2008 MCAS Math Grade 4 Released Items Document by ulz11512

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									X. Mathematics, Grade 4
                           Grade 4 Mathematics Test
The spring 2008 grade 4 MCAS Mathematics test was based on learning standards in the Massachusetts
Mathematics Curriculum Framework (2000). The Framework identifies five major content strands,
listed below. Page numbers for the grades 3–4 learning standards appear in parentheses.

    ■ Number Sense and Operations (Framework, pages 22–23)

    ■ Patterns, Relations, and Algebra (Framework, page 32)

    ■ Geometry (Framework, page 40)

    ■ Measurement (Framework, page 48)

    ■ Data Analysis, Statistics, and Probability (Framework, page 56)

The Mathematics Curriculum Framework is available on the Department Web site at
www.doe.mass.edu/frameworks/current.html.

In Test Item Analysis Reports and on the Subject Area Subscore pages of the MCAS School Reports and
District Reports, Mathematics test results are reported under five MCAS reporting categories, which are
identical to the five Framework content strands listed above.

Test Sessions
The MCAS grade 4 Mathematics test included two separate test sessions. Each session included multiple-
choice, short-answer, and open-response questions.

Reference Materials and Tools
Each student taking the grade 4 Mathematics test was provided with a plastic ruler and a grade 4
Mathematics Tool Kit. A copy of the tool kit follows the final question in this chapter. An image of the
ruler is not reproduced in this publication.

The use of bilingual word-to-word dictionaries was allowed for current and former limited English
proficient students only, during both Mathematics test sessions. No calculators, other reference tools, or
materials were allowed.

Cross-Reference Information
The table at the conclusion of this chapter indicates each item’s reporting category and the Framework
learning standard it assesses. The correct answers for multiple-choice and short-answer questions are also
displayed in the table.




                                                   260
                                                     Mathematics
                                                             SeSSion 1
                                You may use your tool kit and MCAS ruler during this session.
                                     You may not use a calculator during this session.

DIRECTIONS
This session contains twelve multiple-choice questions, two short-answer questions, and
three open-response questions. Mark your answers to these questions in the spaces provided in your
Student Answer Booklet.
ID:228590 3221504_AR1.eps, 3221504_ B Common                            ID:227459 EBH239_map.eps A Common

●
   1	      Angelo used the rule “add 4, subtract 2” to
           make a number pattern, as shown below.
                                                                          2	
                                                                        ●          The map below shows Kim’s
                                                                                   neighborhood.

                                                                                        Kim’s Neighborhood
           11         15        13        17        15       19

                  4        –2         4        –2        4
                                                                                                         Elm Drive




                                                                                                                     Pine Road
                                                                                              e
           Which of the following number patterns



                                                                                              u
                                                                                          ven
           uses the same rule?
                                                                                        kA
                                                                                     Oa
           A.                                                                                        Main Street
                  10 14 18 14 12 16

           B.                                                                       M
                  10 14 12 16 14 18                                                   ap
                                                                                         le
                                                                                              La
                                                                                                ne

           C.
                  10 14 10 18 22 20
                                                                                   Which street is parallel to Main Street?
           D.                                                                      A. Elm Drive
                  10 14 16 18 24 26
                                                                                   B. Maple Lane
                                                                                   C. Oak Avenue
                                                                                   D. Pine Road




                                                                  261
Mathematics                                                                                              Session 1
ID:227363 227363_clues.eps C Common                       ID:227464 EBH243_lines_of_symmetry. B Common

●
  3	       Jamal’s clues about his mystery number
           are shown in the box below.
                                                          ●
                                                            5	       Which of the following shapes has
                                                                     more than one line of symmetry?


                                                                     A.
                           My number has

                               5 tens
                               8 thousands
                               2 ones
                               6 ten thousands                       B.
                               0 hundreds


           What is Jamal’s mystery number?
                                                                     C.
           A.     5,826
           B.     6,285
           C. 68,052
           D. 86,520
                                                                     D.


ID:227388 C Common

●
  4	       Mr. Dolan bought 9 boxes of erasers.
           There were 12 erasers in each box.
           How many erasers did Mr. Dolan buy?

           A.     96
           B.     98
           C. 108
           D. 120




                                                    262
Mathematics                                                                                       Session 1
ID:227510 EBH264_school.eps [stem_0 D Common

●
 6         The tally chart below shows the different ways the 24 students in Ms. Mitchell’s class get
           to school.

