contains an error. ● Example: Only 10.00 or 8.75 (or Total Cost from Part 1) is mentioned. ● Example: No “Yes, No” answer is given, but work is correct and complete. Note: Do not give credit for “Yes” or “No” answer without any valid support. ELKINS ELEMENTARY (NEVIN) MATH RELEASED ITEMS – 4TH GRADE UPDATED 7/2008 28 Use the table below to answer question 6. Hector’s Table State Park Approx. Miles From Little Rock Pinnacle Mountain 10 Woolly Hollow 40 Village Creek 90 Crater of Diamonds 100 Bull Shoals 120 6. Hector made the table above for his family to compare the approximate distance from their home in Little Rock to several state parks. How many more miles is it to Village Creek State Park than to Woolly Hollow State Park? A. 40 * B. 50 C. 80 D. 90 2004 – % Use the chart below to answer question 35. Super Cinema Theaters Adult admission $6.25 Children $3.75 Large popcorn $4.00 Small popcorn $3.00 Large soda $1.89 Small soda $0.99 35. Mr. Dunbar took his five-year-old daughter to the movies. After paying for the admission for each of them, he bought a large popcorn and 2 small sodas. How much did he spend? A. $14.98 * B. $15.98 C. $16.88 D. $17.98 2004 – % ELKINS ELEMENTARY (NEVIN) MATH RELEASED ITEMS – 4TH GRADE UPDATED 7/2008 29 NO.3.4.5 Use estimation strategies to solve problems and judge the reasonableness of the answer 6. Maria bought 10 plants for her garden. Each plant cost $7.97. What would be the estimated total cost of Maria’s plants? A $ 8.00 B $10.00 * C $80.00 D $90.00 2008 - 39. Which state has a population that is about 2,000,000 greater than that of Arkansas? Population of Arkansas and Its Border States State Population Texas 22,118,509 Tennessee 5,841,748 Missouri 5,704,484 Louisiana 4,496,334 Oklahoma 3,511,532 Mississippi 2,881,281 Arkansas 2,725,714 A. Tennessee B. Missouri * C. Louisiana D. Oklahoma 2007 – % 12. Randy has 3 bags of marbles. Each bag has 86 marbles. About how many marbles does Randy have in all? A. 83 B. 89 C. 240 * D. 270 2006 – % ELKINS ELEMENTARY (NEVIN) MATH RELEASED ITEMS – 4TH GRADE UPDATED 7/2008 30 6. The bicycle repair person told Jon that it would cost about $60.00 to fix his bike. If the repair person rounded the bill to the nearest ten dollars, which of the following could have been the actual amount? A. $49.95 B. $52.60 * C. $58.45 D. $65.80 2005 – % AR4M03N103NXXX-015B 12. Randy counted 5,624 tickets sold for the school carnival. What is this number rounded to the nearest hundred? A. 5,000 * B. 5,600 C. 5,700 D. 6,000 2005 – % 35. The distance from Austin’s house to his grandparents’ house is 234 miles. About how many miles, rounded to the nearest hundred, is this? * A. 200 B. 230 C. 240 D. 300 2005 – % ELKINS ELEMENTARY (NEVIN) MATH RELEASED ITEMS – 4TH GRADE UPDATED 7/2008 31 A.4.4.1 Identify a number that is more or less than any whole number using multiples of 10, 100 and/or 1000 Ex. 100 more than 4987 is 5087 ELKINS ELEMENTARY (NEVIN) MATH RELEASED ITEMS – 4TH GRADE UPDATED 7/2008 32 A.4.4.2 Use repeating and growing numeric and geometric patterns to make predictions and solve problems 9. Lee found 5 rocks each day for 5 days to add to his rock collection. Which pattern can Lee use to count his rocks? A 5 7 9 11 13 B 5 15 25 35 45 * C 5 10 15 20 25 D 17 19 21 23 25 2008 - 19. If the pattern below continues, how many squares will be in Figure 5? A. 4 B. 11 C. 13 * D. 17 2007 – % 5. 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, 7 * B. 7, 4 C. 4, 8 D. 8, 4 2006 – % ELKINS ELEMENTARY (NEVIN) MATH RELEASED ITEMS – 4TH GRADE UPDATED 7/2008 33 B. Karen wants to make a bookmark out of leather. She is planning the design below on paper before she starts cutting the leather. 1. Using Karen’s pattern, complete the design for the bookmark. 2. How many of each shape will she need to cut out to make her bookmark? 3. 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 3. 2006 – /8 SOLUTION AND SCORING PART 1 1 point possible 1 point: The last 4 top and bottom sections of the bookmark (positions 7- 10) are correctly completed, as shown in the diagram below: Note: Top and bottom row do not have to be aligned. PART 2 1 point possible 1 point: Correct number of shapes: 10 squares, 5 rhombuses, 5 circles (shapes may be named or drawn). Or Correct # of squares, rhombuses and circles based on Part 1 answer. PART 3 2 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 or the nd st 2 row is a repeat of the 1 row. Note: Design must be different from the original bookmark. 2 points: Correct and complete design that contains all of the following: • 10 squares, 5 rhombuses, 5 circles OR Equal #’s of each shape. • The pattern is repeating horizontally, repeats at least once and has no errors. Or 1 point: Partially correct design: • Design uses 10 Squares, 5 rhombuses, 5 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. ELKINS ELEMENTARY (NEVIN) MATH RELEASED ITEMS – 4TH GRADE UPDATED 7/2008 34 4. Laura kept track of the growth of her ivy plant. It was 6 inches long when she planted it, and it grew about 2 inches each week. About how many inches long was it by the end of the fourth week? A. 8 B. 10 C. 12 * D. 14 2005 – % Use the chart below to answer question 23. IN OUT A B 5 10 10 20 20 40 40 80 80 ? 23. Mrs. Bunch put the pattern above on the board. Which number would correctly complete the pattern? A. 100 B. 120 C. 140 * D. 160 2005 – % Use the pattern below to answer question 26. AR4M03P106NXXX-043B 1 6 11 16 21 . . . 26. In the pattern above, each number increases by how many? A. 1 * B. 5 C. 21 D. 26 2005 – % 23. What number comes next in the pattern? 1, 2, 4, 7, 11, __ A. 15 * B. 16 C. 18 D. 22 2004 – % ELKINS ELEMENTARY (NEVIN) MATH RELEASED ITEMS – 4TH GRADE UPDATED 7/2008 35 31. What is the rule for the pattern below? 2 4 7 14 17 34 37 A. Add 2, then add 3 in a repeating pattern. B. Double each number. C. Double the first number, then double the next number, then subtract 1. * D. Double the first number, then add three to the next number. 2004 – % D. Dwight and his brother, Jim, decided what they would like to eat for breakfast every day for a month. They each began filling in the calendar above with their favorite breakfast foods. 1. If Dwight’s pattern on the calendar above continues, how many times during the month will he have eggs? Explain your answer using words, numbers, and/or pictures. 2. If both Dwight’s and Jim’s patterns continue, how many days during the month will both boys have the same thing for breakfast? Explain your answer using words, numbers, and/or pictures. BE SURE TO LABEL YOUR RESPONSES 1 AND 2. 2004 – /8 SOLUTION AND SCORING Part 1: (2 points possible) ELKINS ELEMENTARY (NEVIN) MATH RELEASED ITEMS – 4TH GRADE UPDATED 7/2008 36 1 point for correct answer of Dwight eats eggs 10 times, AND 1 point for correct and complete procedure shown and/or explained. ● Give credit for the following explanations or equivalent (Answer might not be “10.”): “He has eggs on the 2nd ,5th ,8th, 11th, 14th, 17th, 20th, 23rd, 26th, and 29th;” or “He has eggs on the 2nd and every third day after that;” or 31/3 = 10 r1; or Correct number of times eggs are eaten each week (1 + 3 + 2 + 2 + 2); or Calendar is correctly filled out indicating days when Dwight eats eggs. (Dates do not have to be circled.) Note: Do not give credit for incorrect or incomplete procedures: ● Student continues the pattern past May 31st. (Incorrect procedure. This usually follows an answer of “He has eggs 11 times.”) ● “The pattern is CEW,” or “I did the pattern.” (Incomplete procedure.) Part 2: (2 points possible) 1 point for correct answer of they will eat the same things 11 times, AND 1 point for correct and complete procedure shown and/or explained. ● Give credit for the following explanations or equivalent (Answer might not be “11.”): “They will both have – ♦ Cereal on the 1st, 7th, 13th, 19th, 25th, and 31st; and ♦ Waffles on the 6th, 12th, 18th, 24th, and 30th,” or “They will eat the same things on the following dates: 1, 6, 7, 12, 13, 18, 19, 24, 25, 30, and 31,” or “They will both have cereal on the first day of the month and every sixth day after that. They will both have waffles every sixth day,” or Correct number of times they have the same breakfast each week (1 + 2 + 3 + 3 + 2), or Calendar is correctly filled out indicating days when they eat the same thing. (Dates do not have to be circled.) ELKINS ELEMENTARY (NEVIN) MATH RELEASED ITEMS – 4TH GRADE UPDATED 7/2008 37 APRIL SUN. MON. TUE.WED. THUR. FRI. SAT. 1 2 3 4 5 6 7 basketball soccer football basketball soccer football basketball 8 9 10 11 12 13 14 soccer football basketball soccer football basketball soccer 15 16 17 18 19 20 21 football 22 23 24 25 26 27 28 29 30 C. Jake and Timothy play sports in the neighborhood every day. The calendar above shows how many times they have played basketball, soccer, and football so far during the month of April. 1. If this pattern continues, what sport will Jake and Timothy play on Saturday, April 21? Explain your answer using words and/or numbers. 2. How many times will Jake and Timothy play soccer during the month of April? Explain your answer using words and/or numbers. BE SURE TO LABEL YOUR RESPONSES 1 AND 2. 2003 – /8 SOLUTION Part 1: Football Work/Explanation: Response states any of the following: • Football is played every third day. OR • 21 is a multiple of 3. OR • Student fills in calendar with appropriate sport for April 16 through April 21. OR • Explains that the pattern is “basketball, soccer, football” and if started on the 16th, ELKINS ELEMENTARY (NEVIN) MATH RELEASED ITEMS – 4TH GRADE UPDATED 7/2008 38 football would be played on the 21st. OR • Equivalent work or explanation. Part 2: 10 Work/Explanation: Response states any of the following: • Soccer is played 5 times during the first 15 days of April, so they will play 5 times during the last 15 days of the month. OR • 30 ÷ 3 = 10. OR • Student fills in or lists appropriate soccer dates on calendar through April 29. OR • Equivalent work or explanation. Scoring (4 total points possible) Part 1: (2 points possible) • 1 point for correct answer of Football, AND • 1 point for correct and complete work or explanation. Part 2: (2 points possible) • 1 point for correct answer of 10. AND • 1 point for correct and complete work or explanation. ELKINS ELEMENTARY (NEVIN) MATH RELEASED ITEMS – 4TH GRADE UPDATED 7/2008 39 A.4.4.3 Determine the relationship between sets of numbers by selecting the rule (2 step rule in words) 9. Pam created the table below using a 2-step rule. X Y 2 5 3 7 4 9 5 11 What did Pam do to create her set of numbers? A. Add 4 to the x-value, and then subtract 1. * B. Multiply the x-value by 2, and then add 1. C. Add 2 to the x-value, and then add 1 more. D. Multiply the x-value by 2, and then subtract 1. 2007 – % 25. Toby recorded the height of a plant for four weeks. He noticed a pattern. Week Height 1 2 inches 2 5 inches 3 11 inches 4 23 inches What is the rule for the changes in height? A. Add 3. B. Add 12. C. Double each number. * D. Multiply each number by 2 and add 1. 2007 – % 30. Mr. Teck wrote the sets of numbers below on the board. (5, 9) (6, 12) (7, 15) (8, 18) What rule did Mr. Teck use to determine the value of the second number in each set? A. Add 4 to the first number. B. Multiply the first number by 2. C. Multiply the first number by 2, and then add 1. * D. Subtract 2 from the first number, and then multiply by 3. 