Accommodations Toolkit

Manipulatives: States' Accessibility Policies, 2021

Share this page

National Center on Educational Outcomes (NCEO)

This summary of states’ accessibility policies for manipulatives is part of the Accommodations Toolkit published by the National Center on Educational Outcomes (NCEO)[1]. The toolkit also contains a summary of the research literature on manipulatives

Accessibility policies often have several tiers of accessibility features: universal features, designated features, and accommodations[2]. Manipulatives can include lots of different physical and virtual math tools (e.g., abacus, cubes, tiles, rods, blocks, counters/chips), and states sometimes have different policies for each specific type of manipulative. Figure 1 summarizes how states included manipulatives in their accessibility policies for students with disabilities in 2021. Figure 2 summarizes how states included manipulatives in their accessibility policies for English learners. Table 1 shows how manipulatives was included in the policies, while Table 2 contains additional details and specifications.

Figure 1. States’ Accessibility Policies for Students with Disabilities for Manipulatives, 2021

Math

  • Universal Features (U): 3 States
  • Designated Features (D): 3 States
  • Accommodations (A):42 States

Science

  • Universal Features (U): 2 States
  • Designated Features (D): 5 States
  • Accommodations (A): 32 States

Figure 2. States’ Accessibility Policies for English Learners for Manipulatives, 2021

Math

  • Universal Features (U): 3 States
  • Designated Features (D): 3 States
  • Accommodations (A):2 States

Science

  • Universal Features (U): 2 States
  • Designated Features (D): 5 States
  • Accommodations (A): 2 States

Table 1. Accommodations Policies for Manipulatives by State, 2021

U = Universal Feature, D = Designated Feature, A = Accommodation, ELA = English Language Arts, X = Allowed, SD = Allowed for Students with Disabilities, E = Allowed for English Learners, P = Prohibited, Blank cell = no policy found, N = Notes in Table 2

State

Math

Science

Notes

(See Table 2)

U

D

A

U

D

A

Alabama

SD

SD

N

Alaska

SD

SD

N

Arizona

SD

N

Arkansas

SD

N

California

SD

X

SD

N

Colorado

SD

SD

N

Connecticut

SD

N

Delaware

SD

SD

N

District of Columbia

SD

N

Florida

SD

SD

N

Georgia

SD

SD

N

Hawaii

SD

SD

N

Idaho

SD

SD

N

Illinois

SD

N

Indiana

SD

SD

N

Iowa

SD

SD

N

Kansas

Kentucky

SD

SD

N

Louisiana

SD

N

Maine

Maryland

SD

N

Massachusetts

SD

N

Michigan

SD

SD

N

Minnesota

X

SD

N

Mississippi

SD

SD

N

Missouri

SD

SD

N

Montana

SD

N

Nebraska

SD

SD

N

Nevada

SD

SD

N

New Hampshire

SD

SD

N

New Jersey

SD

SD

N

New Mexico

SD

SD

N

New York

SD

N

North Carolina

SD

SD

N

North Dakota

X

SD

X

SD

N

Ohio

X

SD

X

SD

N

Oklahoma

SD

SD

N

Oregon

X

SD

X

X

N

Pennsylvania

SD, E

SD, E

N

Rhode Island

SD

X

N

South Carolina

South Dakota

SD

SD

N

Tennessee

SD

N

Texas

X

X

N

Utah

X

SD, E

N

Vermont

SD

SD

N

Virginia

SD

N

Washington

SD

SD

N

West Virginia

SD

SD

N

Wisconsin

SD

SD

N

Wyoming

SD

SD

N

Total (Students with Disabilities)

3

3

46

2

5

32

Total (English Learners)

3

3

2

2

5

2

Note: Blank cell = no policy found

Table 2. Details and Specifications: States’ Manipulatives Accessibility Policies

State

Details/Specifications

Alabama

Accommodation (Math, Science):

Abacus: Students with a visual impairment who regularly use an abacus may use this device in place of using scratch paper. Setting: Large group, small group, or individual. Considerations/Constraints: Student must have an IEP or Section 504 Plan. Set Up: The student can test with other online testers in a large group setting. The school or district is responsible for providing the Abacus, and it must be a support the student uses regularly in the classroom. The tests are timed.

Alaska

Accommodation (Math, Science):

Math manipulatives: Student use of physical objects for math items. Multiplication tables and number lines may be used on select sections of the math content assessment where calculators are allowed. See Test Administration Directions and the Assessment Calculator Policy. See the Handbook for the Participation Guidelines for list of additional allowable and non-allowable math manipulatives.

Arizona

Accommodation (Math):

Abacus: Students may use an abacus without restrictions for any Math test or a talking calculator for students taking Part 1 of the 7th or 8th grade Math test or any part of the 10th grade Math test.

Arkansas

Accommodation (Math):

Abacus: An instrument for performing calculations by sliding counters along rods or in grooves. Recommended Usage: Examinees with visual impairments. This accommodation may only be used for the mathematics test. Extra testing time may be needed when providing this accommodation.

California

Designated Feature (Science):

100s number table: This is paper-based table for reference, listing numbers 1–100, available from Smarter Balanced https://www.caaspp.org/rsc/pdfs/CAASPP.hundreds-number-table.pdf PDF .

Multiplication table: A paper-based multiplication table (1–12) for reference will be available from Smarter Balanced at https://www.caaspp.org/rsc/pdfs/CAASPP.multiplication-table.pdf PDF .

