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Alternate Assessments Measured Against
Grade-level Achievement Standards: The Massachusetts "Competency Portfolio"
NCEO Synthesis Report 59
Published by the National Center on Educational Outcomes
Dan Wiener
Massachusetts Department of Education
January 2006
Any or all portions of this document
may be reproduced and distributed without prior permission, provided the source
is cited as:
Wiener, D. (2006). Alternate
assessments measured against grade-level achievement standards: The
Massachusetts "Competency Portfolio" (Synthesis Report 59). Minneapolis,
MN: University of Minnesota, National Center on Educational Outcomes. Retrieved
[today's date], from the World Wide Web: http://education.umn.edu/NCEO/OnlinePubs/Synthesis59.html
Background
Alternate assessment originated in Kentucky in 1992 (National
Alternate Assessment Center, 2005), and was mandated nationally by the
Individuals with Disabilities Education Act of 1997. Alternate assessment acts
as a mechanism for inclusion in large-scale educational assessments for those
students with disabilities who cannot participate in regular state and district
assessments, even with accommodations and modifications. The No Child Left
Behind Act of 2001 (NCLB), the Individuals with Disabilities Educational
Improvement Act of 2004 (IDEA), and subsequent regulations reinforce the
requirement that states develop alternate assessments for students who need them
in order to be appropriately included in assessment and accountability systems.
The law and regulations also clarify that alternate assessments on grade-level
achievement standards can be designed to assess the achievement of students with
disabilities other than the most significant cognitive disabilities, who, often,
cannot show what they know on the general assessment, even with accommodations.
NCLB requires that alternate assessments for these students must be comparable
to the general assessment both in content standard coverage and achievement
standards. Regardless of whether alternate or grade-level achievement standards
are set, all assessment options are to be aligned to grade-level content
standards.
In addition, several states have implemented graduation tests
as a condition of receiving a high school diploma. There is much that states
must still do to expand opportunities for students with disabilities to
demonstrate what they know and can do through ways other than those typically
used in large-scale assessments. One option that states have considered is to
provide students with alternative methods for showing proficiency (Krentz,
Thurlow, Shyyan, & Scott, 2005).
To ensure full participation in assessment and accountability
systems, whether for NCLB accountability purposes or for graduation or
promotion, students with disabilities unable to take statewide paper-and-pencil
tests may require alternate assessments. Some of these students have significant
cognitive disabilities and are working substantially below the performance
expectations of other students in their grade. Sometimes, though, the nature of
the student’s primary disability is not cognitive, though still complex and
significant enough to require an alternate assessment, for example a student
with cerebral palsy or an intensive emotional disability. This latter group of
students may be working at or close to a performance level comparable with
typical peers, but cannot take the on-demand paper-and-pencil test, even with
accommodations, due to their disability. The alternate assessments taken by
these students must be able to measure their performance against grade-level
achievement standards, rather than the alternate achievement standards normally
associated with students with the most significant cognitive disabilities.
The focus of this discussion will be on those students who
require alternate assessments based on grade-level achievement standards, and
how such alternate assessments can reliably measure their achievement in a
manner that is equivalent to students who are taking the regular state
assessment for that grade. The Massachusetts Department of Education (the
"Department") has developed an alternate assessment based on grade-level
achievement standards consisting of a structured portfolio of student work
collected over a period of time, and reviewed by experts in the content area.
This option can be used for two purposes: to ensure appropriate participation
for all students in system accountability for NCLB purposes and to ensure
appropriate assessments for all students for the purpose of competency
determination for a diploma. In this paper, the "competency portfolio" will be
discussed, including how the model was developed and validated, and how a small
but growing number of students are using this format as an alternative pathway
to participate in the Massachusetts Comprehensive Assessment System (MCAS) and,
ultimately, satisfy the state’s graduation requirement.