2007 – % ELKINS ELEMENTARY (NEVIN) MATH RELEASED ITEMS – 4TH GRADE UPDATED 7/2008 40 31. What is the rule for the pattern below? 2 4 3 6 5 10 9 . . . A. Add 2, and then subtract 1. B. Divide by 2, and then add 1. C. Multiply by 2, and then add 1. * D. Multiply by 2, and then subtract 1. 2007 – % 1. What is the missing operation in the pattern below? Input n 10 11 12 13 14 15 Output ? 3 4 5 6 7 8 A. add 7 B. add 10 C. subtract 3 * D. subtract 7 2006 – % 13. What is the rule for the number pattern below? 1,125 225 45 9 A. add 900 B. divide by 2 * C. divide by 5 D. subtract 900 2006 – % 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? * A. add 100 B. add 117 C. divide by 100 D. divide by 117 2006 – % ELKINS ELEMENTARY (NEVIN) MATH RELEASED ITEMS – 4TH GRADE UPDATED 7/2008 41 B. Use these equations to answer the questions that follow. 6+5= 60 + 50 = 600 + 500 = 6,000 + 5,000 = 1. Find each sum above. 2. What pattern do you notice? 3. Explain how you could use this pattern to find the sum of 6,000 + 8,000. BE SURE TO LABEL YOUR RESPONSES 1, 2, AND 3. 2005 – /8 SOLUTION AND SCORING Part 1: (1 point possible) Answer: 1 point for 4 correct answers given: 11; 110; 1,100; 11,000. OR ½ point for 2 or 3 correct answers given. Part 2: (1 point possible) Answer: 1 point for correct and complete statement of the pattern. ● Give credit for the following explanations or equivalent: “The sum of 6 + 5 = 11. All the answers start with 11 and add a pattern of zeros; first one, then two, then three,” or “Each sum has the same number of zeros after ‘11’ that are in each addend. Example: 60 and 50 each have one ‘0.’ Therefore, their sum would be 110,” or “Add a 0 every time.” Note: Do not give credit for incomplete explanations. ● Example: “I added zeros.” ● Example: “Add a 0 to the 5 and 6” (only addresses the addends). Part 3: (2 points possible) Answer: 2 points for correct and complete explanation. ● Give credit for the following explanations or equivalent: 6 + 8 = 14; add 3 zeros to get 14,000, or 6 + 8 = 14 and add 3 zeros, or 6 + 8 = 14 and add zeros to get 14,000, or 6 + 8 60 + 80 600 + 800 6,000 + 8,000. Give full credit with or without sums of 14, 140, 1,400, 14,000. OR 1 point for incomplete or vague explanation, but understanding of pattern is shown. ● Give credit for the following or equivalent: 14 140 1400 14,000 (only sums given), or “Add 6 + 8 = 14 and add 0’s” (incomplete), or Student uses given pattern (6 + 5, etc.) to find 6,000 + 8,000. ▲ Example: “I could add 6,000 + 5,000 and then add 3,000.” Note: Do not give credit for 6,000 + 8,000 = 14,000 only. ELKINS ELEMENTARY (NEVIN) MATH RELEASED ITEMS – 4TH GRADE UPDATED 7/2008 42 Use the chart below to answer question 33. ISABEL’S SAVINGS CHART Week’s Saved 2 3 4 5 Total Saved $8.00 $12.00 $16.00 $20.00 33. The chart above shows the pattern of Isabel’s savings over a 5-week period. What is the rule Isabel used to create this pattern? * A. add 4 B. subtract 4 C. divide by 4 D. multiply by 2 2003 – % Use the information below to answer question 36. Amount of Distance Time Traveled Traveled 10 minutes 5 miles 20 minutes 10 miles 30 minutes 15 miles 40 minutes 20 miles 50 minutes 25 miles 36. Bridget’s dad kept count of how far he bicycled over a period of 50 minutes. If this pattern continues, how many miles will Bridget’s dad have traveled in 90 minutes? A. 30 miles * B. 45 miles C. 60 miles D. 90 miles 2003 – % ELKINS ELEMENTARY (NEVIN) MATH RELEASED ITEMS – 4TH GRADE UPDATED 7/2008 43 A.5.4.1 Select and/or write number sentences (equations) to find the unknown in problem-solving contexts involving two-digit by one-digit division using appropriate labels 3. Mrs. Barwick bought 18 boxes of colored pencils for her students. There are 72 pencils in all. If n = the number of pencils in a box, which equation (number sentence) can Mrs. Barwick use to find the number of colored pencils in each box? * A 72 ÷ n = 18 B 72 x n =_ 18 C 72 - 18 =_ n D 72 + 18 = n 2008 - 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? * A. 30 ÷ 5 = n B. 30 × 5 = n C. 30 – 5 = n D. 30 + 5 = n 2006 – % ELKINS ELEMENTARY (NEVIN) MATH RELEASED ITEMS – 4TH GRADE UPDATED 7/2008 44 A.5.4.2 Express mathematical relationships using simple equations and inequalities (>, <, =, ≠ ) Ex. 4 x 5 ____ 8 x 2 + 3 12. Kim wrote the following number sentence (inequality) on the board. 3 × 6 − 4 < 6[ ]3 Which symbol will make the number sentence true? A. + B. − * C. × D. ÷ 2007 – % 2. Mr. Douglas asked each of his fourth-grade students to write an inequality statement. Which one of the following inequality statements is true? A. 1258 < 1249 B. 76,849 > 76,890 * C. 94,682 > 94,628 D. 1,238,489 < 1,219,999 2003 – % 10. Maria collects pictures of butterflies. She has 140 pictures. Of these, 80 pictures show butterflies. Which equation can you use to show pictures without butterflies? A. 140 + 80 = N * B. 140 – 80 = N C. 140 × 80 = N D. 140 ÷ 80 = N 2003 – % 15. Which comparison is correct? * A. 0,500 < 550 B. 0,300 > 2,850 C. 4,300 = 3,400 D. 9,919 < 9,919 2003 – % ELKINS ELEMENTARY (NEVIN) MATH RELEASED ITEMS – 4TH GRADE UPDATED 7/2008 45 A.5.4.3 Use a variable to represent an unknown quantity in a number sentence involving contextual situations and find the value Ex. Susie bought 48 pencils. If the pencils came in packages of 12, how many packages of pencils did she buy? P = 48 ÷ 12 21. Eleven students paid a total of $55 to go on a field trip. Which equation (number sentence) shows how much money each student paid (n), if each student paid an equal amount? * A. 55 ÷ 11= n B. 11 × 55 = n C. 55 – 11 = n D. 55 + 11 = n 2007 – % 24. Marguerite needs 24 squares to make one patchwork quilt. She wants to make 6 quilts. Which mathematical sentence shows how many squares she needs? A. 24 ÷ 6 = n B. 6 ÷ 24 = n * C. 24 × 6 = n D. 4 × 24 = n 2007 – % AR4M03P104NXXX-104B 29. In the equation below, what is the value of n? (81 − 9) ÷ n = 9 A. 0 * B. 8 C. 72 D. 81 2005 – % 1. Which number will make the equation true? (10 + n) – (2 × 3) = 8 * A. 4 B. 9 C. 10 D. 16 2004 – % ELKINS ELEMENTARY (NEVIN) MATH RELEASED ITEMS – 4TH GRADE UPDATED 7/2008 46 37. What number does n represent in order for the statement below to be true? 6×3=2×n A. 1 B. 3 C. 5 * D. 9 2004 – % AR4M01P104NXXX-085D 20. Mr. Dove wrote the number sentence N ÷ 3 = 9 on the board. What number could replace N to make this number sentence true? A. 3 B. 6 C. 12 * D. 27 2003 – % 24. LaToya made up this number sentence: N × 4 = 2 × 8. What number could replace N to make LaToya’s number sentence true? A. 2 * B. 4 C. 16 D. 64 2003 – % ELKINS ELEMENTARY (NEVIN) MATH RELEASED ITEMS – 4TH GRADE UPDATED 7/2008 47 A.6.4.1 Create a chart or table to organize given information and to understand relationships and explain the results Ex. Troy must read independently for 2 hours a week. If Troy reads 20 minutes a day, how long will it take him to read a total of two hours? 4. Marley tracked the number of minutes she spent writing in her journal in the table below. Time Spent Writing in My Journal Day Total Minutes 1 20 2 ? 3 60 4 80 5 100 If Marley wrote in her journal the same number of minutes each day, how many total minutes did she write by the end of Day 2? A 20 B 30 * C 40 D 80 2008 - 36. Lisa must walk the family dog for 30 minutes each day. The table below shows the total amount of time she has walked the dog so far this week. DAY TOTAL TIME FOR THE WEEK 1 1 hour 2 2 1 hour 3 1 1 hour 2 4 ? 5 ? 6 ? 7 ? According to the table, how much time will Lisa have spent walking the dog by the end of the 7th day? 1 A. 2 hours B. 2 hours 2 1 C. 3 hours * D. 3 hours 2 2007 – % ELKINS ELEMENTARY (NEVIN) MATH RELEASED ITEMS – 4TH GRADE UPDATED 7/2008 48 A. Cheryl has a new 20-gallon fish tank. She only has a 1-quart pitcher that she will use to fill the tank. She started making the table below to help her find out how many times she would need to fill and pour with her quart pitcher. Number of 1 2 3 4 5 6 7 8 9 10 Gallons Number of 4 8 Quarts 1. In your answer document, copy and complete Cheryl’s table, showing the relationship between quarts and gallons. 2. How many times will Cheryl need to fill and pour her pitcher in order to fill her 20-gallon tank? Explain your answer using words and/or numbers. BE SURE TO LABEL YOUR RESPONSES 1 AND 2. 2007 – /8 SOLUTION AND SCORING PART 1 2 points possible 2 points: Chart is correct and complete, as shown in the diagram below. Note: Work is not required. Note: 1 & 2 Gallons and 4 & 8 Quarts (given) may be missing but are required for a score of 4. Labels (# of Gallons, # of Quarts) may be missing, but are required for a score of 4. Ex: OR 1 point: Chart is incomplete or incorrect due to one of the following: • 1 or more #s are incorrect due to one calculation, counting or copy error. Correct procedure used: 4 is added to all entries to get the next entry, or each entry for # of gallons is multiplied by 4. Ex: Response contains 1 calculation error. Error: 20+4=23, others from that point on are correct based on error (+4). • Chart is incomplete: One entry is missing from 12–40. The #s listed are correct. Ex: • The # of Quarts (12–40) are correct and complete but they aren’t associated with corresponding # of Gallons. Ex: Note: Do not give credit if work contains more than 1 calculation error or ELKINS ELEMENTARY (NEVIN) MATH RELEASED ITEMS – 4TH GRADE UPDATED 7/2008 49 incorrect procedure is used. PART 2 2 points possible 1 point: Correct answer: 80, or correct answer based on calculation in Part 1. AND 1 point: Correct and complete procedure shown and/or explained. Work may contain a calculation error or may be based on a calculation, counting, or copy error in Part 1. Give credit for the following or equivalent: • 20 × 4 = # (4 quarts/gallon, has 20 gallons), or • 40 (or # of quarts for 10 gallons in Part 1) × 2 = #, or • The chart is extended to 20 gallons and is completed correctly, or multiples of 4 from 44 to 80 are listed: 44, 48, 52, 56, 60, 64, 68, 72, 76, 80 (may be based on incorrect entry in Part 1), or • 10/40 = 20/x, x = #, or • “The chart shows that it would take 40 quarts to fill a 10-gallon tank. A 20- gallon tank is 2 times larger, so it would need two times as much water so I doubled 40.” Note: Do not give credit for incomplete work or explanation. Ex: “I counted by 4’s” Use the chart below to answer question 39. IN OUT 8 16 9 18 10 20 12 24 14 ? 39. The chart above shows a relationship between the numbers in the “IN” column and the numbers in the “OUT” column. What number would complete the chart above? A. 16 B. 26 * C. 28 D. 32 2005 – % 2. Mr. Preddy put the chart below on the board. He asked his students, “If the pattern continues, which pair of numbers would come next?” What answer should the students have given? A. 55, 10 * B. 60, 12 C. 75, 15 D. 90, 18 2004 – % ELKINS ELEMENTARY (NEVIN) MATH RELEASED ITEMS – 4TH GRADE UPDATED 7/2008 50 Use the chart below to answer question 15. Pattern Chart A B 6 12 12 24 24 48 ? ? 