2006 Mathematics Released Items for Grades 3

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2006 Mathematics Released Items for Grades 38

• Beverly Neitzel
• Mathematics Initiative Director
• 360/725-6352beverly.neitzel_at_k12.wa.us

Mary Holmberg Mathematics Initiative
TOSA 360/725-6235Mary.Holmberg_at_k12.wa.us
http//www.k12.wa.us/assessment/WASL/Mathematics/d
efault.aspx
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Youre Kidding! You count the WASL?
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Agenda

• Introduction
• Scoring with Newly Released Items
• Released Item Documents (RIDs) with Lessons
  Learned
• Where are we, and what else can we do?
• Questions and Evaluation
• Break 230245 p.m.

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A View of Mathematics from OSPI

• Mathematics is a language and science of
  patterns.
• Mathematical content (EALR 1) must be embedded in
  the mathematical processes (EALRs 25).
• For all students to learn significant
  mathematics, content must be taught and assessed
  in meaningful situations.

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Big Ideas

• How can we use the knowledge of standards and
  assessment to plan for instruction?
• How can we use what we learn from student work to
  further students understanding in mathematics?

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Scoring Training

• Knowledge of Standards
• Knowledge of Assessment
• Evidence of Understanding
• Using Knowledge to Further Student Understanding

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Scoring Training Process

• Teachers
• do item and share solutions
• match item with item specification
• examine rubric
• review anchor papers
• score practice papers
• Back to Big Ideas

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How to Read RIDs

• Terry Letter
• How to Use
• Ideas
• Introduction
• Item
• Score Points
• Tools Y N X
• Strand
• Item Specification
• Performance Data
• School
• District
• State
• Student Example
• 3 Examples of Score Points of 4, 3, 2, 1
• 1 Example of Zero Score Point

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Lessons Learned from Scoring Student Work
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Run-On Equations

• Students are using run-on equations to support
  work. Run-on equations give false information
  and do not earn points for supporting work.
• Example of a run-on equation
• 10 17 27 3 24
• Remedy Have students use only one equal sign per
  equation.

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Showing Work

• Short answer and extended response items require
  students to show evidence of procedures, and/or
  strategies.
• Students should show work to support their
  answers on Tools Days and on days when tools are
  not allowed.
• Examples of ways to help students earn points
• Have students show all mathematical decisions.
• Encourage students to record any conversion
  factor that they use.

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Showing Work

• Show work using words, numbers, and/or pictures
  does not mean all of the ways.
• Students who write a narrative of how they
  solved a problem have added no additional
  information and may include a contradiction in
  the narrative.

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Showing Work

• When students provide more than one answer,
  scorers will not choose which one is correct.
• When students write over an answer, they are not
  making their answers clear enough to score.
• Students can earn points for work that is crossed
  out if it is correct and supports their answer.
• Students should cross out work, rather than
  erase. When students erase work, they show no
  evidence of strategy or procedure.

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Labels

• Missing and/or incorrect labels are a common
  reason students lose points.
• Money 1.80 (One dollar and eighty cents) is
  mislabeled in the following ways
• 180 1.80 1.80 1.80
  1.8
• When students are given inches in a prompt, their
  answers are mislabeled feet.

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Labels

• When reading data from a graph, students often
  ignore the unit provided in the label of an axis
  or provide an incorrect label in their answer.
• Students mislabel or leave the labels off linear,
  square, and/or cubic measures.
• Instead of 35 ft², students mistakenly write 35²
  ft.

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Labels

• Use (") symbol for inch and (') symbol for foot
  with a raised 2 to mean squared is incorrect.
• Example 25'² and 25²' are both incorrect.
• Mislabeled time units include
• forgetting the morning or afternoon label.
• forgetting the colon.
• using a decimal point instead of a colon.

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Conclusion and Support

• Students need practice drawing conclusions and
  giving quantitative support for their
  conclusions.
• Valid conclusions are based on the data or
  describe the data.
• Support uses the specific data and/or information
  specific from the item.

