3Rd Grade Fraction Worksheets by hkf42269

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									Presented by Anise Flowers, Ph.D.
    Measurement Consultant
             The Power of Three!

Diagnostic    ASSIST™       Essential
Assessment    computer      Resources
              scoring and   intervention
              reporting     program
             Introduction KeyMath3
             Diagnostic Assessment
• Nationally standardized and criterion
  referenced diagnostic assessment of
  mathematics concepts and skills
• Untimed and individually administered
• Covers full spectrum from rote counting
  to factoring polynomials & solving linear
• Designed to meet requirements for RtI
  Service Delivery Model for Tiers II and III.

• KeyMath3 measures a student’s
  understanding and application of critical
  math concepts
• Age Range: 4:6 through 21:11
• Content Range: Pre-K through 9
• 30-90 minute administration time
• Convenient computer scoring
• Essential Resources intervention material
              KM3 - Key Features

• Aligned to the National Council of
  Teachers of Mathematics (NCTM)
  Principles and Standards of Mathematics
  – Most state Math standards aligned to NCTM
    Principles and Standards
• Ability to measure progress in 3 month
  – Useful for Progress Monitoring and Response
    to Intervention Models (RtI)
           KeyMath3 Revisions:
             What’s New?
• Includes Algebra at all levels
• New Subtests
• All new items
• Updated norms
• More emphasis on math communication,
  connections, & reasoning
• Linked to interventions
• 372 full color items in each form
• 3,360 individuals from 4 years 6 months to 21
  years 11 months old
• Both “Age” and “Grade” for Fall and Spring 2006
• Norms for the entire assessment and for specific
• Norm sample matched to 2005 U.S. census for
   – Sex, ethnicity, socioeconomic status, region
     and Special Education classification

•   Measure math proficiency
•   Measure student progress
•   Develop instructional plans
•   Support educational placement decisions
          Examiner Qualifications

• Minimum of bachelor’s degree including
  – Coursework in principles of measurement and
    in interpretation of tests
  – Formal training in mathematics
• Users include, but are not limited to
  – Educational diagnosticians
  – School psychologists
  – Special Education professionals
                 Other Users

• Title 1 Teachers
• General educators with struggling
• Math Teachers and Coaches
                KM3 Diagnostic
              Assessment Program
• Manual
• Two easels
• Record form (A or B) and student
  response booklet for computation
• ASSIST computer scoring and reporting
• Also needed: pen or pencil & calculator
  – Calculator for 3rd grade & up on Applied
    Problem Solving subtest
               Administration Time

•   PreK – K:          15 - 35 minutes
•   Grades 1 -2:       35 – 60 minutes
•   Grades 3 – 7:      60 - 80 minutes
•   Grades 8-12:       75 – 90 minutes

• Areas may be administered individually
    – Focus on students area of greatest need
    – Shorter administration time
             10 NCTM Standards

• Five Content
  – Number and Operations, Algebra, Geometry,
    Measurement, Data Analysis & Probability
  – Match Basic Concepts subtests
• Five Process
  – Problem Solving, Connections,
    Communication, Representation, Reasoning
    & Proof
  – Incorporated into the KeyMath3 items
    throughout the 10 subtests
        NCTM Standards Match

Subtests          Content Standards
                    Numeration &
Algebra                Algebra
Geometry             Geometry
Measurement         Measurement
Data Analysis &    Data Analysis &
Probability          Probability
       NCTM Process Standards

• Problem Solving
   – Solving problems when method for solution
     is not readily apparent
• Connections
   – Connecting mathematical concepts & skills
     in a variety of contexts
• Communication
   – Communicating ideas & explaining
        NCTM Process Standards

• Representation
  – Using symbolic expressions, diagrams,
• Reasoning & Proof:
  – Using reasoning to form insights, recognize
    patterns, explore phenomena, make
    conjectures, & justify results
             KeyMath3 Content

• Basic Concepts (Conceptual Knowledge)
• Operations (Computational Skills)
• Applications (Problem Solving)

    The same as KeyMath-R/NU
            Basic Concepts Subtests

•   Numeration
•   Algebra
•   Geometry
•   Measurement
•   Data Analysis and Probability
           Basic Concepts Subtests:

