VIEWS: 5 PAGES: 28 POSTED ON: 10/4/2012 Public Domain
Grade 8 NAEP Estimation and Computation Questions Multiple- Percent Question Alaska Grade Level Choice or Correct Number Expectation Question Aligns Description of NAEP Question Constructed by and Page To Response Alaska Number Students E&C-2 adding, subtracting, Add two 3-digit numbers MC 93% Q1, P. 2 multiplying or dividing integers or positive rational numbers E&C-2 Identify solution method that uses MC 84% Q2, P. 3 multiplication E&C-2 Given a context, identify a multiple of 6 MC 86% Q3, P. 4 E&C-2 Subtract two-digit number from three-digit CR 89% Q4, P. 5 number E&C-2 Solve a multi-step word problem MC 81% Q5, P. 7 E&C-2 Solve a multi-step money word problem MC 74% Q6, P. 8 E&C-2 Solve a word problem with simple MC 63% Q7, P. 9 fractions E&C-2 Solve problem using multiplication and MC 48% Q8, P. 10 division E&C-2 Determine distance between points from a MC 26% Q9, P. 11 written description E&C-2 Solve a multi-step story problem CR 76% Q10, P. 13 E&C-2 Solve and explain a word problem CR 75% Q11, P. 15 involving remainders E&C-2 Solve a story problem with multiple CR 41% Q12, P. 18 operations E&C-3 using percents and Compare percent reduction CR 24% Q13, P. 21 percentages (e.g., tax, discount) E&C-3 Solve a story problem involving percent MC 38% Q14, P. 24 increase E&C-3 Find the percent of a tip on a restaurant MC 26% Q15, P. 25 bill E&C-4 converting between Convert a written number to decimal form MC 72% Q_16, P. 26 equivalent fractions, decimals, or percents E&C-5 using ratio and proportion Use proportional reasoning to find the MC 41% Q_17, P. 27 distance between two towns along a line E&C-5 Identify equivalent ratio MC 63% Q_18, P. 28 Grade 8 NAEP Estimation and Computation Questions GLE: E&C-2 adding, subtracting, multiplying or dividing integers or positive rational numbers Description: Add two 3-digit numbers Add: 1. 238 + 462 A) 600 B) 690 C) 700 D) 790 Key: C 2003 National Performance Results Score Percentage of Students Correct 91% Incorrect 7% Omitted 2% Note: These results are for public and nonpublic school students. Percentages may not add to 100 due to rounding. Alaska students: 93% Correct A B C* D Omitted Missing Row Row Row Row Row Row Pct. Pct. Pct. Pct. Pct. Pct. All students 2 5 91 # 2 # -2- Grade 8 NAEP Estimation and Computation Questions GLE: E&C-2 adding, subtracting, multiplying or dividing integers or positive rational numbers Description: Identify solution method that uses multiplication Carla has 12 boxes that each weigh the same amount. What would be a quick way for her to find the 2. total weight of the 12 boxes? A) Add 12 to the weight of one of the boxes. B) Subtract 12 from the weight of one of the boxes. C) Divide the weight of one of the boxes by 12. D) Multiply the weight of one of the boxes by 12. KEY: D 2003 National Performance Results Score Percentage of Students Correct 81% Incorrect 18% Omitted 1% Note: These results are for public and nonpublic school students. Percentages may not add to 100 due to rounding. Alaska Students: 84% Correct A B C D* Omitted Missing Row Row Row Row Row Row Pct. Pct. Pct. Pct. Pct. Pct. All students 6 2 10 81 1 # -3- Grade 8 NAEP Estimation and Computation Questions GLE: E&C-2 adding, subtracting, multiplying or dividing integers or positive rational numbers Description: Given a context, identify a multiple of 6 Six students bought exactly enough pens to share equally among themselves. Which of the following 3. could be the number of pens they bought? A) 46 B) 48 C) 50 D) 52 KEY: B 2003 National Performance Results Score Percentage of Students Correct 83% Incorrect 16% Omitted 1% Note: These results are for public and nonpublic school students. Percentages may not add to 100 due to rounding. Alaska Students: 86% Correct A B* C D Omitted Missing Row Row Row Row Row Row Pct. Pct. Pct. Pct. Pct. Pct. All students 10 83 4 2 1 # -4- Grade 8 NAEP Estimation and Computation Questions GLE: E&C-2 adding, subtracting, multiplying or dividing integers or positive rational numbers Description: Subtract two-digit number from three-digit number 4. Subtract 972 - 46 Answer: _________________________ Scoring Guide Solution: 926 Score & Description Correct Correct response Incorrect #4 1018 (Student added instead of subtracting) Incorrect #3 826 Incorrect #2 934 Incorrect #1 Any incorrect response other than those described in 2, 3, and 4. *The use of more than one incorrect category in this question enabled NAEP to gather data on common student errors. Any response that fell into one of the incorrect categories earned no credit. -5- Grade 8 NAEP Estimation and Computation Questions Question Four: Subtract two-digit number from three-digit number 2005 National Performance Results Score Percentage of Students Incorrect #1 7% Incorrect #2 2% Incorrect #3 3% Incorrect #4 0% Correct 88% Omitted 1% Off task 0% Note: These results are for public and nonpublic school students. Percentages may not add to 100 due to rounding. Alaska Students: 89% Correct Incorrect Incorrect Incorrect Incorrect #1 #2 #3 #4 Correct Omitted Off task Missing Row Row Row Row Row Row Row Row Pct. Pct. Pct. Pct. Pct. Pct. Pct. Pct. All 7 2 3 # 88 1 # # students -6- Grade 8 NAEP Estimation and Computation Questions GLE: E&C-2 adding, subtracting, multiplying or dividing integers or positive rational numbers Description: Solve a multi-step word problem Carl has 3 empty egg cartons and 34 eggs. If each carton holds 12 eggs, how many more eggs are 5. needed to fill all 3 cartons? A) 2 B) 3 C) 4 D) 6 Key: A 2003 National Performance Results Score Percentage of Students Correct 80% Incorrect 19% Omitted 1% Note: These results are for public and nonpublic school students. Percentages may not add to 100 due to rounding. Alaska Students: 81% Correct A* B C D Omitted Missing Row Row Row Row Row Row Pct. Pct. Pct. Pct. Pct. Pct. All students 80 6 6 6 1 # -7- Grade 8 NAEP Estimation and Computation Questions GLE: E&C-2 adding, subtracting, multiplying or dividing integers or positive rational numbers Description: Solve a multi-step money word problem 6. How much change will John get back from $5.00 if he buys 2 notebooks that cost $1.80 each? A) $1.40 B) $2.40 C) $3.20 D) $3.60 KEY: A 2003 National Performance Results Score Percentage of Students Correct 73% Incorrect 26% Omitted 1% Note: These results are for public and nonpublic school students. Percentages may not add to 100 due to rounding. Alaska Students: 74% Correct A* B C D Omitted Missing Row Row Row Row Row Row Pct. Pct. Pct. Pct. Pct. Pct. All students 73 13 6 7 1 # -8- Grade 8 NAEP Estimation and Computation Questions GLE: E&C-2 adding, subtracting, multiplying or dividing integers or positive rational numbers Description: Solve a word problem with simple fractions Jim has 3/4 of a yard of string which he wishes to divide into pieces, each 1/8 of a yard long. How 7. many pieces will he have? A) 3 B) 4 C) 6 D) 8 KEY: C 2003 National Performance Results Score Percentage of Students Correct 55% Incorrect 43% Omitted 2% Note: These results are for public and nonpublic school students. Percentages may not add to 100 due to rounding. Alaska Students: 63% Correct A B C* D Omitted Missing Row Row Row Row Row Row Pct. Pct. Pct. Pct. Pct. Pct. All students 15 21 55 8 2 1 -9- Grade 8 NAEP Estimation and Computation Questions GLE: E&C-2 adding, subtracting, multiplying or dividing integers or positive rational numbers Description: Solve problem using multiplication and division Fifteen boxes each containing 8 radios can be repacked in 10 larger boxes each containing how 8. many radios? A) 8 B) 10 C) 12 D) 80 E) 120 KEY: C 2003 National Performance Results Score Percentage of Students Correct 47% Incorrect 52% Omitted 1% Note: These results are for public and nonpublic school students. Percentages may not add to 100 due to rounding. Alaska Students: 48% Correct A B C* D E Omitted Missing Row Row Row Row Row Row Row Pct. Pct. Pct. Pct. Pct. Pct. Pct. All 8 7 47 19 18 1 1 students - 10 - Grade 8 NAEP Estimation and Computation Questions GLE: E&C-2 adding, subtracting, multiplying or dividing integers or positive rational numbers Description: Determine distance between points from a written description 9. The map above gives the distances, in miles, between various