Accommodation:

100s number table (Math): A paper-based number table (1–100) for reference in all grades is available from Smarter Balanced (https://www.caaspp.org/rsc/pdfs/CAASPP.hundreds-number-table.pdf PDF ).

Abacus (Math, Science): This accommodation may be used in place of scratch paper for students who typically use an abacus.

Multiplication table (Math): For math, a paper-based multiplication table (1–12) for all grades is available from Smarter Balanced for reference (https://www.caaspp.org/rsc/pdfs/CAASPP.multiplication-table.pdf PDF ).

Colorado

Accommodation (Math, Science):

Abacus/Tactile Math Manipulatives: Available only to students with an IEP or 504 plan with a documented diagnosis of blindness/visual impairment. The student uses the calculator or abacus used during daily instruction on all units of the science assessment and the calculator sections/units of the math assessment. Students with a documented diagnosis of blindness including visual impairment may use an abacus or talking calculator for calculation on the paper-based test. The student’s work on the abacus (or brailler) is recorded in the test book by the Test Administrator for constructed response items. All extra/adaptive papers used by the student during the assessment are secure materials. Return extra/adaptive papers to the SAC for secure destruction.

Connecticut

Accommodation (Math):

100s Number Table: (Grades 3-8) A paper-based table listing numbers from 1-100 is available from Smarter Balanced for reference. Students with visual processing, or spatial perception needs, may find this beneficial, as documented in their IEP or 504 Plan.

Abacus: This tool may be used in place of scratch paper for students who typically use an abacus during instruction as documented in the student’s IEP or Section 504 Plan. This accommodation is only available for the Smarter Balanced Mathematics Assessment.

Multiplication Table (Grades 3-8): A paper-based (digits 1-12) Multiplication Table is available for students in Grades 3-8 for the Smarter Balanced Mathematics Assessment. This tool may be used for reference by students with an IEP or 504 Plan documenting the need for this accommodation. These students typically demonstrate a persistent calculation disability (i.e., dyscalculia).

Manipulatives (Grades 4-8): Math manipulatives are available on the Smarter Balanced Math Assessments to allow eligible students to use concrete mathematical tools strategically to support their decision making. Math manipulatives may be requested via the petition process for students using this accommodation in daily instruction as indicated in their Individualized Education Program (IEP) or Section 504 Plan. Students eligible for this special documented accommodation are typically identified as students with visual disabilities or math-related disabilities, such as dyscalculia, and are typically students with Learning Disabilities, Autism, Visual Impairments, or Intellectual Disabilities. The petition application must include a description of the math manipulative(s) used in instruction and assessment, the submission of the IEP or Section 504 Plan, as well as additional documented evidence of the math-related disability, such as a recent Educational/Psychological evaluation or Mathematics Assessments. Upon approval, specific guidance will be provided about administering the math assessment using this specific special documented accommodation. Guidance includes, but is not limited to, the requirement that the student:

  • is tested separately from other students not using manipulatives during assessment;
  • uses manipulatives that are consistent with those used during instruction and that the manipulatives are made available in an organized manner; and
  • selects and uses the manipulative(s) independently without teacher prompting or direction.

The use of this special documented accommodation may require the student to be provided additional time for participation in the Smarter Balanced Assessment.

Delaware

Accommodation:

100s Number Table (Math, Science): A paper-based table listing numbers from 1–100 available from DeSSA for reference. Students with visual processing or spatial perception needs may find this beneficial, as documented in their IEP or 504 plan.

Abacus (Math, Science): Some students, including students with visual impairments or with documented processing impairments, who typically use an abacus may use an abacus in place of using scratch paper.

Math Manipulatives (Math): Available for students who are tactile learners or who have a documented need through an IEP or 504 Plan and uses manipulatives to solve math tasks during classroom instruction. Manipulatives should not have any markings such as marked fraction blocks. Possible suggestions include: straws, unifix cubes, counting bears, etc.

Multiplication Table (Math): A paper-based multiplication table containing numbers 1–12 is available from Smarter Balanced for reference – See Appendix A-11 For students with a documented and persistent calculation disability (i.e., dyscalculia).

District of Columbia

Accommodation (Math):

Mathematics tools (on non-Calculator Sections of Mathematics Assessments): Allowable mathematics tools include:

  • Arithmetic tables (e.g., addition charts, subtraction charts, multiplication charts; division charts).
  • Two-color chips (e.g., single-sided or double-sided).
  • Counters and counting chips.
  • Abacus
  • Square tiles.
  • Base 10 blocks.
  • 100s chart.

A student with a visual impairment may need other mathematics tools, such as a large print ruler (embedded ruler is designed in 18 point font), braille ruler, tactile compass, or braille protractor. Note that braille mathematics kits will include the appropriate grade-level braille ruler and braille protractors.

Florida

Accommodation (Math, Science):

A student with a visual impairment may use an abacus and products such as the Graphic Aid for Mathematics, Math Window®, and the geoboard. These devices are approved substitutes for paper-and-pencil computation.

A student may use blank mathematics grids/guides to organize mathematical computation.

Multiplication charts/tables may not be used.

Manipulative materials, including but not limited to counters, base-10 blocks, clock faces, or geometric shapes may not be used except when approved by FDOE for use with braille test materials. Real coins may be used to represent coins depicted in test items. Coins may not be used as counting devices.

Georgia

Accommodation (Math, Science):

Abacus: Allowed for students with visual impairments only.

Hawaii

Accommodation (Math, Science):

100s number table: A paper-based table listing numbers from 1–100 available from Smarter Balanced for reference. Students with visual processing or spatial perception needs may find this beneficial, as documented in their IEP or 504 plan.

