English Vocabulary for Mathematics

Free ESL in Canada English lessons for international students to study Mathematics in Canada or USA during an exchange program. Mathematics vocabulary is necessary for exchange students to succeed during an exchange program in the USA or Canada. Other grammar topics include vocabulary, parts of speech, sentence structure, punctuation, tenses, verbals, conditionals and writing.

algebraic expression. One or more variables and possibly numbers and operation symbols. For example, 3x + 6, x, and 5x are algebraic expressions.

algorithm. A systematic procedure for carrying out a computation. For example, the addition algorithm is a set of rules for finding the sum of two or more numbers.

alternate angles. Two angles on opposite sides of a transversal when it crosses two lines. The angles are equal when the lines are parallel. The angles form one of these patterns

analog clock. A timepiece that indicates the time through the position of its hands.

attribute. A quantitative or qualitative characteristic of an object or a shape, for example, colour, size, thickness. bar graph. See under graph.

bias. An emphasis on characteristics that are not typical of an entire population.

binomial. An algebraic expression with two terms, for example, 2x + 4y, 5k - 3n, and 2y2 + 5.

bisector. A line that divides a segment, an angle, a line, or a figure into two equal halves.

calculation method. Any of a variety of methods used for solving problems, for example, estimation, mental calculation, pencil-and-paper computation, the use of technology (including calculators, computer spreadsheets).

capacity. The greatest amount that a container can hold; usually measured in litres or millilitres.

census. The counting of an entire population.

coefficient. Part of a term. In a term, the numerical factor is the numerical coefficient, and the variable factor is the variable coefficient. For example, in 5y, 5 is the numerical coefficient and y is the variable coefficient.

complementary angles. Two angles whose sum is 90º.

composite number. A number that has factors other than itself and 1. For example, the number 8 has four factors: 1, 2, 4, and 8.

computer spreadsheet. Software that helps to organize information using rows and columns.

concrete materials. Objects that students handle and use in constructing their own understanding of mathematical concepts and skills and in illustrating that understanding. Some examples are base ten blocks, centicubes, construction kits, dice, games, geoboards, geometric solids, hundreds charts, measuring tapes, Miras, number lines, pattern blocks, spinners, and tiles. Also called manipulatives.

cone. A three-dimensional figure with a circular base and a curved surface that tapers proportionately to an apex.

congruent figures. Geometric figures that have the same size and shape.

conservation. The property by which something remains the same despite changes such as physical arrangement.

coordinate plane. A plane that contains an X-axis (horizontal) and a Y-axis (vertical). Also called Cartesian coordinate grid or Cartesian plane.

coordinates. An ordered pair used to describe a location on a grid or plane. For example, the coordinates (3, 5) describe a location on a grid found by moving 3 units horizontally from the origin (0, 0) followed by 5 units vertically.

data. Facts or information.

database. An organized and sorted list of facts or information; usually generated by a computer.

degree. A unit for measuring angles.

dependent variable. A variable that changes as a result of a change in the independent variable.

diameter. A line segment that joins two points on the circumference of a circle and passes through the centre.

displacement. The amount of fluid displaced by an object placed in it.

distribution. A classification or an arrangement of statistical information.

equation. A mathematical statement that has equivalent terms on either side of the equal sign.

equivalent fractions. Fractions that represent the same part of a whole or group, for example, 1/3 , 2/6, 3/9, 4/12.

equivalent ratios. Ratios that represent the same fractional number or amount, for example, 1:3, 2:6, 3:9.

estimation strategies. Mental mathematics strategies used to obtain an approximate answer. Students estimate when an exact answer is not required and estimate to check the reasonableness of their mathematics work. Some estimation strategies are: clustering. A strategy used for estimating the sum of numbers that cluster around one particular value. For example, the numbers 42, 47, 56, 55 cluster around 50. So estimate 50 + 50 + 50 + 50 = 200.

rounding. A process of replacing a number by an approximate value of that number. For example, rounding to the nearest tens for 106 is 110.

event. One of several independent probabilities.

experimental probability. The chance of an event occurring based on the results of an experiment.