15. Mrs. Gordon put the chart above on the board. What pair of numbers would come next in the pattern? A. 30, 60 B. 30, 96 C. 48, 60 * D. 48, 96 2004 – % ELKINS ELEMENTARY (NEVIN) MATH RELEASED ITEMS – 4TH GRADE UPDATED 7/2008 51 A.7.4.1 Identify, describe and generalize relationships in which quantities change proportionally Ex. If a car travels at a rate of 50 mph, how far will it travel in three hours? hours 1 2 3 miles 50 100 150 26. It is 150 miles between Little Rock and Ashdown. Driving at 50 miles per hour, how many hours will the trip take? * A. 3 1 B. 2 2 C. 2 1 D. 3 2 2006 - % ELKINS ELEMENTARY (NEVIN) MATH RELEASED ITEMS – 4TH GRADE UPDATED 7/2008 52 G.8.4.1 Identify, describe and classify three-dimensional solids by properties including the number of vertices, edges, and shapes of faces using models 7. How many edges does the brick below have? A4 B6 C9 * D 12 2008 - 20. Which of the following is most like a cylinder? * A. soda can B. stop sign C. cereal box D. front door of a house 2006 – % 24. How many more vertices does a cube have than a triangular prism? * A. 2 B. 6 C. 8 D. 14 2006 – % ELKINS ELEMENTARY (NEVIN) MATH RELEASED ITEMS – 4TH GRADE UPDATED 7/2008 53 Use the figures below to answer question 5. 5. Mr. Joyner asked his students to construct 3-D shapes using construction paper and tape. Which of the following shapes could Marlene make from the three shapes above? A. cone B. cube * C. cylinder D. rectangular prism 2005 – % 7. Aaron has paper cut-outs of a rectangle and two circles. Which of the following 3-dimensional shapes could Aaron make using all three of his cut-out shapes? A. a cone B. a sphere * C. a cylinder D. a rectangular prism 2003 – % 12. How many faces does a cube have? A. 4 B. 5 * C. 6 D. 7 2003 – % ELKINS ELEMENTARY (NEVIN) MATH RELEASED ITEMS – 4TH GRADE UPDATED 7/2008 54 18. How many figures (circle, triangle, rectangle, square . . .) do you need to make the cylinder below? A. 2 congruent circles and 1 triangle * B. 2 congruent circles and 1 rectangle C. 2 congruent circles and 1 trapezoid D. 2 congruent circles only 2003 – % 26. Which figure below could be folded to make a cube? A. B. * C. D. 2003 – % ELKINS ELEMENTARY (NEVIN) MATH RELEASED ITEMS – 4TH GRADE UPDATED 7/2008 55 G.8.4.2 Identify regular and irregular polygons including octagon See the Polygons page in the Appendix 15. Which statement best describes the polygons below? A. Both are regular. * B. Both are irregular. C. Both are congruent. D. Both are pentagons 2007 – % B. Susan wrote the clues below to describe a mystery shape. • It is a quadrilateral. • It has only one set of parallel sides. • It has no right angles. • It has only one line of symmetry. You may use your pattern blocks to help answer Parts 1 and 2. 1. In your answer document, draw and name Susan’s mystery shape. 2. Draw and label a rhombus, and give three “mystery shape” clues for it. BE SURE TO LABEL YOUR RESPONSES 1 AND 2. 2007 – /8 SOLUTION AND SCORING PART 1 2 points possible 1 point: Correct drawing of a trapezoid. Ex: AND trapezoid 1 point: Correct name of “Trapezoid.” PART 2 2 points possible 2 points: Correct drawing of a rhombus, as shown below. rhombus Note: The label of “rhombus” is only required for a score of 4. A drawing of a square is acceptable because a square is a rhombus. And Response contains any 3 clues that correctly describe a rhombus. ELKINS ELEMENTARY (NEVIN) MATH RELEASED ITEMS – 4TH GRADE UPDATED 7/2008 56 Examples: • I am a quadrilateral. • I am a parallelogram or I am like a diamond. • I have 4 sides, lines, or edges (“edges” is not acceptable for a score of 4). • I have 4 vertices or corners (“points” is not acceptable). • The lengths of all of my sides are equal. • I am an equilateral. • My opposite sides are parallel. • I have 2 sets of parallel sides. • I have 2 lines of symmetry. • I have 2 obtuse angles. • I have 2 acute angles. • The measures of my opposite angles are equal. • My diagonals are perpendicular. • My diagonals bisect each other. • My diagonals bisect my angles. Note: If a drawing of a square is given, score clues accordingly. OR 1 point: Response contains either of the following: • Correct drawing of a rhombus but clues are incomplete or missing, or • Drawing of rhombus is missing or not obviously incorrect. 3 correct clues for a rhombus are listed with no incorrect clues included. Note: No credit is given in Part 2 if the diagram is incorrect. 37. I am a polygon. I have 6 sides. What is my name? A. square B. octagon * C. hexagon D. quadrilateral 2006 – % Use the figure below to answer question 1. 1. Ms. Sutton drew the rhombus above on the board. She asked her students to describe the shape. Which of the following is a correct description of the shape? A. 4 even sides; 4 right angles; 2 sets of parallel lines B. 4 uneven sides; 2 acute angles; 2 obtuse angles; 2 sets of parallel lines * C. 4 even sides; 2 acute angles; 2 obtuse angles; 2 sets of parallel lines D. 4 even sides; 2 acute angles; 2 obtuse angles; 1 set of parallel lines 2005 – % ELKINS ELEMENTARY (NEVIN) MATH RELEASED ITEMS – 4TH GRADE UPDATED 7/2008 57 Use the graph below to answer question 3. PLAN FOR THE WALKWAY 9 ft. 3 ft. 3. Caleb wants to help his dad build a walkway to his front door using square tiles. If each tile is 1 square foot, how many tiles will Caleb and his dad need? A. 6 B. 12 C. 24 * D. 27 2005 – % Use the pictures below to answer question 18. Group A Group B 18. What rule was used for sorting the objects above? * A. Group A: objects without angles Group B: objects with angles B. Group A: objects that are food Group B: objects with angles C. Group A: objects that are balls Group B: objects with angles D. Group A: objects that are round Group B: objects that are triangular 2005 – % ELKINS ELEMENTARY (NEVIN) MATH RELEASED ITEMS – 4TH GRADE UPDATED 7/2008 58 28. Mr. Taylor told his math students to guess what pattern block he was holding. He gave the following clues: • It has 4 sides. • All of its sides are equal. • It has no right angles. What is it? A. triangle B. hexagon * C. rhombus D. trapezoid 2004 – % 32. I am Sam the Robot. My head is a hexagon. My legs are right triangles. My body is a trapezoid. Which robot am I? * A. B. C. D. 2004 – % ELKINS ELEMENTARY (NEVIN) MATH RELEASED ITEMS – 4TH GRADE UPDATED 7/2008 59 G.8.4.3 Identify, draw, and describe a line, line segment, a ray, an angle, intersecting, perpendicular, and parallel lines 2. Which of the following represents two line segments? * A. B. C. D. 2008 - 34. Mr. Thompson showed his class a line segment and a ray that are parallel to one another. Which figure did he show them? A. B. C. * D. 2007 – % ELKINS ELEMENTARY (NEVIN) MATH RELEASED ITEMS – 4TH GRADE UPDATED 7/2008 60 G.8.4.4 Identify and describe intersecting, perpendicular and parallel lines in problem solving context 1. Which term describes the relationship of the bookcase shelves? * A. parallel B. intersecting C. line segment D. perpendicular 2007 – % 6. Which shape does not have parallel sides? * A. B. C. D. 2003 – % ELKINS ELEMENTARY (NEVIN) MATH RELEASED ITEMS – 4TH GRADE UPDATED 7/2008 61 G.8.4.5 Classify angles relative to 90° as more than, less than or equal to 8. Which clock below has hands at an angle less than 90 degrees? * A. B. C. D. 2007 – % 27. Which two shapes have at least one angle that is greater than 90°? A. E and H * B. F and G C. G and H D. E and F 2007 – % ELKINS ELEMENTARY (NEVIN) MATH RELEASED ITEMS – 4TH GRADE UPDATED 7/2008 62 G.9.4.1 Determine the result of a transformation of a two-dimensional figure as a slide (translation), flip (reflection) or turn (rotation) and justify the answer 38. Which shows the figure below after it has been flipped (reflected)? A. B. C. * D. 2007 – % Use the figure below to answer question 8. FIGURE 1 8. Which figure is the flip image of Figure A above? * A. B. C. D. 2004 – % ELKINS ELEMENTARY (NEVIN) MATH RELEASED ITEMS – 4TH GRADE UPDATED 7/2008 63 G.10.4.1 Locate and identify points on a coordinate grid and name the ordered pair (quadrant one only) using common language and geometric vocabulary (horizontal and vertical) ELKINS ELEMENTARY (NEVIN) MATH RELEASED ITEMS – 4TH GRADE UPDATED 7/2008 64 G.11.4.1 Construct a three-dimensional model composed of cubes when given an illustration AR4M05G1101Y078-078B 37. Abner is building a fort with his friends. If he uses at least 25 blocks, which figure could be a model of his fort? (There are no hidden blocks.) I II III IV A. I * B. II C. III D. IV 2007 – % Use the figure below to answer question 30. 30. How many blocks are there in the figure above? A. 14 B. 18 * C. 28 D. 34 2005 – % ELKINS ELEMENTARY (NEVIN) MATH RELEASED ITEMS – 4TH GRADE UPDATED 7/2008 65 G.11.4.2 Create new figures by combining and subdividing models of existing figures in multiple ways and record results in a table Ex . 4. If Alan combines the two triangles below, what type of parallelogram could he make? A. trapezoid B. rhombus * C. rectangle D. square 2007 – % 14. Joey covered a hexagon pattern block using 3 triangles and 1 other shape. What is the other shape? You may use your pattern blocks to help you. A. square B. triangle C. rhombus * D. trapezoid 2006 – % ELKINS ELEMENTARY (NEVIN) MATH RELEASED ITEMS – 4TH GRADE UPDATED 7/2008 66 15. How many triangle pattern blocks are needed to cover the figure below? You may use your pattern blocks to help you. A. 3 B. 4 * C. 12 D. 13 2006 – % 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.) A. B. C. * D. 2006 – % ELKINS ELEMENTARY (NEVIN) MATH RELEASED ITEMS – 4TH GRADE UPDATED 7/2008 67 D. Casey used four pattern blocks to create the design below. 1. Name the four pattern blocks Casey used. You may use your pattern blocks to help you find the answer. 2. 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 1 AND 2. 2006 – /8 SOLUTION AND SCORING PART 1 2 points possible 2 points: Answer is correct and complete: 2 Hexagons, 1 Trapezoid and 1 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 do not give credit if quadrilateral is used for both the trapezoid & square. Or 1 point: Partially correct answer. Give credit for the following: • Hexagon, Trapezoid and Square (correct shapes, no #’s) Or rd • 2 names & #’s are correct, 3 has correct drawing of remaining shape, but name may be incorrect or missing. PART 2 ELKINS ELEMENTARY (NEVIN) MATH RELEASED ITEMS – 4TH GRADE UPDATED 7/2008 68 2 points possible 2 points: Correct and complete answer. Give credit for the following: Note: If incorrect name(s) are given in Part 1, do not penalize again. Credit can be given if answer is “correct” based on Pt. 1 answer. • Correct shapes and # of shapes (> 4) needed to make new design with support explaining or showing why they will work: Ex: 1 hexagon, 3 trapezoids and 1 square with given diagram correctly divided. Ex: “4 trapezoids, 3 triangles and one square because 2 trapezoids could make up each hexagon and 3 triangles could make up one trapezoid.” Ex: “2 hexagons, 1 square, 1 triangle, 1 rhombus since a trapezoid can be made up of 1 triangle and 1 rhombus.” Ex: 5 trapezoids and 1 square with given diagram correctly divided. Ex: “15 triangles and 1 square because 6 triangles make up 1 hexagon and 3 triangles make up 1 trapezoid so 6 + 6 + 3 = 15 triangles, + 1 square.” Or • Correct and complete drawing of given design divided up into more than 4 pattern blocks. Or 1 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. Use the figure below to answer question 13. 