DRAFT - Mathematics for English Language Learners Project

DRAFT 

Spanish Translations of Some Common Mathematics 

Terms used in Middle School and High School 

Dr. Bill Jasper, Project Leader 

(jasper@shsu.edu) 

Sam Houston State University 

Project Team 

Dr. Bill Jasper, Dr. Sylvia Taube, Carolyn Long 

Dr. John Huber, Dr. Mary Swarthout, Lolita Gerardo, Dr. Mark Klespis 

June 2007 

Spanish Translations of Some Common Mathematics Terms used in Middle School and High School, 

created by SHSU MELL Group (jasper@shsu.edu) June 2007


1 

Spanish Translations of Some Common Mathematics Terms used in Middle 

School and High School 

This product was created by a team of Sam Houston State University educators. No 

claim is made that every possible vocabulary term is covered for TAKS tests. 

Ninety vocabulary terms were selected for this product to support the needs of 

mathematics teachers in grades 7-11. Each mathematics term is provided in English and 

Spanish, along with a pronunciation guide, in order to best support those teachers of ELL 

students who are not bilingual. Because a very high portion of ELL students in Texas are 

Hispanic, Spanish was chosen as the second language for the glossary. 

Teachers may make copies and use this product in their classrooms to augment the 

learning of necessary mathematics vocabulary. Some teachers may prefer to provide the entire 

glossary to their students, to pre-teach vocabulary prior to concept development. Others may 

decide to have their students develop their own glossary as terms are introduced during lessons 

or by content strands. 

During the development of this product, we attempted to simplify the mathematics 

language used to define each term, without compromising the mathematics content appropriate 

for each term. After inputs from Texas teachers, we added a drawing or example for each term 

to assist our English Language Learners. 

We hope that this product is helpful to teachers of ELL students, and that it will enhance 

the mathematics understanding of English Language Learners in Texas. Any comments or 

suggestions concerning this product should be directed to Dr. Bill Jasper at jasper@shsu.edu. 




2 

Spanish Translations of Some Common Mathematics Terms used in 

Middle School and High School 

English term Spanish term Description/meaning Drawing/example 

angle 

arc length 

ángulo 

ahn’-goo-loh 

longitud de un 

arco 

lohn’-hee-tood 

deh oon ahr-koh 

A figure formed by 

two non-collinear rays 

that have the same 

endpoint. The two 

rays are called the 

sides of the angle. 

Their common 

endpoint is the vertex. 

the length of a portion 

of the circumference 

of a circle 

A 

arc AB 

The portion of the circle between 

A and B is the arc AB 

B 

area 

área 

ah’-reh-ah 

the number of square 

units that cover a 

figure 

axis of 

symmetry 

eje de simetría 

eh-heh deh 

see-meh-tree’-ah 

a line over which a 

graph is the mirror 

image of itself. Also 

called a line of 

symmetry. 

Area = 2 X 4 = 8 sq. units 





3 

circumference 

circunferencia 

Cartesian sistema a rectangular system 

coordinate cartesiano de for graphing ordered 

system coordenadas 

ses-the’-mah 

cahr-teh-see-ah’- 

noh deh coh-ordeh-na’-thas 

pairs with x- 

coordinates and 

y-coordinates 

seer-coon-fehrehn-seea 

length of the curve 

that forms the circle. 

congruent triángulos triangles whose 

triangles congruentes 

2 2 

completing the completar el adding a term to an 

2 2 ! 3 " ! 3 " 

square cuadrado expression of the form x + 3x = x + 3x 

+ $ % # $ % 

2 2 

2 

& ' & ' 

ax + bx to produce a 

2 

cohm-pleh-thar binomial square. ! 3 " 9 

= x 

ehl 

$ + % # 

& 2 ' 4 

coo-ah-drah-tho 

concrete modelos representations of Manipulatives such as 

models concretos functional algebra tiles, color tiles, and 

relationships with pattern blocks 

mo-deh-los manipulatives or realcon-cre-tos 

world examples 

tree-ahn’-goolohscohn-grooehn-tehs 

corresponding sides 

and angles have the 

same measures 

ABC ! DEF 

conjecture 

conjetura 

cohn-heh-too’-rah 

a generalization 

based on inductive 

reasoning 

after measuring and finding 

the sum of the interior angles 

of several different triangles, a 

conjecture would be that the 

sum is always 180 degrees. 





constant rate 

of change 

cube 

tasa de cambio 

constante 

tah’-sah deh 

cahm’-bee-oh 

cons-tan-te 

cubo 

koo-boh 

where one variable 

changes at the same 

proportion to another 

variable 

a solid figure with six 

faces, each of which 

is a square 

an example is the slope of a 

line, where ratio of the 

change in vertical distance to 

the change in horizontal 

distance is constant. 

