NY Grade 5 Math flashcards

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

Order of operations

The agreed sequence for evaluating expressions: grouping symbols first, then multiplication and division from left to right, then addition and subtraction from left to right.

Numerical expression

A combination of numbers and operation signs with no equals sign, such as 6 + 4 × 3. It can be evaluated to a single value.

Variable

A letter or symbol that stands for an unknown or changing number in an expression or equation, such as n in 5n + 1.

Evaluate an expression

To substitute a given value for each variable and simplify using order of operations, for example 2x + 3 at x = 6 equals 15.

Pattern rule

A description of how a sequence changes, either recursive (add 4 each time) or explicit (term n equals 4n − 1).

Equation vs. inequality

An equation states two expressions are equal using =; an inequality states one is greater or less using <, >, ≤, or ≥.

Place value in decimals

Positions to the right of the decimal are tenths, hundredths, thousandths, and so on; each place is one tenth of the place to its left.

Multiplying by powers of ten

Multiplying by 10, 100, or 1,000 shifts the decimal point one, two, or three places to the right; dividing shifts it left.

Expanded form of decimals

Writing a decimal as a sum of its place values, such as 5.308 = 5 + 0.3 + 0.008.

Comparing decimals

Compare digits place by place from left to right after lining up decimal points; the first place that differs decides which number is greater.

Rounding decimals

Locate the place being rounded, then check the digit to its right: 5 or more rounds up, 4 or less keeps the digit unchanged.

Standard algorithm for multiplication

Multiply by each digit of the second factor, shift each partial product one place left, then add the partial products to get the product.

Remainder in division

The amount left over when a whole number does not divide evenly; it is always less than the divisor.

Equivalent fractions

Fractions that name the same amount, produced by multiplying or dividing numerator and denominator by the same nonzero number, as 2/3 = 8/12.

Common denominator

A shared denominator for two or more fractions, needed before adding or subtracting; the least common denominator gives the simplest computation.

Multiplying fractions

Multiply numerator by numerator and denominator by denominator; the result of two fractions less than 1 is smaller than either factor.

Dividing by a unit fraction

Dividing a whole number by 1/b is the same as multiplying by b, so 6 ÷ 1/4 = 24.

Unit fraction divided by whole number

Splitting a unit fraction into equal parts gives a smaller unit fraction: 1/2 ÷ 3 = 1/6.

Scaling by a fraction

Multiplying by a factor greater than 1 enlarges the number, a factor between 0 and 1 shrinks it, and a factor of 1 leaves it unchanged.

Improper fraction

A fraction whose numerator is greater than or equal to its denominator, such as 9/4, equal to the mixed number 2 1/4.

Customary length units

12 inches = 1 foot, 3 feet = 1 yard, and 5,280 feet = 1 mile; multiply to convert to smaller units, divide for larger.

Metric unit conversions

Metric units relate by powers of ten: 1 kilometer = 1,000 meters, 1 meter = 100 centimeters, 1 kilogram = 1,000 grams.

Volume of a rectangular prism

V = length × width × height, or base area × height; the answer is reported in cubic units such as cubic centimeters.

Additive volume

A solid built from non-overlapping rectangular prisms has a total volume equal to the sum of the volumes of its parts.

Line plot with fractions

A number line marked with X's for each data value; the fair share equals the sum of all values divided by the number of X's.

Coordinate plane axes

The horizontal x-axis and vertical y-axis meet at the origin (0, 0); an ordered pair (x, y) is read horizontally first, then vertically.

Quadrilateral hierarchy

A classification in which every square is also a rectangle and a rhombus, and every rectangle and rhombus is a parallelogram.

Trapezoid

A quadrilateral with at least one pair of parallel sides; the parallel sides are called bases.

Triangle angle sum

The three interior angles of any triangle always add to 180 degrees, which allows finding a missing angle.

Quadrilateral angle sum

The four interior angles of any quadrilateral always add to 360 degrees, since it can be split into two triangles.

Reflection over x-axis

A flip over the horizontal axis that changes (x, y) to (x, −y); the x-coordinate stays the same and the y-coordinate changes sign.

Translation

A slide of a figure in the coordinate plane that changes position but not size, shape, or orientation; side lengths and angles stay equal.