Mathematics Flashcards
Reducing Fractions
dividing the numerator and denominator by any common factors to put the fraction in lowest terms
2/4 = 1/2, 3/9 = 1/3
Prime Factorization
the process of writing a number in terms of its prime factors
12 = 2x2x3
Common Denominator
when 2 fractions share the same total parts of whatever item or items are being represented
1/3 and 2/3
Proportion
A statement that two ratios are equivalent.
2/3 = 4/6
Multiplicative Identity
a number that, when multiplied by x, yields x. one or forms of one such as x/x
6x1 = 6
Prime Numbers
natural numbers greater than 1 that have no numbers that will divide into them without a remainder
2, 3, 5, 7….
Benchmark Fraction
an easily remembered fraction that can be used to make problems simpler
1/10, 1/4, 1/2, etc.
Ratio
A comparison that shows the relative size of two or more values.
The ratio of boys to girls is: 4 to 5; 4:5; 4/5; 0.8.
Composite numbers
natural numbers that have numbers that divide into them
4,6,8,9 …
Exponential Form
Using base-10 numbers with exponents in expanded form or writing the prime factorization of a number using exponents
5,232 = 2x2x2x2x3x109 = 2^4x3x109
Expanded Form
break apart each digit in the number and show the digits true value
4,358 = 4000 + 300 + 50 + 8
Scientific Notation
Numbers expressed as the product of a base-10 number and a number between 1 and 10
2.56 x 10 = 25.6 4.32 x 10^-4 = 0.000432
Absolute Value
The distance a number is from zero; always a positive number
Absolute Value of 5 and -5 is 5
Factor Tree
A visual process to find the factors of a number
Base 10 Number system
each place location for a number has a value that is a power of 10
10, 100, 1000, 10000
Improper Fraction
A fraction where the numerator is larger than the denominator
3/2 7/4
Real Numbers
numbers that have a specific value
π, -2, 3, 4, 1/2
Mixed Number
A whole number with a fraction
3 1/2 4 2/5
Magnitude
The size of a number
Prime Factor
a prime number or term that can be multiplied by another to get a number.
2 x 6 = 12, 2 is a prime factor
Greatest common factor (GCF) / Greatest Common Divisor
the largest number that will divide evenly into two or more numbers
For 12 and 15, GCF = 3
Least Common Multiple (LCM)
the smallest number two or more numbers will divide into evenly
For 12 and 15, LCM = 60
Irrational Numbers
real numbers that CANNOT be represented exactly as a ratio of two integers. pi (π)
Relatively Prime
two numbers are relatively prime if they share no common factors 34 and 15
Unit Fraction
1 over any rational number. The inverse of a whole number. 1/2, 1/3, 1/19
Factors
Values that are multiplied to get another number. Some factors of 12 are 3 and 4 because 3 x 4 = 12
Decimal Fractions
fractions with a denominator of 10 1/10 = 0.1
Number Line
a straight line where each number is equal distance from the next one
Denominator
the bottom term of a fraction in 1/10 the denominator is 10
Numerator
the top term of a fraction In 1/10 the numerator is 1
Fractions
represent partial numbers 1/2 = one half of one unit = 50%
Percentages
A way to represent part-to-whole relationships, where the percent is the part out of 100. 35% = 35/100 = 0.35
Concrete Representations
Creative writing written in verse and often including rhymes or heavy use of figurative language
Manipulatives
Abstract Thinking
Using numbers or letter variables in an equation
13x = y
Proportional Manipulatives
objects that are proportional to each other with respect to shape and size
Tangrams
Symbolic Stage / Representational Stage
Drawing pictures or symbols to represent numbers in an equation Squares
Estimating
rounding numbers or approximating them to quickly perform math operations
23 + 39 -> 20 + 40 so the answer is about 60
Non-proportional Manipulatives
objects that are not proportional to each other with respect to shape and size. Often all of the items are the same size.
