Math

Ensure you have a strong grasp of the Pearson alternative text general guidelines before starting any alt text project.

Pearson uses the principles of MathSpeak when authoring alternative text for images containing STEM content. Using MathSpeak grammar rules provides students with print disabilities a description of what would be naturally spoken in the classroom and does not overwhelm them with information that is not needed to understand the content.

The following topics address guidance when authoring image descriptions:

When working in the MathXL space, also review Section 8.1 Alt Text which is an excerpt of the MathXL Content Standards & Development Guidelines.



Numbers and Dates

  • Cardinal numbers (1, 2, 3, 4…) – are announced correctly by screen readers. Numbers can stay as cardinal numbers.
  • Ordinal numbers (1st, 2nd, 3rd, 4th…) – are not announced correctly by screen readers. When writing alternative text descriptions, write out the words “first, second, third, fourth…”.
  • In cases where double or triple-digit numbers are present such as 22nd and 158th, numbers should be written as “twenty-second” and “one hundred and fifty-eighth”.
  • Numbers with decimals (3.5) – are read correctly by screen readers. Numbers with decimal points are correctly read without the need to write out the number or decimal point. The number 3.5 is announced as “3 point 5”.
  • Roman Numerals – some screen readers may read them incorrectly. For example, Roman numeral 5 which is the letter V is announced as the letter V and not 5. When using Roman numerals in alt text, write it out as “Roman numeral 5” and avoid using the Roman numerical system.
    Exception: When students are learning Roman numerals, the description may require special handling to best address the level and context of the content.
  • Dates – When writing:
    • Months – Avoid using abbreviations, write out the whole word.
    • Day – Use cardinal numbers instead of ordinal numbers.
    • Year – Use a space in the middle of the 4-digit number so screen readers announce the year as we speak it naturally. For example, the year “1968” should be written as “19 68”. This will ensure all screen readers announce it as intended.

Basic Math Symbols

SymbolAlternative TextGuidance
++use the symbol and not the word plus
minus

negative
5 minus 2 = 3

negative 2
Use the words minus and negative as appropriate.
xtimes
÷divided by
/over, per, divided byUse “over” and “per” as appropriate. Only use “divided by” for the forward slash character when used for division.
==Use the equals symbol except when a math object starts with an equal symbol (e.g., a step in a solution) then use the word “equals”.
( )left paren
right paren
Use the shortened form instead of writing out the full word. This helps with reducing character counts within the alt text description.

Subscripts and Superscripts

Prior to December 2023, Pearson advised authors to indicate subscripts and superscripts when describing STEM elements in alternative text. However, moving forward, only denote them when necessary for the user to grasp the equation’s meaning.

When a title comes up for re-edition, STEM elements which include subscripts or superscripts, it is not required to edit previously written descriptions. It is acceptable to maintain the alternative text previously written and follow the “refreshed” guidelines for new alternative text.

The shortened form “sub” and “super” are highly recommended for two main reasons:

  1. Fosters brevity.
  2. Reduces the alt text character count which is helpful when trying to stay under 255 characters.

In the following examples, subscripts and superscripts are NOT needed to understand the content:

Math ExpressionAlternative Text
H2OH 2 O
CHC H 4
x5x to the fifth power
f-1(x)f inverse of x
d2y / dx2d 2 y over d x squared
1s22s22p63s23p21 s 2, 2 s 2, 2 p 6, 3 s 2, 3 p 2

Examples when subscripts/superscripts are NEEDED in alt text to avoid ambiguity: 

ExpressionAlternative Text
P1V1=P2V2P sub 1 V sub 1 = P sub 2 V sub 2
z1 = r1(cos θ1 + i sin θ1)z sub 1 equals r sub 1 left paren cosine theta sub 1 plus i sine theta sub 1 right paren
anpn + an-1pn-1 + . . .a sub n times p to the n power plus a sub n minus 1 baseline p to the n minus 1 power plus ellipsis

Scientific Notation/Numbers with Powers

ExpressionAlternative TextGuidance
10210 squared
10310 cubed
10510 to the fifth powerUsing the word “raised” in the description should be avoided since it is known “fifth power” is raised.
10-110 to the negative first power
10-210 to the negative second power
10-310 to the negative third power
2.37 x 1022.37 times 10 squared
7 x 10227 times 10 to the twenty-second powerIt is grammatically incorrect to use “20 second” as an alt text for “22”. Logically 22 should be written as “twenty second”.