Abacus: This tool may be used in place of scratch paper for students who typically use an abacus. Some students, including students with visual impairments or with documented processing impairments, who typically use an abacus may use an abacus in place of using scratch paper.

Multiplication table: A paper-based multiplication table containing numbers 1–12 will be available from Smarter Balanced for reference. For students with a documented and persistent calculation disability.

Idaho

Accommodation:

100s number table (Math): A paper-based table listing numbers from 1–100 available from Smarter Balanced for reference. Download the 100s Number Table by Smarter Balanced. Students with visual processing or spatial perception needs may find this beneficial, as documented in their IEP or 504 Plan.

Abacus (Math, Science): This tool may be used in place of scratch paper for students who typically use an abacus. Some students, including students with visual impairments or with documented processing impairments, who typically use an abacus may use an abacus in place of using scratch paper.

Multiplication table (Math): A paper-based multiplication table containing numbers 1–12 will be available from Smarter Balanced for reference. Download the Multiplication Table by Smarter Balanced. For students with a documented and persistent calculation disability (i.e., dyscalculia).

Illinois

Accommodation (Math):

Mathematics tools (on non-Calculator Sections of Mathematics Assessments): Allowable mathematics tools include:

  • Arithmetic tables (e.g., addition charts, subtraction charts, multiplication charts; division charts).
  • Two-color chips (e.g., single-sided or double-sided).
  • Counters and counting chips.
  • Abacus
  • Square tiles.
  • Base 10 blocks.
  • 100s chart.

A student with a visual impairment may need other mathematics tools, such as a large print ruler (embedded ruler is designed in 18 point font), braille ruler, tactile compass, or braille protractor. Note that braille mathematics kits will include the appropriate grade-level braille ruler and braille protractors.

Indiana

Accommodation (Math, Science):

Hundreds chart: For students with visual processing or visual perception difficulties, a paper-based 1-100 chart may be used. (ILEARN Mathematics 3-8, ILEARN Science grades four and six and I AM Mathematics three through eight, I AM Science grades four and six).

Multiplication table: For students with visual processing, or visual perception difficulties, a paper-based 9x9 multiplication table may be used. (ILEARN Mathematics three through eight, ILEARN Science grades four and six, I AM Mathematics three through eight, I AM Science grades four and six and ILEARN Biology).

Iowa

Accommodation (Math, Science):

Abacus: An abacus may be provided in place of scratch paper. Students with visual impairments who typically use an abacus may be provided this accommodation.

Multiplication table: A paper copy of a single digit (1-9) multiplication table is made available to the student. Students with a documented and persistent calculation disability (e.g., dyscalculia) may benefit from this accommodation.

Kentucky

Accommodation (Math, Science):

Manipulatives: If a student has manipulatives marked on their student plan and have used them throughout the school year, he/she may use the manipulatives on the test as long as they are considered appropriate for a state assessment (free of content, no guidance to a response). Any student that receives this accommodation should be tested in a one-on-one environment. The manipulatives should be placed at a central location that is not on the student’s direct testing surface. Students cannot be prompted to use manipulatives once the test has commenced. The proctor can, however, prior to testing begins show the student where the manipulatives are located so they are aware they are available and where to find the manipulatives. Manipulatives must be free of content of any kind when first presented to the student. This includes any numbers, letters, pictures, sketches or designs that can be considered content.

Louisiana

Accommodation (Math):

Math Tools (for non-calculator sections of Mathematics Assessments): Allowable mathematics tools include:

  • Arithmetic tables (e.g., addition charts, subtraction charts, multiplication charts, division charts).
  • Two-color chips (e.g., single-sided or double-sided)
  • Counters and counting chips
  • Square tiles
  • Base 10 blocks
  • 100s chart

Those tools are only allowable for students who have a disability that severely limits or prevents their ability to perform basic calculations, including an inability to perform single-digit addition, subtraction, multiplication, or division. However, mathematics tools may not subvert the construct of the assessment. A visual impairment student may need other mathematics tools, such as a large print ruler (embedded LEAP 2025 ruler is designed in 18-point font), braille ruler, tactile compass, or braille protractor.

Maryland

Accommodation (Math):

Mathematics Tools (on Calculator sections of the Mathematics Assessments): If a student’s disability affects mathematics calculation, reasoning or access, a calculator or other mathematical tool may be needed. Some students may need to use mathematical tools such as a large print ruler, braille ruler, tactile compass, braille protractor. Sometimes other mathematical tools are needed by students with disabilities such as arithmetic tables, two-color chips, counters and counting chips, square tiles, base ten blocks, or 100s charts.

Mathematics Tools (on non-Calculator sections of the Mathematics Assessments).

Massachusetts

Accommodation (Math):

Mathematics tool (including addition/subtraction or multiplication/division tables; or manipulatives) on the non-calculator session of the Mathematics test or retest: This accommodation is intended for a small number of students with documented disabilities that severely limit or prevent them from performing basic calculations without a calculation device or other mathematics tool, as documented in locally administered diagnostic evaluations, even after varied and repeated attempts to teach the student to do so. The student must meet all of the following criteria:

  • be virtually unable to calculate (i.e., unable to perform single-digit addition, subtraction, multiplication, or division without a calculation device or other mathematics tool); and
  • uses the calculation device or tool during routine instruction in mathematics; and
  • receives ongoing intervention to learn the skill. The student’s IEP or 504 plan must specify which calculation device or tool will be used (e.g., calculator or multiplication table).