4 

cylinder 

dependent 

event 

dependent 

variable 

cilindro 

see-leen’-droh 

evento 

dependiente 

eh-ben’-to 

deh-pehn-deeehn’-te 

Variable 

dependiente 

bah-ree-ah-bleh 

deh-pehn-deeehn’-teh 

a solid figure whose 

top and bottom are 

circular and parallel to 

each other 

in probability, an 

event that depends on 

some previous 

outcome 

the output variable 

whose value is 

determined by the 

independent variable 

(input variable) and 

the rule applied 

pick a card from a deck of 

playing cards, do not replace 

it, and then pick another card. 

The pick of the second card is 

dependent on which card was 

picked on the first draw 

income = (number of hours 

worked) times 

($ per hour) 

Dependent variable is 

income, which depends on 

the number of hours worked. 

diagram 

diagrama 

dee-ah-grah’-mah 

a picture or drawing 

that represent the 

functional relationship 

between two variables 

diameter 

diámetro 

dee-ah’-meh-troh 

a line segment with 

endpoints on the 

circle and that 

contains the center 

(connects two points 

on the circle) 

dimension dimensión in flat (plane) figures, 

the length and width 

A 

AB is the diameter of the circle 

B 





dee-mehnseeohn’ 

of the figure; in solid 

figures, the length, 

width, and height of 

the figure 

2D 

3D 

5 

direct 

variation 

domain 

variación directa 

bah-ree-ahseeohn’ 

dee-rehk-tah 

dominio 

doh-mee’-nee-oh 

when the y value of a 

function varies at the 

same proportional 

rate as the x value of 

the function ! 

the input values of a 

function (independent 

variable) 

! 

y = 4x 

y will always be 4 times 

whatever x is 

y = 2x 

For every x value input into 

the function (the domain), the 

y value is twice as much 

edge 

arista 

ah-ris-tah 

a line segment on a 

solid figure where two 

faces intersect. 

equation 

event 

ecuación 

eh-koo-ahseeohn’ 

evento 

eh-ben’-to 

a mathematical 

sentence that states 

that two expressions 

are equal 

a subset of a sample 

space ! 

y = "2x " 3 

rolling a die and getting a 4 is 

an event 





experimental 

probability 

face 

probabilidad 

experimental 

proh-bah-bee-leedahd 

ehks-peh-reemehn-tahl 

cara 

cah-rah 

the probability of an 

event determined by 

observation or 

measurement 

a flat surface of a 

solid figure 

toss a coin 100 times and you 

had 60 heads and 40 tails. 

The experimental probability 

for getting a head is 60/100 or 

3/5 

6 

function 

(functional 

relationship) 

graph 

función 

foon-seeohn’ 

gráfica 

grah’-fee-cah 

a relation where each 

input is paired with 

exactly one output 

and is based on some 

rule or description ! 

the solution set of an 

equation or inequality 

on a Cartesian 

coordinate system 

y = 2x " 3 

Each different value for x 

gives a different value for y 





hypotenuse 

hipotenusa 

ee-poh-the-noosah 

the side of a right 

triangle opposite the 

right angle 

7 

independent evento in probability, an pick a card from a deck of 

event 

independiente event that does not 

depend on some 

previous outcome 

playing cards, replace it , and 

then pick another card. The 

eh-ben’to 

een-deh-pehndee-ehn’-te 

pick of the second card does 

not depend on which card was 

picked on the first draw 

independent variable the variable whose income = (number of hours 

variable 

inequality 

linear function 

independiente 

desigualdad 

bah-ree-ah’-bleh 

een-deh-pehndee-ehn-teh 

deh-see-goo-ahldahd 

función lineal 

value is subject to 

choice (input variable) 

a mathematical 

sentence that shows a 

greater than, greater 

than or equal, less 

than, or less than or 

equal relationship ! 

between two 

expressions 

a function that can be 

represented by a 

straight line on a 

graph. The function 

would have a constant 

rate of change ! 

worked) times 

($ per hour) 

Independent variable is 

number of hours worked. 

y " 3x + 4 

y = 0.5x + 7 

foon-see-ohn’ leeneh-ahl 

logical razonamiento reasoning based on a geometric proof uses logical 

reasoning lógico 

rah-soh-nah-meeehn’-to 

loh’-heeko 

inferences of logic reasoning to take what 

information is given and to use 

mathematical definitions, 

axioms, and theorems to 

determine a result. 





