MELL English/Spanish Math Terms - Texas State …tsusmell.org/downloads/Products/Classroom Resources/MELL_MathTer… · Each mathematics term is provided in English and Spanish, along

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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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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].


arc AB

The portion of the circle betweenA and B is the arc AB

B

A

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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.


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.


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


!

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


!

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


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.


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


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


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


!

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


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


!

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


!

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


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


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


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.


Documents

MELL English/Spanish Math Terms - Texas State …tsusmell.org/downloads/Products/Classroom Resources/MELL_MathTer… · Each mathematics term is provided in English and Spanish, along