coins
Manipulatives
Objects used to represent numbers in an equation
Blocks, Coins
Word Wall
An on-going bulletin board with common terms used frequently in the classroom. Vocabulary words are added as they are introduced
Division Property of Equality
If the quantities on each side of an equal sign are both divided by the same amount, the resulting statement will still be equal. If a = b and c ≠ 0, then a ÷ c = b ÷ c
Combine Like Terms
A method of simplifying an algebraic expression by adding or subtracting the coefficients of like terms. 2x + 4x = 6x
Subtraction Property of Equality
If the quantities on each side of an equal sign have the same amount subtracted from them, the resulting statement will still be equal. If a = b, then a – c = b – c
Multiplication Property of Equality
If the quantities on each side of an equal sign are both multiplied by the same amount, the resulting statement will still be equal. If a = b, then ac = bc
Order of Operations (PEMDAS)
A set order in which multi-step equations must be solved: Parenthesis, Exponents, Multiplication and Division (L to R), Addition and Subtraction (L to R)
Like Terms
Terms with the same variable and exponent combination. 2x and 5x
Addition Property of Equality
If the quantities on each side of an equal sign have the same amount added to them, the resulting statement will still be equal. If a = b, then a + c = b + c
Distributive Property
An number in front of a group of terms will multiply all terms in the grouping individually a(b+c) = ab + ac
Linear Expression
An expression that does not contain any exponents 2x + 3
Algebra
The branch of mathematics in which letters and symbols are used to represent unknown values.
Perpendicular Lines
Lines that intersect at a right (90º) angle. They have slopes that are opposite reciprocals, meaning their signs (positive or negative) are opposite and their fractions are flipped. y=2/5x+3 and y=-5/2x-4
Expression
Numbers, symbols, and operators grouped together to show the value of something.
3x - 4y + 6 is an expression. Note that it differs from an equation because there is no equal sign and therefore cannot be solved, only simplified.
Parallel Lines
lines that are coplanar and never intersect because they are changing at the same rate (same slope) y=2x+4 and y=2x-5
Coefficient
A number that multiplies a variable.
In the expression 3x+1, 3 is the coefficient of x.
Equation
A statement that 2 expressions are equal.
2x + 4 = 6 is an example of an equation. Note that it differs from an expression because it has an equal sign and therefore can be solved.
Inequality
A statement that 2 expressions are not equal.
2x + 3 > 6
Variable
A letter or non-numeric symbol that represents an unknown value.
In the expression 2x+4y-5, there are 2 variables: x and y.
Constant
A number without a variable. It is called a constant because its value does not change (it stays constant). In the expression 2x+4y-5, there is one constant: -5.
Term
Each part of an expression that is separated by a + or - sign.
In the expression 2x+4y-5, there are 3 terms: 2x, 4y, and -5.
System of Equations
A set of two or more equations or inequalities with the same set of variables, or unknowns.
2x + 4y = 10 5x - 6y = 12
International System of Units (SI) / The Metric SystemInternational System of Units (SI) / The Metric SystemInternational System of Units (SI) / The Metric SystemInternational System of Units (SI) / The Metric SystemInternational System of Units (SI) / The Metric System
a system of measurement used throughout the world meters, liters, grams
Grams (g)
the base metric unit of masS
Liters (l)
the base metric unit of volume
Meter (m)
the unit for distance in the metric system
The pool was 6 m deep.
English system / Imperial system
a system of measurement used in the United States using units such as feet, pounds and ounces
Unit analysis
the process of converting within or between systems by multiplying by factors of 1 in various forms
Dimensional analysis
the process of converting within or between systems by multiplying by factors of 1 in various forms
Proportion
A statement that two ratios are equivalent.
2/3 = 4/6
Positive Skew / Skewed Right
distribution with a tail that pulls to the right, towards the larger numbers. reflects a bunching of data at the lower end of the distribution.
Negative Skew / Skewed Left
distribution of data with a tail that pulls to the left, toward the smaller numbers. reflects a bunching of data at the upper end of the distribution.
Normal Distribution
graph with a bell-shaped curve, where the graph is symmetric and has no skew.
Range (stats)
The difference between the highest data value and the lowest data value.
Standard Deviation
An average of how far each data point is away from the mean. A higher standard deviation indicates higher variability in the data (the data are more spread out). The Greek symbol sigma (σ) is used to represent standard deviation.
Mean
The mean is found by adding all of the numbers in a data set and dividing that sum by the number of numbers in the data set. The mean is commonly known as the average and the Greek symbol is often used to represent the mean.
Range (stats)
The difference between the highest data value and the lowest data value.