13. Ward made the above design with pattern blocks. If he makes a congruent design with triangular pattern blocks, how many triangles will he use? (You may use your pattern blocks to help you.) A. 3 * B. 6 C. 8 D. 9 2005 – % ELKINS ELEMENTARY (NEVIN) MATH RELEASED ITEMS – 4TH GRADE UPDATED 7/2008 69 Use the figure below to answer question 36. 36. The area of a trapezoid pattern block is equal to 3 triangular pattern blocks. How many triangles would be needed to find the area of a hexagon? (You may use your pattern blocks to help you.) A. 2 B. 3 * C. 6 D. 7 2005 – % E. Emily took the hexagon pattern shape above and cut it symmetrically into two equal pieces, cutting from one vertex to another across the shape. 1. What shape are the two new pieces? Use words or a picture to explain your answer. 2. If Emily cuts the hexagon on all lines of symmetry, what shape will the new pieces be? Use words or a picture to explain your answer. BE SURE TO LABEL YOUR RESPONSES 1 AND 2. 2005 – /8 SOLUTION AND SCORING Part 1: (2 points possible) Answer: 1 point for correct answer of “Trapezoid” or “Quadrilateral.” Note: Give credit for a drawing of a trapezoid (with no name or incorrect name) if no credit is given for the work or explanation in Part 1. Note: Do not give credit for “Trapezoid” or “Quadrilateral” if the explanation includes a diagram of a hexagon that is divided into shapes, none of which are trapezoids or quadrilaterals. AND Work: 1 point for the following work or explanations: ● One of the following diagrams of a hexagon cut symmetrically from 1 vertex to another: ● Correct and complete definition of trapezoid. ELKINS ELEMENTARY (NEVIN) MATH RELEASED ITEMS – 4TH GRADE UPDATED 7/2008 70 Example: “She would have two trapezoids since each shape would have 4 sides with just 1 pair of sides being parallel.” Part 2: (2 points possible) Answer: 1 point for correct answer of “Triangle.” Note: Give credit for a drawing of a triangle (no name) if no credit is given for the work or explanation in Part 2. Note: Do not give credit for “Triangle” if the explanation includes a diagram of a hexagon that is divided into shapes, none of which are triangles, or multiple answers are given. AND Work: 1 point for the following work or explanation: ● Correct drawing of hexagon with anywhere from 3 lines of symmetry (connecting the opposite vertices, or connecting the midpoints of opposite sides, resulting in 6 triangles) up to all 6 lines of symmetry (resulting in 12 triangles), as shown below: 3 Lines of Symmetry Connecting Opposite Vertices All 6 Lines of Symmetry Connecting Opposite Vertices and Midpoints of Opposite Sides , or ● “If she cut the hexagon on all lines of symmetry, she will have 6 triangles (or 12 triangles).” Note: Do not give credit for incomplete procedure (< 3 lines of symmetry), vague explanations, or explanations that basically repeat the prompt. ● Example: “If I draw all of the lines of symmetry, I’ll get triangles.” Use the figure below to answer question 12. 12. Annie made a pattern block design using 1 hexagon and 2 trapezoids. How many equilateral triangles will cover this design? (You may use your pattern blocks to help you find the answer.) A. 3 B. 6 * C. 12 D. 14 2004 – % ELKINS ELEMENTARY (NEVIN) MATH RELEASED ITEMS – 4TH GRADE UPDATED 7/2008 71 M.12.4.1 Recognize that 60 seconds equals 1 minute 8. Marsha jumped rope for 1 minute without stopping. How many seconds did she jump? A 10 seconds B 30 seconds * C 60 seconds D 90 seconds 2008 - 21. One morning it took Carlos 167 seconds to brush his teeth. How many minutes and seconds did it take him to brush his teeth? * A. 2 minutes and 47 seconds B. 3 minutes and 67 seconds C. 4 minutes and 17 seconds D. 16 minutes and 7 seconds 2004 – % ELKINS ELEMENTARY (NEVIN) MATH RELEASED ITEMS – 4TH GRADE UPDATED 7/2008 72 M.12.4.2 Distinguish the temperature in contextual problems using the Fahrenheit scale on a thermometer 17. Mr. Barnhill has the temperature in his house set to a comfortable level—not too hot, not too cold. What temperature would the thermometer show? A. 25°F B. 45°F * C. 72°F D. 99°F 2005 – % 20. Kathy is wearing a heavy coat, scarf, mittens, and a hat. Which temperature is it most likely outside? A. 35°C * B. 35°F C. 68°C D. 68°F 2004 – % ELKINS ELEMENTARY (NEVIN) MATH RELEASED ITEMS – 4TH GRADE UPDATED 7/2008 73 M.12.4.3 Use the relationship among units of measurement Length: Capacity: Weight: 12 in = 1 ft 2 cups = 1 pint 16 ounces = 1 lb 3 ft = 1 yd 2 pints = 1 quart 36 in = 1 yd 4 quarts = 1 gallon 100 cm = 1 m 11. Felton weighed 8 apples and found that they weighed 2 pounds. Approximately how much does 1 apple weigh? A. 2 oz * B. 4 oz C. 16 oz D. 32 oz 2006 – % 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? A. 2 feet * B. 6 feet C. 34 feet D. 72 feet 2006 – % 39. Craig’s little brother weighed 5 pounds and 8 ounces when he was born. How many ounces did he weigh? A. 40 B. 44 C. 80 * D. 88 2006 – % AR4M03M103NXXX-114A 8. Malek jumped a distance of 6 feet on his dirt bike. How many yards did he jump? * A. 2 B. 3 C. 4 D. 6 2005 – % ELKINS ELEMENTARY (NEVIN) MATH RELEASED ITEMS – 4TH GRADE UPDATED 7/2008 74 1 10. It is exactly 6 feet from Jomarie’s desk to the classroom door. How far is 2 that in inches? A. 62 inches B. 72 inches * C. 78 inches D. 84 inches 2005 – % 1 22. Sarah is 4 feet tall. How tall is Sarah in inches? 2 A. 45 inches B. 48 inches * C. 54 inches D. 56 inches 2005 – % 4. Last week, Mark’s pet bunny weighed 12 ounces. This week, it had gained 4 more ounces. How much does it weigh now? * A. 1 pound B. 8 ounces C. 16 pounds D. 48 ounces 2004 – % 27. Jim’s fish tank holds 40 quarts of water. How many gallons of water does that equal? * A. 10 B. 20 C. 40 D. 60 2004 – % 36. Pinnacle Mountain has a height of 1,011 feet. What would be its height in yards? * A. 337 yards B. 975 yards C. 1,014 yards D. 3,033 yards 2004 – % ELKINS ELEMENTARY (NEVIN) MATH RELEASED ITEMS – 4TH GRADE UPDATED 7/2008 75 C. Barb and William are each growing sweet potato vines. Barb’s plant measures one-and-a-half feet long. William’s plant measures 24 inches long. 1. Whose plant is longer? Explain your answer using words and/or numbers. 2. How much must William’s plant grow before it is one yard long? Explain your answer using words and/or numbers. BE SURE TO LABEL YOUR RESPONSES 1 AND 2. 2004 – /8 SOLUTION AND SCORING Part 1: (2 points possible) 1 point for correct answer of William’s plant is longer. ● Note: Do not give credit if there is clear evidence of incorrect procedure. AND 1 point for correct conversion of Barb’s 1 ½ foot plant into 18 inches or William’s 24 inch plant into 2 feet shown and/or explained. ● Give credit for any of the following explanations or equivalent: 12 + 6 = 18 and 24 >18, or 24/12 = 2 and 2 >1 ½, or “Twenty-four inches equals two feet, so William’s plant is longer,” or “His plant is longer since a foot and a half would only be eighteen inches.” ● Do not give credit for the following incomplete explanations: “His plant is 6 inches longer,” or “His plant is longer since 24 inches is longer than 1 ½ feet.” Part 2: (2 points possible) 1 point for correct answer of “12 inches” or “1 foot.” Label must be correct. AND 1 point for correct procedure shown and/or explained. ● Give credit for any of the following explanations or equivalent: There are 36 inches in a yard. William’s plant is 24 inches long. The difference is 12 inches, or 1 yard = 3 feet and he has 2 feet. Therefore, it needs to grow 1 foot, or 1 yard = 36 inches. 36 - 24 = 12 inches. OR ● Answer is incorrect due to a calculation or copy error, but correct procedure is used. Example: 36 - 24 = 11 inches. ♦ Note: Credit will be received for the procedure, but not for the answer. ELKINS ELEMENTARY (NEVIN) MATH RELEASED ITEMS – 4TH GRADE UPDATED 7/2008 76 5. Alex drew a floor plan of her house. What is the length in feet of Alex’s house from the corner of the kitchen to the corner of the baby’s room? A. 04 feet B. 05 feet C. 20 feet * D. 40 feet 2003 – % 13. Lee’s mother has a 32-fluid-ounce pitcher filled with milk. How many cups can she fill? (8 fluid ounces = 1 cup) * A. 004 B. 024 C. 040 D. 256 2003 – % 17. Four feet equals ________. A. 3 inches B. 4 inches C. 12 inches * D. 48 inches 2003 – % ELKINS ELEMENTARY (NEVIN) MATH RELEASED ITEMS – 4TH GRADE UPDATED 7/2008 77 27. A Ferris wheel at the fair is 208 feet high. About how high is the Ferris wheel in yards? * A. 069 yards B. 104 yards C. 205 yards D. 624 yards 2003 – % ELKINS ELEMENTARY (NEVIN) MATH RELEASED ITEMS – 4TH GRADE UPDATED 7/2008 78 M.12.4.4 Create and complete a conversion table to show relationships between units of measurement in the same system ELKINS ELEMENTARY (NEVIN) MATH RELEASED ITEMS – 4TH GRADE UPDATED 7/2008 79 M.13.4.1 Using a calendar to determine elapsed time from month to month AR4M05M1301NXXX-111A 10. Mrs. Merchant’s students wrote in their journals every day beginning on January 31st. They wrote their last journal entries on February 9th. How many total days did the students write in their journals? A 8 days B 9 days * C 10 days D 22 days 2008 - 5. José’s school has a week-long spring break starting on March 28. On what date will the school reopen? * A. April 4 B. April 5 C. April 11 D. March 12 2007 – % ELKINS ELEMENTARY (NEVIN) MATH RELEASED ITEMS – 4TH GRADE UPDATED 7/2008 80 Use the calendar below to answer question 9. 9. The calendar above shows that John cleans his hamster’s cage every 3 days and his gerbil’s cage every 5 days. If this pattern continues, how many times during the month of July will he clean both cages on the same day? A. 1 * B. 2 C. 6 D. 9 2005 – % Use the calendar below to answer question 7. MAY SUN MON TUE WED THUR FRI SAT 1 2 3 4 5 6 SWIM 7 8 9 10 11 12 13 14 15 16 17 18 19 20 SWIM 21 22 23 24 25 26 27 28 29 30 31 7. Jane has swim practice on the first and third Monday of each month. What will be the date of her first swim practice in June? A. 1st * B. 5th C. 15th D. 29th 2004 – % ELKINS ELEMENTARY (NEVIN) MATH RELEASED ITEMS – 4TH GRADE UPDATED 7/2008 81 M.13.4.2 Solve problems involving conversions between minutes and hours 10. It took Sara 1 hour and 30 minutes to do her homework, and she practiced piano for 45 minutes. What was the total amount of time Sara spent doing homework and practicing piano? A. 1 hour and 15 minutes B. 1 hour and 30 minutes * C. 2 hours and 15 minutes D. 2 hours and 25 minutes 2007 – % IMPORTANT: This item appeared in the Grade 4 Benchmark Examination test booklet as item 12 and again as item 48. Students were required to answer this item correctly only once. Answering correctly for item 12 but incorrectly for item 48 (or vice versa) resulted in a student receiving credit for the item. The student’s score was not harmed by the duplication of the item. 28. Justine can run one-fourth of a mile in 120 seconds. How many minutes is that? * A. 2 B. 4 C. 20 D. 30 2005 – % 30. During the month of February, a student in fourth grade read for a total of 1,680 minutes. For how many minutes did the student read each day if she read for the same number of minutes on each of the 28 days in February? A. 0028 * B. 0060 C. 0070 D. 1,680 2003 – % 31. Troy must read independently for 2 hours per week. If Troy reads for 20 minutes per day, how many days will it take him to read for a total of 2 hours? A. 20 + 120 = B. 120 − 20 = C. 120 × 20 = * D. 120 ÷ 20 = 2003 – % ELKINS ELEMENTARY (NEVIN) MATH RELEASED ITEMS – 4TH GRADE UPDATED 7/2008 82 34. Students in Mr. Kon’s science class want to determine which hours of the day are the warmest and the coolest. They put a beaker of water outside in the sun and recorded the temperature of the water at 4 different times for one week. What are the best times for the students to record their data? * A. 8:15 a.m., 12:00 noon, 1:30 p.m., and 4:00 p.m. B. 1:30 p.m., 3:30 p.m., 5:30 p.m., and 7:30 p.m. C. 8:15 a.m., 9:15 a.m., 10:15 a.m., and 11:15 a.m. D. 4:00 p.m., 6:00 p.m., 8:00 p.m., and 10:00 p.m. 2003 – % 1 35. It takes 3 hours to drive from Fayetteville to Little Rock. If you leave 2 Fayetteville at 4:15 p.m., what time will you arrive in Little Rock? DEPARTS FAYETTEVILLE, AR 4:15 P.M. A. 4:45 p.m. B. 7:15 p.m. * C. 7:45 p.m. D. 8:00 p.m. 2003 – % ELKINS ELEMENTARY (NEVIN) MATH RELEASED ITEMS – 4TH GRADE UPDATED 7/2008 83 M.13.4.3 Restate the time in multiple ways given an analog clock to the nearest one-minute 32. What is another way you could write “5 minutes before 9 o’clock”? A. 5:09 B. 8:11 * C. 8:55 D. 9:05 2005 – % ELKINS ELEMENTARY (NEVIN) MATH RELEASED ITEMS – 4TH GRADE UPDATED 7/2008 84 M.13.4.4 Determine elapsed time in contextual situations to five-minute intervals with beginning time unknown Ex. Mary watched a movie for 1 hour and 15 minutes. The movie ended at 8:15. When did the movie begin? 