•   Early number awareness
•   Place value and number sense
•   Magnitude of numbers
•   Fractions
•   Decimals
•   Percentages
•   Exponents, integers, multiples, & factors
          Basic Concepts: Numeration

Grade Level: 3rd grade
• Representation process standard because it shows
alternative representations of the number 253.
• Connections process standard because it connects the
student’s understanding of addition and place value.
                  Basic Concepts:

Grade Level: 6th grade
• Connections process standard because it
requires the student to link his/her understanding
of decimal and fraction.
           Basic Concepts Subtests:

•   Early algebraic awareness
•   Algebraic uses of numbers & geometry
•   Symbolic representation
•   Ratio & proportion
•   Coordinate graphing
            Basic Concepts: Algebra

Grade Level: 3rd grade
• Connections process standard– it requires the student to
connect their understanding of multiplication to sets of
objects presented in rows.
• Representation process standard–it requires the student
to recognize an alternative representation of
multiplication – repeated addition.
               Basic Concepts: Algebra

Grade Level: 8th grade
• Both the Problem Solving and the Representation
process standards. Without the benefit of a solution that
is evident, the student must apply strategies to identify a
mathematical relationship between the numbers in the
two columns then choose the function that represents
that relationship.
           Basic Concepts Subtests:

•   Early geometric awareness
•   Two-dimensional shapes
•   Three-dimensional shapes
•   Lines & angles
•   Formulas
•   Grids & coordinate plans
            Basic Concepts: Geometry

Grade Level: 8th grade
• Communication process standard because the student is
required to precisely express the mathematical concept of
• Reasoning and Proof process standard is addressed
because the student must use reasoning to formulate the
           Basic Concepts Subtests:

•   Early awareness of measurement
•   Standard units
•   Time
•   Money
                     Basic Concepts:

Grade Level: 2nd Grade
• Problem Solving process standard because the solution is
not readily apparent. Applying trial and error with various
coin values is a common strategy for this problem.
                    Basic Concepts:

Grade Level: 9th grade
• Reasoning and Proof process standard by requiring the
student to development an argument.
• Communication process standard because the student must
explain with accurate mathematical language.
• Connection process standard because it applies math in a
real-world context.
           Basic Concepts Subtests:
          Data Analysis & Probability

•   Early awareness of data & probability
•   Charts, tables & graphs
•   Graphical representation
•   Statistics
•   Probability
                   Basic Concepts:
             Data Analysis and Probability

Grade Level: 3rd grade
• Reasoning process standard as
it requires a degree of
reasoning for young students to
recognize that the only real
choice is the question with
three options.
• Data are represented in a bar chart; thus, it addresses the
Representation process standard. Connections process standard
because it applies to a situation not that unfamiliar to students
that is outside of mathematics.
                      Basic Concepts:
                     Data Analysis and

Grade Level: 5th grade
• Reasoning and Proof process
standard as the student must
identify which of the four options is most likely
• Communications process standard as they then have to
explain their reasoning
• Connections process standard because it connects to a topic
familiar to students and that is outside of mathematics.
             Operations Subtests

• Mental Computation and Estimation
• Addition and Subtraction*
• Multiplication and Division*

*Items mixed and ordered by relative
           Operations Subtests:
           Mental Computation
              & Estimation
• Early awareness of mental computation
• Mental computation
   – Chains
   – Whole numbers
   – Rational numbers
• Estimation
   – Whole numbers
   – Rational numbers
   Operations: Mental
Computation and Estimation
   Operations: Mental
Computation and Estimation
              Operations Subtests:
             Addition & Subtraction

• Algorithms to add & subtract whole
  – Involves regrouping & multidigit numbers
• Algorithms to add & subtract rational
  – Explores decimals, fractions, & mixed
• Integers
• Algebra
  – Explores monomials & polynomials.
              Operations Subtests:
             Multiplication & Division
• Algorithms to multiply & divide whole
  – Involves regrouping & one/two-digit
    multipliers & divisors
• Algorithms to multiply & divide rational
  – Explores decimals, fractions, & mixed
• Integers
• Algebra
  – Explores monomials & polynomials.
             Applications Subtests