Manipulatives and other mathematics tools (excluding calculators and arithmetic tables) must be approved by the Department prior to their use on MCAS tests. Please contact Student Assessment Services at 781-338-3625 or mcas@doe.mass.edu to request approval.

Michigan

Accommodation:

Multiplication Table (grade 4 and above only; Math): The multiplication table is allowed for use by online or paper/pencil M-STEP mathematics test takers in grades 4–7. For some assessments, this paper-based single-digit (1-9) multiplication table will be available for students who have a documented need in their IEP or 504 Plan, such as a persistent calculation disability (such as dyscalculia).

Abacus (Math, Science): Some students with visual impairments who typically use an abacus may use an abacus in place of using scratch paper during the assessment.

Counters, coins, base-10 blocks or other manipulatives for solving mathematics problems (Math, Science): Some students may find that visual or physical objects are helpful for them in providing concreteness of mathematical concepts.

Minnesota

Universal Feature (Grade 11; Math):

Since a calculator is allowed on all items in the grade 11 Mathematics MCA, the use of mathematics manipulatives, a multiplication table, or an abacus is considered a general support and not documented as an accommodation. These supports must be used in an individual setting with the online test or paper test materials. Mathematics manipulatives (like unifix cubes or base-10 blocks) can be the same color or different colors, but they must not be grouped or organized by the Test Monitor. Manipulatives that have any numbers or writing on them are not allowed; multiplication and hundreds tables provided by MDE are the exception. MDE does not produce a comprehensive list of allowable manipulatives; email mde.testing@state.mn.us for specific questions about providing manipulatives for statewide testing. Paper versions of the multiplication and hundreds tables posted on PearsonAccess Next (Preparing for Testing > Mathematics Accommodations) may be provided during testing. If students use the same table(s) for instruction and testing, Test Monitors must ensure that they do not have any additional writing on them before they are used for testing. If they do, a clean copy must be provided. The table(s) must be collected at the end of each test session and kept as a secure material, as students may have written parts of test items on them. Following test administration, the tables must be securely disposed of. Note: Mathematics manipulatives, multiplication and hundreds tables, and an abacus are accommodations for grades 3–8 (refer to Table 10 for additional information).

Accommodation (Grades 3-8; Math):

Mathematics manipulatives, multiplication and hundreds tables, and an abacus are considered accommodations for the grades 3–8 Mathematics MCA. Mathematics manipulatives (like unifix cubes or base-10 blocks) can be the same color or different colors, but they must not be grouped or organized by the Test Monitor. With the exception of multiplication and hundreds tables, manipulatives that have any numbers or writing on them are not allowed. MDE does not produce a comprehensive list of allowable manipulatives; email mde.testing@state.mn.us for specific questions about providing manipulatives. Paper versions of the multiplication and hundreds tables posted on PearsonAccess Next (Preparing for Testing > Mathematics Accommodations) may be provided during testing. If students use the same table(s) for instruction and testing, Test Monitors must ensure that they do not have any additional writing on them before testing. If they do contain any writing, a clean copy must be provided. The tables must be collected at the end of each test session and kept as a secure material, as students may have written parts of test items on them. Following test administration, the tables must be securely disposed of. The student must use a paper test book in an individual setting and only use the mathematics manipulatives, multiplication/hundreds tables, or an abacus on the segments where calculators are allowed. Note that because the use of any of these accommodations requires students to move from an online test to a paper test, students lose the benefits of online testing, including access to interactive test items and an adaptive test tailored to their skill level. A 12-point regular print test book will be automatically shipped if this code is indicated in Pretest Editing by Jan. 21; after this date, the test book must be ordered as an additional order in PearsonAccess Next. All student responses must be entered online by district staff within the testing window. Refer to Entering Student Responses Online for MCA Paper Accommodations earlier in this chapter.

Notes for mathematics manipulatives, multiplication/hundreds tables, or an abacus: Since a calculator is allowed on all sections/segments of the grade 11 Mathematics MCA, the use of any of these is not indicated as an accommodation for grade 11 Mathematics MCA. If a student’s IEP or 504 plan indicates the use of any of these (HC) and a 12-point regular print test book (12), only one code can be indicated in Pretest Editing; a 12-point test book is automatically sent when either code is indicated by Jan. 21. If a student’s IEP or 504 plan indicates the use of any of these (HC) and script (MS), only the MS is indicated in Pretest Editing; a 12-point test book is automatically sent when the script is indicated by Jan. 21. If a student’s IEP or 504 plan indicates the use of any of these (HC), MS, and 12, only the MS code is indicated in Pretest Editing; a 12-point test book is automatically sent when the script is indicated by Jan. 21.

Mississippi

Accommodation (Math, Science):

Abacus: Only a student who is visually-impaired may use the abacus to solve mathematics problems.

Missouri

Accommodation (Math, Science):

Abacus: Students with this accommodation in their IEP/504 plan may have access to an abacus.

Multiplication table: Students in grades 4-8 with this accommodation in their IEP/504 plan may have access to a single digit multiplication table.

Montana

Accommodation (Math):

100s number table: A paper-based table listing numbers from 1–100 available from Smarter Balanced for reference. Students with visual processing or spatial perception needs may find this beneficial, as documented in their IEP or 504 plan.

Abacus: This tool may be used in place of scratch paper for students who typically use an abacus. Some students, including students with visual impairments or with documented processing impairments, who typically use an abacus may use an abacus in place of using scratch paper.