12. When Marissa went to the amusement park, it took her 1 hour and 10 minutes to wait in line and ride the roller coaster. The ride ended at 11:55 A.M. 1. At what time did Marissa begin waiting in line to ride the roller coaster? Explain your answer using words and/or numbers. 2. Marissa got in line for the bumper boats at 12:30 P.M. The ride began at 1:10 P.M. How long did Marissa stand in line? Explain your answer using words and/or numbers. BE SURE TO LABEL YOUR RESPONSES 1 AND 2. 2008 - ELKINS ELEMENTARY (NEVIN) MATH RELEASED ITEMS – 4TH GRADE UPDATED 7/2008 85 11. José attended a science program that lasted 1 hour and 10 minutes. The program ended at 3:20 P.M. What time did the program begin? A. 4:30 P.M. B. 4:20 P.M. C. 2:20 P.M. * D. 2:10 P.M. 2007 – % 16. On Saturday night, Roberto’s family watched a movie that lasted 2 hours and 10 minutes. If the movie ended at 9:10 P.M., what time did the movie start? * A. 7:00 P.M. B. 7:10 P.M. C. 11:00 P.M. D. 11:20 P.M. 2007 – % Use the information below to answer question 13. SCHEDULE FOR FEEDING SNAKES 10:00 A.M. 12:00 P.M. 2:00 P.M. 4:00 P.M. 13. Sandra’s fourth-grade class went to the Little Rock Zoo on a field trip. Her group arrived at the snake exhibit at 10:25 A.M. How long will the group have to wait to see the next snake feeding? A. 2 hours B. 35 minutes * C. 1 hour, 35 minutes D. 2 hours, 35 minutes 2004 – % AR4M02M301NXXX-095B 38. Pat’s coach told the team to arrive at the ballpark 45 minutes before their baseball game. The game begins at 6:00 P.M. What time should Pat arrive at the ballpark? A. 4:45 P.M. * B. 5:15 P.M. C. 5:30 P.M. D. 6:45 P.M. 2004 – % ELKINS ELEMENTARY (NEVIN) MATH RELEASED ITEMS – 4TH GRADE UPDATED 7/2008 86 M.13.4.5 Apply money concepts in contextual situations Ex. determine the better buy determine change back with the least amount of currency compare money 28. Brian has $6.50 in quarters. How many quarters does Brian have? A. 4 B. 12 C. 24 * D. 26 2007 – % C. Thomas, Sam, and David all put their coins together to buy a set of comic books. Altogether, they paid $4.48. 1. Thomas contributed 7 quarters, 4 dimes, 2 nickels, and 3 pennies. How much money did Thomas contribute? Explain your work using words, numbers, and/or pictures. 2. David contributed only nickels and dimes for a total of $1.20. What are two possible combinations that he could have used? Explain your work using words, numbers, and/or pictures. BE SURE TO LABEL YOUR RESPONSES 1 AND 2. 2005 – /8 SOLUTION AND SCORING Part 1: (2 points possible) Answer: 1 point for correct answer of ($)2.28. AND Work: 1 point for correct and complete procedure showing how to determine the answer. ● Give credit for the following work and/or explanations or equivalent. Work may contain a calculation or copy error. 7(.25) + 4(.10) + 2(.05) + 3(.01) = Total Amount, or 1.75 + .40 + .10 + .03 = Total Amount, or Correct number of each coin drawn with correct $ values indicated. Do not give credit if coins only have “Q”, “D”, “N”, etc. Note: Do not give credit for partial or incomplete work. ● Example: “I added 7 quarters, 4 dimes, 2 nickels and 3 pennies.” Part 2: (2 points possible) Answer: 1 point for 2 correct combinations of nickels and dimes (combinations listed below). ● Example: 8 nickels and 8 dimes, and 6 nickels and 9 dimes. OR ½ point for 1 correct combination. ● Example: 2 nickels and 11 dimes. Nickels Dimes Total ELKINS ELEMENTARY (NEVIN) MATH RELEASED ITEMS – 4TH GRADE UPDATED 7/2008 87 # $ # $ $1.20 2 .10 11 1.10 " 4 .20 10 1.00 " 6 .30 9 .90 " 8 .40 8 .80 " 10 .50 7 .70 " 12 .60 6 .60 " 14 .70 5 .50 " 16 .80 4 .40 " 18 .90 3 .30 " 20 1.00 2 .20 " 22 1.10 1 .10 " AND Work: ½ point (1 point total) for work showing why each combination of nickels and dimes will total $1.20 as shown in the $ columns of the chart above. ● Example: 6 nickels = .30, and 9 dimes = .90. ● Example: Correct drawing with correct $ values indicated. Note: Work may contain a calculation or copy error. Do not give credit for partial or incomplete work. 5. Kisha visited the Aerospace Education Center in Little Rock with her family. She bought a toy airplane for $4.88 in the gift shop. She gave the salesperson $5.00. How much change should Kisha receive? * A. $0.12 B. $0.22 C. $1.12 D. $1.88 2004 – % 39. Alex went to a movie. His ticket cost $5.75, and he bought a popcorn and soda for $3.50. His change was $10.75. What amount of money did he take to the movie? A. $ 9.25 B. $10.00 * C. $20.00 D. $21.25 2004 – % ELKINS ELEMENTARY (NEVIN) MATH RELEASED ITEMS – 4TH GRADE UPDATED 7/2008 88 M.13.4.6 Read temperatures on Fahrenheit and Celsius scales ELKINS ELEMENTARY (NEVIN) MATH RELEASED ITEMS – 4TH GRADE UPDATED 7/2008 89 M.13.4.7 Use appropriate customary and metric measurement tools for length, capacity and mass 1 28. What is the length, measured to the nearest inch, of the plastic fork below? 2 Use your ruler to help you. A. 4 inches 1 B. 4 inches 2 * C. 5 inches 1 D. 5 inches 2 2006 – % 32. Jacob drew the map below to show the distance he drives from his house to the mall. Based on Jacob’s scale, what is the distance? Use your ruler to help you. * A. 3 miles B. 4 miles C. 7 miles D. 8 miles 2006 – % ELKINS ELEMENTARY (NEVIN) MATH RELEASED ITEMS – 4TH GRADE UPDATED 7/2008 90 2. Which of the following units would you use to measure the weight of a penny? A. tons * B. grams C. pounds D. kilograms 2005 – % Use the figure below to answer question 16. 16. How long is the rod above, to the nearest half inch? 1 * A. 4 in. 2 B. 5 in. C. 11 cm 1 D. 11 cm 2 2004 – % 34. Sandra brought a bottle of soda to share at her class party. What is most likely the size of the bottle? * A. 2 liters B. 20 liters C. 2 milliliters D. 20 milliliters 2004 – % ELKINS ELEMENTARY (NEVIN) MATH RELEASED ITEMS – 4TH GRADE UPDATED 7/2008 91 Use the figure below to answer question 8. 8. Which measurement best describes the length of a jump rope? A. 07.3 inches * B. 07.3 feet C. 07.3 yards D. 73.0 feet 2003 – % ELKINS ELEMENTARY (NEVIN) MATH RELEASED ITEMS – 4TH GRADE UPDATED 7/2008 92 M.13.4.8 Estimate and measure length, capacity/volume and mass using appropriate customary and metric units 1 Length: inch, 1 cm 2 Perimeter: inches, feet, centimeters, meters Area: square inches, square feet, square centimeters, square meters Weight: pounds/ounces Mass: kilograms/grams Capacity: cups, pints, quarts, gallons Volume: liters 1 27. Which length, rounded to the nearest inch, best describes the toy cheetah 2 below? Use your ruler to help you. * A. 4 inches 1 B. 4 inches 2 C. 5 inches 1 D. 5 inches 2 2006 – % ELKINS ELEMENTARY (NEVIN) MATH RELEASED ITEMS – 4TH GRADE UPDATED 7/2008 93 37. Roberto’s pet rabbit weighs 3 kilograms. If his cat weighs the same as his rabbit, how many grams does the cat weigh? A. 0003 grams B. 0030 grams C. 0300 grams * D. 3000 grams 2003 – % ELKINS ELEMENTARY (NEVIN) MATH RELEASED ITEMS – 4TH GRADE UPDATED 7/2008 94 M.13.4.9 Use strategies for finding the perimeter of a rectangle 3. How many yards of fencing would it take to surround a dog’s play area that is a square measuring 412 yards per side? A. 16 yards B. 1612 yards * C. 18 yards D. 25 yards 2006 – % Use the picture below to answer question 11. 11. What is the perimeter of the swimming pool, in meters? A. 80 B. 85 * C. 90 D. 110 2005 – % ELKINS ELEMENTARY (NEVIN) MATH RELEASED ITEMS – 4TH GRADE UPDATED 7/2008 95 Use the picture below to answer question 27. 27. Marla wants to glue a piece of yarn around the outer edge of the picture frame above. How many inches of yarn does she need to cut? A. 12 B. 14 * C. 24 D. 35 2005 – % Use the diagram below to answer question 17. 17. The basketball court above is 94 feet long and 50 feet wide. What is the perimeter of this basketball court? A. 0,144 ft B. 0,188 sq ft * C. 0,288 ft D. 4,700 sq ft 2004 – % ELKINS ELEMENTARY (NEVIN) MATH RELEASED ITEMS – 4TH GRADE UPDATED 7/2008 96 Use the figure below to answer question 4. 4. What is the perimeter of the rug above? A. 07 ft. B. 11 ft. C. 12 ft. * D. 14 ft. 2003 – % 21. Sam makes his own frames to display his photography. The shop sells 48-inch wood strips for framing. If all of Sam’s frames are 4 in. × 6 in. rectangles, how many frames can he make from 1 strip? * A. 2 B. 3 C. 8 D. 12 2003 – % ELKINS ELEMENTARY (NEVIN) MATH RELEASED ITEMS – 4TH GRADE UPDATED 7/2008 97 E. Mrs. Needham wants to put a border around the edge of the bulletin board above. 1. What is the perimeter of the bulletin board? Explain your reasoning with words and/or pictures. 2. Mrs. Needham has 20 feet of border. Is that enough to go around the bulletin board? Explain your reasoning with words and/or pictures. BE SURE TO LABEL YOUR RESPONSES 1 AND 2. 2003 – /8 SOLUTION Part 1: Perimeter is 18 feet. Work/Explanation: 3 + 3 + 6 + 6 = 18 feet. OR Equivalent work or explanation. Part 2: Yes, there is enough. Work/Explanation: She has enough since she only needs 18 ft and she has 20 ft of border. OR 18 < 20. OR 20 – 18 = 2. OR Equivalent work or explanation. Scoring (4 total points possible) Part 1: (2 points possible) • 1 point for correct answer of 18. (Note: Give credit for 18 if work includes 6 × 3 (student might be grouping), but do not give credit for 18 if it is evident that the incorrect procedure was used: e.g., work includes L × W = 6 × 3 = 18.) Work/Explanation: • 1 point for correct and complete procedure for perimeter: L + L + W + W = P. (Note: Work might have a calculation or copy error. Do not give credit for 6 × 3.) Part 2: (2 points possible) If the answer in Part 1 is 18, or incorrect due to a calculation error with correct procedure used: • 2 points for correct Y/N corresponding to answer in Part 1, and clear, correct work/explanation in Part 2. OR • 1 point for correct Y/N corresponding to answer in Part 1, but work/explanation in ELKINS ELEMENTARY (NEVIN) MATH RELEASED ITEMS – 4TH GRADE UPDATED 7/2008 98 Part 2 is vague, incomplete, or absent. OR • 1 point for missing Y/N answer with clear and correct work/explanation in Part 2. If the answer in Part 1 is incorrect due to a procedural error: • 1 point for correct Y/N corresponding to answer in Part 1 with at least some correct work/explanation in Part 2. OR • 1 point for missing Y/N answer with clear and correct work/explanation in Part 2. ELKINS ELEMENTARY (NEVIN) MATH RELEASED ITEMS – 4TH GRADE UPDATED 7/2008 99 M.13.4.10 Use strategies for finding the area of a rectangle 26. Kara put wallpaper on one wall in her room, as shown below. How much wallpaper did she use? A. 20 sq ft B. 40 sq ft * C. 96 sq ft D. 98 sq ft 2007 - % D. Rachel and Hannah are getting new desks for their rooms. Their parents said that the larger desk should go in the larger room. Below is a grid model of each girl’s room and the two desks. 