• Foundations of Problem Solving
  – Identify missing elements in a problem,
    operations needed, or optimal strategy
• Applied Problem Solving
  – Math problems in real-world contexts
  – Requires standard & non-standard problem
    solving strategies
              Applications Subtests:
             Foundations of Problem
• Analysis of problems
  – Whether sufficient information is present
  – Operations needed
  – Relationships in relevant information
• Word problems
  – Creating word problems and creating clues
• Problem-solving strategies
  – Identify strategies that would address
             Applications: Foundations
                of Problem Solving

Grade Level: 1st-2nd
• Representing information
for word problems in the
form of a number sentence
is a foundational part of
formal problem solving
•Content Standard- Algebra
               Applications: Foundations
                  of Problem Solving

Grade Level: 7-8th grade
• Connections- student must
connect this information to the
concept of volume while also maintaining the correct units.
•Content Standard - Measurement
             Applications Subtests:
            Applied Problem Solving

•   Numeration
•   Algebra
•   Geometry
•   Measurement
•   Data Analysis and Probability
                 Applications: Applied
                   Problem Solving

Grade Level: 8th grade
•Process Standards - Communication, Problem Solving,
Connections, Reasoning and Proof
•Content Standard - Numeration
                  Applications: Applied
                    Problem Solving

Grade Level: 2nd grade
• Representation - Information given is expressed or
represented in a number sentence.
•Content Standard – Data Analysis & Probability

• Areas may be administered individually
  – Tailor intervention to that area
  – Assess effectiveness of intervention for that
  – Monitor progress in that area

• Parallel Forms A and B
  – Alternate every three months
  – Forms matched statistically and by content
                KeyMath3 Screening

• Administer 5 Basic Concepts subtests to
  obtain information on essential math
• Administration time
  – Prek-2nd:    15-30 minutes
  – 3rd – 12:    35-45 minutes
              KeyMath™-3 Content
               Areas & Subtests
                    Total Test


 Numeration      Mental Computation   Foundations of
                 & Estimation         Problem Solving
 Algebra         Addition &           Applied Problem
 Geometry        Subtraction          Solving
                 Multiplication &
 Measurement     Division
 Data Analysis
 & Probability
               KeyMath3 Scores

• For Areas (Basic Concepts, Operations, and
  Applications) and Total Test:
   – Standard Scores
      (x=100, SD=15,Range 55-145)
   – Confidence Intervals
   – Grade Equivalent or Age Equivalent
   – Percentile Rank
                KeyMath3 Scores

• For Subtests:
   – Scaled Scores (x =10, SD=3,Range 1-19)
   – Confidence Intervals
   – Grade Equivalent or Age Equivalent
             Descriptive Categories

                Scale Score     Standard Score

Well-below        2 or below      70 or below
Below average         5-7           71-85

Average              8-12           86-114

Above average        13-15         115-129

Well-above        16 or above    130 or above
         Scoring Program: ASSIST

• Quickly and accurately scores the test
• Pinpoints student’s strengths & weaknesses
• Linked to Essential Resources intervention
• Provides the assessment link for the RtI
• Available in Network Client/Server version
  in 2008
ASSIST Data Entry Options
ASSIST Data Entry Options
ASSIST™ Report Options
             ASSIST Reports

•   Score Summaries
•   Area Comparisons
•   Score Profiles
•   Score Summary Narrative
•   Item and Functional Range Analysis
•   Progress Report (GSV)
•   Parent/Caregiver Letter
        ASSIST Score Summary

• Norm-referenced scores
• An excellent tool for identifying and
  prioritizing instructional programs
• Easily and quickly identify an examinee’s
  lowest and highest areas of functioning
ASSIST Score Summary
                    Score Profile

  – Presents a graphical representation of an
    examinee’s subtest scale scores, and area
    and total test standard scores
  – Quickly and easily identify student’s
    strengths and weaknesses
• Interpretation:
  – Facilitates prioritizing instruction
  – Supports analysis of severity of a
    performance deficit
ASSIST Score Profiles
        ASSIST Area Comparisons

