SAE: MATH

subitize

The ability to look at a number pattern and instantly recognize the quantity in the arrangement without counting. For example, the student is able to instantly recognize the quantities on the faces of die represented by dot patterns. It is also considered an important component of number sense.

volume

The amount of space a shape contains. it is measured in cubic units.

geometry

The branch of mathematics that deals with the deduction of the properties, measurements, and relationships of points, lines, angles, and figures in space from their defining conditions by means of certain assumed properties of space.

ratio

The comparison of two numbers or quantities; another use of fractions.

range

The difference between the largest quantity and smaller quantity in a data set

perimeter

The distance around a polygon

median

The middle quantity of a set of data arranged according to size ( or numerical order); for an even number of quantities, the median average of the middle two quantities.

mode

The number that occurs with the greatest frequency in a set of data. There may be one or more modes or no mode for a set of data.

operations

The operations indicate what is to be done with the numbers involved in a given mathematical situation. The main four operations are additions, subtractions, multiplications, and divisions

modeling

The process of choosing and using appropriate mathematics and statistics to analyze empirical situations, to understand them better, and to improve decisions. Modeling links classroom mathematics and statistics to everyday life, work, and decision - making ( National Governors Association Center for Best Practices & Council of Chief State School Officers, 2014; see www.corestandards.org/Math/ Practice for more information).

multiples

The product of any numbers or symbols that you multiply together; for example, 30 is a multiple of 5 and 6 because 5 X 6 = 30; similarly 30 is a multiple of 1 and 30 because 1 X 30 = 30.

mean

The sum of a set of quantities divided by the total number of quantities; also known as average.

natural numbers

They are counting numbers ( 1, 2, 3, 4, 5,....).

symbolic level

A cognitive level that involves the use of symbols to represent mathematical ideas. For example, using the numeral "5" or the number name "five" to represent the numerical value of number five.

exponent

A number or symbol (like a letter), placed above and to the right of the expression, which is called the base of the expression to which the exponent applies. The exponent indicates the number of times the base is used as a factor multiplied by itself. For example, the exponent 3 in the expression 8^3 indicates the 8 is multiplied by itself three times: 8 X 8 X 8. The exponent x in the expression (a + b) ^x indicates (a + b) is multiplied by itself x times.

number

A number represents the cardinality or the idea of how many objects are contained in a set.

prime number

A number with exactly two whole- number factors ( 1 and the number itself). The first several prime numbers are 1 , 2 , 3, 5 , 7, 11, 13, and 17.

numeral

A numeral is the symbolic representation of a numerical quantity; for example, the numeral written as "5" represents symbolically how many objects are contained in a set- in this case, five objects,

square

A parallelogram with all equal sides and four right angles.

rhombus

A parallelogram with all equal sides; opposite sides are parallel and opposite angles are equal.

rectangle

A parallelogram with four right angles

prism

A polyhedron that has two congruent and parallel faces with all other faces being parallelograms

pyramid

A polyhedron with one base, all other faces are triangles that intersect at a common point called a vertex.

kite

A quadrilateral with adjacent sides of equal length and opposite sides of different lengths.

trapezoid

A quadrilateral with exactly one pair of parallel sides.

parallelogram

A quadrilateral with exactly two pairs of parallel sides.

variable

A quantity that may assume any numerical value or set of numerical values.

rate

A ratio in which the measuring units describing two quantities being compared are different. For example, Gill drove the car at 65 miles per hour, or you can get 12 cans for $3. See also unit rate

graph

A representation of data that compares two variables or displays information in a pictorial or graphical form.

rational numbers

A set of numbers that contains integers and positive and negative fractions; expressed as the ratio of two integers , a/b, where b>0; for example, 2/5, -3/8, or 7/1=7

proportion

A statement indicating that two ratios are equal; for example, at the market, if four apples cost $1.20, then eight apples should cost $2.40

frequency table

A table for organizing a set of data that shows the number of pieces of data that shows the number pieces of data that fall within given intervals or categories.

sphere

A three- dimensional figure in which all points on the surface are the same distance from the center of the sphere, a ball.