Mathematical Expressions

Property/CategoryExpressionAlternative TextGuidance
Boyle’s Law P1V1 = P1V2P sub 1 V sub 1 = P sub 2 V sub 2For this mathematical expression, it is necessary to use subscripts and superscripts to avoid ambiguity. The abbreviation “sub” is preferred because it has fewer characters.
Charles’ LawV1/T1=V2/T2V sub 1 divided by T sub 1 = V sub 2 divided by T sub 2.For this mathematical expression, it is necessary to use subscripts and superscripts to avoid ambiguity. The abbreviation “sub” is preferred because it has less characters.
Mathematical equation (example 1)
Mathematical equation example 1, alt text is written in next column.
v sub y squared = v sub 0 y baseline squared plus 2 a sub y delta yFor this mathematical expression, it is necessary to use subscripts and superscripts to avoid ambiguity.
Baseline is used after the description of the subscripts whenever there is more than one subscript character present for any term for better clarity. Whenever there is only one subscript character associated with a term, no need to use “baseline” after the description of the subscripts.
Mathematical equation (example 2)
Mathematical equation example 2, alt text in next column.
Gamma = StartFrac 1 over StartRoot 1 minus StartFrac 2 over plus or minus StartRoot 1 minus j EndRoot EndFrac EndRoot EndFrac for all j less than or equal to negative 3.
Mathematical equation (example 3)
Mathematical equation example 3, alt text in next column.
X sub k = StartFrac 1 over Uppercase N EndFrac times summation from n equals 0 to uppercase N minus 1 of x sub n times e to the i 2 pi k times StartFrac n over uppercase N EndFrac power.
Fractions (Example 1)
fraction example 1, alt text in next column.
a + StartFrac b over c EndFracNote: a + b over c would be ambiguous and could be interpreted as (a + b)/c or a + (b/c)
Fractions (Example 2)
fraction example 2, alt text in next column.
StartFrac a + b over c EndFracNote: a + b over c would be ambiguous and could be interpreted as (a + b)/c or a + (b/c)
Logarithmslog4 xlog base 4 of x
Limits
Limits expression, alt text in next column.
the limit as x approaches zeroLimits are written with “lim” on the baseline and
X right arrow zero
is placed directly below “lim” and centered.

Other Mathematical Notation

Property/CategoryExpressionAlternative TextGuidance
Line labels or calculator notationL1 or X1L sub 1 or X sub 1
Number base systems3245 or 324five3 2 4 base 5not three hundred twenty-four
Matrix elementsa32a sub 3 2not thirty-two (3 represents the row number and 2 represents the column number)
Exponential functionexe to the xusually omit “raised”
Exponential function
Exponential function, alt text in next column
e to the x squaredusually omit “raised”
Inverse functionf -1(x)f inverse of x
Inverse trig functionsin-1xinverse sine of xThe word inverse is typically stated before the trigonometric function.

Derivatives

Property/CategoryExpressionAlternative TextGuidance
Derivatives (prime notation)y′, y″, y‴y prime, y double prime, y triple prime
Derivatives (n notation)f (n), f (5)enth derivative of f,
fifth derivative of f
Second derivativesd2y / dx2d two y over d x squared
Second order partial derivatives2f / ∂y∂xPartial 2 f over partial y partial x

Molecular Formulae

ExpressionAlternative TextGuidance
H2OH 2 0Omit the word “subscript” to mirror how it is pronounced naturally in speaking. Place a space between each letter/number.
CH4C H 4Omit the word “subscript” to mirror how it is pronounced naturally in speaking. Place a space between each letter/number.
Al2(SO4)3A l 2 left paren S O 4 right paren sub 3Use subscript and parenthesis abbreviations to clarify what subscript 3 is modifying.
(NH4)2SO4Left paren N H 4 right paren sub 2 S O 4Here it is necessary to use subscript and parenthesis abbreviations, so the expression is not ambiguous.
H2SO4H 2 S O 4
CH3CH2CH3C H 3 C H 2 C H 3
CH3(CH2)3CH3C H 3 left paren C H 2 right paren sub 3 C H 3
SO42-S O 4 2 minusFor ions and molecular formulae, charges appear as superscript numbers followed by a plus or minus sign. It is understood that numbers following an element symbol are subscript, and charges are superscript. 
In this example, it is clear which symbols represent the charge. Thus, superscript is not needed and can be omitted.
O2- 

O2 
O super 2 minus

O 2 super minus
When writing alt text add superscript when there is ambiguity. Here you need to indicate the superscript position. If not, the oxide and superoxide ions would both be read as “O 2 minus”.
ClC l super minusWhen writing alt text add superscript to ions with charges of plus or minus 1, which are represented by a superscript plus or minus symbol only.
In this example the chloride ion has a charge of minus 1. So, the ion symbol Cl- would be read aloud as “C l minus” but when writing alt text indicate the “super” position to avoid ambiguity.