• Allows direct comparison of an
  individual’s performance in one area with
  his or her performance in the other areas
• Indicates level of statistical significance
  of the difference
• Indicates frequency of that difference in
  the norm sample
ASSIST Area Comparisons
           ASSIST Score Summary

• Describes student’s subtest, area, and
  total test scores.
• Explains percentile ranks and descriptive
• Describes a student’s mathematical
  performance in relation to a nationally
  representative sample of individuals of
  the same grade or age
ASSIST Score Summary Narrative
        ASSIST Item and Functional
              Range Analysis
• Identifies KeyMath-3 DA items that fall
  within an individual’s functional range
• Notes items that may require particular
• Presents the behavioral objective
  measured by each of the items included
  in the analysis
• Identifies appropriate lessons in the
  KeyMath-3 Essential Resources
ASSIST Item and Functional
      Range Analysis
              Functional Range:

• Pay attention to items in functional range
  answered incorrectly
• Look for relationships among these items
  which might represent an instructional
• Identify concepts & skills that are
  prerequisites for subsequent learning
• Appendix F lists objectives for each item
               Functional Range:

• Look for relationships between
  Numeration subtest and each of the
  others – since number concepts are
  foundational to other skills
• Computation skills facilitate applied
  problem solving
• Also consider student’s current grade
  level – have they received instruction on
  this objective?
                  Focus Items:

• Items below the functional range which
  were answered incorrectly
   – Reflects gaps in understanding
   – Skills that need particular attention
• Items above the functional range which
  were answered correctly
   – Exceptional Competence with
     particular skill
           KeyMath3 Developmental
To Measure Growth
• Grade Equivalents
• Age Equivalents
• Growth Scale Value (GSV) – available only with
  the ASSIST scoring program
              Measuring Growth

• Growth Scale Value (GSV)
  – Based on IRT ability Scale
  – Designed for measuring change
  – Reflects absolute performance like a raw
    score not relative standing (normative)
  – Allows direct comparison of GSV scores
    obtained on the alternate forms of an area
  – Useful for documenting progress (AYP)
  – Helpful in measuring response to intervention
ASSIST™ Report Options
       ASSIST Progress Report

•Evaluates the effectiveness of math
intervention programs for individuals and groups
•GSVs have a significant advantage for
measuring growth and tracking progress over
standard scores and percentile ranks
•Report can be obtained for Total Test and each
of the 3 Areas
        ASSIST Progress Report

Answers the following questions:
1) How much gain occurred? (GSV units per year)
2) Is that gain significant?
   • If not significant – they are not responding
      adequately to the intervention
   • If significant – then they are showing
      progress that is reliably greater than zero
      (no growth)
3) How does the student’s growth compare to
  the population?
           ASSIST Progress Report

• Shows percentile rank, change in GSV
  since 1st administration, and growth rates
• Grade level expressed in grade & month
  of the year (August is 0)
• Change over baseline significantly greater
  than zero indicated with an asterisk
           ASSIST Progress Report

• Vertical axis is GSV scores
• Horizontal is grade or age level
• Curved line is average GSV OF NORM
• Student’s GSV scores are connected red
• Dashed line is student’s growth average
  across administrations – shows growth
            ASSIST Parent/Caregiver
•Provides a means of communicating an
examinee’s test results to his or her parents or
caregivers through a one-page letter

•Briefly describes the various features of the test
and provides content area and total test
percentile ranks and descriptive categories
  •Useful in communicating an examinee’s test
ASSIST Parent Caregiver Report

       Internal Consistency of Form A

Grade Basic    Operations Applications   Total

 K-5      .92        .89           .85     .95

6-12      .96        .94           .89     .98

              Basic      Operations   Applications Total

Alternate-       .94        .93           .88       .96

Test-retest      .95        .93           .93       .97
           Concurrent Validity – KeyMath™-3
                  with Sections of:
            Basic                 Problem
          Concepts   Operations    Solving
KTEA-II      .79        .82          .68     (gr k-5)
ITBS         .78        .75          .75     (gr k-8)
GMADE        .83        .63          .75     (gr k-5)
MAP          .81        .80          .75     (gr k-5)