locations in a state park. Traveling the shortest possible total distance along the paths shown on the map, from the visitor center Teresa visits the cave, waterfall, and monument, but not necessarily in that order, and then returns to the visitor center. If she does not retrace her steps along any path and the total distance that Teresa travels is 14.7 miles, what is the distance between the cave and the monument? A) 2.2 miles B) 2.5 miles C) 2.7 miles D) 3.0 miles E) 3.2 miles - 11 - Grade 8 NAEP Estimation and Computation Questions Question Nine: Determine distance between points from a written description KEY: E 2005 National Performance Results Score Percentage of Students Correct 22% Incorrect 75% Omitted 2% Note: These results are for public and nonpublic school students. Percentages may not add to 100 due to rounding. Alaska Students: 26% Correct A B C D E* Omitted Missing Row Row Row Row Row Row Row Pct. Pct. Pct. Pct. Pct. Pct. Pct. All 12 20 27 17 22 2 4 students - 12 - Grade 8 NAEP Estimation and Computation Questions GLE: E&C-2 adding, subtracting, multiplying or dividing integers or positive rational numbers Description: Solve a multi-step story problem A club needs to sell 625 tickets. If it has already sold 184 tickets to adults and 80 tickets to 10. children, how many more does it need to sell? Answer: _________________________ - 13 - Grade 8 NAEP Estimation and Computation Questions Question Ten: Determine distance between points from a written description Scoring Guide Solution: 361 Score & Description Correct Correct response Incorrect #4 104 or 441 or 545 Incorrect #3 889 Incorrect #2 264 ( 184 + 80 ) Incorrect #1 Any incorrect response other than those described in 2, 3, and 4. *The use of more than one incorrect category in this question enabled NAEP to gather data on common student errors. Any response that fell into one of the incorrect categories earned no credit. 2005 National Performance Results Score Percentage of Students Incorrect #1 17% Incorrect #2 2% Incorrect #3 0% Incorrect #4 3% Correct 77% Omitted 1% Off task 0% Note: These results are for public and nonpublic school students. Percentages may not add to 100 due to rounding. Alaska Students: 76 % Correct - 14 - Grade 8 NAEP Estimation and Computation Questions GLE: E&C-2 adding, subtracting, multiplying or dividing integers or positive rational numbers Description: Solve and explain a word problem involving remainders A high school orders 11 buses to transport 418 students. If each bus can seat 35 students, will the 11. number of buses ordered be enough to provide a seat for each student? ()Yes ()No Show all of your work or explain your thinking even if you use mental math. - 15 - Grade 8 NAEP Estimation and Computation Questions Question Eleven: Solve and explain a word problem involving remainders Scoring Guide Solution: 418 ÷ 11 = 38 per bus which is 3 more students than 35, or 3 more students would have to fit in each bus OR is 3 more students than can fit in a bus OR buses (must include .9) OR 11 × 35 is less than 418 Score & Description Correct Correct response Note: Explanation must indicate that 11 buses will only seat 385 students. This may also be illustrated by an example such as 11 × 35 = 385 OR 418 ÷ 35 = 11 with a remainder of 33 OR needs 33 more seats Incorrect Any incorrect or incomplete response An incorrect response includes an incorrect computation In this question the student needed to apply multiplication or division to solve a word problem, and then interpret the answer in the context of the question. To earn full credit the student needed to explain either that there were not enough seats on 11 buses for 418 students or that 418 students would require more than 11 buses. - 16 - Grade 8 NAEP Estimation and Computation Questions Question Eleven: Solve and explain a word problem involving remainders 2003 National Performance Results Score Percentage of Students Incorrect 19% Correct 77% Omitted 4% Note: These results are for public and nonpublic school students. Percentages may not add to 100 due to rounding. Alaska Students: 75% Correct - 17 - Grade 8 NAEP Estimation and Computation