Instructional Materials - rpdp.net 4 CRT 2013.pdf · domains, the types of questions included in these instructional materials allow for the assessment of different levels of cognitive

Nevada

DEPARTMENTOFEDUCATION

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Grade 4MATHEMATICS

Copyright © 2013 by the Nevada Department of Education

InstructionalMaterialsfor THE

CrITErIoNrEfErENCEDTEST

Page iCopyright © 2013 by the Nevada Department of Education

Dear Educators, The following materials, developed as a collaborative effort between the Nevada Department of Education and WestEd, a nonprofit research, development, and service agency, are designed to be used as part of a guided instructional activity to support student performance on items aligned to the Common Core Standards. We have provided p-values (the proportion of students who got the item correct) for the multiple-choice items that were field tested in the 2011-2012 administration. The p-values indicate how students performed on the items. In addition, we are providing the percentage of students selecting each response option. The p-values, combined with the item-level percentages by response option, provide valuable data to the field as to what types of errors students are making. For mathematics, no p-value is reported if that item did not appear on the field test. In mathematics, some field test items have been used as a model to mirror the content being assessed and therefore the p-values are based on the field test version of the item and not the actual item as it appears in these materials. These items are indicated by an asterisk. To further understanding of constructed-response items, scoring guides and annotated student examples have been included. While these materials can provide students with practice in answering assessment items, we believe it is critical that these materials be used to help students understand the elements of the state assessment and guide them in the use of effective strategies that will support their ability to comprehend and take a variety of assessments. If you choose, however, to use these support documents solely as a practice activity, we highly recommend that you go back over each item with students and investigate each response to better understand their knowledge of the assessment. Vocabulary Knowledge The Nevada Department of Education believes that students are not thoroughly being taught the content vocabulary of the Nevada Mathematics Content Standards. For example, equation, expression, coordinate, function, histogram, analyze, and justify are terms used in the assessments at grade-appropriate levels. Students in Nevada, therefore, must have repeated experiences with speaking, listening, reading, and writing the vocabulary of the standards. Students should be able to use the vocabulary of the standards when they are engaged in classroom discussion, read them in assessments, and effectively use the vocabulary in their writing. Types of Questions and Support Documents The mathematics assessment includes two types of questions—multiple-choice questions for all grades (3 – 8 and high school) and constructed-response questions for grades 4 – 8.

JAMES W. GUTHRIE Superintendent of Public Instruction

STATE OF NEVADA TEACHER LICENSURE SOUTHERN NEVADA OFFICE

9890 S. Maryland Parkway Suite 221

Las Vegas, Nevada 89183 RORIE FITZPATRICK Deputy Superintendent

Instructional, Research, and Evaluative Services

(702) 486-6458 Fax: (702) 486-6450

DEBORAH CUNNINGHAM Deputy Superintendent

SATELLITE OFFICE Administrative and

Fiscal Services

DEPARTMENT OF EDUCATION 700 E. Fifth Street

Carson City, Nevada 89701-5096 (775) 687-9217 · Fax: (775) 687-9101

www.doe.nv.gov

ADDRESSES/MAPS http://www.doe.nv.gov

Page iiCopyright © 2013 by the Nevada Department of Education

To help prepare students for constructed-response questions, we have provided you with:

1. the student checklist (included in the student test booklet at grades 4 and 5) 2. the general student rubric (included in the student test booklet at grades 6 – 8) 3. item-specific rubrics 4. annotated student work

With the use of these materials, students can become familiar with the different types of questions used on the state and future assessments. They can learn to use the checklist or rubric to determine if they have answered the constructed-response questions completely. Familiarity with the tools provided as part of the assessment and the vocabulary of the standards can result in less anxiety on the part of students and teachers. (Please note that the student checklist and general rubric can be on the walls of your classroom throughout the school year. As you assign constructed-response questions, students can use these tools as they develop their answers.) Depth of Knowledge (DOK) Levels - In addition to measuring a broad spectrum of mathematics content domains, the types of questions included in these instructional materials allow for the assessment of different levels of cognitive complexity. The Nevada Proficiency Examination Program in mathematics includes items to assess three Depth of Knowledge levels. These DOK levels are based on descriptions developed by Dr. Norman Webb and adapted for Nevada's mathematics assessments. We suggest that you engage students in question writing so they not only can recognize these levels of complexity, but can begin to formulate them as well. The following are the three DOK levels used on Nevada’s mathematics assessments:

DOK Level 1: Recall - Level 1 requires the recall of facts or use of basic skills. A level 1 item consists of literal recall from text, paraphrasing, or simple understanding of a single word or phrase. A level 1 item may require a simple connection between sentences, which may be considered a very basic inference.

