Praxis Elem CKT Math flashcards

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

Place value of a digit

The value a digit has because of its position; in 5,283 the 8 means 8 tens, or 80, since each place is ten times the place to its right.

Standard algorithm for addition

Add digits column by column from the right, regrouping ten ones as one ten, ten tens as one hundred, and so on, carrying to the next column.

Distributive property in multiplication

Multiplying a sum equals the sum of the products: a × (b + c) = (a × b) + (a × c). Partial-products methods depend on this property.

Commutative property

Order does not change the result of addition or multiplication: a + b = b + a and a × b = b × a. It does not hold for subtraction or division.

Associative property

Grouping does not change a sum or product: (a + b) + c = a + (b + c) and (a × b) × c = a × (b × c). It fails for subtraction and division.

Identity and zero properties

Adding 0 or multiplying by 1 leaves a number unchanged. Multiplying any number by 0 gives 0, and 0 divided by a nonzero number is 0.

Equivalent fractions

Fractions naming the same amount, such as 1/2, 2/4, and 5/10. Multiplying or dividing numerator and denominator by the same nonzero number produces an equivalent fraction.

Comparing fractions

Use common denominators, common numerators, or benchmarks such as 1/2. With equal denominators, the larger numerator gives the larger fraction.

Fraction multiplication meaning

Multiplying by a fraction means taking that part of a whole: 3/4 × 8 means three-fourths of 8, which is 6.

Dividing by a unit fraction

Dividing by 1/n is the same as multiplying by n, because the question asks how many 1/n pieces fit in the whole. For example, 4 ÷ 1/3 = 12.

Decimal place values

Positions to the right of the decimal point are tenths, hundredths, thousandths, and so on, each worth one-tenth of the place before it.

Rounding whole numbers

Locate the target place, then check the digit to its right. If that digit is 5 or more, round up; if it is 4 or less, keep the target digit.

Prime and composite numbers

A prime has exactly two factors, 1 and itself, such as 7 or 13. A composite has more than two factors, such as 12. The number 1 is neither.

Greatest common factor

The largest number dividing two or more numbers evenly. GCF(12, 18) = 6, useful for simplifying fractions such as 12/18 to 2/3.

Least common multiple

The smallest nonzero number that is a multiple of two or more numbers. LCM(4, 6) = 12, used to find common denominators.

Order of operations

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

Perimeter versus area

Perimeter is the distance around a figure, measured in linear units. Area is the surface covered, measured in square units, as in length × width for a rectangle.

Volume of a rectangular prism

Volume equals length × width × height, reported in cubic units. It also equals base area times height for any prism with a uniform cross-section.

Triangle area formula

Area of a triangle is one-half times base times height, where height is perpendicular to the chosen base, not necessarily a side length.

Quadrilateral classification

A square has four equal sides and four right angles. It is also a rectangle, rhombus, and parallelogram, since those categories overlap by shared properties.

Coordinate plane ordered pairs

A point is named (x, y): x gives horizontal distance from the origin and y gives vertical distance. The origin is (0, 0).

Mean of a data set

The arithmetic average: add all values and divide by the number of values. The mean is affected by outliers more than the median is.

Median and mode

Median is the middle value when data are ordered; for an even count, average the two middle values. Mode is the value occurring most often.

Unit rate

A rate expressed per one unit, found by dividing the first quantity by the second. If 3 pounds cost $6, the unit rate is $2 per pound.

Concrete to abstract progression

Instruction moves from manipulatives to pictorial representations to symbols, so students build meaning before memorizing procedures such as regrouping.

Procedural versus conceptual knowledge

Procedural knowledge is skill in carrying out steps; conceptual knowledge is understanding why they work. Effective instruction connects both rather than drilling alone.

Formative assessment in mathematics

Ongoing checks of student understanding, such as exit tickets or error analysis, used to adjust instruction rather than to assign final grades.

Diagnosing a computation error

Compare a student's work with the correct procedure to locate the faulty step, distinguishing a misapplied rule from a misunderstanding of the underlying concept.

Number talk routine

A brief whole-class discussion in which students solve a computation mentally and share strategies, building flexibility and fluency with number relationships.

Manipulatives for base ten

Blocks representing ones, tens, hundreds, and thousands let students physically trade ten of one unit for one of the next, making regrouping visible.

Fraction models

Area models, set models, and number lines represent fractions differently; number lines are especially useful for showing magnitude and equivalence.

Mathematical discourse moves

Teacher actions such as revoicing student thinking, asking for justification, and comparing strategies to develop reasoning and precise mathematical language.