mathematical propiedades rules or relationships the commutative property 

properties matemáticas that are valid for a set 

of numbers 

proh-pee-eh-dah’- 

dehs 

mah-teh-mah’- 

tee-cahs 

states that, for any real 

numbers a and b, 

a + b = b + a 

mean media the calculated for the data set {80, 76, 89, 

average of a set of 91} the mean is 

meh-dee-ah numbers, found by 

adding all of the (80 + 76 + 89 + 91) 

numbers in the set 

4 

together and dividing 

by the number of 336/4 = 84 

numbers in the set 

median mediana 

meh-dee-ah-nah 

the middle value (or 

the average of the 

middle two values) of 

a set of data arranged 

in numerical order 

for the data set 

{2, 3, 4, 6, 8, 10, 15}, the 

median is 6 

midpoint of a 

segment 

mode 

model 

punto medio de 

un segmento 

poon-to meh-deeoh 

deh oon sehgmehn-toh 

moda 

moh-thah 

modelo 

moh-deh’-loh 

the point on a line 

segment that is equal 

distance from the two 

endpoints 

in a data set, the 

number or element 

that occurs most 

often. 

a representation of a 

mathematical concept 

(such as physical, 

algebraic, or 

geometric 

representations) 

8 cm 8 cm 

midpoint 

for the data set 

{5, 8, 6, 7, 8, 1, 4, 8}, the 

mode is 8 

algebra tiles are used to 

represent algebraic 

relationships. 

represents a variable x and 

8 

monomial 

monomio 

moh-noh’-mee-oh 

a term that is a 

number, a variable, or 

the product of a 

number and one or 

more variables 

represents a value of 1 

3 

x 

3y 2 

4m 2 n 





net 

desarrollo 

des-ah-ro-yo 

a diagram of a twodimensional 

shape 

that can be folded to 

form a three 

dimensional shape 

9 

ordered pair 

parabola 

par ordenado 

pahr 

ohr-deh-nah-tho 

parábola 

pah-rah’-boh-lah 

a pair of numbers in 

which the order they 

are written is 

important. 

the set of points in a 

plane equidistant from 

a point called the 

focus and a line called 

the directrix. 

(3,6) is a different ordered 

pair than (6,3) 

parallel lines 

pattern 

líneas paralelas 

lee’-neh-ahs 

pah-rah-leh-lahs 

patrón 

pah-trohn’ 

two lines in a plane 

that do not intersect 

a sequence of 

observations that 

follows a trend 

3 + 5 = 8 

7 + 13 = 20 

21 + 3 = 24 

perimeter 

perímetro 

peh-ree’-meh-troh 

the sum of the lengths 

of the sides of a 

polygon 

an odd whole number plus 

another odd whole number 

equals an even number. 

11 cm 

E 

5 cm 

D 

9 cm 

F 

9cm + 5cm + 11cm 

= 25cm 





perpendicular 

lines 

líneas 

perpendiculares 

lee’-neh-ahs 

pehr-pehn-deecoo-lahr-ehs 

two lines in a plane 

that form right angles 

at their point of 

intersection 

pi pi a number that 

expresses the ratio of 

a circle’s 

circumference and its 

diameter. 

polynomial 

expressions 

possible 

outcome 

probability 

problem 

solving 

strategies 

properties of 

equality 

expresiones 

polinómicas 

reh-sool-tah’-tho 

poh-see’-bleh 

probabilidad 

ex-pre-sion-ehs 

poh-lee-noh’- 

mee-cas 

resultado posible 

proh-bah-bee-leedahd’ 

estrategias para 

resolución de 

problemas 

ehs-trah-the-heahs 

pah-rah 

re-soh-looseeohn 

deh prohbleh-mahs 

propiedades de la 

igualdad 

proh-pee-eh’- 

dahd-ehs deh la 

ee-goo-ahl-dahd 

proporción 

a monomial or the 

sum or difference of 

monomials 

one of the elements or 

events in the sample 

space. 

a measure of the 

chance or likelihood of 

an event to occur. 

techniques or 

approaches for 

solving a problem 

the reflective, 

symmetric, transitive, 

and substitution 

properties 

2x 

4x 2 – 3x + 2 

if you pull a card from a deck 

of 52 cards, an ace of spades 

is a possible outcome. 

the probability of drawing a 

heart out of a standard deck 

of playing cards is 13/52 or 1/4 

strategies may include make a 

list, look for a pattern, make a 

drawing, solve an easier 

problem, etc. 

see each definition for specific 

examples of each equality 

property 

proportion 

an equation that 

8 

states that two ratios 11 = 14 x 

proh-pohrseeohn’ 

are equal 


created by SHSU MELL Group (jasper@shsu.edu) June 2007 ! 