Why Students Take Alternate Assessments
First, it is important to clarify why students take alternate
assessments of any type. There are many reasons why a student with a disability
might need an alternate assessment. IEP teams must make careful decisions about
how each student will participate in statewide assessments, based on their
knowledge of and familiarity with the student and his or her prior instructional
and assessment experiences. State assessment policies must also require teams to
revisit previous assessment decisions on an annual basis and make adjustments to
their earlier determinations, as needed, rather than maintaining a student on an
alternate assessment participation track for the duration of his or her
education. Students should also be permitted to take standard tests with
accommodations when this is appropriate and possible in certain subjects, while
taking alternate assessments in another.
Students with the most significant cognitive disabilities
comprise the majority of students taking alternate assessments. These students
are required to work on grade-level content standards, but will likely be
focusing on these standards at levels of complexity substantially below that of
their non-disabled peers. As a result, the standard test at their grade-level
would not allow the student access to the assessment in order to participate,
nor would it yield meaningful results or information needed to improve
subsequent instruction for the student.
Students with other significant (non-cognitive) disabilities
may also require alternate assessments, but for different reasons, especially
when the effects of their disabilities cannot be overcome in order to
participate in standard tests. The number of such students is relatively low in
Massachusetts, about 5-6% of the number of students taking alternate assessments
based on alternate achievement standards. Some of these students might be able
to take the general assessment if appropriate accommodations were identified,
available, and provided, though not always.
At whatever rate and frequency the disabilities of these
students hinder their participation in general assessments, they are entitled to
take assessments that allow them to demonstrate knowledge and skills at the
highest and most challenging levels of complexity. This means the alternate
assessment must measure the same grade-level achievement as their peers, though
using a different assessment format and context.
These students present a dilemma to states charged by law
with assessing all students using valid and reliable methods. They exist in
small, but significant numbers, and without their meaningful participation in
appropriate assessments, the state’s assessment system cannot truly be said to
be fully inclusive. Still, few states have developed alternate assessments based
on grade-level achievement standards. This places these students in a difficult
and vulnerable position. Their IEP teams are forced to choose from among several
unsuitable assessment options, and it raises the possibility of legal challenges
in states where graduation testing requirements may restrict their access to a
diploma.
Why Students Take Alternate Assessments based on Grade-level
Achievement Standards?
It is important to review characteristics of students who
require alternate assessments based on grade-level achievement standards
in order to understand why it is necessary to develop alternate assessments for
them. The following profiles are meant to expand an awareness of the
characteristics of these students, though it is not meant to be an exhaustive
list. The intent is to illustrate the attributes that should impel IEP teams to
consider alternate assessments based on grade-level achievement standards for
these students, due to the complexity, severity, and exceptional nature of their
disabilities. Examples of these students might include:
-
Students unable to "maintain sufficient concentration" to
participate in standard testing, even with test accommodations, as a
consequence of a severe emotional disability, traumatic brain injury, autism
or Aspberger’s Syndrome, or other disability or combination of disabilities.
-
Students for whom the "demands of a prolonged test
administration" would present a significant challenge, as a consequence of a
health-related, multiple physical, or other disability.
-
Students who require "more time than is reasonable or
available" for testing, even with the allowance of extended time, as a
consequence of cerebral palsy, deaf-blindness, or a significant motor,
communication, or other disability.
-
Students for whom the "format of the standard test is
inappropriate," and the necessary accommodations are unavailable or would
"give away" or hint at the answers.
-
Students who do not have significant cognitive
disabilities, but whose disabilities result in other "unique and significant
challenges" to taking the standard test.
From the qualities listed above, it should be clear to
policy-makers and members of IEP teams that such students cannot participate in
standard paper and pencil on-demand tests, even with accommodations, without
seriously compromising the validity of those results. Alternate assessments
based on alternate achievement standards are likewise inappropriate.
When its statewide assessment advisory committee recommended
to the Massachusetts Department of Education in 1999 that students with "unique
and significant challenges" also be permitted to take alternate assessments, and
that the alternate assessment ultimately allow them to meet the state’s
graduation requirement, the idea of a "competency portfolio" was born.
Challenges in Determining an "Equivalent" Performance on
Alternate Assessments
IEP teams in Massachusetts have been trained to recognize the
characteristics of students who should be considered for alternate assessments,
including both students with the most significant cognitive disabilities and
those with "unique and significant" (primarily non-cognitive) disabilities.
