Accommodations Toolkit

Math Charts/Tables: States’ Accessibility Policies, 2022

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National Center on Educational Outcomes (NCEO)

This summary of states’ accessibility policies for math charts/tables 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 math charts/tables.

Accessibility policies often have several tiers of accessibility features: universal features, designated features, and accommodations.[2] Figure 1 summarizes how states included math charts/tables in their accessibility policies for students with disabilities in 2022. Figure 2 summarizes how states included math charts/tables in their accessibility policies for English learners in 2022. Table 1 shows how math charts/tables was included in the policies, while Table 2 contains additional details and specifications.

Figure 1. States’ Accessibility Policies for Students with Disabilities for Math Charts/Tables, 2022

Math

  • Universal Features (U): 2 States
  • Designated Features (D): 2 States
  • Accommodations (A): 31 States

Science

  • Universal Features (U): 1 States
  • Designated Features (D): 3 States
  • Accommodations (A): 15 States

Figure 2. States’ Accessibility Policies for English Learners for Math Charts/Tables, 2022

Math

  • Universal Features (U): 2 States
  • Designated Features (D): 2 States
  • Accommodations (A): 1 States

Science

  • Universal Features (U): 1 States
  • Designated Features (D): 3 States
  • Accommodations (A): 0 States

Table 1. Accommodations Policies for Math Charts/Tables by State, 2022

U = Universal Feature, D = Designated Feature, A = Accommodation, ELA = English Language Arts, X = Allowed, SD = Allowed for Students with Disabilities, E = 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

Alaska

SD

SD

N

Arizona

Arkansas

California

SD

X

N

Colorado

Connecticut

SD

N

Delaware

SD

SD

N

District of Columbia

SD

Florida

P

P

P

P

P

P

N

Georgia

Hawaii

SD

SD

N

Idaho

SD

N

Illinois

SD

N

Indiana

SD

SD

N

Iowa

SD

SD

N

Kansas

Kentucky

Louisiana

SD

N

Maine

Maryland

SD

N

Massachusetts

SD

N

Michigan

SD

N

Minnesota

X

SD

N

Mississippi

Missouri

SD

SD

N

Montana

SD

N

Nebraska

SD

SD

N

Nevada

SD

SD

N

New Hampshire

SD

N

New Jersey

SD

SD

N

New Mexico

SD

SD

N

New York

SD

N

North Carolina

North Dakota

SD

SD

N

Ohio

X

SD

X

SD

N

Oklahoma

Oregon

SD

X

N

Pennsylvania

Rhode Island

South Carolina

South Dakota

SD

SD

N

Tennessee

Texas

X

X

N

Utah

X

SD, E

N

Vermont

SD

SD

N

Virginia

SD

N

Washington

SD

N

West Virginia

SD

N

Wisconsin

Wyoming

Total (Students with Disabilities)

2

2

31

1

3

15

Total (English Learners)

2

2

1

1

3

0

Table 2. Details and Specifications: States’ Math Tables Accessibility Policies

State

Details/Specifications

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.

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 (Math):

100s number table: 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 ).

Multiplication table: 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 ).

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.

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).

Delaware

Accommodation (Math, Science):

100s Number Table: 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.

Accommodation (Math):

Multiplication Table: 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).
  • 100s chart.

Florida

Multiplication charts/tables may not be used.

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.

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 (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.

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.

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).
  • 100s chart.

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):

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.

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).
  • 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.

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.

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).

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.

Missouri

Accommodation (Math, Science):

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.

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.

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 (Math):

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.

New Jersey

Accommodation (Math, Science):

Mathematics tools: Allowable mathematics tools include:

  • Arithmetic tables (e.g., addition charts, subtraction charts, multiplication charts; division charts).
  • 100s chart.

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 Dakota

Accommodation (Math, Science):

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.

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

Oregon

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.

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.

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).

Texas

Designated Feature (Math, Science):

Calculation aids: 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

  • grade-appropriate multiplication grid without special numbers (e.g., perfect squares) indicated.

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.

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.

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.

Washington

Accommodation (Math):

100s number table: 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.

Multiplication table: 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 (Math):

Multiplication table: 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: 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.

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:

  • Lazarus, S. S., Quanbeck, M., & Goldstone, L. (2022). Math charts/tables: States’ accessibility policies, 2022 (NCEO Accommodations Toolkit #22b). National Center on Educational Outcomes.

The Center is supported through a Cooperative Agreement (#H326G210002) 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. Consistent with EDGAR §75.62, the contents of this report were developed under the Cooperative Agreement from the U.S. Department of Education, but do 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