                                                How We Get to School
                                               Way    Number of Students
                                               car
                                               bus
                                               bike
                                               walk

           Which circle graph best represents the information in the tally chart?


           A. How We Get to School                              C. How We Get to School


                                                                                         car
                          car           bus
                                                                            bus            walk
                         bike          walk
                                                                                         bike



           B. How We Get to School                              D. How We Get to School



                          car                                                car
                                         bus                                               bus
                       walk                                                bike
                                                                                  walk
                              bike




                                                      263
Mathematics                                                                                                 Session 1
                                                                ID:227592 AL4213_Scale.eps A Common
ID:218935 TK0407_map.eps D Common

●
  7	       The grid below shows the locations of
           some places in Jim’s neighborhood.
                                                                ●
                                                                  9	       The scale shown below is balanced. Each

                                                                                  has the same weight, and each
                                      1 block
                                                                           has the same weight.
              8
                      Jim’s                     1 block
              7
                      house
              6
                                    Library
              5
              4
              3
                                    School
              2
                      Park
              1
                                                                           How many               are needed to balance
                  0   1 2 3 4 5 6 7 8
                                                                           five       ?
           Moving along the grid lines, what is the
                                                                           A. 10
           least number of blocks from Jim’s house
           to the school?                                                  B. 11
                                                                           C. 15
           A. 3
                                                                           D. 18
           B. 4
           C. 6
           D. 7



ID:229061 C Common

●
  8	       What is the solution to the following
           problem?
                        162  3  ?

           A. 50 R2
           B. 51 R1
           C. 54
           D. 57




                                                          264
Mathematics                                                                                   Session 1

Question 10 is an open-response question.
            •    BE SURE TO ANSWER AND LABEL ALL PARTS OF THE QUESTION.
            •    Show all your work (diagrams, tables, or computations) in your Student Answer Booklet.
            •    If you do the work in your head, explain in writing how you did the work.
Write your answer to question 10 in the space provided in your Student Answer Booklet.
ID:250869 TK0464_Park.eps, Perimete Common

●
  10	      The grid below represents Ginger’s garden.

                                             Ginger’s Garden




                                                                                 1 foot

                                                                        1 foot

           a. What is the perimeter, in feet, of Ginger’s garden? Show or explain how you got your answer.



                                                   Perimeter is the
                                                   distance around
                                                       a shape.




           b. What is the area, in square feet, of Ginger’s garden? Show or explain how you got your answer.


           Ginger wants to increase the area of her garden so that it is 96 square feet. Her garden will
           still be a rectangle.

           c. What could be the length and width of Ginger’s garden after she increases the area? Show
              or explain how you got your answer.




                                                     265
Mathematics                                                                            Session 1

Questions 11 and 12 are short-answer questions. Write your answers to these questions in the
boxes provided in your Student Answer Booklet. Do not write your answers in this test booklet. You
may do your figuring in the test booklet.
ID:227603 Common

●
  11	     What is the value of  that makes the number sentence below true?
                                                  2    160




ID:247633 Common

●
  12      Write a decimal that is equivalent to the fraction below.

                                1
                                4




                                                    266
Mathematics                                                                                Session 1

Question 13 is an open-response question.
           •   BE SURE TO ANSWER AND LABEL ALL PARTS OF THE QUESTION.
           •   Show all your work (diagrams, tables, or computations) in your Student Answer Booklet.
           •   If you do the work in your head, explain in writing how you did the work.
Write your answer to question 13 in the space provided in your Student Answer Booklet.
ID:250554 Common

●
  13	     The chart below shows the numbers of students at four different schools.

                                                           Number of
                                         School
                                                            Students
                                       Pine Street            517
                                       Apple Lane             675
                                       Sanders                419
                                       East Side              566

          a. Use estimation to decide which school has about 100 fewer students than Apple Lane
             School. Show or explain your estimation strategy.


          All the students at the schools are going to form two teams for a reading contest.
              • There will be two schools on each team.
               • The teams will each have about the same number of students.

          b. Use estimation to decide which two schools should be on each team. Show or explain your
             estimation strategy.