Multiplication table: A paper-based multiplication table containing 1-12 will be available from Smarter Balanced for reference. For students with a documented and persistent calculation disability (i.e., dyscalculia).

Nebraska

Accommodation (Math, Science):

Mathematical supports: This accommodation is for students who need additional supports for math (e.g. abacus, calculation device, number line, addition/multiplication charts, base-ten blocks, various types of counters, fraction tiles and pies without numerical labels, coins, clock with or without numbers shown on clock face; clock should not have gears, etc.) Student’s disability affects math calculation but not reasoning.

Nevada

Accommodation (Math, Science):

100s number table: A paper-based table listing numbers from 1–100 available from Smarter Balanced for reference. Students with visual processing or spatial perception needs may find this beneficial, as documented in their IEP or 504 plan.

Abacus: This tool may be used in place of scratch paper for students who typically use an abacus. Some students, including students with visual impairments or with documented processing impairments, who typically use an abacus may use an abacus in place of using scratch paper.

Multiplication table: A paper-based multiplication table containing numbers 1–12 will be available from Smarter Balanced for reference. For students with a documented and persistent calculation disability (i.e., dyscalculia).

New Hampshire

Accommodation:

100s Number Table (grades 4-8, Math): A paper-based table listing numbers from 1–100. Students with visual processing or spatial perception needs may find this beneficial, as documented in their IEP or 504 plan.

Abacus (Math, Science): This tool may be used in place of scratch paper for students who typically use an abacus. Some students with visual impairments who typically use an abacus may use an abacus in place of using scratch paper.

New Jersey

Accommodation (Math, Science):

Mathematics tools: Allowable mathematics tools include:

  • Arithmetic tables (e.g., addition charts, subtraction charts, multiplication charts; division charts).
  • Two-color chips (e.g., single-sided or double-sided).
  • Counters and counting chips.
  • Square tiles.
  • Base 10 blocks.
  • 100s chart.

A student with a visual impairment may need other mathematics tools, such as a large print ruler (embedded ruler is designed in 18-point font), braille ruler, tactile compass, or braille protractor. Note that braille mathematics kits will include the appropriate grade-level braille ruler and braille protractors.

New Mexico

Accommodation (Math, Science):

Math manipulatives: For students who are blind or visually impaired, have specific learning disabilities, or are otherwise health impaired. 3-D objects used in place of paper materials or images on computer screen. Manipulatives include: touch point numbers, counting blocks/beans/etc., abacus, number line, numbers chart, Braille ruler, Braille protractor.

New York

Accommodation (Science):

Use of mathematics tables (science only), use of number line, abacus.

North Carolina

Accommodation (Math, Science):

Cranmer abacus: Available for Mathematics (Grades 3–8) and Science (Grades 5 and 8). The Cranmer abacus is a tool that may be used as a testing accommodation. The Cranmer abacus is not a substitute for a calculator but can serve as a paper substitute for some students. As with all accommodations for North Carolina tests, (1) the use must be documented in the current IEP or Section 504 Plan, and (2) the accommodation must be routinely used during instruction and similar classroom tests.

North Dakota

Universal Feature (Math, Science):

Math tools: Learners may use digital or physical tools, such as rulers, number lines, or math manipulatives.

Accommodation (Math, Science):

Abacus: This tool may be used in place of scratch paper for students who typically use an abacus.

100s Number Table: A paper-based table listing number from 1-100.

Multiplication table:  A paper-based single digit (1-9) multiplication table is made available to the learner.

Ohio

Designated Feature (Math, Science):

Calculator or fact charts – handheld: Students may use handheld calculators and fact charts (addition, subtraction, multiplication or division only) for calculator-allowable mathematics tests or parts of test and the physical science test. Additional calculator guidance is in the Test Administration Manuals. The red TI-30X IIS is the only handheld calculator that can be used in place of the online calculator during the mathematics and science OGT.

Rulers, angled-rulers, compasses and protractors: Students may be familiar with these tools from instruction at various grade levels and want to use them on the test. While these tools are not required for testing, districts may choose to provide them to students or allow students to provide their own. The tools cannot contain any additional writing or information that may provide an unfair testing advantage. Examples of additional writing could include but are not limited to multiplication tables, formulas or conversion charts. A student with a visual impairment may need adapted mathematical tools such as a large print ruler, Braille ruler, tactile compass or Braille protractor.

Accommodation:

Calculator or fact charts on non-calculator mathematics test or part of test (Math): The student uses a handheld or embedded calculator or fact chart (addition, subtraction, multiplication or division only) on a non-calculator mathematics test or part of test. Both parts of grades 3 through 5 mathematics tests and part 1 of grades 6 and 7 mathematics tests are non-calculator tests.

Mathematical tools (Math, Science):

Allowable tools include:

  • 100s chart
  • Abacus/Rekenrek
  • Algebra Tiles
  • Base 10 blocks
  • Counters and counting chips
  • Cubes
  • Fraction tiles and pies without numerical labels
  • Square tiles
  • Two-colored chips

Student uses these tools and manipulatives to assist mathematical problem solving. These manipulatives allow the flexibility of grouping, representing or counting without numeric labels. Tools that give students answers (e.g., fraction tiles with numerical labels) or lead a student to use a specific strategy (e.g., number lines) are not allowed. These types of tools can be effective for instruction and while students may create their own during testing as a strategy, they may not be provided to students on Ohio state tests. For information about fact charts, see calculation device or fact charts on non-calculator mathematics test or part of test in this section. Information about rulers, angled-rulers, compasses and protractors is located in the non-embedded designated supports section of this manual. The Department will review and revise this list annually as needed. Allowable for mathematics and science tests only.