exponential form. A shorthand method for writing repeated multiplication. In 53, 3, which is the exponent, indicates that 5 is to be multiplied by itself three times. 53 is in exponential form.

expression. A combination of numbers and variables without an equal sign, for example, 3x + 5.

formula. A set of ideas, words, symbols, figures, characters, or principles used to state a general rule. For example, the formula for the area of a rectangle is A = l x w.

frequency. The number of times an event or item occurs.

frequency distribution. A table or graph that shows how often each score, event, or measurement occurred.

graph. A representation of data in a pictorial form.
Some types of graphs are:
bar graph. A diagram consisting of horizontal or vertical bars that represent data.
broken-line graph. On a coordinate grid, a display of data formed by line segments that join points representing data.
circle graph. A graph in which a circle used to represent a whole is divided into parts that represent parts of the whole.
comparative bar graph. A graph consisting of two or more bar graphs placed side by side to compare the same thing. Also called double bar graph.
concrete graph. A graph in which real objects are used to represent pieces of information.
coordinate graph. A grid that has data points named as ordered pairs of numbers, for example, (4, 3).
histogram. A type of bar graph in which each bar represents a range of values, and the data are continuous.
pictograph. A graph that illustrates data using pictures and symbols.

improper fraction. A fraction whose numerator is greater than its denominator, for example, 12/5.

independent events. Two or more events for which the occurrence or non-occurrence of one does not change the probability of the other.

independent variable. A variable that does not depend on another for its value; a variable that the experimenter purposely changes. Also called cause variable.

inequality. A statement using symbols to show that one expression is greater than (>), less than (<), or not equal to another expression.

integer. Any one of the numbers. . . , -4, -3, -2, -1, 0, 1, 2, 3, 4, . . .

integral exponent. A power that has an integer as an exponent.

intersecting lines. Two lines with exactly one point in common, the point of intersection.

interval. A space between two points. For example, 0-10 represents the interval from 0 to 10 inclusively.
irrational number. A number that cannot be represented as a terminating or repeating decimal.
irregular polygon. A polygon whose side and angle measures are not equal.

isometric dot paper. Dot paper formed by the vertices of equilateral triangles, used for three-dimensional drawings. Also called triangular dot paper or triangle dot paper.

isosceles triangle. A triangle that has two sides of equal length.

linear dimension. Dimension involving the measurement of only one linear attribute, for example, length, width, height, depth.

linear relationship. A relationship that has a straight-line graph.

line of best fit. A line that can sometimes be determined on a scatter plot. If a line of best fit can be found, a relationship exists between the independent and dependent variables.

line of symmetry. A line that divides a shape into two parts that can be matched by folding the shape in half.

many-to-one correspondence. The matching of elements in two sets in such a way that more than one element in one set can be matched with one and only one element in another set, for example, 3 pennies to each pocket.

mass. The amount of matter in an object; usually measured in grams or kilograms.

mathematical communication. The use of mathematical language by students to: respond to and describe the world around them; communicate their attitudes about and interests in mathematics; reflect and shape their understandings of and skills in mathematics. Students communicate by talking, drawing pictures, drawing diagrams, writing journals, charting, dramatizing, building with concrete materials, and using symbolic language, (e.g., 2, >, =).

mathematical concepts. The fundamental understandings about mathematics that a student develops within problem-solving contexts. mathematical language. terminology (e.g., factor, pictograph, tetrahedron); pictures/diagrams (e.g., 2 x 3 matrix, parallelogram, tree diagram); symbols, including numbers (e.g., 2, 1/4), operations (e.g., 3 x 8 = [3 x 4] + [3 x 4]), and relations (e.g., 1/4 <).

mathematical procedures. The skills, operations, mechanics, manipulations, and calculations that a student uses to solve problems.

mean. The average; the sum of a set of numbers divided by the number of numbers in the set. For example, the average of 10 + 20 + 30 is 60 ÷ 3 = 20.

measure of central tendency. A value that can represent a set of data, for example, mean, median, mode. Also called central measure.

median. The middle number in a set of numbers, such that half the numbers in the set are less and half are greater when the numbers are arranged in order. For example, 14 is the median for the set of numbers 7, 9, 14, 21, 39. If there is an even number of numbers, the median is the mean of the two middle numbers. For example, 11 is the median of 5, 10, 12, and 28.