                                                     267
Mathematics                                                                                            Session 1

Mark your answers to multiple-choice questions 14 through 16 in the spaces provided in your
Student Answer Booklet. Do not write your answers in this test booklet. You may do your figuring in
the test booklet.
ID:218881 A Common                                      ID:219003 TK0433_spinners.eps [opt_ A Common

●
  14	      Which number is equivalent to three
           hundredths?
                                                        ●
                                                          16	       On which of the following spinners
                                                                    is the arrow most likely to land on a
                                                                    section labeled B?
           A. 0.03
           B. 0.30                                                  A.
           C. 3.00
                                                                                Y               B
           D. 300

                                                                                B               G

ID:218884 B Common

●
  15	      Ms. Caruso wants to arrange 16 desks
           in rows to form a square.
                                                                    B.
           Which of the following number
           sentences shows how all of the desks                                     G       Y
           can be arranged in rows to form a
           square?                                                            B                  B
           A. 2  8  16                                                            Y       G
           B. 4  4  16
           C. 4  12  16
           D. 8  8  16
                                                                    C.
                                                                                    B       Y
                                                                              G                  B

                                                                              Y                  Y
                                                                                    B       G



                                                                    D.

                                                                               Y                G



                                                                                        B



                                                  268
Mathematics                                                                                  Session 1

Question 17 is an open-response question.
           •   BE SURE TO ANSWER AND LABEL ALL PARTS OF THE QUESTION.
           •   Show all your work (diagrams, tables, or computations) in your Student Answer Booklet.
           •   If you do the work in your head, explain in writing how you did the work.
Write your answer to question 17 in the space provided in your Student Answer Booklet.
ID:250841 Common
Use the two triangles labeled 1 from your tool kit to answer question 17.

●
  17	     For all parts of this question, the triangles should be lying flat on your desk.
               • The triangles must be label side up.
               • The triangles may touch but not overlap.

          a. Put the triangles together so that a side labeled a is next to a side labeled c. What shape
             did you make when you put the two triangles together in this way? Explain how you know.

          b. Put the triangles together so that the sides labeled b are next to each other. What shape did
             you make when you put the two triangles together in this way? Explain how you know.

          c. Make a shape with the two triangles that is different from the shapes you made in
             parts (a) and (b). Only congruent sides may touch, and they must match exactly. In your
             Student Answer Booklet, trace your shape and label the sides of both triangles with the
             correct letters.

          d. What shape did you make in part (c)? Explain how you know.




                                                     269
                                         Mathematics
                                              SeSSion 2
                        You may use your tool kit and MCAS ruler during this session.
                             You may not use a calculator during this session.

DIRECTIONS
This session contains seventeen multiple-choice questions, three short-answer questions, and
two open-response questions. Mark your answers to these questions in the spaces provided in your
Student Answer Booklet.
ID:250435 B Common                                         ID:247703 EBH526_A_B.eps A Common

 
● 18	      There are 22 students in a class. There
           are  students absent today.
                                                             20	
                                                           ●          Figure G, figure H, and a line are
                                                                      shown below.
           Which of the following represents the
           number of students who are in class
           today?

           A. 22  
           B. 22  
           C. 22  
           D. 22  

                                                                                 G                    H
ID:228799 C Common

●
  19	      The population of Keith’s hometown
           is 57,619. What is 57,619 rounded to
           the nearest thousand?
                                                                      Ping believes that figure G and figure H
           A. 55,000                                                  are congruent.
           B. 57,000                                                  Which of the following best describes
           C. 58,000                                                  how Ping could move figure G so that it
           D. 60,000                                                  exactly covers figure H?

                                                                      A. Reflect (flip) figure G over the line.

                                                                      B. Translate (slide) figure G over the line.

                                                                      C. Rotate (turn) figure G 90° clockwise,
                                                                         and translate (slide) it over the line.

                                                                      D. Rotate (turn) figure G 90° clockwise,
                                                                         and then reflect (flip) it over the line.




                                                     270
Mathematics                                                                                 Session 2
ID:247536 EBH488_groups.eps [opt_a0 A Common

●
  21	      Juan used a model to solve the problem below.


                                Bob had 28 strawberries to share equally among 4 friends.

                                How many strawberries did each friend get?

           Which of the following could be Juan’s model?