DOK Level 2: Use of Concepts and Skills - Level 2 requires comprehension and mental processing of text or portions of text. A level 2 item includes the engagement of some mental processing beyond recalling or reproducing a response. A level 2 item requires the application of skills and concepts. Some important concepts are covered but not in a deeply complex way.

DOK Level 3: Strategic Thinking and Problem Solving - Level 3 requires abstract reasoning, critical thinking, and/or the application of abstract concepts to new situations.

We hope that interaction with these instructional support materials will lead to lowered anxiety and better understanding of the assessment task that is being presented to students. If you have questions about the mathematics materials or how to embed this information into your curriculum, please contact Tracy Gruber at [email protected]. Cindy Sharp Nevada Department of Education

Page 1Copyright © 2013 by the Nevada Department of Education

MathematicsGrade 4

Name:

Did I think about the question (and/or directions) thatI read?

Did I use the words in bold print in the question to giveme information?

Did I show all my work and include each step needed to complete the problem?

If I used a diagram, did I label each part of the diagramclearly?

Did I answer all parts of the question?

4th Grade Written-Response Checklist

Yes No

Yes No

Yes No

Yes No

This booklet contains mathematics questions for you to answer. There are two types of questions in this booklet. For the multiple-choice questions, you will be given four answer choices—A, B, C, and D. You are to choose the correct answer from the four choices. Each question has only one right answer. The written-response question requires you to give a written response to a question as indicated in the booklet. You will be given a separate sheet of paper to answer this question.

You may use the checklist below to help you do a good job when you are answering the written-response question.

Yes No

Grade 4 Mathematics� Instructional Materials

Go OnCopyright © 2013 by the Nevada Department of Education Page 2

■1Which statement represents the equation 2 8 16× = ?

A The number 2 is 8 less than 16 .B The number 8 is 2 times as many as 16 .C The number 16 is 8 more than 2 .D The number 16 is 2 times as many as 8 .

■2There are 282 paper clips in each of 3 boxes. There are 172 paper clips in a bag. Which is the best ESTIMATE of the total number of paper clips in the 3 boxes and the bag?

A between 400 and 600 paper clipsB between 700 and 900 paper clipsC between 1,000 and 1,200 paper clipsD between 1,600 and 1,800 paper clips

■3There are 5 shelves on a wall at a shoe store. There are 8 shoeboxes on each shelf. Each shoebox contains 2 shoes. Which equation can be used to find the total number of shoes (t) in all the shoeboxes on the shelves?

A t = 5 + 8 + 2B t = 5 × 8 + 2C t = 5 × 8 × 2D t = 5 + 8 – 2

■4Lee buys 15 packages of cookies. Each package contains 35 cookies. Lee takes all the cookies and puts an equal number of cookies on each of 6 plates, with some cookies remaining. What is the greatest number of cookies Lee could place on each plate and the number of cookies remaining?

A 86 cookies on each plate, with 9 cookies remaining

B 87 cookies on each plate, with 3 cookies remaining

C 87 cookies on each plate, with 5 cookies remaining

D 88 cookies on each plate, with 3 cookies remaining

■5Which number is a multiple of 8 ?

A 18B 35C 74D 96



■6Dylan makes a pattern that starts with the number 55 . He uses the rule “subtract 5” to make his pattern. Which statement about the numbers in Dylan’s pattern is true?

A Every number in the pattern is divisible by both 2 and 5 .

B Every number in the pattern is divisible by both 5 and 11 .

C Every third number in the pattern is divisible by both 3 and 5 .