Mira. A transparent mirror used in geometry to locate reflection lines, reflection images, and lines of symmetry, and to determine congruency and line symmetry.

mixed number. A number that is the sum of a whole number and a fraction, for example, 81/4.

mode. The number that occurs most often in a set of data. For example, in a set of data with the values 3, 5, 6, 5, 6, 5, 4, 5, the mode is 5.

modeling. A representation of the facts and factors of, and the inferences to be drawn from, an entity or a situation.

monomial. An algebraic expression with one term, for example, 2x or 5xy2.

multiple. The product of a given number and a whole number. For example, 4, 8, 12, . . . are multiples of 4.

multiplication. An operation that combines numbers called factors to give one number called a product. For example, 4 x 5 = 20; thus factor x factor = product.

multi-step problem. A problem whose solution requires at least two calculations. For example, shoppers who want to find out how much money they have left after a purchase follow these steps:
Step 1 - Add all items purchased (subtotal).
Step 2 - Multiply the sum of purchases by % of tax.
Step 3 - Add the tax to the sum of purchases (grand total).
Step 4 - Subtract the grand total from the shopper's original amount of money.

natural numbers. The counting numbers 1, 2, 3, 4, . . .

net. A pattern that can be folded to make a three-dimensional figure.

network. A set of vertices joined by paths.

non-standard units. Measurement units used in the early development of measurement concepts, for example, paper clips, cubes, hand spans, and so on.

number line. A line that matches a set of numbers and a set of points one to one.

number operations. Mathematical processes or actions that include the addition, subtraction, multiplication, and division of numbers.

nth term. The last of a series of terms.

obtuse angle. An angle that measures more than 90º and less than 180º.

one-to-one correspondence. The matching of elements in two sets in such a way that every element in one set can be matched with one and only one element in another set.

ordered pair. Two numbers in order, for example, (2, 6). On a coordinate plane, the first number is the horizontal coordinate of a point, and the second is the vertical coordinate of the point.

order of operations. The rules used to simplify expressions. Often the acronym BEDMAS is used to describe this calculation process:
brackets
exponents
division or multiplication,
whichever comes first addition or subtraction,
whichever comes first

ordinal number. A number that shows relative position or place, for example, first, second, third, fourth.

parallel lines. Lines in the same plane that do not intersect.

parallelogram. A quadrilateral whose opposite sides are parallel.

perfect square. The product of an integer multiplied by itself. For example, 9 = 3 x 3; thus 9 is a perfect square.

perpendicular lines. Two lines that intersect at a 90º angle.

place value. The value given to the place in which a digit appears in a numeral. In the number 5473, 5 is in the thousands place, 4 is in the hundreds place, 7 is in the tens place, and 3 is in the ones place.

plane shape. A two-dimensional figure.

polygon. A closed figure formed by three or more line segments. Examples of polygons are triangles, quadrilaterals, pentagons, octagons.

polyhedron. A three-dimensional object that has polygons as faces.

polynomial. An algebraic expression. Examples of polynomials are 6x, 3x - 2, and 4x2 + 5x - 4.

population. The total number of individuals or items.

primary data. Information that is collected directly or first-hand. Data from a person-on-the-street survey are primary data. Also called first-hand data or primary-source data.

prime factorization. An expression showing a composite number as a product of its prime factors. The prime factorization for 42 is 2 x 3 x 7.

prime number. A whole number greater than 1 that has only two factors, itself and 1. For example, 7 = 1 x 7.

prism. A three-dimensional figure with two parallel and congruent bases. A prism is named by the shape of its bases, for example, rectangular prism, triangular prism.

probability. A number that shows how likely it is that an event will happen.

proper fraction. A fraction whose numerator is smaller than its denominator, for example, 2/3.

proportion. A number sentence showing that two ratios are equal, for example, 2/3 = 6/9.