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Comparisons in Mathematics

• Students can include how things are alike and/or
  different.
• Students need to use two terms to describe a
  difference.
• Students need to correctly use and apply the
  words more, most, always, never, and almost.
  More is a comparative word and needs to show how
  and what is being compared.
• Example Don has more apples than Juan.

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Comparisons in Mathematics

• Students should use attributes not opinions.
• Example 1
• Opinion
• These are pretty these are not.

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Comparisons in Mathematics

• Example 2
• Insufficient comparison
• The first building has squares.
• Better comparison
• These are squares the others are not squares
  because the sides are not equal.

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Comparisons in Mathematics

• Example 3
• Insufficient comparison
• The snakes are longer. (Missing second term.)
• Better comparison
• The snakes are longer than the worms.

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Defies Reality

• Remind students to check for the reasonableness
  of their answers. They are submitting answers
  that defy reality.

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Number Sense

• Misplacement of the decimal point is scored as a
  conceptual error not a computation error.
• When a student writes 315 instead of 31.5, it is
  considered a conceptual error not a computation
  error.

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Number Sense

• Students have difficulties labeling fractional
  parts.
• Examples of mislabels

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Number Sense

• Students have trouble graphing inequalities on a
  number line.
• Examples of correctly graphed inequalities
• 2 lt p

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Number Sense

• 2 p

or
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Number Sense

• Students do not know how to represent a remainder
  in decimal form.
• Student writes an answer as 12.3 instead of 12 ¾
  on the answer line.

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Number Sense

• Students do not understand the meaning of the
  remainder in division problems.

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Measurement

• Students have difficulty computing with time and
  representing the answers.
• 1210 means 12 hours ten minutes elapsed time.
• 12.1 hours means 12 hours 6 minutes.
• 1210 P.M. means 10 minutes after 12 noon.
• Students continue to use 100 minutes for one hour
  instead of sixty minutes for one hour, when
  computing elapsed time.

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Algebraic Sense

• When students are asked to write an expression or
  equation for a given picture or illustration, the
  expression or equation should be connected to the
  picture or illustration.

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Algebraic Sense

• Students need to understand the difference
  between expressions and equations and a correct
  way to represent expressions and equations using
  variables.
• Examples of expressions
• Examples of equations

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Algebraic Sense

• Students need to use the variable given in the
  prompt.
• Students do not understand how to define
  variables. They give the value of the variable
  instead of what the variable means.
• Students need practice writing expressions and
  equations that represent a situation. They can
  solve a problem, but do not write an equation or
  expression that represents what they have done.

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Algebraic Sense

• Students are using words or a mixture of words
  and symbols when asked to write an equation using
  variables.
• Students in upper grades need practice writing
  equations with two variables. As always,
  students should define any variables they use.

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Geometric Sense

• When plotting points on a coordinate grid,
  students are showing the tracking lines that help
  them locate the points.

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Geometric Sense

• Students need practice sorting figures using more
  than one attribute i.e. four-sided figures with
  exactly one line of symmetry.
• When sorting figures with specific attributes,
  students mistakenly assume that there is an equal
  number of figures for each attribute.

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Geometric Sense

• Students need to use a ruler or straight edge
  when drawing figures.

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Probability and Statistics

• Students need to understand measures of central
  tendency mean, median, and mode.
• Students do not make lists of all possible
  outcomes.
• Students have difficulty determining
  probabilities of dependent events.

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Solves Problems/Reasons Logically

• Students should answer the question that is being
  asked.

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Communication

• When students are asked to write questions or
  information that can be obtained from data given,
  they should use the information, rather than just
  restate the information given.

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Communication

• Students have difficulty writing questions that
  can be answered from given information.
• When students write
• The cost of a milkshake and a donut
• They do not receive credit because it is not a
  question.
• They should write
• What is the cost of a milkshake and a donut?

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Communication

• An expression or an equation is not a question.
• An example of student work that will not receive
  points for a question is x y 2.
• Students are using the word it without
  providing information to whom or what is being
  referred. Students should avoid the use of it.
  Students should clarify all pronouns.

