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Spanish Translations of Some Common Mathematics Terms used in Middle School and High School
Dr. Bill Jasper, Project Leader ([email protected])
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 ([email protected]) June 2007
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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 [email protected].
Spanish Translations of Some Common Mathematics Terms used in Middle School and High School, created by SHSU MELL Group ([email protected]) June 2007
arc AB
The portion of the circle betweenA and B is the arc AB
B
A
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Spanish Translations of Some Common Mathematics Terms used in Middle School and High School
English term Spanish term Description/meaning Drawing/example angle ángulo
ahn’-goo-loh
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.
arc length longitud de un arco
lohn’-hee-tood deh oon ahr-koh
the length of a portion of the circumference of a circle
area área
ah’-reh-ah
the number of square units that cover a figure
Area = 2 X 4 = 8 sq. units 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.
Spanish Translations of Some Common Mathematics Terms used in Middle School and High School, created by SHSU MELL Group ([email protected]) June 2007
2ax bx+
3 DRAFT English term Spanish term Description/meaning Drawing/example Cartesian sistema a rectangular system coordinate cartesiano de for graphing ordered system coordenadas
ses-the’-mah cahr-teh-see-ah’-noh deh coh-or-deh-na’-thas
pairs with x-coordinates and y-coordinates
circumference circunferencia
seer-coon-feh-rehn-seea
length of the curve that forms the circle.
completing the completar el adding a term to an square cuadrado
cohm-pleh-thar ehl coo-ah-drah-tho
expression of the form to produce a
binomial square.
2 2
2 2
2
3 33 3
2 2
3 9
2 4
x x x x
x
! " ! "+ = + + #$ % $ %
& ' & '
! "= + #$ %& '
concrete modelos representations of Manipulatives such as models concretos functional algebra tiles, color tiles, and
relationships with pattern blocks mo-deh-los manipulatives or real-con-cre-tos world examples
congruent triángulos triangles whose triangles congruentes
tree-ahn’-goo-lohscohn-groo-ehn-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.
Spanish Translations of Some Common Mathematics Terms used in Middle School and High School, created by SHSU MELL Group ([email protected]) June 2007
4 DRAFT English term Spanish term Description/meaning Drawing/example constant rate of change
tasa de cambio constante
tah’-sah deh cahm’-bee-oh cons-tan-te
where one variable changes at the same proportion to another variable
an example is the slope of a line, where ratio of the change in vertical distance to the change in horizontal distance is constant.
cube cubo
koo-boh
a solid figure with six faces, each of which is a square
cylinder cilindro
see-leen’-droh
a solid figure whose top and bottom are circular and parallel to each other
dependent event
evento dependiente
eh-ben’-to deh-pehn-dee-ehn’-te
in probability, an event that depends on some previous outcome
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
dependent variable
Variable dependiente
bah-ree-ah-bleh deh-pehn-dee-ehn’-teh
the output variable whose value is determined by the independent variable (input variable) and the rule applied
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) AB is the diameter of the circle
BA
dimension dimensión in flat (plane) figures, the length and width
Spanish Translations of Some Common Mathematics Terms used in Middle School and High School, created by SHSU MELL Group ([email protected]) June 2007
!
y = 4x
!
y = 2x
5 DRAFT English term Spanish term Description/meaning Drawing/example
dee-mehn-seeohn’
of the figure; in solid figures, the length, width, and height of the figure
2D
3D
direct variation
variación directa
bah-ree-ah-seeohn’ dee-rehk-tah
when the y value of a function varies at the same proportional rate as the x value of the function
y will always be 4 times whatever x is
domain dominio
doh-mee’-nee-oh
the input values of a function (independent variable)
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 ecuación
eh-koo-ah-seeohn’
a mathematical sentence that states that two expressions are equal
!
y = "2x " 3
event evento
eh-ben’-to
a subset of a sample space
rolling a die and getting a 4 is an event
Spanish Translations of Some Common Mathematics Terms used in Middle School and High School, created by SHSU MELL Group ([email protected]) June 2007
!