Units of the Properties

Property/CategoryExpressionAlternative TextGuidance
Energy/enthalpyKJ mol-1kilojoules per moleUse the elaborate description of units to avoid ambiguity that would arise due to the use of alphabets, since an alphabet may represent units for different properties. For ex., kelvin is represented by K and kilo is represented by k. Similarly, “m” may represent mass or meter.
EntropyJ mol-1 k-1joules per mole per kelvinIt is preferable to use the elaborate description of units to avoid ambiguity that would arise due to the use of alphabets, since an alphabet may represent units for different properties. For ex., kelvin is represented by K and kilo is represented by k. Similarly, “m” may represent mass or meter.
First order rate constants-1per secondIt is preferable to use the elaborate description of units to avoid ambiguity that would arise due to the use of alphabets, since an alphabet may represent units for different properties. For ex., kelvin is represented by K and kilo is represented by k. Similarly, “m” may represent mass or meter.
Temperature-Kelvin scaleKKelvinIt is preferable to use the elaborate description of units to avoid ambiguity that would arise due to the use of alphabets, since an alphabet may represent units for different properties. For ex., kelvin is represented by K and kilo is represented by k. Similarly, “m” may represent mass or meter.
Densitykg m-3kilogram per cubic meterIt is preferable to use the elaborate description of units to avoid ambiguity that would arise due to the use of alphabets, since an alphabet may represent units for different properties. For ex., kelvin is represented by K and kilo is represented by k. Similarly, “m” may represent mass or meter.
Complex Derived Unit – Wattkg m2 s-3 or
start frac kilogram meters squared over second cubed end frac
Kilogram meters squared per second cubed“Derived” units are formed by combining “base” units such as kilograms, meters, and seconds. This example shows the derived unit we usually refer to as a “watt.” In physics calculations, we must often write out derived units in terms of their base units, so that the base units can be recombined or canceled. There are two basic rules for writing out derived or composite units in terms of their base units.

Rule 1: If the derived unit includes a sequence of more than one base unit, the number (singular, plural) of the last base unit should match the associated value. This is true even if the last base unit has an exponent. For example, the unit for moment of inertia is “kilogram meter squared.” The base unit “meter” is last. So, this unit will be singular or plural depending on the associated value. We write “1 kilogram meter squared” and “3 kilogram meters squared.” We do not change “kilogram,” however. If the derived unit is a fraction, this rule only applies to a sequence of base units in the numerator. The units in the denominator should always be singular.

Rule 2: If a sequence of base units includes a unit of distance raised to the second or third power, do not use “square” or “cubic” before the unit. For the example in column 2, we write “kilogram meters squared per second cubed” rather than “kilogram square meters per second cubed.”
Densityg mL-1gram per milliliterIt is preferable to use the elaborate description of units to avoid ambiguity that would arise due to the use of alphabets, since an alphabet may represent units for different properties. For ex., kelvin is represented by K and kilo is represented by k. Similarly, “m” may represent mass or meter.
Densityg cm-3gram per cubic centimeterIt is preferable to use the elaborate description of units to avoid ambiguity that would arise due to the use of alphabets, since an alphabet may represent units for different properties. For ex., kelvin is represented by K and kilo is represented by k. Similarly, “m” may represent mass or meter.
Specific Conductance/conductivitySm-1Siemens meter inverseIt is preferable to use the elaborate description of units to avoid ambiguity that would arise due to the use of alphabets, since an alphabet may represent units for different properties. For ex., kelvin is represented by K and kilo is represented by k. Similarly, “m” may represent mass or meter.
Accelerationms-2meter per second squaredIt is preferable to use the elaborate description of units to avoid ambiguity that would arise due to the use of alphabets, since an alphabet may represent units for different properties. For ex., kelvin is represented by K and kilo is represented by k. Similarly, “m” may represent mass or meter.

Dated: 2024-01-17