Guidelines for IEP team decision-making on alternate assessment participation
have been circulated since 1999.
In broadening the participation criteria to include both
groups of students, the alternate assessment itself had to become sufficiently
flexible to accommodate the creation and scoring of portfolios for students
working at levels of complexity ranging from substantially below to comparable
with, and even above, the level of their non-disabled grade-level peers.
As a result, the reporting system required a seamless
progression of achievement levels reflecting student performance based on
alternate as well as grade-level achievement standards. Figure 1 shows how the
Massachusetts Comprehensive Assessment System (MCAS) integrated its performance
levels for statewide reporting on alternate assessments to allow comparisons of
all students taking alternate assessments, whether measured against alternate or
grade-level achievement standards.
Figure 1. Performance Levels on MCAS and MCAS-Alt

Design and Implementation of Alternate
Assessments Based on Grade-level Achievement Standards
Portfolios do not assess student learning precisely in the
same way as standard assessments, due in part to the large number of learning
standards and skills required for documentation. However, portfolios have
several distinct advantages over on-demand tests, including demonstration of
growth and learning over a period of time, development of an individualized
learning sequence and pace of instruction (Seidel et al., 1997), and relieving
students of the intense physical and emotional demands of test-taking. New
methods and criteria for examining student work will need to be established for
this alternate assessment, and information will need to be included with student
work telling how the instructional tasks were conducted, and describing the
frequency and types of assistance, if any, given to the student.
Further, the design of these methods and criteria must be
based on a foundation of rigorous and challenging content. Thus, the direct
participation and involvement of content experts is perhaps the most critical
element in the design of an alternate assessment based on grade-level
achievement standards, since individuals most familiar with the standards in the
content area are those who are most qualified to identify the key skills and
content to be assessed, and to assist the state in determining the benchmarks
needed to reach each level of achievement.
The role of content experts in developing the Massachusetts
"competency portfolio" was identified in early discussions. It became obvious
that not every learning standard assessed on the general assessment could be
documented in a portfolio, due to the unrealistic amount of time and effort such
a range of learning standards would entail. Particularly, in a state like
Massachusetts with a state requirement to demonstrate competency in English
language arts (ELA) and mathematics, practitioners had to agree on the primacy
of certain learning standards, so students could demonstrate proficiency in
essential areas deemed most significant by secondary-level content experts.
These experts assisted the Department in identifying the most critical standards
for documentation, and continue to advise the Department on fine-tuning this
process.
States must be thorough, thoughtful, and collaborative in
their approach to developing alternate assessments based on grade-level
achievement standards because of the inherent differences in assessment formats,
particularly when results are used to determine high stakes for students, such
as promotion or graduation. Massachusetts students, for example, must eventually
pass the grade 10 MCAS assessments in English language arts and mathematics as
part of the state’s requirement to earn a diploma. The cut score for passing
these standard assessments is a score of 220 on the tests, the lowest scaled
score within the needs improvement performance level. Performance levels
on MCAS tests are scaled as follows: warning/failing (200-218); needs
improvement (220-238); proficient (240-258); advanced
(260-280). Although performance at the needs improvement level in grade
10 is sufficient for students to meet the state’s graduation requirement, a
score of proficient is required to meet the federal definition of
proficiency for No Child Left Behind.
While some students with disabilities in Massachusetts score
at the needs improvement and proficient levels on their grade 10
assessments, those who do not are encouraged to work until the end of grade 12,
or longer, to achieve a score of at least needs improvement and earn
their diplomas. It is important for states to provide incentives to continue the
intensive instruction of these students beyond grade 10, even though their
scores do not count in the AYP calculations of their schools and districts, and
to provide them with academic support programs and opportunities to take
successive retests. It is equally important that IEP teams be permitted to
designate these students for alternate assessments, when necessary, and that
these students be permitted to meet all state requirements to graduate when they
take these alternate assessments. Taking an alternate assessment should not
automatically remove any student from the possibility of earning a diploma,
since in many cases it is not known precisely how much these students are
capable of learning.
