Praxis 5272 flashcards

33 cards. Read the term and the definition here. The deck at the top of this page is optional.

Standards for Mathematical Practice

Eight habits describing how students engage mathematics, including persevering, reasoning, constructing arguments, modeling, using tools strategically, attending to precision, using structure, and expressing repeated reasoning.

Modeling cycle

A problem-solving process that identifies real quantities, represents them mathematically, computes, interprets results in the original context, and validates or revises the model as needed.

Proportional relationship test

Two quantities are proportional only when their ratio stays constant and the graph is a straight line through the origin; constant difference alone does not indicate proportionality.

Counterexample

A single case that satisfies a statement's conditions but makes the conclusion false; it disproves a general claim, whereas examples alone cannot prove one.

Multiplicative versus additive comparison

Additive comparison asks how many more by subtraction; multiplicative comparison asks how many times as many by division or scaling by a factor.

Order of operations

Evaluate grouping symbols first, then exponents, then multiplication and division left to right, then addition and subtraction left to right.

Divisibility by 3 and 9

A whole number is divisible by 3 or 9 exactly when the sum of its digits is divisible by 3 or 9 respectively.

Dividing by a fraction

Dividing by a fraction is multiplying by its reciprocal, and it can be interpreted as asking how many groups of that fraction fit into the dividend.

Percent change formula

Percent change equals new value minus old value, divided by old value, times one hundred; successive changes multiply rather than add.

Rational versus irrational numbers

Rational numbers can be written as a ratio of integers and have terminating or repeating decimals; irrational numbers such as pi or the square root of two do not.

Integer sign rules

A product or quotient is negative when there is an odd number of negative factors and positive when there is an even number.

Scientific notation

A number written as a times ten to a power, where a is at least one and less than ten; multiplying adds exponents and dividing subtracts them.

Slope formula

Slope equals the change in y divided by the change in x between two points, describing steepness and direction of a line.

Parallel and perpendicular slopes

Parallel lines have equal slopes; perpendicular lines have slopes that are negative reciprocals, so their product equals negative one.

Linear system solution count

Two linear equations have one solution when slopes differ, no solution when slopes match but intercepts differ, and infinitely many when the equations are equivalent.

Inequality reversal rule

Multiplying or dividing both sides of an inequality by a negative number reverses the inequality symbol, because the order of numbers flips.

Definition of a function

A relation in which each input value corresponds to exactly one output value; its graph passes the vertical line test.

Exponential growth formula

Growth is modeled by a times the quantity one plus r raised to t, where a is the initial amount, r the rate per period, and t the number of periods.

Distributive property

Multiplying a sum by a factor gives the same result as multiplying each addend by the factor and adding, as in a times b plus c equals ab plus ac.

Triangle angle sum

The interior angles of any triangle add to 180 degrees; an exterior angle equals the sum of the two remote interior angles.

Area of a trapezoid

Area equals one half times the sum of the two parallel bases times the height between them.

Volume of a cone

Volume equals one third times the base area times the height, which is one third pi r squared h for a circular cone.

Pythagorean theorem

In a right triangle the sum of the squares of the two legs equals the square of the hypotenuse; the converse identifies right triangles.

Scale factor effects

Under similarity, lengths scale by factor k, areas by k squared, and volumes by k cubed.

Mean versus median

The mean is the sum divided by the count and is pulled by outliers; the median is the middle value and resists extreme values.

Interquartile range

The difference between the third quartile and the first quartile, measuring the spread of the middle half of a data set and resisting outliers.

Independent event probability

For independent events, the probability of both occurring is the product of their individual probabilities.

Unit conversion strategy

Multiply by conversion fractions arranged so unwanted units cancel; metric prefixes change by powers of ten and customary equivalents must be memorized.

Constructed-response scoring

Hand-scored items award credit for correct reasoning and supporting work, so showing steps and labeling units can earn partial credit even after an error.

Place value

Each digit's value depends on its position; in base ten, moving one place left multiplies value by ten and moving right divides by ten.

Measures of center and spread

Center describes a typical value using mean, median, or mode; spread describes variability using range, interquartile range, or standard deviation.

Coordinate plane transformations

Reflections flip a figure over an axis, rotations turn it about a point, and translations slide it; these preserve size and shape, while dilations change size.

Equivalent expressions

Expressions are equivalent when they produce the same value for every input; combining like terms and factoring are common ways to create equivalent forms.