Oklahoma

Accommodation (Math, Science):

Abacus: Students who have a visual impairment/blindness or access mathematical calculations tactilely may use an abacus.

Oregon

Designated Feature (Math):

Abacus (for Math, all grades): The abacus, also called a counting frame, is a calculating tool. This tool may be used by students who typically use an abacus.

Manipulatives (for Math, all grades): Manipulatives used during testing must be listed in this table and should be used during instruction so they are familiar to students. Using manipulatives not included in this list will result in a testing impropriety and student test invalidation.

Manipulatives are tactile tools that provide concrete representations of mathematical ideas.

Allowable manipulatives:

  • Algebra tiles
  • Base-ten blocks or pieces
  • Colored chips, including those with positive and negatives sides
  • Counters (e.g., beans, blocks, craft sticks, tiles, or similar)
  • Cruisenaire rods
  • Dot paper (square or hex)
  • Fraction strips or fraction pieces (unlabeled only)
  • Geoboard and bands
  • Geometric shapes (2D and 3D)
  • Interlocking cubes (e.g., Unifix, Omnifix)
  • Number rack (rekenrek)
  • Pattern blocks
  • Trays, containers, or bags for storage and/or sorting

Additional manipulatives may be requested.

The intent of this support is to make students’ testing environment more consistent with their learning environment. Students who benefit from the use of manipulatives during instruction may use this support during their assessment. Manipulatives are available to help students think, not to give them answers.

Guidelines for administration:

  • Manipulatives must neither directly provide students with answers nor identify the process by which students may determine the answer
  • Manipulatives must be provided to the student in a tray, container, or bag before testing begins
  • Manipulatives must be stored at the student’s testing area to minimize movement
  • Manipulatives must not be labeled (e.g., fractions, decimals, numerals, text)
  • Students must work individually with manipulatives
  • Students are not to be coached as to which manipulatives to use, nor on how to use them

The use of this designated support may result in additional logistical considerations for the testing environment and may result in the student needing additional overall time to complete the assessment.

Accommodation (Math):

100s Number Table: A paper-based table listing numbers from 1-100. Students with visual processing or spatial perception needs may find this beneficial, as documented in their IEP or 504 plan.

Multiplication Table (grade 4 and above math items): A paper-based 1-12 multiplication table. For students with a documented and persistent calculation disability (i.e., dyscalculia).

Universal Feature (Science):

Multiplication Table: All students in grades 5, 8, and 11 may use a multiplication table (1-12) either as a chart on the wall or on a piece of paper to assist them on the OSAS Science Assessment.

100s Number Table: A paper-based table listing numbers from 1–100 is available.

Designated Feature (Science):

Abacus: The abacus, also called a counting frame, is a calculating tool. This tool may be used by students who typically use an abacus.

Manipulatives (for all grades):

Manipulatives used during testing must be listed in this table and should be used during instruction so they are familiar to students. Using manipulatives not included in this list will result in a testing impropriety and student test invalidation. Manipulatives are tactile tools that provide concrete representations of mathematical ideas.

Allowable manipulatives:

  • Algebra tiles
  • Base-ten blocks or pieces
  • Colored chips, including those with positive and negatives sides
  • Counters (e.g., beans, blocks, craft sticks, tiles, or similar)
  • Cruisenaire rods
  • Dot paper (square or hex)
  • Fraction strips or fraction pieces (unlabeled only)
  • Geoboard and bands
  • Geometric shapes (2D and 3D)
  • Interlocking cubes (e.g., Unifix, Omnifix)
  • Number rack (rekenrek)
  • Pattern blocks
  • Trays, containers, or bags for storage and/or sorting

Additional manipulatives may be requested.

The intent of this support is to make students’ testing environment more consistent with their learning environment. Students who benefit from the use of manipulatives during instruction may use this support during their assessment. Manipulatives are available to help students think, not to give them answers.

Guidelines for administration:

  • Manipulatives must neither directly provide students with answers nor identify the process by which students may determine the answer
  • Manipulatives must be provided to the student in a tray, container, or bag before testing begins
  • Manipulatives must be stored at the student’s testing area to minimize movement
  • Manipulatives must not be labeled (e.g., fractions, decimals, numerals, text)
  • Students must work individually with manipulatives
  • Students are not to be coached as to which manipulatives to use, nor on how to use them

The use of this designated support may result in additional logistical considerations for the testing environment and may result in the student needing additional overall time to complete the assessment.

Pennsylvania

Accommodation (Math, Science):

Grade specific ruler and/or protractor tools provided with the PSSA test materials. No math tools provided with Keystone Exam materials; student may use a straight edge tool (not a ruler) for the Algebra I exam. Cranmer abacus and Math Window (these two are for braille users only). Number lines; high contrast ruler/protractor or tactile ruler/protractor (only for students with IEP or 504 Plan). Note: A number grid or hundreds chart is not allowable.

Rhode Island

Designated Feature (Science):

Student uses arithmetic tables for addition, subtraction, multiplication, and division, including an abacus or other manipulatives.

Accommodation (Math):

Student uses arithmetic tables for addition, subtraction, multiplication, and division, including an abacus or other manipulatives.

South Dakota

Accommodation (Math, Science):

100s Number Table: A paper-based table listing numbers from 1–100. A copy is available in the resource section. Students with visual processing or spatial perception needs may find this beneficial, as documented in their IEP or 504 plan.

