# Alaska GLE: E&C-2 by Fp05N61

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```									               Grade 8
NAEP Estimation and Computation
Questions

Multiple-     Percent    Question
Expectation Question Aligns           Description of NAEP Question                 Constructed   by         and Page
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
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.

A            B              C*             D                 Omitted           Missing
Row          Row            Row            Row               Row               Row
Pct.         Pct.           Pct.           Pct.              Pct.              Pct.
All students 2            5              91             #                 2                 #

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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.

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.

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

Scoring Guide

Solution:
926
Score & Description
Correct
Correct response

Incorrect #4

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%

Note:

     These results are for public and nonpublic school students.

     Percentages may not add to 100 due to rounding.

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

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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.

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.

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.

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.

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.

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.

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?

- 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%

Note:

   These results are for public and nonpublic school students.

   Percentages may not add to 100 due to rounding.

- 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.

- 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%

Note:

      These results are for public and nonpublic school students.

      Percentages may not add to 100 due to rounding.

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:
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.

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.

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.

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.

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.

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.

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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