10



Pythagorean teorema de a formula that shows 

theorem Pitágoras the relationship 

among the lengths of 

the three sides of a 

right triangle: 

a 2 + b 2 = c 2 , where c 

is the hypotenuse, 

and a and b are the 

legs of the triangle. 

teh-oh-reh-mah 

deh pee-tah’-gohrahs 

quadratic función a function of the form 

function cuadrática f (x) = ax 2 + bx + c , 

where a, b, and c are 

foon-see-ohn’ 

! 

real numbers and a ≠ 

coo-ah-drah’-teekah 

! functions must have ! 

0. Quadratic 

an x 2 term 

radius radio 

a line segment from 

the center of a circle 

rah’-dee-oh to a point on the 

circumference (half of 

the diameter) 

C 

a 2 + b 2 = c 2 

5 2 +12 2 =13 2 

25 +144 =169 

169 =169 

D 

b 

c 

f (x) = 2x 2 " 4x + 3 

C 

B 

A 

a 

11 

CD is the radius of the circle 

range 

rango/ recorrido/ 

contradominio 

ran-go / re-coree-do 

/ con-trahdo-mee-nee-oh 

the output values 

(y-coordinates on a 

graph) of a function 

if the domain (input values of 

x) are 1 and 2 for the function 

y = 3 x, then the range 

(values of y) are 3 and 6. 

ratio 

razón 

rah-sohn’ 

a comparison of two 

or more quantities. 

200miles 

9gallons 


created by SHSU MELL Group (jasper@shsu.edu) June 2007 

!



rectangle 

reflection 

rectángulo 

rehk-tahn’-gooloh 

reflexión 

reh-flek-seeohn’ 

a quadrilateral with 

four right angles 

a congruence 

transformation that 

reflects (flips) a figure 

over a line called the 

line of reflection. 

12 

reflective 

property 

propiedad 

reflexiva 

for all real numbers a, 

a = a 

4 = 4 

regular 

polygon 

relation 

right angle 

right triangle 


dahd 

reh-fleh-see-bah 

polígono regular 

poh-lee’-goh-noh 

reh-goo-lar 

relación 

reh-lah-seeohn’ 

ángulo recto 

ahn’-goo-loh 

rehk-toh 

triángulo 

rectángulo 

tree-an’-goo-loh 

rehk-tan-gu-lo 

a polygon that is both 

equilateral (sides 

same length) and 

equiangular (angles 

same measure) 

a set of ordered pairs, 

which describe a 

relationship between 

two variables. For a 

relation, it is 

acceptable for each 

input value to be 

paired with more than 

one output 

an angle with a 

measure of 90 

degrees 

a triangle that 

contains one 90- 

degree (right) angle 

! 

A = {(1,2), (2, 4), (3,6)} 

Or 

B = {(1,2), (1,4), (1,8)} 





rotation 

rotación 

roh-tah-seeohn’ 

a congruence 


rotates (turns) a figure 

about a fixed point 

13 

sales tax 

sample space 

scatter plot 

sector 

impuesto 

eem-poo-ehs’-toh 

espacio muestral 

ehs-pah’-seeoh 

moo-ehs-trahl’ 

gráfica de 

dispersión 

grah’-fee-cah deh 

dees-pehrseeohn’ 

sector 

sehk-tohr 

an amount added to 

the cost of items, 

calculated as a 

percentage of the cost 

the set of all possible 

outcomes for an 

experiment. 

a graph in which the 

data are shown as 

points in a coordinate 

plane. Scatter plots 

show the relationship 

between two 

variables. 

a region of a circle 

bounded by two radii 

and their intercepted 

arc 

a sales tax of 8.5% on a $50 

purchase would be $4.25 

(50 x 0.085) 

the sample space for tossing a 

6-face die is 

S = {1, 2, 3, 4, 5, 6} 

. . 

Ht . . 

. . 

Wt 

. 

similar figures 

slope of a line 

figuras similares 

fee-goo-rahs 

see-mee-lah-rehs 

pendiente de una 

línea 

pehn-dee-ehn’- 

teh oo-nah leenehah 

figures that have the 

same shape but may 

have different sizes. 