           A.                                                         C.




           B.                                                         D.




                                                                           XXXX




                                                          271
Mathematics                                                                                     Session 2
ID:273868 EBH479_candy_bars.eps D Common                 ID:247759 EBH544_line.eps C Common

●
  22	      Ken is using the two rectangles shown
           below to compare fractions.
                                                         Use your MCAS ruler to answer question 23.

                                                         ●
                                                           23	      Julie drew the line segment shown below.



                                                                    Keegan drew a line segment that was
                                                                    2 inches longer than Julie’s line segment.
                                                                    Which of the following is closest to the
                                                                    length of Keegan’s line segment?
                                                                          1
                                                                    A.            inch
                                                                          4

                                                                    B. 2 1 inches
                                                                              4

                                                                    C. 4 1 inches
                                                                              4
           Which of the following is true?
                 1       1                                          D. 6 1 inches
           A.    3
                     
                         2
                                                                              4

                 1       3
           B.    3
                     
                         6

                 1       3
           C.    3
                     
                         6
                                                         ID:247586 D Common


                 1       2
                                                         ●
                                                           24	      All the students in Mr. Conner’s class are
                                                                    working in groups. There are 6 groups of
           D.    3
                     
                         6                                          4 students and 1 group of 3 students.
                                                                    What is the total number of students in
                                                                    Mr. Conner’s class?

                                                                    A. 18
                                                                    B. 24
                                                                    C. 26
                                                                    D. 27




                                                   272
Mathematics                                                                                           Session 2
ID:222172 3247438_AR1.eps, 3247438_ C Common                     ID:250317 A Common

●
  25	      Two number sentences are shown below.                 ●
                                                                   26	      Erin recorded the height of a tomato
                                                                            plant each week for four weeks. Which
                                                                            of the following would be best for Erin
                           4
                           4                   9
                                               9                            to use to display the change in the
                                                                            height of the tomato plant?
                                               11
                                               11
                                                                            A. a line graph
                                                                            B. a pictograph
           What values for    and                   make                    C. a circle graph
           both number sentences true?                                      D. a Venn diagram


           A.
                           7              4


           B.
                           6              5


           C.
                           5              6


           D.
                           2              9




                                                           273
Mathematics                                                                                 Session 2

Question 27 is an open-response question.
           •   BE SURE TO ANSWER AND LABEL ALL PARTS OF THE QUESTION.
           •   Show all your work (diagrams, tables, or computations) in your Student Answer Booklet.
           •   If you do the work in your head, explain in writing how you did the work.
Write your answer to question 27 in the space provided in your Student Answer Booklet.
ID:250388 Common

●
  27	     Lee wrote the number sentence shown below to represent the rule for his input-output table.
                                               input     output
                                                ↓    ↓
                                                n3 p


          a. Copy Lee’s table below into your Student Answer Booklet. Use Lee’s number sentence to
             complete the table.

                                                Lee’s Table
                              Input       n      1       2        5   10     12
                              Output      p



          b. Lee’s friend Maya wrote the input-output table below.

                                               Maya’s Table
                              Input       n      5       6        8   12     21
                              Output      p      3       4        6   10     19

               Write a number sentence to represent the rule for Maya’s table. Use n for the input and p
               for the output.


          c. A new input-output table is shown below.

                              Input       n      1       2        5    7
                              Output      p      4            20      28     36

               What are the missing numbers that complete the input-output table? Show or explain how
               you got each of your answers.




                                                       274
Mathematics                                                                                   Session 2

Questions 28, 29, and 30 are short-answer questions. Write your answers to these questions in the
boxes provided in your Student Answer Booklet. Do not write your answers in this test booklet. You
may do your figuring in the test booklet.
ID:219076 TK0465-bags-of-marbles.ep Common

●
  28	      Cassie has three black marbles and four white marbles, as shown below. Each marble is the
           same shape and size.




           Cassie will put all her marbles into a bag. She will pick a marble out of the bag without looking.
           What is the probability that Cassie will pick a black marble? Write your answer as a fraction.




                                                     275
Mathematics                                                                          Session 2

Write your answers to questions 29 and 30 in the boxes provided in your Student Answer Booklet.


ID:219075 TK0461-alan.eps Common

●
  29	      Alan painted his name on a grid, as shown below.




                                              = 1 square unit

           What is the total area, in square units, that Alan painted?