In each of the classes of 2003 and 2004 in Massachusetts,
80-82% of students with disabilities met the threshold for graduation by the end
of grade 12. As of this writing, about seventy-five Massachusetts students have
successfully earned their diplomas by taking alternate assessments based on
grade-level achievement standards. The process of reviewing the portfolios is
described more fully in the next section.
The "Competency Portfolio" Review Process
The evidence in the MCAS Alternate Assessment (MCAS-Alt)
portfolio determines whether a student’s performance will be measured based on
grade-level achievement standards or alternate achievement standards. During the
portfolio review process, scorers (primarily special educators) determine
whether a portfolio demonstrates student performance either at, or close to,
grade-level complexity and expectations. Through this winnowing process,
portfolios identified as "at or close to grade-level expectations" are set aside
and subsequently reviewed by content experts who verify that the portfolio
should indeed be reviewed based on grade-level achievement standards. The expert
panels then review for depth, breadth, and overall comparability with a student
who has passed the corresponding MCAS test, based on their familiarity with the
learning standards and with the performance expectations for students who have
passed the grade 10 tests. Specific requirements to meet the Competency
Determination standard are described in the Appendix.
For students in grades 3–8, where the stakes are arguably
lower (i.e., no retention or promotion, although sanctions may result for
schools and districts based on AYP determinations), the alternate assessment
based on grade-level expectations is nevertheless held to high standards for
breadth, depth, and quantity. Documentation is required in at least three
learning standards in each of three "strands" (or subdomains) in the content
area being assessed. When work samples are determined to be at a level of
complexity comparable with a student in that grade, as determined by a panel of
content experts in grades 3–8, and the work is both accurate and independently
produced by the student, then the student earns a score of needs improvement,
proficient, or advanced, based on an equivalent performance of a
student scoring at these performance levels on the test.
At grade 10, the requirements to meet the graduation standard
were set considerably higher. Content experts advised the Department that
evidence of only three learning standards per strand would be inadequate to meet
the Competency Determination standard. Portfolio submission requirements for
grade 10 students were developed with specific products in mind, based on
learning standards selected for documentation by curriculum and assessment
experts in English and math.
With support from technical advisors and state contractors,
the Department developed separate requirements for the English language arts and
mathematics competency portfolios. Since the ELA general assessment is primarily
an assessment of language, reading comprehension, and writing skills, test
developers and assessment experts conceived a portfolio based on writing samples
that responded to a piece of grade 10 literature in which the student addressed
themes in the work, rather than simplistic plot summaries. Students were
required to show successive drafts and revisions, with self-generated edits
guided by teachers’ comments and feedback. Specific ELA competency portfolio
requirements are shown in the Appendix.
Math test developers and curriculum framework writers,
on the other hand, took a more prescriptive approach to the math competency
portfolio. They identified between two and four learning standards in each of
five Math "strands" for documentation in the portfolio through a collection of
work samples focused on each required standard. The selected learning standards
typically were either the most difficult, most comprehensive, or those that
subsumed other standards within them. In some strands (geometry, for example),
teachers and students could choose any three standards on which to base their
work samples. In other strands, specific standards were pre-selected for
documentation. Students are required to solve problems accurately and
independently, and to show all steps in solving the problems, plus show evidence
of applying the standard in novel situations, rather than simply recalling or
repeating information.
A Level of Complexity ("5") was added to the MCAS-Alt scoring
rubric to reflect a student who had submitted work of this depth and breadth. A
score of 5 is necessary for a student to "pass" the assessment in order to earn
a Competency Determination. Figure 2 shows the Level of Complexity scoring area
in the MCAS-Alt scoring rubric, reflecting a range of complexity and alignment
of portfolio evidence with grade-level academic learning standards.