The lengths of 

corresponding sides 

of similar figures are 

proportional 

the change in vertical 

distance divided by 

the change in 

horizontal distance 

! 

for the equation 

y = 3x + 5 , 

the slope of the line is 3, 

which shows a vertical 

change of 3 units for every 1 

unit of horizontal change 





slope-intercept 

form of a 

linear function 

sphere 

square 

forma pendienteintercepción 

de 

una función lineal 

fohr-mah pehndee-ehn-te 

! 

een-tehr-sehpsee-ohn 

deh 

oonah func-seeon 

lee-nehal 

esfera 

ehs-feh’-rah 

cuadrado 

koo-ah’-drah-do 

y = mx + b , where m is 

the slope and b is the 

y-intercept 

! 

the set of points in 

space that are an 

equal distance from 

the center of the 

figure. 

a rectangle whose 

four sides are 

congruent 

for the equation 

y = "2x " 3 , the slope is -2 

and the 

y-intercept is -3 

14 

substitution 

property 

surface area 

propiedad de 

sustitución 


dahd 

deh soos-tee-tooseeohn’ 

área total 

ah’-reh-a 

toh-tal 

for all real numbers a 

and b, if a = b, then a 

may replace b or b 

may replace a in any 

statement ! 

for a solid figure, the 

sum of the areas of all 

the faces or surfaces 

than enclose the solid 

if y = 6 , then 6 may be 

substituted for y in the 

expression 2y + 3 , giving a 

value of 15 for the expression 

! 

37mm 

37mm 

37mm 

surface area is sum of the areas 

of the 6 squares that make up 

the sides of the cube 

The surface area of this cube 

is 6 X 37 2 = 8214 mm 2 





symmetric 

property 

system of 

linear 

equations 

table 

tessellation 

propiedad 

simétrica 


dahd 

see-meh’-treecah 

sistema de 

ecuaciones 

lineales 

sees-the’-ma deh 

eh-koo-ahseeohn’-ehs 

leeneh-ah’-lehs 

tabla 

tah-blah 

teselación 

the-she-la-seeon’ 

for all real numbers a 

and b, if a = b, then b 

= a 

! 

two or more linear 

equations that are 

considered or plotted 

together 

a display of 

mathematical data, ! 

usually in a vertical or 

horizontal manner 

an arrangement of 

closed figures that 

completely cover a 

surface, without any 

gaps or overlaps 

If 

2x = 6. Then 

! 

y = 2x + 3 

2y = "2x +12 

Solving : 

x = 1 

y = 5 

6 = 2x 

x 2 4 6 

y 5 9 13 

15 

theoretical 

probability 

probabilidad 

teórica 

proh-bah-bee-leedahd’ 

teh-oh’-ree-cah 

the probability of an 

event determined by 

the ratio of the 

number of favorable 

outcomes to the 

number of possible 

outcomes in the 

sample space 

when a coin is tossed, the 

theoretical probability of 

getting a head is ½ 





transitive 

property 

translation 

transversal 

trigonometric 

ratios 

propiedad 

transitiva 

proh-pee-eh-dahd 

trahn-see-tee’-ba 

traslación 

tras-lah-seeohn’ 

transversal 

trahns-behr-sahl 

razones 

trigonométricas 

rah’-so-nes treegoh-no-meh’-treecas 

for all real numbers a, 

b, and c, if a = b and 

b = c, then a = c 

a congruence 


slides a figure in the 

plane without 

changing its 

orientation or size 

a line that intersects 

two or more different 

lines in a plane. 

When the lines are 

parallel, certain angle 

measurements are 

equal 

relationships between 

the sides of right 

triangles. Most 

commonly used are 

the sine, cosine, and 

tangent 

if a = 2 and 

2 = c, then a = c 

A 

5 

C 

12 

13 

The sine of angle A is 12/13 

B 

16 

variable 

variable 

bah-ree-ah-bleh 

a symbol (usually a 

letter) used to 

represent an unknown 

number in a given set 

of numbers 

in the expression, 

4 n + 2, the “n” is a variable 





vertex 

vértice 

behr’-tee-ceh 

the point on the axis 

of symmetry of a 

parabola equidistant 

from the focus and the 

directrix. 

17 

volume 

volumen 

boh-loo-mehn 

the measured size 

(how much it will hold) 

of a solid figure; 

measurement given in 

“cubic” units 

x-intercept 

intercepción x 

een-tehr-cehpseeohn’ 

eh-kees 

the value(s) of x 

where a graph 

intersects the x-axis. 

y-intercept 

Intercepción y 

een-tehr-cehpseeohn’ 

yah 

the value of y where a 

graph intersects the y- 

axis.

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