y = 2x " 3
6 DRAFT English term Spanish term Description/meaning Drawing/example experimental probability
probabilidad experimental
proh-bah-bee-lee-dahd ehks-peh-ree-mehn-tahl
the probability of an event determined by observation or measurement
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
face cara
cah-rah
a flat surface of a solid figure
function (functional relationship)
función
foon-seeohn’
a relation where each input is paired with exactly one output and is based on some rule or description
Each different value for x gives a different value for y
graph gráfica
grah’-fee-cah
the solution set of an equation or inequality on a Cartesian coordinate system
Spanish Translations of Some Common Mathematics Terms used in Middle School and High School, created by SHSU MELL Group ([email protected]) June 2007
7 DRAFT English term Spanish term Description/meaning Drawing/example hypotenuse hipotenusa
ee-poh-the-noo-sah
the side of a right triangle opposite the right angle
independent evento in probability, an pick a card from a deck of event independiente
eh-ben’to een-deh-pehn-dee-ehn’-te
event that does not depend on some previous outcome
playing cards, replace it , and then pick another card. The 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 independiente
bah-ree-ah’-bleh een-deh-pehn-dee-ehn-teh
value is subject to choice (input variable)
worked) times ($ per hour) Independent variable is number of hours worked.
inequality desigualdad
deh-see-goo-ahl-dahd
a mathematical sentence that shows a greater than, greater than or equal, less than, or less than or equal relationship between two expressions
!
y " 3x + 4
linear function función lineal
foon-see-ohn’ lee-neh-ahl
a function that can be represented by a straight line on a graph. The function would have a constant rate of change !
y = 0.5x + 7
logical razonamiento reasoning based on a geometric proof uses logical reasoning lógico
rah-soh-nah-mee-ehn’-to loh’-hee-ko
inferences of logic reasoning to take what information is given and to use mathematical definitions, axioms, and theorems to determine a result.
Spanish Translations of Some Common Mathematics Terms used in Middle School and High School, created by SHSU MELL Group ([email protected]) June 2007
8 DRAFT English term Spanish term Description/meaning Drawing/example mathematical propiedades rules or relationships the commutative property properties matemáticas
proh-pee-eh-dah’-dehs mah-teh-mah’-tee-cahs
that are valid for a set of numbers
states that, for any real numbers a and b, a + b = b + a
mean media the calculated for the data set {80, 76, 89,
meh-dee-ah average of a set of numbers, found by
91} the mean is
adding all of the (80 + 76 + 89 + 91) numbers in the set together and dividing
4
by the number of numbers in the set
336/4 = 84
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
punto medio de un segmento
poon-to meh-dee-oh deh oon sehg-mehn-toh
the point on a line segment that is equal distance from the two endpoints
8 cm 8 cm
midpoint
mode moda
moh-thah
in a data set, the number or element that occurs most often.
for the data set {5, 8, 6, 7, 8, 1, 4, 8}, the mode is 8
model modelo
moh-deh’-loh
a representation of a mathematical concept (such as physical, algebraic, or geometric representations)
algebra tiles are used to represent algebraic relationships.
represents a variable x and
represents a value of 1 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
3 x 3y2
4m2n
Spanish Translations of Some Common Mathematics Terms used in Middle School and High School, created by SHSU MELL Group ([email protected]) June 2007
9 cm
11 cm
5 cm
D
E
F
9 DRAFT English term Spanish term Description/meaning Drawing/example net desarrollo
des-ah-ro-yo
a diagram of a two-dimensional shape that can be folded to form a three dimensional shape
ordered pair par ordenado
pahr ohr-deh-nah-tho
a pair of numbers in which the order they are written is important.
(3,6) is a different ordered pair than (6,3)
parabola parábola
pah-rah’-boh-lah
the set of points in a plane equidistant from a point called the focus and a line called the directrix.
parallel lines líneas paralelas
lee’-neh-ahs pah-rah-leh-lahs
two lines in a plane that do not intersect
pattern patrón
pah-trohn’
a sequence of observations that follows a trend
3 + 5 = 8 7 + 13 = 20 21 + 3 = 24
an odd whole number plus another odd whole number equals an even number.
perimeter perímetro
peh-ree’-meh-troh
the sum of the lengths of the sides of a polygon
9cm + 5cm + 11cm = 25cm
Spanish Translations of Some Common Mathematics Terms used in Middle School and High School, created by SHSU MELL Group ([email protected]) June 2007
10 DRAFT English term Spanish term Description/meaning Drawing/example perpendicular lines
líneas perpendiculares
lee’-neh-ahs pehr-pehn-dee-coo-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
expresiones polinómicas
ex-pre-sion-ehs poh-lee-noh’-mee-cas
a monomial or the sum or difference of monomials
2x
4x2 – 3x + 2
possible outcome
resultado posible
reh-sool-tah’-tho poh-see’-bleh
one of the elements or events in the sample space.