Pythagorean theorem. In a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the other two sides.

quadrilateral. A polygon with four straight sides.

radius. A line segment whose endpoints are the centre of a circle and a point on the circle.

range. The difference between the highest and lowest number in a group of numbers. For example, in a data set of 8, 32, 15, 10, the range is 24, that is, 32 - 8.

rate. A comparison of two numbers with different units, such as kilometres and hours, for example, 100 km/h.

ratio. A comparison of numbers with the same units, for example, 3:4 or 3/4. rational number. A number that can be expressed as the quotient of two integers where the divisor is not 0.

reflection. A transformation that turns a figure over an axis. The figure does not change size or shape, but it does change position and orientation. A reflection image is the result of a reflection. Also called flip.

regular polygon. A closed figure in which all sides and angles are equal.

rotation. A transformation that turns a figure about a fixed point. The figure does not change size or shape, but it does change position and orientation. A rotation image is the result of a rotation. Also called turn.

rotational symmetry. A shape that fits onto itself after a turn less than a full turn has rotational symmetry. For example, a square has a turn symmetry of order 4 because it resumes its original orientation after each of 4 turns: 1/4 turn, 1/2 turn, 3/4 turn, and full turn. Also called turn symmetry.

sample. A small, representative group chosen from a population and examined in order to make predictions about the population. Also called sampling.

scale drawing. A drawing in which the lengths are a reduction or an enlargement of actual lengths.

scalene triangle. A triangle with three sides of different lengths.

scatter plot. A graph that attempts to show a relationship between two variables by means of points plotted on a coordinate grid. Also called scatter diagram.

scientific notation. A way of writing a number as the product of a number between 1 and 10 and a power of 10. In scientific notation, 58 000 000 is written 5.8 x 107.

secondary data. Information that is not collected first-hand, for example, data from a government document or a database. Also called second-hand data or secondary-source data.

sequence. A succession of things that are connected in some way, for example, the sequence of numbers 1, 1, 2, 3, 5, . . .

seriation line. A line used for the ordering of objects, numbers, or ideas.

shell. A three-dimensional figure whose interior is completely empty.

SI. The international system of measurement units, for example, centimetre, kilogram. (From the French Système International.)

similar figures. Geometric figures that have the same shape but not always the same size.

simple interest. The formula used to calculate the interest on an investment: I = PRT where P is the principal, R is the rate of interest, and T is the time chosen to invest the principal.

simulation. A probability experiment to test the likelihood of an event. For example, tossing a coin is a simulation of whether the next person you meet is a male or a female.

skeleton. A three-dimensional figure showing only the edges and vertices of the figure.

standard form. A way of writing a number in which each digit has a place value according to its position in relation to the other digits. For example, 7856 is in standard form.

supplementary angles. Two angles whose sum is 180º.

surface area. The sum of the areas of the faces of a three-dimensional object.

survey. A sampling of information, such as that made by asking people questions or interviewing them.

symbol. See under mathematical language.

systematic counting. A process used as a check so that no event or outcome is counted twice.

table. An orderly arrangement of facts set out for easy reference, for example, an arrangement of numerical values in vertical or horizontal columns.

tally chart. A chart that uses tally marks to count data and record frequencies.

tangram. An ancient Chinese puzzle made from a square cut into seven pieces: two large triangles, one medium-sized triangle, two small triangles, one square, and one parallelogram.

theoretical probability. The number of favorable outcomes divided by the number of possible outcomes.

transformation. A change in a figure that results in a different position, orientation, or size. The transformations include the translation (slide), reflection (flip), rotation (turn), and dilatation (reduction or enlargement).

translation. A transformation that moves a figure to a new position in the same plane. The figure does not change size, shape, or orientation; it only changes position. A translation image is the result of a translation. Also called slide.

trapezoid. A quadrilateral with exactly one pair of parallel sides.

tree diagram. A branching diagram that shows all possible combinations or outcomes.

variable. A letter or symbol used to represent a number.

Venn diagram. A diagram consisting of overlapping circles used to show what two or more sets have in common.

vertex. The common endpoint of the two segments or lines of an angle.

volume. The amount of space occupied by an object; measured in cubic units such as cubic centimetres.

For Intermediate and Advanced Mathematics Vocabulary please go to the ESL in Canada Sentence Master Grammar Reference or Exchange Student Survival Guide. You can also order the complete Sentence Master Grammar Reference CD for additional explanations and examples.

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