Praxis Elem CKT Math key terms

Instantly recognizing how many items are in a small group without counting them one by one. Seeing four dots arranged in a square and knowing it is four is an example.

The understanding that the last number said when counting a set tells how many objects are in that set. A child who counts five blocks and answers 'five' shows this principle.

Matching exactly one number word, or one object, to each item being counted. Touching each bear once while saying a number illustrates this counting principle.

Knowing that the count of a set does not change when objects are rearranged or spread out. A child with this understanding knows a scattered row of seven counters is still seven.

Recognizing that an operation can be undone or mentally reversed. Knowing that adding then subtracting the same amount returns the original number is one example.

The system in which a digit's value depends on its position in a number. In 352, the 3 means three hundreds, the 5 means five tens, and the 2 means two ones.

Manipulatives representing ones (small cubes), tens (rods), hundreds (flats), and thousands (large cubes). They let students build and trade quantities to model regrouping in addition and subtraction.

Writing a number as the sum of the values of its digits. The number 4,067 in expanded form is 4,000 + 60 + 7.

Trading ten units in one place for one unit in the next larger place, or the reverse. It is used when adding or subtracting digits whose sum exceeds nine or whose top digit is too small.

A line marked with evenly spaced points representing numbers in order. It supports comparing numbers, rounding, and modeling addition, subtraction, and fractions as distances.

Replacing a number with a nearby number of a specified place value. The result is chosen by checking the digit to the right of that place against the midpoint five.

Finding a reasonable approximate answer or quantity rather than an exact one. Strategies include rounding, front-end estimation, and using compatible numbers to simplify computation.

Numbers adjusted to values that are easy to compute with mentally, often used in estimation. For example, 198 + 305 can be estimated as 200 + 300.

Operations that undo each other, such as addition and subtraction or multiplication and division. They are used to solve equations and to check answers.

A set of related equations using the same three numbers. From 3, 4, and 12 come 3 × 4 = 12, 4 × 3 = 12, 12 ÷ 4 = 3, and 12 ÷ 3 = 4.

The rule that changing the order of addends or factors does not change the result. For example, 8 + 5 equals 5 + 8, and 6 × 7 equals 7 × 6.

The rule that grouping addends or factors differently does not change the result. For example, (2 + 3) + 4 equals 2 + (3 + 4).

The rule that multiplying a sum by a number equals multiplying each addend by that number and adding the products. For example, 6 × 14 equals 6 × 10 plus 6 × 4.

The separate products formed when multiplying multi-digit numbers place by place, then added together. For 23 × 4, the partial products are 80 and 12, totaling 92.

A rectangle diagram whose side lengths represent factors and whose area represents their product. It visually explains multiplication, partial products, and fraction multiplication.

An arrangement of objects in equal rows and columns. Arrays model multiplication and division and connect to the area model.

Numbers multiplied together to produce a product. In 3 × 7 = 21, the factors are 3 and 7; the factors of 21 are 1, 3, 7, and 21.

The products formed when a number is multiplied by whole numbers. The multiples of 4 include 4, 8, 12, 16, and so on.

A whole number greater than one with exactly two distinct factors, one and itself. Examples include 2, 3, 5, 7, and 11.

A whole number greater than one that has more than two factors. For example, 12 is composite because it is divisible by 1, 2, 3, 4, 6, and 12.

Fractions that name the same amount even though their numerators and denominators differ. For example, one-half, two-fourths, and three-sixths are equivalent.

A familiar fraction such as one-half, one-fourth, or three-fourths used to judge the size of other fractions. Comparing a fraction to one-half helps students estimate and order values.

A shared multiple of the denominators of two or more fractions, used to compare or add them. For one-third and one-fourth, twelve is a common denominator.

A fraction written so that the numerator and denominator share no common factor greater than one. For example, eight-twelfths simplifies to two-thirds.

A number written with a decimal point to represent tenths, hundredths, and smaller place values. The digits to the right of the point follow the same base-ten pattern as whole numbers.

A comparison of two quantities by division. A class with 6 girls and 4 boys has a ratio of girls to boys of 6 to 4, or three to two.

A rate expressed per one unit of the second quantity. If 3 pounds of apples cost 6 dollars, the unit rate is 2 dollars per pound.

Reasoning with relationships in which two quantities change by the same factor. It supports solving problems about scaling recipes, maps, and constant speed.

The distance around the outside of a two-dimensional shape. For a rectangle it equals twice the sum of the length and width.

The amount of surface a two-dimensional figure covers, measured in square units. A rectangle's area equals its length times its width.

The average found by dividing the sum of a data set by the number of values. The mean of 2, 4, and 9 is 5.

The middle value of a data set ordered from least to greatest. If there is an even number of values, it is the mean of the two middle values.

Ongoing checks of student understanding used to adjust instruction while learning is in progress. Exit tickets, questioning, and quick quizzes are common examples.

A physical object students handle to model mathematical ideas. Counters, fraction tiles, and base-ten blocks are manipulatives that bridge concrete experience and abstract symbols.