if you pull a card from a deck of 52 cards, an ace of spades is a possible outcome.
probability probabilidad
proh-bah-bee-lee-dahd’
a measure of the chance or likelihood of an event to occur.
the probability of drawing a heart out of a standard deck of playing cards is 13/52 or 1/4
problem solving strategies
estrategias para resolución de problemas
ehs-trah-the-he-ahs pah-rah re-soh-loo-seeohn deh proh-bleh-mahs
techniques or approaches for solving a problem
strategies may include make a list, look for a pattern, make a drawing, solve an easier problem, etc.
properties of equality
propiedades de la igualdad
proh-pee-eh’-dahd-ehs deh la ee-goo-ahl-dahd
the reflective, symmetric, transitive, and substitution properties
see each definition for specific examples of each equality property
proportion proporción
proh-pohr-seeohn’
an equation that states that two ratios are equal
!
8
11=14
x
Spanish Translations of Some Common Mathematics Terms used in Middle School and High School, created by SHSU MELL Group ([email protected]) June 2007
!
f (x) = ax2
+ bx + c
CD is the radius of the circle
D C
11 DRAFT English term Spanish term Description/meaning Drawing/example Pythagorean teorema de a formula that shows theorem Pitágoras
teh-oh-reh-mah deh pee-tah’-goh-rahs
the relationship among the lengths of the three sides of a right triangle:
a2 + b2 = c2, where c is the hypotenuse, and a and b are the legs of the triangle.
b
c
a
C B
A
!
a2
+ b2
= c2
52
+122
=132
25 +144 =169
169 =169
quadratic función a function of the form function cuadrática
foon-see-ohn’ coo-ah-drah’-tee-kah
, where a, b, and c are real numbers and a ≠ 0. Quadratic functions must have an x2 term
!
f (x) = 2x2" 4x + 3
radius radio
rah’-dee-oh
a line segment from the center of a circle to a point on the circumference (half of the diameter)
range rango/ recorrido/ contradominio
ran-go / re-co-ree-do / con-trah-do-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
Spanish Translations of Some Common Mathematics Terms used in Middle School and High School, created by SHSU MELL Group ([email protected]) June 2007
12 DRAFT English term Spanish term Description/meaning Drawing/example rectangle rectángulo
rehk-tahn’-goo-loh
a quadrilateral with four right angles
reflection reflexión
reh-flek-seeohn’
a congruence transformation that reflects (flips) a figure over a line called the line of reflection.
reflective property
propiedad reflexiva
proh-pee-eh’-dahd reh-fleh-see-bah
for all real numbers a, a = a
!
4 = 4
regular polygon
polígono regular
poh-lee’-goh-noh reh-goo-lar
a polygon that is both equilateral (sides same length) and equiangular (angles same measure)
relation relación
reh-lah-seeohn’
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
A = {(1,2), (2, 4), (3,6)}
Or
B = {(1,2), (1,4), (1,8)}
right angle ángulo recto
ahn’-goo-loh rehk-toh
an angle with a measure of 90 degrees
right triangle triángulo rectángulo
tree-an’-goo-loh rehk-tan-gu-lo
a triangle that contains one 90-degree (right) angle
Spanish Translations of Some Common Mathematics Terms used in Middle School and High School, created by SHSU MELL Group ([email protected]) June 2007
!
y = 3x + 5
13 DRAFT English term Spanish term Description/meaning Drawing/example rotation rotación
roh-tah-seeohn’
a congruence transformation that rotates (turns) a figure about a fixed point
sales tax impuesto
eem-poo-ehs’-toh
an amount added to the cost of items, calculated as a percentage of the cost
a sales tax of 8.5% on a $50 purchase would be $4.25 (50 x 0.085)
sample space espacio muestral
ehs-pah’-seeoh moo-ehs-trahl’
the set of all possible outcomes for an experiment.
the sample space for tossing a 6-face die is S = {1, 2, 3, 4, 5, 6}
scatter plot gráfica de dispersión
grah’-fee-cah deh dees-pehr-seeohn’
a graph in which the data are shown as points in a coordinate plane. Scatter plots show the relationship between two variables.
. . .
Ht . . . .