scalene triangle

A triangle in which all three sides are different lengths.

equilateral triangle

A triangle in which all three sides are the same length

isosceles triangle

A triangle in which at least two sides are the same length.

right triangle

A triangle in which one angle measures exactly 90 degrees.

obtuse triangle

A triangle in which one angle measures more than 90 degrees.

exponential notation

A way to represent repeated multiplication in a simpler manner. For example, 3 multiplied by itself four times or 3 X 3 X 3 X 3 can be represented as 3 ^4, which is equal to 81. Remember that 3^4 is not equivalent to 3 X 4 or 4 X 3.

factors

Any of the numbers or symbols that you multiply together to get another number or product. For example, 5 and 6 are factors of 30 because 5 X 6 = 30; similarly, 1 and 30 are factors of 30 because 1 X 30= 30

properties

Aspects of a shape that define the shape

fractions

Can be expressed as a ratio of two whole numbers, a/b where b>0; for example, 1/2, 2/3, and 12/4

pictograph

Diagram or graph using pictured objects, icons, or symbols, to convey ideas or information.

octagon

Eight - sided polygon

similar

Figures of the same shape, but a different size

pentagon

Five- sided polygon

frequency

For a collection of data, the number of items in a given category

quadrilateral

Four - sided polygon

transitivity principle for indirect measurement

If the length of object A is greater than the length of object B, and the length of object B is greater than the length of object C, then the length of object A is greater than the length of Object C. This principle applies to measurement of other quantities as well ( National Governors Association Center for Best Practices & Council of Chief State Schools Officers, 2014).

computation strategy

Purposeful manipulations that may be chosen for specific problems, may not have a fixed order, and may be aimed at converting one problem into another

slope

Rate of change of one variable in relation to a second variable

percent

Refers to the number of parts out of 100 parts; For example, 76 percent ( written 76%) indicates that you have 76 parts out of 100 parts.

heptagon

Seven- sided polygon

hexagon

Six - sided polygon

manipulatives

Small objects that can be touched and moved about by students in ways that enable descriptions and learning to come alive. They are used to help students internalize mathematics concepts and work with abstract ideas at a concrete- level; for example, base ten blocks are used to help students understand place value ideas.

line graph

Statistical graph that uses lines to show how values change over time.

faces

Surfaces of a polyhedron

congruent

exactly the same; congruent figures are the same shape and same size

automaticity

instant recall of a math fact without having to think about it

composite number

numbers composed of several whole-number factors. For example, 30 is a composite number because it is composed of several whole-number factors other than 1 and itself, like 2,3,5,6,10,and 15

base

side of a polygon in relation to a height; side of a polygon that forms a 90-degree angle with the height

decagon

ten-sided polygon

area

the amount of surface that a shape covers; measures in square units

circumferences

the distance around a circle

commutative property

the order in which you add two terms together or multiply two terms together does not affect the sum of product. In addition, the order of additional can be reversed: a+b=b+a. In multiplication, the order of multiplication can be reversed: a*b=b*a

average

the sum of a set of quantities divided by the total number of quantities; also known as mean

classifications

those names given to shapes that use properties to classify but also take into account the relationships between different classifications of shapes. Classifications use the properties of shapes to lead to a hierarchical structure

distibutive property

when a sum or difference is multiplied by a common term, each part of the sum or difference can be multiplied by the common term and then added or subtracted. A number multiplied by a sum/ difference can be found by multiplying each term of the sum/ difference by the multiplier: a * (b+c)= a * b+ a * c

associative property

when more than two terms are added together or multiplied together, the order in which the terms are paired does not affect the sum or product. In addition, the sum of three or more addends can be found in any order: a+(b+c)=(a+b)+c. In multiplication, the product of three or more factors can be found in any order: a*(b*c)=(a*b)*c

nonagon

Nine- sided polygon

numerator

In a fraction of the form a/ b where a is any integer except zero =, a represents the numerator of the fraction. The numerator expresses the number equal parts taken from the whole after the whole is divided into equal parts. For example, in the fraction 4/ 8 the 4 indicates the number of equal parts that were taken from a whole that was divided into 8 equal parts.