KTEA-II     .85         .87         .76      (gr 6-12)
GMADE       .83         .84         .74      (gr 6-12)
MAP         .86         .87         .82      (gr 6-12)
Clinical Group         Mean Difference
LD Math                -15.6
LD Reading             -12.5
Combined LD Math and   -22.2
Mild Intellectual      -34
ADHD                   -1.1
Gifted and Talented    16.6
             Essential Resources

• Interventions integrated with KeyMath-3
  content, organization and range
• Three program levels
  – Level I: Pre-K – grade 2 [June 2008]
  – Level II: grades 3 – 5 [June 2008]
  – Level III: grades 6 – 8 [Coming soon…]
               Essential Resources
• Comprehensive supplement to a basal
  mathematics program
• Provides alternative teaching presentations
• Clearly identify concepts and skills
• Maintains conceptual continuity through careful
  pacing and thoroughness
• Facilitates precise teaching through unique
• Connects directly with KeyMath™ 3 Assessment
              Essential Resources

• Organized into 10 content strands
  – Content clusters within each strand
     • Individual lessons & activities within
• Lessons can be covered in a single class
• ER can be used with individual, small
  group, or whole class
                 Essential Resources
• Two easels
  – Teaching in individual or small group
  – Easel Activity Display develops concepts and skills
    through the use of representations, structured
    discussions, and specific activities.
• Manual
  – Contains several hundred masters for guided &
    independent practice
  – Contains images from easel to produce
    transparencies or use with a computer.
       KM-3 Essential Resources

• ASSIST links directly to recommended
  instructional materials based on the
  student’s KeyMath-3 DA results
• OR material can be used independently,
  incorporating these engaging activities
  into a teaching program
  – Conveniently organized for easy browsing
          Essential Resources Steps
• Obtain recommended lessons from the
  Diagnostic Assessment results
• Review for appropriateness for the student
• Administer Readiness assessment
• Teach the specific lesson with Guided practice
• Student completes Independent practice
• Administer Review assessment
• If needed, re-teach lesson with variations
• Administer Mastery assessment
        KM-3 Essential Resources

• Targeted materials to build a customized
  instructional program for your student:
  – Over 400 Lessons with activities per level
  – Over 200 guided and nearly 450 independent
    worksheets per level
  – Nearly 150 assessments per level including
    readiness, review, mastery and alternative
  – Progress Monitoring Report – one for each of
    the 10 content strands
         KM-3 Essential Resources

• Automatically
  lessons based
  on DA results
            KM-3 Essential Resources

• Conveniently
  of all
            Easel Teacher Display

• Convenient
• Reverse side
  of Student
• Specific
                    Student Display
    Engaging +
 Easel or CD +
 for use with
      small or
large groups
     Clip-ins – +
 and opaque
                Guided Practice

• Used during the
  lesson – tied to
  lesson display
• Available on CD –
  print as many as you
         Independent Practice

• Used by students
  during class time,
  after school or as
• Reduced verbal
  load from the
  guided practice
         Readiness Assessment

• Available at the
  cluster level
• Determine whether
  the student has the
  needed to learn the
  lesson you are
  about to teach
            Review Assessment

• Available at the
  cluster level
• Determine whether
  the student has
  mastered the
             Mastery Assessment

• Similar to the
  review assessment
• Useful when re-
  teaching the lesson
  is necessary
         Alternative Assessment

• Useful with
  students who
  are unable to
  take traditional
            Progress Monitoring

• Record for each of the 10 content strands
• Monitor individual student progress with
  KM3 ER assessments as you move through
  the lessons
• Monitor progress and determine any
  needed adjustments to student
  instructional plan
             Progress Monitoring

• Track student
  over time
• Determine
  to education
                         KeyMath3 & RTI
         Additional diagnostic assessment with KeyMath3
              Interventions from Essential Resources
         May include Special Education referral/placement

            KeyMath3 Diagnostic Assessment for students
             not responding to Tier 1 interventions
 KeyMath3 Essential Resources – Lessons specified by DA results
Track progress using Cluster Review & Mastery assessments in ER
                  Retest with DA after 3 months
Math screening for all students (such as BASI, GMADE
                     or PASeries)
                                   Schema adapted from Michelle Windmueller


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