Alaska GLE: E&C-2 by Fp05N61

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									               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 -

								
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