Figure 2. MCAS-Alt Scoring Rubric: Level of Complexity
|
1 |
2 |
3 |
4 |
5 |
|
Portfolio reflects little or no basis on
Curriculum Frameworks learning standards in this strand. |
Student primarily addresses social,
motor, and communication “access skills” during instruction based on
Curriculum Frameworks learning standards in this strand. |
Student addresses “entry points,” or
modified (i.e. less difficult) Curriculum Frameworks learning
standards below grade-level expectations in this strand. |
Student addresses a narrow sample of
Curriculum Frameworks learning standards (1 or 2) at
grade-level expectations in this strand. |
Student addresses a broad range of
Curriculum Frameworks learning standards (3 or more) at
grade-level expectations in this strand. |
Opportunities to Resubmit Portfolios for
Graduation Beyond Grade 10
Students are given multiple opportunities beyond grade 10 to
pass these assessments and earn a diploma by resubmitting their competency
portfolios with additional work samples in grades 11 and 12, and even beyond
grade 12. A detailed summary of the portfolio review is returned to each school
that allows educators to focus instruction in precisely the areas in which it is
needed, and resubmit the enhanced portfolio, until such time as the student
demonstrates competency on the grade-level content. The decision to resubmit a
competency portfolio beyond grade 10 is at the discretion of the student’s
IEP/504 team, based on whether the student, in their judgment, is approaching a
grade 10 level of achievement.
It is clear that portfolio submissions will need to occur
over the course of several school years for some students beginning in grade 10.
A collaborative approach among general and special educators will be needed to
do this effectively. There is now ample evidence to indicate that this portfolio
process has fostered both that collaboration and thoughtful, long-range planning
among general and special educators for these students.
Conclusion
States will need to document the validity of assessments used
to assess and report the academic performance of all students, based on the
requirements in the No Child Left Behind law. A small but significant number of
these students will not be able to take the standard test because of the nature
and complexity of their disabilities, but are also ill-suited to take alternate
assessments based on alternate achievement standards, since their knowledge and
skills are at comparable levels with their non-disabled peers. The assessment
results of these students based on either of these existing assessment formats
will be invalid for the purpose of reporting and accountability. A more flexible
and responsive approach is needed to assess these students. As assessments are
used to make decisions that have a direct impact on students, states will run
the risk of being held accountable by the public to show that results were
obtained using fair and precise assessments.
States in increasing numbers are also looking to verify that
students graduating from high school can demonstrate the core competencies
acknowledged as important in becoming productive citizens and lifelong learners.
These states must balance resources and capacity, external pressures, and
political concerns in considering whether and how to implement graduation
requirements for students. Approaches that rely on the use of only one
assessment method by which students can meet these high-stakes requirements will
inevitably be challenged by the families of students who claim to have these
skills and competencies, but cannot demonstrate them effectively on standard
tests. States must therefore decide whether to develop alternative pathways to a
diploma for the comparatively small number of students who need them. In so
doing, they will ensure that their assessment system remains responsive to the
needs of a full range of students, so all will have the opportunity to
demonstrate their skills effectively. This report presented one such model of an
alternative pathway used by a state to meet diploma requirements.
References
National Alternate Assessment Center. (2005). The
assessment triangle and students with significant cognitive disabilities: Models
of student cognition. Lexington, KY: Interdisciplinary Human Development
Institute, University of Kentucky.
Krentz, J., Thurlow, M., Shyyan, V., & Scott, D. (2005).
Alternative routes to the standard diploma (Synthesis Report 54).
Minneapolis, MN: University of Minnesota, National Center on Educational
Outcomes.
Massachusetts Department of Education. (1999).
Participation guidelines for MCAS alternate assessment. Malden, MA: Author.
Massachusetts Department of Education. (2004). 2005
educator’s manual for MCAS alternate assessment. Malden, MA: Author
Massachusetts Department of Education. (2000).
Massachusetts mathematics curriculum framework. Malden, MA: Author.
Massachusetts Department of Education. (2001)
Massachusetts English language arts curriculum framework. Malden, MA:
Author.
Seidel, S., Walters, J., Kirby, E., Olff, N., Powell, K.,
Scripp, L., & Veneema, S. (1997). Portfolio practices: Thinking through the
assessment of children’s work. Cambridge, MA: President and Fellows of
Harvard College.