Abacus: This tool may be used in place of scratch paper for students who typically use an abacus. Some students, including students with visual impairments or with documented processing impairments, who typically use an abacus may use an abacus in place of using scratch paper.

Multiplication Table: A paper-based multiplication table containing numbers 1-12. A copy is available in the resource section. For students with a documented and persistent calculation disability (i.e., dyscalculia).

Tennessee

Accommodation (Math):

Visual Representations for Math: Test administrator ensures the student has access to the necessary manipulatives for testing (e.g., abacus, cubes, tiles, rods, or blocks). This would not include things such as multiplication charts/tables, number lines etc. typically used by students with math deficits who are not visually impaired. This accommodation is only applicable for students with a visual impairment and may not be used on the non-calculator sections of the assessment. This accommodation may be used in place of scratch paper for students who typically use an abacus or other manipulatives.

Texas

Designated Feature:

Calculation aids (Math, Science): This designated support provides an alternate method of computation for a student who is unable to effectively use paper-and-pencil methods.

For a student who meets the eligibility criteria, this designated support may be used on

  • STAAR grades 3–7 mathematics
  • STAAR grade 5 science
  • STAAR Spanish grades 3–5 mathematics
  • STAAR Spanish grade 5 science

A student may use this designated support if he or she

  • receives Section 504 or special education services,
  • routinely, independently, and effectively uses it during classroom instruction and classroom testing, and
  • meets at least one of the following for the applicable grade.

Grades 3 and 4

  • The student has a physical disability that prevents him or her from independently writing the numbers required for computations and cannot effectively use other accessibility features to address this need (e.g., whiteboard, graph paper).
  • The student has an impairment in vision that prevents him or her from seeing the numbers they have written during computations and cannot effectively use other accessibility features to address this need (e.g., magnifier).

Grades 5 through 7

  • The student has a physical disability that prevents him or her from independently writing the numbers required for computations and cannot effectively use other accessibility features to address this need (e.g., whiteboard, graph paper).
  • The student has an impairment in vision that prevents him or her from seeing the numbers they have written during computations and cannot effectively use other accessibility features to address this need (e.g., magnifier).
  • The student has a disability that affects mathematics calculations. Even after intensive instruction and remediation, the student is consistently unable to memorize basic addition, subtraction, multiplication, or division facts or perform the steps in an algorithm correctly when solving problems.

This designated support may include only

  • basic (i.e., four-function) handheld calculator or calculator application, including large-key or speech-output
  • basic calculator available as an online embedded support on STAAR
  • abacus or Cranmer modified abacus
  • 0–9 addition grid without special numbers (e.g., even numbers) indicated
  • grade-appropriate multiplication grid without special numbers (e.g., perfect squares) indicated

Mathematics Manipulatives (Math): These designated supports are concrete objects or pictures of concrete objects for a student to move and touch in order to visualize abstract concepts.

For a student who meets the eligibility criteria, this designated support may be used on

  • STAAR grades 3–8 mathematics, Algebra I, and Algebra II
  • STAAR Spanish grades 3–5 mathematics

A student may use this designated support if that student routinely, independently, and effectively uses it during classroom instruction and classroom testing.

This designated support may include only

  • real or play money (both heads and tails)
  • clocks with or without numbers shown on clock face; the clock should NOT have gears
  • base-ten blocks
  • various types of counters (e.g., two-sided chips, blocks, numerals with printed or raised dots)
  • algebra tiles; the tiles should NOT contain words, labels, pictures, acronyms, mnemonics, numbers, symbols, or variables
  • fraction pieces (e.g., fraction bars, fraction circles); the fraction pieces should NOT contain labels (e.g., labels that show individual fractions, equivalencies, or cumulative sequence)
  • geometric figures that are grade- or course-appropriate; the figures may be provided in either three-dimensional form or two-dimensional form, but NOT in both forms; the figures should NOT contain words, labels, colors used as labels, pictures, acronyms, mnemonics, numbers, symbols, or variables. Providing a pictorial model of a geometric figure in one form (e.g., net) and a supplement aid of the same figure in another form (e.g., three-dimensional solid) is NOT allowed.

Utah

Universal Feature (Math):

Computation tables: Not allowed for grades 3-5; Embedded grade 6 segment 2, grades 7 & 8.

Accommodation (SWD and EL; Math):

Calculation devices and computation tables: 6th grade – handheld allowed during calculator segment 2 only.

All students are allowed to use the online calculation device when it is embedded during the allowed segments of a math assessment. Students in grades 7–12 who require a handheld calculation device or printable computation table can use that resource during the allowed segment of the math assessment. For students in grade 6, the use of a handheld calculation device or printable computation table is considered an accommodation and may be provided (based on need documented in the IEP) during the allowed segment of the assessment. For students in grades 3–5, the use of a handheld calculation device printable computation table is not allowed during any segment of the math assessment. If provided, the test must be reported as modified, and the student will receive a score of non-proficient and be considered a non‐participant for accountability. During instruction, it is important to determine whether the use of a calculation device or computation table is a matter of convenience or a necessary accommodation. It is also important to know the goal of instruction and assessment before making decisions about the use of calculation devices or computation tables. In some cases, calculators may be adapted with large keys or voice output (talking calculators). Examples of calculation devices are calculators, slide rules, and abacuses. Examples of computation tables are number lines and multiplication, division, addition, and subtraction charts.

Visual representation: Visual Representations are manipulatives such as cubes, tiles, rods, blocks, models, etc. They may be used on all sections of the mathematics assessment if they are included in the student’s IEP or 504.