ID:219065 TK0442-number-line.eps Common

●
  30	      Mr. Miller drew the number line shown below.

                                                           P

                                          0                     1        1
                                                                2

           What fraction best represents the location of point P ?




                                                          276
Mathematics                                                                                 Session 2

Question 31 is an open-response question.
           •    BE SURE TO ANSWER AND LABEL ALL PARTS OF THE QUESTION.
           •    Show all your work (diagrams, tables, or computations) in your Student Answer Booklet.
           •    If you do the work in your head, explain in writing how you did the work.
Write your answer to question 31 in the space provided in your Student Answer Booklet.
ID:219127 TK0496_data.eps, TK0469_l Common

●
  31	      On Monday, Ms. Smith asked her students to write the number of hours they spent reading
           over the weekend. Their answers are shown below.


                                                 2       4         6       2

                                                 0       3         2       3

                                                 4       6         4       4

                                                 3       2         8       5

           a. In your Student Answer Booklet, copy the number line below.


                                             0   1   2   3     4   5   6    7     8

                Based on the answers the students wrote, make a line plot using the number line
                you copied. Be sure to label your line plot.


           b. How many of Ms. Smith’s students read 4 or more hours over the weekend? Use your line
              plot to explain how you know.




                                                         277
Mathematics                                                                                     Session 2

Mark your answers to multiple-choice questions 32 through 39 in the spaces provided in your
Student Answer Booklet. Do not write your answers in this test booklet. You may do your figuring in
the test booklet.
ID:218917 TK0395_cds.eps C Common                          ID:247595 C Common

●
  32	      The CDs in the box shown below all
           cost the same amount.
                                                           ●
                                                             34       Mr. Janson bought 47 packs of pencils.
                                                                      There are 22 pencils in each pack.
                                                                      Which of the following has a value that
                                                                      is closest to the number of pencils
                                                                      Mr. Janson bought?

                                                                      A. 40  20
                                                                      B. 40  30
            CDs: 4 for $20.00
                                                                      C. 50  20
                                                                      D. 50  30
           How much does one CD cost?

           A. $4.00
           B. $4.50
           C. $5.00
           D. $5.50



ID:273874 B Common

●
  33	      The Blakes spent $8,762 to paint their
           house. They also spent $987 to repair
           the roof. What was the total amount the
           Blakes spent to paint their house and
           repair the roof?

           A. $7,775
           B. $9,749
           C. $9,750
           D. $18,632




                                                     278
Mathematics                                                                                                              Session 2
ID:250360 SEB_leaf_graph.eps A Common                                               ID:218912 B Common

●
  35	                          The graph below shows how much
                               money Chris earned each day last week
                                                                                    ●
                                                                                      36	      Ms. Martin played a number game with
                                                                                               her class. Every time a student said
                               raking leaves.                                                  a number, Ms. Martin used a rule to
                                                                                               change it to a new number. The table
                                      Money Chris Earned                                       below shows the students’ numbers and
                                        Raking Leaves                                          Ms. Martin’s new numbers.
                          27
                                                                                                             Number Game
                          24
 Money Earned (dollars)




                          21                                                                             Students’       New
                          18
                                                                                                         Numbers       Numbers
                          15                                                                                8              4
                          12                                                                                16             8
                           9                                                                                20            10
                           6                                                                                32            16
                           3
                           0                                                                   Ms. Martin used the same rule each time.
                               Mon. Tue.   Wed.   Thu.   Fri.   Sat.   Sun.                    Which of the following could be
                                                  Day                                          Ms. Martin’s rule?

                               Chris earns $6 per hour for raking                              A. subtract 4
                               leaves. How many hours did he rake                              B. divide by 2
                               leaves on Saturday?
                                                                                               C. subtract 10
                               A.   4 hours                                                    D. divide by 4
                               B.   8 hours
                               C. 12 hours
                               D. 24 hours




                                                                              279
Mathematics                                                                                Session 2
ID:247561 B Common                                    ID:273875 TK0434_hat.eps D Common

●
  37       Which number sentence is not true?         ●
                                                        38	      Marcus will pick a number card from the
                                                                 hat shown below without looking. Each
           A. 7  8  5  15  5                                 number card is the same size and shape.
           B. 7  8  5  15  7
           C. 7  8  5  5  8  7
           D. 7  8  5  8  7  5

                                                                           3 4 2 3 1
                                                                           2 3   1 3
                                                                               2




                                                                 What is the probability that Marcus will
                                                                 pick a card with the number 3 on it?
                                                                      4
                                                                 A.   6

                                                                       6
                                                                 B.   10

                                                                      3
                                                                 C.   6

                                                                       4
                                                                 D.   10




                                                280
Mathematics                                                  Session 2
ID:247623 EBH505_game.eps A Common

●
  39       Pat and Meg wrote their names in some
           of the squares on a grid, as shown below.