Mode
The mode is the most frequent number in a data set. Some sets of data have no mode (if all data values appear in the set the same number of times). Some sets of data have more than one mode (if multiple pieces of data in a set appear the same number of times and appear more than any other data values).
Median
The median is found by first putting all the numbers in order from least to greatest. The median is either the middle number of a set that has an odd quantity of values, or, when there is an even number of values, the median is found by calculating the mean of the middle two numbers.
Dot Plot
a graph that uses dots to show the frequency counts of a group of data. Dot plots are used for small sets of quantitative data. You can easily identify the mode, the shape or skew of the graph, and potential outliers on a dot plot.
Bar Graph
a visual representation of data which compares values in different categories
Categorical Data
data recorded as categories/groups
Line Graph
a visual representation of data which shows change over time or in response to a manipulated variable
Histogram
a visual representation of data, similar to a bar graph, which compares frequencies of different occurrences
Pie Chart
a graph in which a circle is divided into sectors that each represent a proportion of the whole. Pie charts are helpful when displaying the relative distribution of categories.
Quantitative Data
data which is measured and usually expressed numerically
-distance, time, temperature
Box-And-Whisker Plot / Boxplot
A boxplot splits the data set into quartiles, where the middle 50% of the data forms the box and the lower 25% and upper 25% form the whiskers. Boxplots are used with larger sets of data. You can easily identify the median, the shape or skewness of the graph, and the range on a boxplot.
Stem-And-Leaf Plot / Stemplot
plot where each data value is split into a “leaf” (usually the last digit) and a “stem” (the other digits). Stemplots are used for smaller sets of quantitative data. You can easily identify outliers, data clusters, or gaps on a stemplot.
Slant height
the distance from the apex (top) to an edge of the base
Face
the sides of the shape
Circle
The set of all points equidistant (the same distance) from a given point (the center). Circles have no sides nor interior angles.
Equilateral Polygon
polygon with all sides congruent (equal length)
Triangle
polygon with three vertices and three sides
Equilateral Triangle / Equiangular Triangle
A regular polygon of three sides; triangle with all sides congruent to each other and all angles congruent to each other.
Trapezoid
Quadrilateral with one pair of parallel sides and one pair of non-parallel sides
Square
Rectangle with four congruent sides (four sides of the same measure)
Irregular Polygon
polygon with sides and angle measures that are not the same
Rhombus
Parallelogram with all sides of congruent length.
Concave Polygon
polygon that has at least one interior angle that is more than 180⁰; at least one vertex seems to point inward; diagonals pass outside of the polygon
Scalene Triangle
Triangle with no sides or angles congruent to each other. All three sides are of different lengths.
Equiangular Polygon
polygon with all angles congruent (equal measure)
Pyramid
a shape in three dimensions that has a polygon for a base and triangular faces that meet at a point (the apex) Triangular pyramid
Regular Polygon
polygon with all sides congruent to each other and all angle measures congruent to each other
Convex Polygon
polygon for which all interior angles are less than 180⁰; vertices seem to point outward; all diagonals will be contained within the polygon
Parallelogram
Quadrilateral with two pairs of opposite sides that are parallel to each other
Area
the amount of surface inside of a figure
Isosceles Triangle
Triangle with (at least) two sides congruent to each other and their two base angles congruent to each
Edge
where these faces meet
Right Triangle
triangle with one right angle measuring exactly 90⁰
Polygon
multi-sided, closed figure made up of vertices (corners) and sides (segments connecting consecutive corners)
Rectangle
Parallelogram with four right (90°) angles. Both pairs of opposite sides are parallel. Sides do NOT need to be congruent, but can be.
Perimeter
the distance around the outside of a figure
Quadrilateral
polygon with four vertices and four sides Parallelogram
Acute Triangle
Triangle with each angle being an acute angle; each angle measuring less than 90⁰
Obtuse Triangle
Triangle with one obtuse angle; one angle measuring more than 90⁰
Right Prism
a prism that has the two bases aligned with each other vertically, creating sides that are perpendicular to the bases (meet the bases at right angles), creating rectangular faces
Prism
a three-dimensional figure with quadrilateral faces with two Square prism
Oblique Prism
a prism with bases that are not exactly above/below each other, creating faces that are parallelograms (without right angles)
Sphere
set of points in 3-dimensional space that are all the same distance from a given point (the center) Ball
Vertices
the corners of the shape