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Increase Scores

• Answer the question being asked.
• Show work to show how you got your answer.

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What do you see?
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Mathematics Grades 38 and 10
Percent of students meeting standard
100.0
90.0
80.0
70.0
64.5
56.0
60.0
49.6
49.1
50.0
40.0
30.0
20.0
10.0
0.0
Grade 3
Grade 4
Grade 5
Grade 6
Grade 7
Grade 8
Grade 10
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Washingtons Results on the Nations Report
CardMathematics 2005

• National Assessment of Educational Progress (NAEP)

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NAEP Achievement-Level Descriptions

• The three NAEP achievement levels, from lowest to
  highest, are
• Basic denotes partial mastery of the knowledge
  and skills that are fundamental for proficient
  work at a given grade.
• Proficient represents solid academic
  performance. Students reaching this level have
  demonstrated competency over challenging subject
  matter.
• Advanced signifies superior performance.

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NAEP Scale Scores

• NAEP mathematics scores are reported for grades
  4 and 8 on a 0500 scale.
• Beginning in 2002, the national sample sizes have
  increased dramatically. Standard errors, an
  estimate of the uncertainty in data, have been
  reduced due to the increase in national sample
  size.
• While a small1- or 2-pointdifference may not
  have met the have met the standard for
  statistically significant before 2002, that
  same difference may meet that standard in later
  years because of the smaller standard errors.

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NAEPGrade 4
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NAEPGrade 4
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NAEPGrade 4
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NAEPGrade 4
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NAEPGrade 4
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NAEPGrade 8
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NAEPGrade 8
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NAEPGrade 8
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NAEPGrade 8
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NAEPGrade 8
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NAEPGrade 8
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SAT
STATE Participation Rate 2004 2004 Mean 1994 Mean 10 Year Change
New York 87 510 497 13
Connecticut 85 515 497 18
Massachusetts 85 523 500 23
New Jersey 83 514 500 14
New Hampshire 80 521 510 11
D.C. 77 476 468 8
Maine 76 501 490 11
Pennsylvania 74 502 489 13
Delaware 73 499 491 8
Georgia 73 493 474 19
Rhode Island 72 502 488 14
Virginia 71 509 495 14
North Carolina 70 507 482 25
Maryland 68 515 503 12
Florida 67 499 492 7
Vermont 66 512 498 14
Indiana 64 506 493 13
South Carolina 62 495 473 22
Hawaii 60 514 504 10
Oregon 56 528 515 13
Alaska 53 514 502 12
Texas 52 499 500 -1
Washington 52 531 512 19
California 49 519 506 13

• Table 3 Mean SAT Verbal and Math Scores by
  State, with Changes for Selected Years

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SAT
STATE Participation Rate 2004 2004 Mean 1994 Mean 10 Year Change
Washington 52 531 512 19
Oregon 56 528 515 13
Massachusetts 85 523 500 23
New Hampshire 80 521 510 11
California 49 519 506 13
Connecticut 85 515 497 18
Maryland 68 515 503 12
Alaska 53 514 502 12
Hawaii 60 514 504 10
New Jersey 83 514 500 14
Vermont 66 512 498 14
New York 87 510 497 13
Virginia 71 509 495 14
North Carolina 70 507 482 25
Indiana 64 506 493 13
Pennsylvania 74 502 489 13
Rhode Island 72 502 488 14
Maine 76 501 490 11
Delaware 73 499 491 8
Florida 67 499 492 7
Texas 52 499 500 -1
South Carolina 62 495 473 22
Georgia 73 493 474 19
D.C. 77 476 468 8

• Table 3 Mean SAT Verbal and Math Scores by
  State, with Changes for Selected Years

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What Else Can We Do?

• What are you doing in your districts now that is
  working?
• What else can we be doing?

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www.k12.wa.us
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Mathematics Assessment
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Tools/Resources
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Essential Academic Learning Requirements
(EALRs)/Indicators
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Practice and Sample Tests
Released Item Documents (RIDs)
Test and Item Specifications
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GLEs
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Thanks!