1. The area of Rachel’s room is 95 square feet. What is the area of Hannah’s room? Explain your answer using words, numbers, and/or pictures. 2. Which girl will get Desk A? Explain your answer using words, numbers, and/or pictures. BE SURE TO LABEL YOUR RESPONSES 1 AND 2. 2007 – /8 SOLUTION AND SCORING PART 1 2 points possible 1 point: Correct answer: 85 (square feet required for a score of 4). AND 1 point: Correct and complete procedure shown and/or explained. Work may contain a copy, calculation, or counting error ± 1. Give credit for the following or equivalent: ELKINS ELEMENTARY (NEVIN) MATH RELEASED ITEMS – 4TH GRADE UPDATED 7/2008 100 • 8 × 10 = 80, 80 + 5 = #, or • (5 × 9) + (5 × 8) = #, or • 10 × 9 = 90, 90 – 5 = #, or • “The first row has 5, and there are 8 rows of 10, so I added them all up and got 85,” or • The response includes a diagram of the room with squares numbered from 1–85. Note: Do not give credit for incomplete or vague explanations. Ex: “I counted the squares.” PART 2 2 points possible 2 points: Correct answer: Rachel, or correct answer based on an incorrect answer in Part 1 with correct and complete work shown and/or explanation that includes both of the following: • A comparison in words or symbols of the areas of the rooms. • A comparison of the desks using 1 of the following methods: Compares using letters A & B. Ex: A > B Compares areas using #s. Ex: 8 > 6 Names the areas of the desks. Ex: A = 8 and B = 6 Comparative words include “bigger, larger, greater, more than,” etc. Give credit for the following or equivalent: • “Rachel gets Desk A because she has the bigger room since 95 > 85. Desk A is bigger than Desk B since 2 × 4 = 8, 2 × 3 = 6, and 8 > 6,” or • “Rachel gets A, Rooms: 95 > 85, Desks: 8 > 6,” or • “Rachel will because she has the bigger room and Desk A is the bigger desk,” or • “Rachel, because her room has more area and A = 8 and B = 6.” OR 1 point: Give credit for the following or equivalent: Work may contain a copy, calculation, or reasonable counting error. • Correct answer (may be based on incorrect work in Part 1) with incomplete work and/or explanation that includes a comparison of the areas of the rooms OR a comparison of the desks using A & B and/or comparing or naming of the areas of the desks using #s. Ex: “Rachel gets A since A > B” (no comparison of rooms). Ex: “Rachel gets Desk A because she has the bigger room––hers is 95 and Hannah’s is only 85” (no comparison of desks), or • Work or explanation does not included comparative symbols or words, but includes the correct answer (Rachel) and all 4 correct areas. Ex: “Rachel. Rooms: Rachel’s is 95, Hannah’s is 85. Desks: A is 8, B is 6.” Note: Do not give credit for “Rachel gets Desk A” with no comparison of the areas of the rooms or naming the areas and/or comparison of the desks. ELKINS ELEMENTARY (NEVIN) MATH RELEASED ITEMS – 4TH GRADE UPDATED 7/2008 101 19. Mrs. Rodriguez will use 54 square feet of tile to cover her bathroom floor. What are the dimensions of her bathroom? * A. 6 ft by 9 ft B. 7 ft by 8 ft C. 5 ft by 4 ft D. 8 ft by 8 ft 2006 – % A. Cameron drew the rectangle below. The length of Cameron’s rectangle is 3 times its width. 1. What is the length of Cameron’s rectangle? Explain your answer using words, numbers, and/or pictures. 2. What is the area of Cameron’s rectangle? Explain your answer using words, numbers, and/or pictures. BE SURE TO LABEL YOUR RESPONSES 1 AND 2. 2006 – /8 SOLUTION AND SCORING PART 1 2 points possible 1 point: Correct answer: 9 (cm). Note: Do not give credit for answer if incorrect procedure is evident. AND 1 point: Correct procedure shown and/or explained. Work may contain a calculation error. Give credit for the following or equivalent: • 3 x 3 = L (uses fact that length is 3 times the width and w = 3 cm.) • “If the width is 3, just multiply that by 3.” or • 3 + 3 + 9 + 9 = 24 (Finds length based on perimeter, uses Guess & Check) or • 3 + 3 = 6, 24 – 6 = 18, 18 ÷ 2 = L. Note: Do not give credit for incomplete procedure: Ex: L = 9 because 24 – 6 = 18. PART 2 ELKINS ELEMENTARY (NEVIN) MATH RELEASED ITEMS – 4TH GRADE UPDATED 7/2008 102 2 points possible 1 point: Correct answer: 27 (square cm) or correct answer based on incorrect answer to Part 1. AND 1 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 1. Give credit for the following or equivalent: • “3 x 9 = Area.” or • “I multiplied the width of 3 by the length of 9.” or • “I multiplied the length times the width, and the length is 9 and the width is 3.” or • Drawing of a 3 x 9 rectangle that is divided into 27 squares. Note: Do not give credit for only repeating the formula LW = Area only. 16. Melissa’s sandbox is 4 feet wide and 6 feet long. Which of the following number sentences would she use to find its area? A. 6 + 4 = n * B. 6 × 4 = n C. 4 + 4 + 6 + 6 = n D. (4 × 4) + (6 × 6) = n 2005 – % 29. Ms. Smith wants to cover the floor of her sun porch with tiles. Which of the following is the correct formula for finding the area of the porch? A. l + w = A * B. l × w = A C. 2l + 2w = A D. l + l + w + w = A 2004 – % ELKINS ELEMENTARY (NEVIN) MATH RELEASED ITEMS – 4TH GRADE UPDATED 7/2008 103 B. A group of students is helping to paint the basketball court at their neighborhood recreation center. They need to find the area of the court in order to buy enough paint. They measured the court and found the length to be 80 feet and the width to be 50 feet. 1. What is the area of the court? Explain your answer using words, numbers, and/or pictures. 2. They need to tape the outer edges before painting. They need to find the perimeter so they will know how much tape they need. How much tape will they need? Explain your answer using words and/or numbers. BE SURE TO LABEL YOUR RESPONSES 1 AND 2. 2004 – /8 SOLUTION AND SCORING Part 1: (2 points possible) 1 point for correct answer of 4,000 (with or without square feet), AND 1 point for correct and complete procedure for finding area shown and/or explained. ● Give credit for the following explanations or equivalent: Area is found by multiplying the length by the width. The length is 80 feet and the width is 50 feet. Therefore, the area is 4,000 (square feet), or A = 80 x 50 = 4,000 (square feet), or Correct procedure (l x w = A) to find area is used, but answer is incorrect due to a calculation or copy error. Note: Do not give credit for copying the formula l x w = A only. Part 2: (2 points possible) 1 point for correct answer of 260 (with or without feet), AND 1 point for correct and complete procedure for finding perimeter shown and/or explained. ● Give credit for the following explanations or equivalent: Perimeter is found by multiplying the length and the width times two, then adding these two numbers. Two times 80 is 160. Two times 50 is 100; therefore 160 added to 100 is 260 feet, or P = 2l + 2w = 2(80) + 2(50) = 160 + 100 = 260 (feet), or ELKINS ELEMENTARY (NEVIN) MATH RELEASED ITEMS – 4TH GRADE UPDATED 7/2008 104 Diagram correctly labeled on all four sides (l = 80, w = 50), or Correct procedure (l + l + w + w = P) to find perimeter is used, but answer is incorrect due to a calculation or copy error. Note: Do not give credit for copying the formula l + l + w + w = P or 2l + 2w = P only. ELKINS ELEMENTARY (NEVIN) MATH RELEASED ITEMS – 4TH GRADE UPDATED 7/2008 105 M.13.4.11 Use strategies to find the volume (cubic units) of rectangular prisms and cubes 35. Thomas built the structure below. What is its volume? A. 12 cubic units B. 16 cubic units * C. 24 cubic units D. 28 cubic units 2007 – % 2. Jamie built a block structure with a volume of 9 cubic units. Which of the structures below did he build? A. Figure 1 B. Figure 2 * C. Figure 3 D. Figure 4 2006 – % ELKINS ELEMENTARY (NEVIN) MATH RELEASED ITEMS – 4TH GRADE UPDATED 7/2008 106 Use the figure below to answer question 14. 14. The figure above is made with cubes which are 1 cm3. What is its volume? A. 6 cm3 B. 12 cm3 * C. 18 cm3 D. 21 cm3 2004 – % 32. Mrs. O’Keefe’s kindergarten students made structures with sugar cubes. The volume of each sugar cube is l cubic inch. Who made the structure with the greatest volume? * A. Amy B. Brent C. Chris D. David 2003 – % ELKINS ELEMENTARY (NEVIN) MATH RELEASED ITEMS – 4TH GRADE UPDATED 7/2008 107 DAP.14.4.1 Create a data collection plan after being given a topic and collect, organize, display, describe and interpret simple data using frequency tables or line plots, pictographs and bar graphs 3. The frequency table below shows how students in Ms. Wheeler’s class voted to name their class pet. How many more students voted for Spike than for Fuzzy and Squirmy combined? A. 1 * B. 3 C. 4 D. 7 2007 – % AR4M05D1401Y142-142B ELKINS ELEMENTARY (NEVIN) MATH RELEASED ITEMS – 4TH GRADE UPDATED 7/2008 108 14. Ms. Judge’s class recorded the daily high temperatures from January 8 through January 12 and made the bar graph below. What was the difference in the high for January 9 and the high for January 10? A. 10°F * B. 15°F C. 35°F D. 50°F 2007 – % ELKINS ELEMENTARY (NEVIN) MATH RELEASED ITEMS – 4TH GRADE UPDATED 7/2008 109 8. Based on the data collection below, how many more fourth-grade students preferred chocolate chip than preferred vanilla? A. 4 B. 5 * C. 19 D. 27 2006 – % 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 2006 – % ELKINS ELEMENTARY (NEVIN) MATH RELEASED ITEMS – 4TH GRADE UPDATED 7/2008 110 Use the chart below to answer question 40. Books Read by Fourth-Graders at Burton Elementary Mrs. Brown’s Class Mrs. Connor’s Class Mr. Sharp’s Class Ms. Jarrell’s Class Key: = 25 books 40. Molly made the pictograph above to show how many books were read by all of the fourth-grade students at Burton Elementary. Students in Ms. Jarrell’s class read a total of 250 books. How many books should Molly display in the row representing Ms. Jarrell’s class? * A. 10 B. 25 C. 250 D. 275 2004 – % ELKINS ELEMENTARY (NEVIN) MATH RELEASED ITEMS – 4TH GRADE UPDATED 7/2008 111 DAP.15.4.1 Represent and interpret data using pictographs, bar graphs and line graphs in which symbols or intervals are greater than one 2. The pictograph below represents the number of pies each fourth-grade teacher made for the bake sale. How many pies did Mrs. McLain make for the bake sale? 1 A. 2 2 1 B. 3 2 * C. 7 D. 12 2007 – % 32. The pictograph below shows the number of books read by each of the fourth- grade classes during a reading contest. How many more books did Mr. Haywood’s class read than did Ms. Kirby’s? A. 10 * B. 25 C. 35 D. 60 2007 – % ELKINS ELEMENTARY (NEVIN) MATH RELEASED ITEMS – 4TH GRADE UPDATED 7/2008 112 C. Taylor walks dogs on the weekends to earn money. The graph below shows the number of times Taylor has walked dogs over the last 6 weekends. 