Questions GLE: E&C-2 adding, subtracting, multiplying or dividing integers or positive rational numbers Description: Solve a story problem with multiple operations Raynold had 31 baseball cards. He gave the cards to his friends. Six of his friends received 3 12. cards each. Seven of his friends received 1 card each. The rest received 2 cards each. How many of his friends received exactly 2 cards from Raynold? - 18 - Grade 8 NAEP Estimation and Computation Questions Question Twelve: Solve a story problem with multiple operations Show all of your work or explain your thinking even if you use mental math. Scoring Guide Solution: 6 x 3 cards = 18 cards 7 x 1 card = 7 cards This totals 25 cards. 31 - 25 = 6 cards left. Dividing 6 by 2 yields 3. So 3 friends receive exactly 2 cards each. NOTE: Response should contain evidence that student found a total, subtracted, and divided. One or more of these may be implied but not stated explicitly by the presence of the numbers 18, 7, 25, and 31. Score & Description Correct Correct response (includes: Subtract 25 from 31 you get 6. Then end up with 3.) Partial Correct number (3) with no work or insufficient work OR Correct process with a computational error (includes dividing by 2 at end) OR Process leading to a response of “6 friends” (i.e., forgets to divide 6 that results from 31 - 25 by 2). The “6” must be present with correct supporting work (and only division by 2 omitted) Incorrect Incorrect response (this includes responses such as those with a computational error and failure to divide by 2 as the last step.) - 19 - Grade 8 NAEP Estimation and Computation Questions Question Twelve: Solve a story problem with multiple operations 2005 National Performance Results Score Percentage of Students Incorrect 29% Partial 20% Correct 49% Omitted 0% Off task 1% Note: These results are for public and nonpublic school students. Percentages may not add to 100 due to rounding. Alaska Students: 41% Correct Incorrect Partial Correct Omitted Off task Missing Row Row Row Row Row Row Pct. Pct. Pct. Pct. Pct. Pct. All students 29 20 49 # 1 8 - 20 - Grade 8 NAEP Estimation and Computation Questions GLE: E&C-3 using percents and percentages (e.g., tax, discount) Description: Compare percent reduction One store, Price Pleasers, reduces the price each week of a $100 stereo by 10 percent of the 13. original price. Another store, Bargains Plus, reduces the price each week of the same $100 stereo by 10 percent of the previous week's price. After 2 weeks, how will the prices at the two stores compare? The price will be cheaper at Price Pleasers. The price will be the same at both stores. The price will be cheaper at Bargains Plus. Show all of your work or explain your thinking even if you use mental math. - 21 - Grade 8 NAEP Estimation and Computation Questions Question Thirteen: Compare percent reduction Scoring Guide Solution: A. Cheaper at Price Pleasers At Price Pleasers the stereo would be $80 after 2 weeks. At Bargain Plus, it would cost $81. OR Successive 10% reductions of the original price will yield greater savings than successive reductions of 10% of the reduced price. Score & Description Correct Correct response—cheaper at Price Pleasers with an explanation that compares price at each store after 2 weeks ($80 vs. $81) OR Cheaper at Price Pleasers with an explanation that generalizes as described in solution above NOTE: Score CORRECT if incorrect answer is B or C with a clear statement that Price Pleasers is cheaper and explanation is correct and complete. Partial Cheaper at Price Pleasers with anything less than a complete explanation OR Computes the correct amount for at least 2 weeks for either Price Pleasers or Bargain Plus, but conclusion is missing, incomplete, or incorrect (if the store is not identified the score is still a 2) Incorrect Incorrect response In this question the student was asked to compare the sale price of a stereo, after 3 weeks, based on two different ways for reducing the price. In one store, the price was reduced each week by a fixed amount (10% of $100, or $10). In the other store the price was reduced each week by a varying amount (10% of the current price, which is less each week). To earn full credit, the student needed to indicate that the price would be less at the first store after 3 weeks and explain how the solution was obtained. Students were permitted to use a calculator. - 22 - Grade 8 NAEP Estimation and Computation Questions Question Thirteen: Compare percent reduction 2003 National Performance Results Score Percentage of Students Correct 25% Incorrect 72% Omitted 4% Note: These results are for public and nonpublic school students. Percentages may not add to 100 due to rounding. Alaska Students: 24% Correct A* B C Omitted Missing Row Row Row Row Row Pct. Pct. Pct. Pct. Pct. All students 25 25 47 4 # - 23 - Grade 8 NAEP Estimation and Computation Questions GLE: E&C-3 using percents and percentages (e.g., tax, discount) Description: Solve a story problem involving percent increase 14. There were 90 employees in a company last year. This year the number of employees increased by 10 percent. How many employees are in the company this year? A) 9 B) 81 C) 91 D) 99 E) 100 KEY: D 2005 National Performance Results Score Percentage of Students Correct 37% Incorrect 62% Omitted 1% Note: These results are for public and nonpublic school students. Percentages may not add to 100 due to rounding. Alaska Students: 38% Correct A B C D* E Omitted Missing Row Row Row Row Row Row Row Pct. Pct. Pct. Pct. Pct. Pct. Pct. All 9 5 6 37 42 1 7 students - 24 - Grade 8 NAEP Estimation and Computation Questions GLE: E&C-3 using percents and percentages (e.g., tax, discount) Description: Find the percent of a tip on a restaurant bill Ms. Thierry and 3 friends ate dinner at a restaurant. The bill was $67. In addition, they left a $13 tip. 15. Approximately what percent of the total bill did they leave as a tip? A) 10% B) 13% C) 15% D) 20% E) 25% KEY: D 2005 National Performance Results Score Percentage of Students Correct 30% Incorrect 68% Omitted 2% Note: These results are for public and nonpublic school students. Percentages may not add to 100 due to rounding. Alaska Students: 26% Correct A B C D* E Omitted Missing Row Row Row Row Row Row Row Pct. Pct. Pct. Pct. Pct. Pct. Pct. All 18 19 25 30 6 2 students - 25 - Grade 8 NAEP Estimation and Computation Questions GLE: E&C-4 converting between equivalent fractions, decimals, or percents Description: Convert a written number to decimal form 16. What is 4 hundredths written in decimal notation? A) 0.004 B) 0.04 C) 0.400 D) 4.00 E) 400.0 KEY: B 2005 National Performance Results Score Percentage of Students Correct 67% Incorrect 32% Omitted 1% Note: These results are for public and nonpublic school students. Percentages may not add to 100 due to rounding. Alaska Students: 72% Correct A B* C D E Omitted Missing Row Row Row Row Row Row Row Pct. Pct. Pct. Pct. Pct. Pct. Pct. All 14 67 9 3 6 1 # students - 26 - Grade 8 NAEP Estimation and Computation Questions GLE: E&C-5 using ratio and proportion Description: Use proportional reasoning to find the distance between two towns along a line On the road shown above, the distance from Bay City to Exton is 60 miles. What is the distance 17. from Bay City to Yardville? A) 45 miles B) 75 miles C) 90 miles D) 105 miles KEY: D 2003 National Performance Results Score Percentage of Students Correct 39% Incorrect 61% Omitted 1% Note: These results are for public and nonpublic school students. Percentages may not add to 100 due to rounding. Alaska Students: 41% Correct A B C D* Row Row Row Row Pct. Pct. Pct. Pct. All students 26 8 26 39 - 27 - Grade 8 NAEP Estimation and Computation Questions GLE: E&C-5 using ratio and proportion Description: Identify equivalent ratio 18. Which of the following ratios is equivalent to the ratio of 6 to 4? A) 12 to 18 B) 12 to 8 C) 8 to 6 D) 4 to 6 E) 2 to 3 KEY: B 2003 National Performance Results Score Percentage of Students Correct 60% Incorrect 39% Omitted 1% Note: These results are for public and nonpublic school students. Percentages may not add to 100 due to rounding. Alaska Students: 63% Correct A B* C D E Omitted Missing Row Row Row Row Row Row Row Pct. Pct. Pct. Pct. Pct. Pct. Pct. All 3 60 11 19 7 1 1 students - 28 -