Vermont

Accommodation (Math, Science):

100s number table: A paper-based table listing numbers from 1–100 available from Smarter Balanced for reference. Students with visual processing or spatial perception needs may find this beneficial, as documented in their IEP or 504 plan.

Abacus: This tool may be used in place of scratch paper for students who typically use an abacus. Some students, including students with visual impairments or with documented processing impairments, who typically use an abacus may use an abacus in place of using scratch paper.

Multiplication table: A paper-based multiplication table containing numbers 1–12 will be available from Smarter Balanced for reference. For students with a documented and persistent calculation disability (i.e., dyscalculia).

Virginia

Accommodation (Math):

Calculator and arithmetic tools: Students with disabilities may use calculators and/or arithmetic tools on sections of the Grades 3-7 Mathematics SOL assessments in which a calculator is not allowed. Arithmetic machines and tables/charts are defined as tools that serve the same function as a simple calculator (e.g., four-function calculator). Examples include multiplication, addition, subtraction, or division charts, tables or machines. In order to use a calculator and/or arithmetic tool, students with disabilities must be found eligible by their IEP Team or 504 Committee using the Calculator Accommodation Criteria Form. If the student is determined eligible, the IEP Team or 504 Committee must document the decision on the student’s IEP or 504 Plan and maintain a copy of the completed and signed Calculator Accommodation Criteria Form in the student’s educational record.

Math aids: Students with disabilities may use approved math aids on Mathematics SOL assessments if the accommodation is documented in the student’s IEP or 504 Plan as a testing accommodation. Examples of approved math aids include: number lines, colored shapes, and fraction circles. For a complete list of both approved and not approved math aids, refer to the document Explanation of Testing Accommodations for Students with Disabilities - Math Aids Accommodation Code 19, available on the Virginia Department of Education website.

Washington

Accommodation:

100s number table (Math):

A paper-based table listing numbers from 1–100 published by Smarter Balanced and available for printing on the WCAP portal. Students with visual processing or spatial perception needs may find this beneficial.

Abacus (Math, Science):

This accommodation may be used in place of scratch paper for students who typically use an abacus. Some students, including students with visual impairments or with documented processing impairments, who typically use an abacus may use an abacus in place of using scratch paper.

Multiplication table (Math):

A paper-based multiplication table containing numbers 1–12, available for printing on the WCAP portal. For students with a documented and persistent calculation disability (e.g., dyscalculia).

West Virginia

Accommodation:

Abacus (Math, Science):

Allowed for: WVGSA Grades 3-8, SAT School Day, and WVASA. Description: This tool may be used in place of scratch paper for students who typically use an abacus. Instructional practices: Students use items to count during their instruction. Counting devices (blocks, tiles, chips, etc.) or scratch paper are utilized to assist the student with mathematical concepts. When to select: Some students with visual impairments who typically use an abacus may use an abacus in place of using scratch paper. Notes for implementation: The abacus should be one the student uses during instruction on a regular basis.

Multiplication table (Math):

Allowed for: WVGSA Grades 3-8 (mathematics Grades 4-8 only) and SAT School Day. Definition: A paper-based single digit (1-9) multiplication table will be available for reference. This accommodation is allowed for Grade 4 and above mathematics items. Instructional practices: Students use a multiplication table (often it is stickers on their desks) during regular instruction and assessments. When to select: For students with a documented and persistent calculation disability (i.e., dyscalculia). Notes for implementation: This accommodation is not allowed for third grade.

100s number table (Math):

Allowed for: WVGSA Grades 3-8 (mathematics Grades 4-8 only) and SAT School Day. Description: A paper-based table listing numbers from 1–100 available for reference – available on the WVGSA portal. This is a non-embedded accommodation for Grades 4 and above mathematics items. Instructional practices: Students who need graphic organizers or manipulatives for visual processing to complete mathematics tasks. When to select: Students with visual processing or spatial perception needs may find this beneficial, as documented in their IEP or 504 plan. Notes for implementation: The table can be printed from the portal for students requiring this accommodation. Use of other 100s number tables is prohibited. Not permitted for 3rd grade.

Wisconsin

Accommodation (Math, Science):

Abacus: An instrument for performing calculations by sliding counters along rods or in grooves. Recommended Usage: Examinees with visual impairments. Personal Needs Profile Selection: Abacus. Notes: This accommodation may only be used for the mathematics test. Extra testing time may be needed when providing this accommodation.

Wyoming

Accommodation (Math, Science):

Abacus: This tool may be used in place of scratch paper for students who typically use an abacus. Some students with visual impairments who typically use an abacus may use an abacus in place of or in addition to scratch paper.

Attribution

All rights reserved. Any or all portions of this document may be reproduced and distributed without prior permission, provided the source is cited as:

  • Quanbeck, M., Lazarus, S. S., & Goldstone, L. (2021). Manipulatives: States’ accessibility policies, 2021 (NCEO Accommodations Toolkit #12b). National Center on Educational Outcomes.

NCEO is supported through a Cooperative Agreement (#H326G160001) with the Research to Practice Division, Office of Special Education Programs, U.S. Department of Education. The Center is affiliated with the Institute on Community Integration at the College of Education and Human Development, University of Minnesota. NCEO does not endorse any of the commercial products used in the studies. The contents of this report were developed under the Cooperative Agreement from the U.S. Department of Education, but does not necessarily represent the policy or opinions of the U.S. Department of Education or Offices within it. Readers should not assume endorsement by the federal government. Project Officer: David Egnor