1. How many more times did Taylor walk dogs during the last 3 weekends than during the first 3 weekends? Explain your answer using words and/or numbers. 2. Taylor charges the dog owners $2.00 per walk. How much money did Taylor earn over the 6 weekends? Explain your answer using words and/or numbers. BE SURE TO LABEL YOUR RESPONSES 1 AND 2. 2007 – /8 SOLUTION AND SCORING PART 1 2 points possible 1 point: Correct answer: 15 (more walks). AND 1 point: Correct and complete procedure shown and/or explained. The student finds 2 totals (work shown or explained) and the difference. Work may contain a calculation or copy error. Give credit for the following or equivalent: • 16 + 4 + 10 = 30, 20 + 10 + 15 = 45 (some grouping is acceptable), 45 – 30 = #, or • “I added the # of walks from the 1st 3 weeks and got 30. I added the # of walks from the last 3 weeks and got 45. Next, I found the difference to get my answer.” OR ½ point: Incomplete, but correct, procedure shown and/or explained. Give credit for the following or equivalent: • 1st 3 weeks: 30, Last 3 weeks: 45, 45-30 = #, or • 1 total correct, 1 total incorrect (no work shown), and correct difference found. ELKINS ELEMENTARY (NEVIN) MATH RELEASED ITEMS – 4TH GRADE UPDATED 7/2008 113 PART 2 1 point: Correct answer: ($) 150.00, or correct answer based on incorrect amount(s) in Part 1. AND 1 point: Correct and complete procedure shown and/or explained. Work may contain a calculation or copy error or may be based on an incorrect amount in Part 1. Give credit for the following or equivalent: Note: Work done in Part 1 does not have to be repeated. • 30 + 45 = 75, 75 x 2 = 150 • 2 × 16 + 2 × 4 + 2 × 10 + 2 × 20 + 2 × 10 + 2 × 15 = # • “There were 30 walks in the 1st 3 weeks and 45 in the last 3 weeks. I added those together and multiplied the sum by 2 to get my answer.” • (T for 1st 3 weeks from Part 1) x 2 + (T for last 3 weeks from Part 1) x 2 = #. OR ½ point: Incomplete, but correct, procedure shown and/or explained. Give credit for the following or equivalent: • 32 + 8 + 20 + 40 + 20 + 30 = # (×2 not shown or explained), or • 30 + 45 = 75, $150.00 made (×2 not shown or explained). Note: Do not give any credit for 30 + 45 = 75 only. 21. Jim and his friends made the table below to show how many seashells they have in their collections. How many seashells do they have in all? 1 A. 13 2 B. 14 1 C. 52 2 * D. 54 2006 – % ELKINS ELEMENTARY (NEVIN) MATH RELEASED ITEMS – 4TH GRADE UPDATED 7/2008 114 E. Joseph made the pictogram below to show the number of hits he had in his last four baseball games. 1. How many hits did Joseph have in Game 2? Explain your answer using words and/or numbers. 2. How many more hits did Joseph have in Game 4 than in Game 3? Explain your answer using words and/or numbers. BE SURE TO LABEL YOUR RESPONSES 1 AND 2. 2006 – /8 SOLUTION AND SCORING PART 1 2 points possible 1 point: Correct answer: 8 (hits). Note: Do not give credit if incorrect procedure is evident. AND 1 point: Correct and complete procedure shown and/or explained. Work may contain a calculation error. Give credit for the following or equivalent: • 4 x 2 = # of hits or • “I multiplied 4 and 2.” or • 2 + 2 + 2 + 2 = # of hits or • 4 + 4 = # of hits or • “I skip counted by 2 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.” PART 2 ELKINS ELEMENTARY (NEVIN) MATH RELEASED ITEMS – 4TH GRADE UPDATED 7/2008 115 2 points possible 1 point: Correct answer: 6 (more hits). Note: Do not give credit if incorrect procedure is evident. Ex: 10 – 4 = 6 AND 1 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) + 1 = 9 Game 3: 2 + 1 = 3 9 – 3 = 6 • “He has 9 hits in game 4 and 3 hits in game 3 so minused 3 from 9.” or • 9 – 3 = # or • 4½ – 1½ = 3 baseballs, 3 x 2 = # or • “I subtracted 3 from 9.” or “I subtracted 9 and 3.” Note: Do not give credit for incomplete procedure: Ex: “He had 9 hits in Game 4 and 3 hits in game 3.” and stops. Note: Do not give credit for vague procedure or procedure stated incorrectly: Ex: “I subtracted 3 and 9.” (order implies 9 is subtracted from 3) Ex: “I subtracted 9 from 3.” (incorrectly stated) Use the chart below to answer question 7. 7. Mr. Kimble asked his students to choose their favorite sport. How many students did not choose soccer? A. 4 B. 7 * C. 11 D. 18 2005 – % ELKINS ELEMENTARY (NEVIN) MATH RELEASED ITEMS – 4TH GRADE UPDATED 7/2008 116 Use the pictograph below to answer question 25. 25. Karen and her friends picked 16 baskets of strawberries. Based on the pictograph above, how many baskets did Amanda pick? A. 1 * B. 4 C. 6 D. 12 2005 – % Use the pictograph below to answer question 37. 37. Based on the data in the pictograph above, which of the following statements is true? A. More people visited in June than in July. B. More people visited in September than in August. C. More people visited in September and October combined than in the other three months combined. * D. More people visited in June and July combined than in the other three months combined. 2005 – % ELKINS ELEMENTARY (NEVIN) MATH RELEASED ITEMS – 4TH GRADE UPDATED 7/2008 117 3. The school librarian made a graph showing the number of books checked out each month by students in the fourth grade. In April, there were 45 books checked out. How many books should be displayed in the graph? A. 05 B. 06 * C. 09 D. 45 2004 – % Use the chart below to answer question 25. The Population of Pulaski County, Arkansas 1960–2000 Year Population 1960 242,980 1970 289,189 1980 340,613 1990 349,660 2000 361,474 AR4M02D102Y061-061B 25. According to the table above, which of the following is a true statement about the population of Pulaski County, Arkansas? A. It has remained the same. * B. It has increased every ten years. C. It has increased every five years. D. It has decreased every ten years. 2004 – % ELKINS ELEMENTARY (NEVIN) MATH RELEASED ITEMS – 4TH GRADE UPDATED 7/2008 118 Use the table below to answer question 33. AR4M02D102Y100-100B 33. Alicia took a survey of the fourth-graders in her class to find out which of the four snacks above they liked best. Which of the following statements is true about the data Alicia collected? A. No fourth-graders liked yogurt. * B. More fourth-graders like cheese and crackers than chips. C. Fourth-graders like chips better than yogurt. D. More fourth-graders prefer yogurt to fruit. 2004 – % 23. Ramiro made a graph showing the number of crickets the class pet turtle ate in a five-day period. How many crickets did it eat in 5 days? * A. 20 B. 40 C. 60 D. 80 2003 – % ELKINS ELEMENTARY (NEVIN) MATH RELEASED ITEMS – 4TH GRADE UPDATED 7/2008 119 Use the figure below to answer question 38. 38. Raul has a game that uses the spinner shown above. What is the probability that a player will spin and land on “RETURN 2 START”? 1 * A. 8 2 B. 8 3 C. 8 7 D. 8 2003 – % 40. Steve and Michael were playing a number game. They turned the 15 cards shown below face down. If Michael chooses one card, what is the probability that he will choose a card with an even number on it? * A. 9 out of 15 B. 1 out of 9 C. 1 out of 15 D. 6 out of 9 2003 – % ELKINS ELEMENTARY (NEVIN) MATH RELEASED ITEMS – 4TH GRADE UPDATED 7/2008 120 B. The chart above shows a record of how much paper was used in one week by five students in Mrs. Drew’s class. 1. How many more sheets of paper did Aaron use than Kayla? Explain your reasoning using wordsand/or numbers. 2. Compare the amount of paper used on Friday to the amount used on Monday. Explain your answer using words and/or numbers. BE SURE TO LABEL YOUR RESPONSES 1 AND 2. 2003 – /8 SOLUTION Part 1: 8 more sheets. Work/Explanation: 26 – 18 = 8. OR Aaron: 26 sheets and Kayla: 18 sheets. The difference is 8. Part 2: More paper was used on Friday. OR Less was used on Monday. OR Symbolic representation of comparison: 32 > 15. Work/Explanation: Friday: 32, Monday: 15. OR 32 – 15 = 17, etc. Scoring (4 total points possible) Part 1: (2 points possible) • 1 point for correct answer of 8. Work/Explanation: • 1 point for correct procedure used: Student finds Aaron’s number – Kayla’s number. (Note: Work might have calculation, counting, or copy error.) Part 2: (2 points possible) • 1 point for correct answer using either of the following: “Friday uses more…”, or Symbolic comparison (F# > M#). (Note: Work might have a calculation, counting, or copy error.) Work/Explanation: ELKINS ELEMENTARY (NEVIN) MATH RELEASED ITEMS – 4TH GRADE UPDATED 7/2008 121 • 1 point for correct work using either of the following: Association of days and numbers: Friday – 32 and Monday – 15, or Subtraction (32 – 15 = 17) without “Friday, Monday” labels. ELKINS ELEMENTARY (NEVIN) MATH RELEASED ITEMS – 4TH GRADE UPDATED 7/2008 122 DAP.15.4.2 Match a set of data with a graphical representation of the data ELKINS ELEMENTARY (NEVIN) MATH RELEASED ITEMS – 4TH GRADE UPDATED 7/2008 123 DAP.16.4.1 Make predictions for a given set of data 5. Barry recorded the temperature over a four-hour period one day in May. If the temperature pattern continues, what will the temperature most likely be at 4:00 P.M.? A 60°F B 65°F * C 75°F D 90°F 2008 - ELKINS ELEMENTARY (NEVIN) MATH RELEASED ITEMS – 4TH GRADE UPDATED 7/2008 124 DAP.17.4.1 Use fractions to predict probability of an event Ex. There are 5 blue tiles, 3 red tiles, and 2 green tiles What is the probability of pulling out a green tile? 6. What is the probability of spinning a number less than 4 on the spinner below? 3 * A. 8 4 B. 8 8 C. 4 8 D. 3 2007 – % AR4M05D1701NXXX-125B 17. Lea has 12 crayons in a bag: 3 green, 5 blue, 2 yellow, 1 black, and 1 brown. What is the probability that Lea will pull out a yellow crayon if she pulls out one crayon without looking? 1 A. 12 2 * B. 12 2 C. 10 1 D. 2 2007 – % AR4M05D1701NXXX-132A ELKINS ELEMENTARY (NEVIN) MATH RELEASED ITEMS – 4TH GRADE UPDATED 7/2008 125 23. At the school carnival, Sue played the “Pop-a-Balloon” game. Inside each of 8 inflated balloons was a slip of paper with the name of a prize written on it. The name of the prize and the number of balloons containing that prize is shown in the table below. Prize Number of Balloons Cupcake 2 Brownie 3 Ice cream 1 Snow cone 2 What is the probability that Sue will win a brownie? 3 * A. 8 3 B. 5 5 C. 8 8 D. 3 2007 – % 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? Jelly beans in the Bag Color Number Black 16 Orange 17 Pink 24 Purple 12 Red 14 Yellow 24 white 17 16 A. 124 12 B. 124 24 * C. 124 124 D. 24 2006 – % ELKINS ELEMENTARY (NEVIN) MATH RELEASED ITEMS – 4TH GRADE UPDATED 7/2008 126 20. Karen’s crayon box contains 3 shades of green, 6 shades of blue, 4 shades of red, and 2 shades of brown. If she picks a crayon from the box without looking, which shade is she least likely to pick? A. red B. blue C. green * D. brown 2005 – % 9. Cliff brought cupcakes to share with his classmates. He brought 12 chocolate and 13 vanilla. What are Jane’s chances of getting a chocolate cupcake? A. 01 out of 25 B. 01 out of 12 * C. 12 out of 25 D. 12 out of 13 2004 – % A. Each of the four counselors at Camp Lake View must choose one camper from his/her group to go waterskiing. Each counselor will put the names of all his/her campers in a bag. One name will be drawn from the bag to select the “winner.” Each group consists of the following: ● Lonnie’s group: 10 boys and 8 girls ● Maria’s group: 8 boys and 10 girls ● James’s group: 9 boys and 9 girls ● Tonya’s group: 6 boys and 12 girls 1. Which of the four groups offers the best chance that a boy will win? Explain your answer using words and/or numbers. 