Appendix A
MCAS-Alt Grade 10 "Competency Portfolio"
Requirements in ELA and Math
Following are the specific
MCAS-Alt portfolio requirements for a student in grade 10 (or beyond) to earn a
Competency Determination:
The student’s portfolio
must:
•
FIVE written work samples
as described below;
•
Multiple drafts
of each work sample
that indicate a progression of the student’s thinking in each successive draft.
Each must:
-
be clearly identified on the first page with a title, the student’s name,
and the date on which it was produced;
-
be written in the words of the student, with independent edits and
meaningful revisions incorporated into subsequent drafts (i.e., not rewritten by
the teacher for the student);
-
include a clear description of the type(s) and frequency of assistance
provided to the student by the teacherPRIVATE "TYPE=PICT;ALT=MS WORD"; and
-
not include
worksheets, short-answer tests, quizzes, or plot summaries.
An
English Language Arts portfolio may include evidence produced and accumulated
over more than one
school year,
beginning as early as grade 9. Evidence may be added to a previously-submitted
portfolio, or replaced with higher-quality work, and the entire portfolio
resubmitted each year beyond grade 10 until the student demonstrates a level of
performance equivalent to that of a student who scored
needs improvement
or higher on the grade 10 ELA MCAS test.
|
English
Language Arts
Strand: |
|
A grade 10
portfolio must include the following components, at minimum, in
order to be considered for the Competency Determination. |
|
Language |
Evidence provided
either in separate work samples or incorporated into the five required
writing samples, that the student understands and is independently able
to analyze and appropriately apply the following:
s
Vocabulary:
words used correctly; literal/figurative
meaning
s
Grammar and usage:
sentence structure and
language conventions
s
Mechanics:
punctuation and spelling |
|
Reading and
Literature
|
Three essays or compositions, including
all drafts, and based on grade 10 literature
in which the student analyzes,
interprets, compares and contrasts, and/or discusses the meaning of the
following:
1.
a work of literary non-fiction,
2.
a work of fiction, and
3.
a work of either poetry or drama. |
|
Composition
|
Two essays or
compositions, including all drafts,
that demonstrate original thinking and
independent editing through several drafts, as follows:
1.
one
essay or composition in which the student identifies and
discusses a theme in literature appropriate to a student in grade 10
and/or connects such a literary theme to his or her life
2.
one
essay or composition, including all drafts, on a topic of the
student’s own choosing that is reflective, persuasive, or fictional |
| |
|
|
|
•
a table of contents
listing each piece of evidence (work sample) submitted, and the strand and
learning standard(s) it purports to address,
•
at least four examples or problems solved correctly by the student
that demonstrate all aspects of each learning standard documented in the
portfolio. Additional examples of each standard are strongly encouraged.
Original evidence, rather than photocopies, is preferred,
•
a Grade 10 Work Description
PRIVATE "TYPE=PICT;ALT=MS WORD"attached to each work sample that documents a
particular learning standard,
•
a score
(% accurate) given by the teacher for each work sample,
•
work samples produced as independently as possible by the student;
corrections made by the teacher may not be submitted as the student's own work,
•
written evidence of the student's thinking and problem-solving,
indicating the process used to solve each problem (i.e., “show all work”),
•
a clear
indication of the type(s) and frequency of assistance provided to the student by
the teacher, either written directly on each piece or described on the
Grade 10 Work Description
Students in grade 10 may
not have had an opportunity to take all mathematics courses needed to satisfy
the requirements listed below. Therefore, a Mathematics portfolio may include
evidence produced over a period of more than one school year, beginning
not earlier than grade 9. Evidence may be added to an existing portfolio and
resubmitted annually beyond grade 10.
