MCAS Accommodation 20
Individualized Mathematics Reference Sheet
Approval Guide for 2015-2016
The following guidelines should be used by schools to create individualized mathematics reference sheets
(a maximum of three pages) for students with disabilities who have MCAS accommodation 20 specified in
an IEP or 504 plan. This guide includes examples of information that is allowed on reference sheets and
information that is not allowed.
All individualized mathematics reference sheets must be submitted to the Department for review and are
approved on a case-by-case basis, regardless of whether they contain only allowable information listed in
this document, or additional information beyond what is listed. The Department’s decision to approve or
deny a particular reference sheet is determined based on whether the reference sheet provides
information that is directly assessed on the MCAS mathematics test in that grade.
The Department encourages schools to develop reference sheets early in the school year and to seek
approval as soon as possible, since students should be comfortable using their reference sheet at the
time of testing. See additional information about the use of accommodation 20 on MCAS tests, including a
mandatory cover sheet and submission deadlines.
Examples of Information Allowed on Individualized Mathematics Reference Sheets, Grades 3–10
Please note the following:
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The examples that follow are intended to guide decision-making on what should be included on a student’s
reference sheet; they should not simply be photocopied and given to a student.
Category headings (like those shown below) may be included if they do not define terms or concepts.
Information included on the standard MCAS mathematics reference sheets provided to students in grades 5
and above may be included on a student’s individualized mathematics reference sheet.
Area and Perimeter formulas
 grades 5 and above only (on standard MCAS
reference sheet)
Checklists of general problem solving strategies
Coordinate grid information
Examples :
𝑦 −𝑦
 𝑚 = 𝑥2 −𝑥1
2
1
 𝑦 = 𝑚𝑥 + 𝑏
 𝑦 − 𝑦 1 = 𝑚(𝑥 − 𝑥1 )
𝑥 +𝑥 𝑦 +𝑦
 𝑀 = ( 1 2 2 , 1 2 2)
 quadrants can be labeled 1-4
Definitions of common variables, only if on general
MCAS reference sheet; otherwise prohibited
Examples:
 𝑙 = 𝑙𝑒𝑛𝑔𝑡ℎ
 𝑤 = 𝑤𝑖𝑑𝑡ℎ
Distance and Quadratic formulas
Example:
𝑥=
−𝑏 ± √𝑏 2 − 4𝑎𝑐
2𝑎
Divisibility rules
 allowed for all grades
Generic steps for solving mathematical problems
Examples:
 “divide, multiply, subtract, check”
 “common denominators”
 “cross cancel”
 “flip and multiply”
 “line up”
 “count them”
 “move it”
 “line up decimals,” “count places to the right of
decimals,” “move decimal over,” “ignore decimal”
Geometric Formulas
Example:

180(𝑛−2)
𝑛
Graphics
 only allowed without labels, headings, or
organizational structure
Greatest Common Factor/Least Common
Denominator/Least Common Multiple
 minimal steps are allowed, without including
definitions
Hundreds chart
 only counting by ones, no shading or highlighting
 can go up to 300
Mnemonic devices
Examples:
 “5 and above, give it a shove”
 “Please Excuse My Dear Aunt Sally” or “PEMDAS”
 King Henry mnemonic for metric system
conversions
Number lines
 positive and negative integers, counting by ones
 no fractions
Operations with Numbers
Examples:
 “same sign = positive”
 “difference sign = negative”
 “SSS” (same sign sum)
 “DSD” (different sign difference)

𝑖𝑠
𝑜𝑓
%
= 100
Place Value
 first initial only of each place value (grades 3–6;
upper grades can have whole words)
Probability
Example:
𝑃=
𝑓𝑎𝑣𝑜𝑟𝑎𝑏𝑙𝑒 𝑜𝑢𝑡𝑐𝑜𝑚𝑒𝑠
𝑝𝑜𝑠𝑠𝑖𝑏𝑙𝑒 𝑜𝑢𝑡𝑐𝑜𝑚𝑒𝑠
Properties of operations
 represent with variables only, no numbers, no
labels
Example:
 𝑎(𝑏 + 𝑐) = 𝑎𝑏 + 𝑎𝑐
Symbols
 “> is greater than”, “< is less than”, “= is equal to”,
and other symbols/descriptors including
congruent, similar, approximately equal, etc.
Unit Conversions
 most unit conversions are allowed for grades 6
and above, but not for grades 3–5
Word banks:
 alphabetical list okay
 no labels, headings, or organization
Percentages
Example:
Examples of Information Not Allowed on Individualized Mathematics Reference Sheets, Grades 3–10

Arithmetic tables
o e.g., addition/subtraction or multiplication/division charts, unless the student also has
nonstandard accommodation 30
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Category headings that define terms or concepts
Definitions of mathematical terms
Graphic illustrations that are labeled or provide definitions of mathematical concepts
Specific examples showing solutions to actual problems