                         Pat       Meg   Pat   Pat


                     Meg           Meg   Meg   Pat


                     Meg           Meg


           Which number sentence shows the
           fraction of squares on the grid that have
           Pat’s name or Meg’s name in them?
                 4         6        10
           A.                 
                12        12        12

                 4         6        10
           B.                 
                12        12        24

                4        6         10
           C.                 
                8        6         14

                4        6         10
           D.                 
                2        2          2




                                                       281
Massachusetts Comprehensive Assessment System
        Grade 4 Mathematics Tool Kit




    a       b          a       b
        1                  1

            c                  c




                    282
                                           Grade 4 Mathematics
                                        Spring 2008 Released Items:
                            Reporting Categories, Standards, and Correct Answers*

                                                                                                            Correct Answer
  Item No.     Page No.                            Reporting Category                        Standard
                                                                                                              (MC/SA)*
      1           261         Patterns, Relations, and Algebra                                  4.P.1              B
      2           261         Geometry                                                         4.G.5               A
      3           262         Number Sense and Operations                                      4.N.1               C
      4           262         Number Sense and Operations                                      4.N.11              C
      5           262         Geometry                                                         4.G.8               B
      6           263         Data Analysis, Statistics, and Probability                       4.D.2               D
      7           264         Geometry                                                         4.G.6               D
      8           264         Number Sense and Operations                                      4.N.13              C
      9           264         Patterns, Relations, and Algebra                                  4.P.4              A
     10           265         Measurement                                                      4.M.4
     11           266         Patterns, Relations, and Algebra                                  4.P.3             80
     12           266         Number Sense and Operations                                      4.N.5             0.25
     13           267         Number Sense and Operations                                      4.N.17
     14           268         Number Sense and Operations                                      4.N.6               A
     15           268         Number Sense and Operations                                      4.N.7               B
     16           268         Data Analysis, Statistics, and Probability                       4.D.6               A
     17           269         Geometry                                                         4.G.9
     18           270         Patterns, Relations, and Algebra                                  4.P.2              B
     19           270         Number Sense and Operations                                      4.N.16              C
     20           270         Geometry                                                         4.G.7               A
     21           271         Number Sense and Operations                                      4.N.8               A
     22           272         Number Sense and Operations                                      4.N.4               D
     23           272         Measurement                                                      4.M.5               C
     24           272         Number Sense and Operations                                      4.N.10              D
     25           273         Patterns, Relations, and Algebra                                  4.P.3              C
     26           273         Data Analysis, Statistics, and Probability                       4.D.1               A
     27           274         Patterns, Relations, and Algebra                                  4.P.6
                                                                                                                   3
     28           275         Data Analysis, Statistics, and Probability                       4.D.4
                                                                                                                   7
     29           276         Measurement                                                      4.M.4              32
                                                                                                                   3
     30           276         Number Sense and Operations                                      4.N.3
                                                                                                                   8
     31           277         Data Analysis, Statistics, and Probability                       4.D.3
     32           278         Patterns, Relations, and Algebra                                  4.P.5              C
     33           278         Number Sense and Operations                                      4.N.12              B
     34           278         Number Sense and Operations                                      4.N.17              C
     35           279         Data Analysis, Statistics, and Probability                       4.D.3               A
     36           279         Patterns, Relations, and Algebra                                  4.P.6              B
     37           280         Number Sense and Operations                                      4.N.9               B
     38           280         Data Analysis, Statistics, and Probability                       4.D.4               D
     39           281         Number Sense and Operations                                      4.N.18              A

* Answers are provided here for multiple-choice items and short-answer items only. Sample responses and scoring guidelines for
  open-response items, which are indicated by shaded cells, will be posted to the Department’s Web site later this year.


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