denominator

In a fraction the form a/b where a is any integer and b is any integer except zero, b represents the denominator of the fraction. It expresses the number of equal parts by which the whole is divided. for example, in the fraction 4/8, the 8 indicates that the whole was divided into eight equal parts

greatest common factor (GFC)

In a set of numbers, the largest whole number that is a factor of all the given numbers. For example, the GCF of 30 and 20 is 10, which is the larges whole- number common factor that divides both numbers evenly.

least common multiple (LCM)

In a set of numbers, the smallest non- zero number that all of given numbers divide into. For example, the LCM of 30 and 20 is 60.

fluency

In mathematics, it is the ability to recall facts with speed, accuracy, and automaticity. Fluency requires time to develop with proper understanding of the operations involved. Sufficient practice, conceptual building blocks, and extra supporting should be provided at each grade level.

integers

Integers represent whole numbers that can be positive, negative, or zero. For example, 23, -23, and 0 are all integers. On a number line, negative numbers are on the left side of zero and positive numbers on the right. An integer without a sign is assumed to be a positive number. All integers can be expressed as as fractions, but not all fractions can be expressed as integers (-25/5 is a fraction that can be expressed as -5).

vertex

Intersection of two edges of a polyhedron

edges

Intersection of two faces of a polyhedron

learning progressions

Involve narrative documents describing the progression of a topic across a number of grade levels, which are informed by research on students' cognitive development and logical structure of mathematics. Also, they can be used to explain why standards are sequenced in a given manner, point out cognitive difficulties and pedagogical solutions, and give more detail on particularly challenging areas of mathematics (The Arizona Board of Regents, 2007, ime.math.arizona.edu/progressions).

height

Minimum distance between two bases; perpendicular distance from one base to another; perpendicular distance from vertex to base.

reflection

Mirror image

translation

Moving a figure along a straight line from one location to another, a slide

rotation

Moving a figure by turning around a given point; a turn

iteration

This process is used to express the length of an object as a whole number of length units, by laying multiple copies of a shorter object (the length unit) end to end. The student also needs to understand that the length measurement of an object is the number of the same- size length units that span it with no gaps or overlaps (National Governors Association Center for Best Practices & Council of Chief State School Officers, 2014).

irrational numbers

This set of numbers includes real numbers that cannot be written as the ratio of two integers. This includes infinite and non- repeating decimals For example, the square root of 2 =square root of 2 = 1.414213... and pi = 3.141592...

polyhedron

Three - dimensional figure figures in which all faces are polygons

triangle

Three- sided polygon

dodecagon

Twelve sided polygon

polygon

Two- dimensional figure that is closed and contains at least three straight sides that meet only at corners

unite rate

When the second term in the rate is 1, the rate is referred to as unit rate. For example, Natalie types 36 words per minute, or Samuel earns $14 per hour.

whole numbers

Whole numbers are natural numbers and zero. Natural numbers are the counting numbers ( 1, 2, 3 , 4, 5 ....)

decimals

a set of numbers based on powers of ten. They are fractions expressed in a decimal notation. The denominators of these fractions are powers of 10 (like 10, 100, 1,000). for example, 0.6 (read six-tenths) is equivalent to 6/10 (dividing the numerator by the denominator

computation algorithm

a set of predefined steps applicable to a class of problems that gives the correct result in every case when the steps are carried out correctly. see also computation strategy (National Governors Association Center for Best Practices & Chief State School Officers, 2014). This may include invented or standard algorithms or strategies

dilation

a shrinking or expanding of a figure

bar graph

a statistical graph used to compare quantities; may be made up of all vertical bars or all horizontal bars; used mainly for purposes of comparison

coordinate system

a system of two or three dimensions that allows for the positioning of points, lines, and shapes in space

cone

a three-dimensional figure that has one circular base and a separate face that comes to a vertex point; similar to a pyramid, but with a circular base

cylinder

a three-dimensional figure that has two circular bases and a curved rectangular face between them; similar to a prism

acute triangle

a triangle in which all three angles measure less than 90 degrees

attributes

aspects of a shape that are particular to a specific shape