D Every third number in the pattern is divisible by both 5 and 9 .

■7Two numbers are shown below.

19,000 1,900

How many times as great is the value of the digit 9 in the number 19,000 as the value of the digit 9 in the number 1,900 ?

A 9 times as greatB 10 times as greatC 19 times as greatD 90 times as great

■8Which expression could be used to find the product of 38 and 24 ?

A 30 20 8 4×( ) + ×( )

B 3 2 3 4 8 2 8 4×( ) × ×( ) × ×( ) × ×( )

C 30 2 30 4 8 2 8 4×( ) + ×( ) + ×( ) + ×( )

D 30 20 30 4 8 20 8 4×( ) + ×( ) + ×( ) + ×( )

■9Russ buys 14 pounds of food for his dog. How many ounces of food does Russ buy for his dog?

A 140 ouncesB 168 ouncesC 196 ouncesD 224 ounces

■10Pentagon EFGHJ is shown below.

H G

J F

E

Which sides of the pentagon are perpendicular?

A side EF and side EJ

B side EF and side FG

C side FG and side GH

D side FG and side HJ



■11A coach plans to buy new soccer balls and uniforms for her team.

• Each ball costs $37 . • Each uniform costs $52 .

The coach will buy 4 balls and 8 uniforms.

A Show or describe an ESTIMATION strategy that would result in an ESTIMATE of $900 as the total cost of the balls and uniforms the coach will buy. Explain why someone might think that $900 is not a reasonable ESTIMATE.

B Find a more reasonable ESTIMATE of the total cost of the balls and uniforms the coach will buy. Show or describe the steps that you took to find the ESTIMATE.

Write your answer to Question 11 on a separate sheet of paper. Be sure to answer Parts A and B.

You may want to go back and check your answers or answer questionsyou did not complete.


Copyright © 2013 by the Nevada Department of Education Page 5


Nevada


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Appendix I

ScoringSupportMaterials

Page 7Copyright © 2013 by the Nevada Department of Education Page 7

ItemNumber Strand DOK P-value A B C D

1 1 1 0.37 13% 37% 13% 37% ✓

2 1 2 0.31 43% 21% 31% ✓ 5%

3* 1 2 0.27 20% 28% 27% ✓ 25%

4* 1 2 0.30 32% 30% ✓ 15% 23%

5* 1 1 0.41 29% 12% 18% 41% ✓

6 2 2 0.29 20% 34% 29% ✓ 17%

7* 1 1 0.36 11% 36% ✓ 14% 39%

8 1 1 0.21 32% 31% 16% 21% ✓

9 3 1 0.25 46% 18% 10% 25% ✓

10* 4 1 0.49 8% 5% 49% ✓ 38%

Correct Answers for Multiple-Choice Items

Detailed objectives for Content Standards and Depth of Knowledge (DOK) descriptions can be found on the Nevada Department of Education web site.

Item Level DataPercentage of Students Selecting

a Given Response

✓ = Correct AnswerP-value is the proportion of students who got the item correct

* This is an item that was developed for these Instructional Materials, and it mirrors content assessed from an item field tested in the 2011-2012 test administration. The p-value and percentages reported here are based on the p-value and percentages of the item from the 2011-2012 field test.


Nevada 4 2011-12Mathematics

Version 1 #47 I-Ref #: WE: Y12_MA2886 Rpt Cat(s): 1.4.6Date: 1/24/12 CCCS: 4.OA.3

Score Description3 Student scores 3 points.2 Student scores 2–2.5 points.1 Student scores 0.5–1.5 points.0 Student’s response provides insufficient evidence of appropriate skills or

knowledge to successfully accomplish the task.Blank No student response.

Score Points

Part A: score 1.5 points correct strategy with correct work/description and completeexplanation

ORscore 1.0 point correct strategy with partially correct work/description and

incomplete explanationORcorrect strategy with correct work/description and complete explanation of an estimate other than $900 (student cannot replicate $900 estimate indicating it is not reasonable)

ORscore 0.5 point correct strategy with no work/description

ORsome correct procedureORvague explanation only

Part B: score 1.5 points correct answer with correct and complete work orexplanation

ORscore 1.0 point correct answer with incomplete work or explanation

ORincorrect answer due to a calculation error (work must be shown)

ORscore 0.5 point correct answer with no work or explanation

ORsome correct procedureORvague explanation only

Note: A student who does not label the total cost in Part B as dollars ($) cannot score a 3.