2. Which of the four groups offers the best chance that a girl will win? Explain your answer using words and/or numbers. BE SURE TO LABEL YOUR RESPONSES 1 AND 2. 2004 – /8 SOLUTION AND SCORING Part 1: (2 points possible) 1 point for correct answer of Lonnie’s group, AND 1 point for correct and complete work or explanation. ● Give credit for the following explanations or equivalent: “Lonnie’s has more boys than any other group and all groups have the same number of kids (or 18 kids),” or “They are the only group with more boys than girls,” or “They have the greatest number of boys and the fewest number of girls of any group,” or “10/18 are boys,” or “There are 10 chances out of 18.” OR ½ point for correct, but incomplete work or explanation. ELKINS ELEMENTARY (NEVIN) MATH RELEASED ITEMS – 4TH GRADE UPDATED 7/2008 127 ● Example: “Lonnie’s group has the most boys (or more boys) than any group. Note: Do not give credit for the following incomplete explanation. ● “Lonnie’s group has more boys than girls.” (Doesn’t say “only group.”) Part 2: (2 points possible) 1 point for correct answer of Tonya’s group, AND 1 point for correct and complete work or explanation. ● Give credit for the following explanations or equivalent: “Tonya’s has more girls than any other group and all groups have the same number of kids (or 18 kids),” or “They have the greatest number of girls and the fewest number of boys of any group,” or “12/18 are girls,” or “There would be 12 chances out of 18.” OR ½ point for correct, but incomplete work or explanation. ● Example: “Tonya’s group has the most girls (or more girls) than any group.” Note: Do not give credit for the following incomplete explanation. ● “Tonya’s group has more girls than boys.” (So does Maria’s group.) ELKINS ELEMENTARY (NEVIN) MATH RELEASED ITEMS – 4TH GRADE UPDATED 7/2008 128 DAP.17.4.2 Conduct simple probability experiments, record the data and draw conclusions about the likelihood of possible outcome (roll number cubes, pull tiles from a bag, spin spinner, or determine the fairness of the game) AR4M05D1702NXXX-133A 22. Maria rolled a number cube 36 times and recorded the numbers she rolled below. Number Number of Times Rolled 1 3 2 6 3 8 4 10 5 4 6 5 If Maria rolls the cube another time, which number is she most likely to roll? * A. 4 B. 6 C. 10 D. 36 2007 – % 16. Carl has a bag of fruit-flavored candy that contains the following pieces: • 3 grape • 5 strawberry • 1 cherry • 2 watermelon Carl pulls a piece of candy from the bag without looking. What is the probability that he picks a watermelon-flavored piece? A. 1 out of 11 * B. 2 out of 11 C. 3 out of 11 D. 5 out of 11 2006 – % ELKINS ELEMENTARY (NEVIN) MATH RELEASED ITEMS – 4TH GRADE UPDATED 7/2008 129 18. Patty is playing a shape game with the spinner below. What is the probability that the pointer will land on a hexagon on her next spin? A. 1 out of 10 B. 2 out of 10 C. 3 out of 10 * D. 4 out of 10 2006 – % 23. On the cube below, the shapes on the faces not showing are triangles. What are the chances the cube will land on a triangle when rolled? A. 1 out of 3 B. 2 out of 6 * C. 4 out of 6 D. 6 out of 4 2006 – % ELKINS ELEMENTARY (NEVIN) MATH RELEASED ITEMS – 4TH GRADE UPDATED 7/2008 130 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. 2006 - % 19. Melissa is first in line to go on the pony ride at the state fair. There are 2 brown ponies, 4 tan ponies, and 3 black ponies. What is the probability that she will get to ride on a black pony? 2 3 A. * B. 9 9 1 4 C. D. 9 9 2004 – % 1. Which two spinners below would give you an equal chance of spinning a C? A. I and II * B. I and III C. II and III D. III and IV 2003 – % ELKINS ELEMENTARY (NEVIN) MATH RELEASED ITEMS – 4TH GRADE UPDATED 7/2008 131 16. Look at the spinner below. How many times is the spinner likely to land on blue in 24 spins? A. 3 B. 6 * C. 12 D. 24 2003 – % 29. Todd has a collection of pro football team T-shirts. He has 4 Miami Dolphin shirts, 3 Jacksonville Jaguar shirts, and 5 from other teams. If Todd selects a shirt at random, what is the probability that he will pick a Dolphin shirt? 1 A. 12 3 B. 12 4 * C. 12 5 D. 12 2003 – % ELKINS ELEMENTARY (NEVIN) MATH RELEASED ITEMS – 4TH GRADE UPDATED 7/2008 132 DAP.17.4.3 Find all possible combinations of two or three sets of objects 22. Ashley is visiting her grandparents for the weekend. Her mom packed 1 pair of black pants, 1 pair of tan shorts, and 4 shirts: white, blue, green, and yellow. How many different outfits can she make from the clothes her mom packed? A. 2 B. 4 C. 6 * D. 8 2004 – % ELKINS ELEMENTARY (NEVIN) MATH RELEASED ITEMS – 4TH GRADE UPDATED 7/2008 133 NO LONGER TESTED Use the chart below to answer question 15. AR4M03D302NXXX-142B Tom’s Math Test Scores 88 97 75 85 71 75 90 15. What is the mean (average) of Tom’s math test scores? A. 75 * B. 83 C. 85 D. 97 2005 – % Use the picture below to answer question 19. 19. Which weight would be the best choice for Latoya to use to weigh her science book? A. one ton B. one gram C. one ounce * D. one kilogram 2005 – % Use the numbers below to answer question 21. 96 86 93 86 99 AR4M03D302Y119- 119B 21. Jorge’s spelling test grades are shown above. What is the mean (average) of his grades? A. 86 * B. 92 C. 93 ELKINS ELEMENTARY (NEVIN) MATH RELEASED ITEMS – 4TH GRADE UPDATED 7/2008 134 D. 94 2005 – % Use the chart below to answer question 33. Glasses of Milk Per Week Week Number of Glasses 1 18 2 21 3 14 4 20 5 12 33. Joanne kept track of the number of glasses of milk that she drank each week for 5 weeks. What was the average number of glasses that she drank per week? A. 5 B. 7 * C. 17 D. 21 2005 – % Use the chart below to answer question 38. Cookies Made for Class Party Blair 28 Michelle 30 Boyd 42 Travis 25 Jean 34 Holly 45 38. The chart above shows how many cookies Blair and her friends made for the class party. What is the mean (average) number of cookies made by the students? A. 23 B. 25 * C. 34 D. 45 2005 – % How Many States Can You Name in One Minute? Name Number of States Laurie 15 Justin 16 Thomas 18 ELKINS ELEMENTARY (NEVIN) MATH RELEASED ITEMS – 4TH GRADE UPDATED 7/2008 135 Serena 9 Mariah 16 Candace 9 Zachary 9 Isabelle 15 Anthony 13 William 10 A. Mrs. Johnson asked a group of students in her class to name as many states in the United States as they could in one minute. The data collection is shown above. 1. What is the mean (average) number of states the group of students could name? Explain your answer using words and/or numbers. 2. What is the mode of the data? Explain your answer using words and/or numbers. BE SURE TO LABEL YOUR RESPONSES 1 AND 2. 2005 – /8 SOLUTION AND SCORING Part 1: (2 points possible) Answer: 1 point for correct answer of 13. Note: Do not give credit if incorrect procedure is used. AND Work: 1 point for correct and complete procedure for Mean shown or explained. Work may contain a calculation or copy error. ● Give credit for the following explanations or equivalent: 15 + 16 + 18 + 16 + 9 + 9 + 15 + 13 + 10 + 9 = Sum Sum ÷ 10 = Mean, or “The average is found by adding all the numbers together (130) and then dividing by the number of pieces of data (10).” Part 2: (2 points possible) Answer: 1 point for correct answer of 9. Note: Do not give credit if incorrect procedure is used. ● Example: 18 – 9 = 9 (range is found). AND Work: 1 point for correct and complete procedure for Mode shown or explained. ● Give credit for the following explanations or equivalent: “The mode is the number that occurs most often,” or “There are three 9’s,” or Numbers are listed and the 9’s are identified in some way (circled). ● Give credit for the following only if a Mode of 9 is given: “I counted how many there were of each number.” Note: Do not give credit for vague explanation. ● Example: “I counted.” ELKINS ELEMENTARY (NEVIN) MATH RELEASED ITEMS – 4TH GRADE UPDATED 7/2008 136 10. Mrs. Andrew’s class collected canned food for a local food drive. They wanted to sort the cans before they donated them. Which of the following is not a way they could group the cans? A. size B. weight C. type of food * D. total number of cans 2004 – % 18. A runner can burn 1,280 calories in 60 minutes. Which of the following number sentences would you use to find out how many calories can be burned in 30 minutes of running? A. 1,280 × 30 = * B. 1,280 ÷ 2 = C. 21,380 − 30 = D. 1,280 × 2 = 2004 – % 24. Which of the following has the most lines of symmetry? A. B. C. * D. 2004 – % Use the table below to answer question 30. Lengths of Snakes at City Zoo Black Rat Snake 72" King Snake 48" Worm Snake 11" Scarlet Snake 15" Brown Snake 13" Ring-neck Snake 15" 30. The table above shows the lengths of the snakes at City Zoo. What is the mode of these lengths? A. 6" * B. 15" C. 29" D. 57" 2004 – % ELKINS ELEMENTARY (NEVIN) MATH RELEASED ITEMS – 4TH GRADE UPDATED 7/2008 137 9. Angelo was asked to find the quotient of two numbers. What operation did he need to do? A. add B. subtract C. multiply * D. divide 2003 – % 11. Find the mean (mean = average) for the set of numbers below. 5, 3, 8, 4, 10, 12 A. 04 * B. 07 C. 08 D. 10 2003 – % 22. Which set of figures is congruent? A. * B. C. D. 2003 – % Use the figure below to answer question 28. 28. Juan put the above shapes in a box because they all follow a common rule. What is one common rule that fits all of the shapes in Juan’s box? A. They all have at least 4 sides. B. They all have at least 3 vertices. C. They all have at least one acute angle. * D. They all are symmetrical. 2003 – % ELKINS ELEMENTARY (NEVIN) MATH RELEASED ITEMS – 4TH GRADE UPDATED 7/2008 138 D. Mrs. Lehman drew the design shown on the grid above. 1. How many completely shaded squares are there in the design? How many half-squares are there in the design? 2. What is the total area of the SHADED part of the design? Explain your reasoning for determining the answer using words, numbers, and/or pictures. BE SURE TO LABEL YOUR RESPONSES 1 AND 2. 2003 – /8 SOLUTION Part 1: Correct answer of 9 (shaded squares) and 12 (half-shaded squares). OR Correct answer of 9 (shaded squares) and 24 (half-squares). Part 2: Correct answer of 15 sq. cm. Work/Explanation: 9 + 12/2 = 9 + 6 = 15 sq. cm. OR Equivalent work or explanation. Scoring (4 total points possible) Part 1: (2 points possible) • 1 point for correct answer of 9 shaded squares, AND • 1 point for correct answer of 12 half-shaded squares or 24 half-squares. Part 2: (2 points possible) • 1 point for correct numerical answer based on shaded answers given in Part 1. (Note: Student might refer to 24 half-squares in Part 1 and refer to 12 half-shaded squares, etc., in Part 2.) AND • 1 point for showing or explaining correct and complete procedure for finding total shaded area. (Note: Work might contain a calculation or copy error.) ELKINS ELEMENTARY (NEVIN) MATH RELEASED ITEMS – 4TH GRADE UPDATED 7/2008 139