|
Mathematics
Strand: |
|
A grade 10
portfolio must include evidence that addresses at least the
following learning standards to be considered for the Competency
Determination: |
|
|
Number Sense and Operations
|
A total of
at least two work samples, one
documenting each of the two learning standards listed below:
10.N.2—Simplify
numerical expressions, including those involving positive integer
exponents or the absolute value [e.g., 3(24 – 1) = 45, 4|3 –
5| + 6 = 14]; apply such simplifications in the solution of problems. |
|
Patterns, Relations,
and Algebra
|
A total of at least
four
work samples, one documenting each of the four learning standards listed
below:
10.P.2—Demonstrate
an understanding of the relationship between various representations of
a line. Determine a line’s slope and x- and y-intercepts from its
graph or from a linear equation that represents the line. Find a linear
equation describing a line from a graph or a geometric description of
the line (e.g., by using the “point-slope” or “slope y-intercept”
formulas). Explain the significance of a positive, negative, zero, or
undefined slope.
10.P.4—Demonstrate
facility in symbolic manipulation of polynomial and rational
expressions by rearranging and collecting terms; factoring [e.g.,
a2 – b2 = (a + b)(a – b); x2 + 10x + 21
= (x + 3)(x + 7); 5x4 + 10x3 – 5x2
= 5x2 (x2 + 2x – 1)]; identifying and canceling
common factors in rational expressions; and applying the properties
of positive integer exponents. [This standard does not include
simple addition, subtraction, and multiplication of polynomials, as
covered in 10.P.3.]
10.P.5—Find
solutions to quadratic equations (with real roots) by factoring,
completing the square, or using the quadratic formula. Demonstrate
an understanding of the equivalence of the methods.
10.P.7—Solve
everyday problems that can be modeled using linear, reciprocal,
quadratic, or exponential functions. Apply appropriate tabular,
graphical, or symbolic methods to the solution. Include compound
interest, and direct and inverse variation problems. Use technology when
appropriate. |
|
|
Geometry |
A total of
at least three work samples, one
documenting each of
any three learning standards
listed below:
10.G.1
—Identify figures using
properties of sides, angles, and diagonals. Identify the figures’
type(s) of symmetry.
10.G.3
—Recognize and solve
problems involving angles formed by transversals of coplanar
lines. Identify and determine the measure of central and inscribed
angles and their associated minor and major arcs. Recognize and solve
problems associated with radii, chords, and arcs within or on the same
circle.
10.G.4
—Apply congruence
and similarity correspondences (e.g.,
DABC
@
DXYZ) and properties of the figures to find missing parts of geometric
figures, and provide logical justification.
10.G.5
—Solve simple triangle
problems using the triangle angle sum property and Pythagorean
theorem.
10.G.6
—Use the properties of
special triangles (e.g., isosceles, equilateral, 30º–60º–90º;
45º–45º–90º) to solve problems.
10.G.7
—Using rectangular
coordinates, calculate midpoints of segments, slopes of lines and
segments, and distances between two points, and apply the results to
the solutions of problems.
10.G.8
—Find linear
equations that represent lines either perpendicular or parallel to a
given line and through a point, e.g., by using the “point-slope” form of
the equation.
|
|
|
Measurement |
A total of
at least three work samples, one
documenting each of the three learning standards listed below:
10.M.1—Calculate
perimeter, circumference, and area of common geometric figures
such as parallelograms, trapezoids, circles, and triangles.
10.M.2—Given
the formula, find the lateral area, surface area, and volume of
prisms, pyramids, spheres, cylinders, and cones (e.g., find the volume
of a sphere with a specified surface area).
10.M.3—Relate
changes in the measurement of one attribute of an object to
changes in other attributes, e.g., how changing radius or height of a
cylinder affects its surface area or volume |
|
|
Data Analysis, Statistics,
and Probability |
A total of
at least two work samples, one
documenting each of the two learning standards listed below:
10.D.1—Select,
create, and interpret an appropriate graphical representation (e.g.,
scatterplot, table, stem-and-leaf plot, box-and-whisker plot, circle
graph, line graph, line plot) for a set of data and use appropriate
statistics (e.g., mean, median, range, mode) to communicate
information about the data. Use these notions to compare different sets
of data.
10.D.2—Approximate
a line of best fit (i.e., draw a trend line) given a set of data
(e.g., scatterplot). Use technology when appropriate. |
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