Nevada 4 2011-12Mathematics

Version 1 #47 I-Ref #: WE: Y12_MA2886 Rpt Cat(s): 1.4.6Date: 1/24/12 CCCS: 4.OA.3

Correct Answers

Part A: $40 10 $400$50 10 $500$400 $500 $900

× =× =

+ =or equivalent strategy

OR

To estimate round the cost of each ball up to $40 and round the cost of each uniform down to $50. Adding the two numbers and then multiplying by 10 would give an estimate of $900.

AND

Sample Explanation:Someone might think $900 is not a reasonable estimate because all four numbers were rounded to the nearest 10. Three of the four numbers were rounded up, and 4 was rounded up a lot to get to 10. Rounding all these numbers up would likely make the estimate too high because there are not really this many balls or uniforms being bought.

Part B: $560

$40 4 $160$50 8 $400$160 $400 $560

× =× =

+ =or equivalent work

OR

Sample Explanation:Round $37 to $40 and $52 to $50. Do not round the number of balls or number of uniforms. Multiply $40 by 4 and $50 by 8 to get $160 and $400; then add the numbers for an estimate of $560.


Student

response

Examples by

Score Point

Nevada



Score Point: 3 The response to Part A includes a correct strategy and complete explanation (1.5). The response to Part B includes a correct answer and complete explanation (1.5).


Score Point: 3 The response to Part A includes a correct strategy and complete explanation (1.5). The response to Part B includes a correct answer and complete explanation (1.5).


Contract: 1378 1 Booklet: 1450002360 Page: 1 of 1 Score: 2 RespCode: MA01047Annotation: A-1.0,B-1.5=2.5 pts. A has identified a strategy that tracks most of what the coach did, but actually goesbeyond the coach's estimate in that they used 12 rather than 10 for the quantity estimate. B has correct answer with work.

Anchor Page 2Score Point: 2 The response to Part A includes a correct strategy and incomplete explanation (1.0). The response to Part B includes a correct answer and complete explanation (1.5).


Contract: 1378 1 Booklet: 1450009204 Page: 1 of 1 Score: 2 RespCode: MA01047Annotation: A-0.5,B-1.5=2.0 pts. A employs an unsusual (and not entirely correct) rounding strategy but has some correctprocedure. B has a correct answer and work.

Anchor Page 3

Score Point: 2 The response to Part A includes some correct procedure and explanation (0.5). The response to Part B includes a correct answer and complete explanation (1.5).


Contract: 1378 1 Booklet: 1450001459 Page: 1 of 1 Score: 1 RespCode: MA01047Annotation: A-0.0,B-1.5=1.5 pts. A is incorrect - the coach is wrong because of my own estimate. B is a correct answerwith work

Anchor Page 4

Score Point: 1 The response to Part A includes no correct explanation (0). The response to Part B includes a correct answer and complete explanation (1.5).


Contract: 1378 1 Booklet: 1450003301 Page: 1 of 1 Score: 1 RespCode: MA01047Annotation: A-0.5,B-0.0=0.5 pts. A correctly identifies the coach's error, but trails off into exact calculation for theexplanation. B is an exact calculation, rounded at the end

Anchor Page 5Score Point: 1 The response to Part A includes some correct procedure (0.5). The response to Part B includes an incorrect answer (0). No credit awarded for calculating an exact answer and rounding.


Nevada


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Appendix II

AdministrativeSupportMaterials


A B C D

Mathematics

Answer Document

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B C D

B C D

B C D

B C D

A B C D

B C D

B C D

B C D

A B C D

1.2.3.4.5.6.7.8.9.

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WRITTEN RESPONSEMATHEMATICSQuestion 16


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James W. GuthrieSuperintendent of Public Instruction

Office of Assessment, Program Accountability, and Curriculum 775-687-9188

CrT • Instructional Materials