Wt
sector sector
sehk-tohr
a region of a circle bounded by two radii and their intercepted arc
similar figures figuras similares
fee-goo-rahs see-mee-lah-rehs
figures that have the same shape but may have different sizes. The lengths of corresponding sides of similar figures are proportional
slope of a line pendiente de una línea
pehn-dee-ehn’-teh oo-nah lee-nehah
the change in vertical distance divided by the change in horizontal distance
for the equation ,
the slope of the line is 3, which shows a vertical change of 3 units for every 1 unit of horizontal change
Spanish Translations of Some Common Mathematics Terms used in Middle School and High School, created by SHSU MELL Group ([email protected]) June 2007
!
y = mx + b
!
y = "2x " 3
!
y = 6
!
2y + 3
37mm
37mm
37mm
surface area is sum of the areasof the 6 squares that make upthe sides of the cube
14 DRAFT English term Spanish term Description/meaning Drawing/example slope-intercept form of a linear function
forma pendiente-intercepción de una función lineal
fohr-mah pehn-dee-ehn-te een-tehr-sehp-see-ohn deh oonah func-seeon lee-nehal
, where m is the slope and b is the y-intercept
for the equation , the slope is -2
and the y-intercept is -3
sphere esfera
ehs-feh’-rah
the set of points in space that are an equal distance from the center of the figure.
square cuadrado
koo-ah’-drah-do
a rectangle whose four sides are congruent
substitution property
propiedad de sustitución
proh-pee-eh’-dahd deh soos-tee-too-seeohn’
for all real numbers a and b, if a = b, then a may replace b or b may replace a in any statement
if , then 6 may be substituted for y in the expression , giving a value of 15 for the expression
surface area área total
ah’-reh-a toh-tal
for a solid figure, the sum of the areas of all the faces or surfaces than enclose the solid
The surface area of this cube is 6 X 372 = 8214 mm2
Spanish Translations of Some Common Mathematics Terms used in Middle School and High School, created by SHSU MELL Group ([email protected]) June 2007
15 DRAFT English term Spanish term Description/meaning Drawing/example symmetric property
propiedad simétrica
proh-pee-eh’-dahd see-meh’-tree-cah
for all real numbers a and b, if a = b, then b = a
If
!
2x = 6 . Then
!
6 = 2x
system of linear equations
sistema de ecuaciones lineales
sees-the’-ma deh eh-koo-ah-seeohn’-ehs lee-neh-ah’-lehs
two or more linear equations that are considered or plotted together
!
y = 2x + 3
2y = "2x +12
Solving :
x =1
y = 5
table tabla
tah-blah
a display of mathematical data, usually in a vertical or horizontal manner
x 2 4 6 y 5 9 13
tessellation teselación
the-she-la-seeon’
an arrangement of closed figures that completely cover a surface, without any gaps or overlaps
theoretical probability
probabilidad teórica
proh-bah-bee-lee-dahd’ 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
Spanish Translations of Some Common Mathematics Terms used in Middle School and High School, created by SHSU MELL Group ([email protected]) June 2007
16 DRAFT English term Spanish term Description/meaning Drawing/example transitive property
propiedad transitiva
proh-pee-eh-dahd trahn-see-tee’-ba
for all real numbers a, b, and c, if a = b and b = c, then a = c
if a = 2 and 2 = c, then a = c
translation traslación
tras-lah-seeohn’
a congruence transformation that slides a figure in the plane without changing its orientation or size
transversal transversal
trahns-behr-sahl
a line that intersects two or more different lines in a plane. When the lines are parallel, certain angle measurements are equal
trigonometric ratios
razones trigonométricas
rah’-so-nes tree-goh-no-meh’-tree-cas
relationships between the sides of right triangles. Most commonly used are the sine, cosine, and tangent
5
12
13
The sine of angle A is 12/13
C
A
B
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
Spanish Translations of Some Common Mathematics Terms used in Middle School and High School, created by SHSU MELL Group ([email protected]) June 2007
17 DRAFT English term Spanish term Description/meaning Drawing/example vertex vértice
behr’-tee-ceh
the point on the axis of symmetry of a parabola equidistant from the focus and the directrix.
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-cehp-seeohn’ eh-kees
the value(s) of x where a graph intersects the x-axis.
y-intercept Intercepción y
een-tehr-cehp-seeohn’ yah
the value of y where a graph intersects the y-axis.
Spanish Translations of Some Common Mathematics Terms used in Middle School and High School, created by SHSU MELL Group ([email protected]) June 2007