NY Grade 5 Math key terms

A combination of numbers and operation signs, such as 3 + 4 × 2, that has no equals sign. It is evaluated by following the order of operations.

The agreed sequence for evaluating an expression: first grouping symbols, then multiplication and division left to right, then addition and subtraction left to right. Following it guarantees everyone gets the same value.

Curved grouping symbols ( ) that enclose part of an expression. Whatever is inside is calculated first, so they can change the value of an expression.

Symbols [ ] and { } used along with parentheses to group parts of an expression. They let a writer show several nested groupings, and the innermost grouping is always computed first.

To find the single numerical value of an expression by carrying out its operations in the correct order. For example, evaluating 2 + 3 × 4 gives 14, not 20.

A letter or symbol, such as n or x, that stands for an unknown or changing number. It lets a rule be written once and applied to many different values.

A mathematical sentence stating that two expressions have the same value, joined by an equals sign. It may be true, false, or true only for certain values of a variable.

An expression is a phrase of numbers and operations with no equals sign, like 5 + 7. An equation is a full sentence with an equals sign, like 5 + 7 = 12, so only equations can be true or false.

A description, often written with a variable, of how each term in a sequence is produced from its position. For example, term n equals 3 × n + 1 generates 4, 7, 10, 13.

Two numbers written in a fixed order as (x, y) to locate a point on a coordinate grid. The first number gives the horizontal distance and the second gives the vertical distance.

The value a digit has because of its position in a number. In 4,072 the 4 means four thousands and the 7 means seven tens, so moving a digit one place left multiplies its value by ten.

A way of writing a number as the sum of the values of its digits, such as 3,506 = 3,000 + 500 + 6. It makes the place value of each digit visible.

The usual way of writing a number using digits in their places, such as 27,408. It contrasts with expanded form and word form.

The numbers 10, 100, 1,000 and so on, formed by multiplying ten repeatedly. Each power of ten is ten times the one before, which explains why our place-value system shifts by tens.

A small raised number showing how many times a base is used as a factor. In 10³ the exponent 3 means 10 × 10 × 10, which equals 1,000.

The dot separating the whole-number part of a decimal from the fractional part. Digits to its right name tenths, hundredths, thousandths, and so on.

A fraction whose denominator is a power of ten, such as 7/100, which can be written in decimal notation as 0.07. Decimals and such fractions name the same values.

Replacing a number with a nearby number of a chosen place value. Look at the digit to the right: 4 or less keeps the digit, 5 or more increases it by one.

A close answer found by rounding or using friendly numbers instead of exact computation. It is used to judge whether an exact answer is reasonable.

A judgment about whether an answer makes sense in the situation and is close to an estimate. Checking reasonableness catches errors such as misplaced decimal points.

The result of multiplying two or more numbers. In 6 × 7 = 42, the product is 42, and 6 and 7 are factors of it.

The result of dividing one number by another. In 56 ÷ 8 = 7, the quotient is 7; a remainder may be left when the division is not exact.

The amount left over when a whole number cannot be divided evenly by another. Dividing 23 by 5 gives quotient 4 with remainder 3, since 4 × 5 + 3 = 23.

A number that names part of a whole or part of a set, written as a numerator over a denominator. In 3/4 the whole is split into 4 equal parts and 3 are taken.

The top number of a fraction. It tells how many equal parts are being described or counted, as the 3 in 3/4.

The bottom number of a fraction. It tells how many equal parts the whole is divided into, as the 4 in 3/4, so a larger denominator means smaller parts.

A fraction with numerator 1, such as 1/5 or 1/12. Every fraction can be built by combining copies of a unit fraction: 3/5 is three copies of 1/5.

Different fractions that name 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.

A fraction written with the smallest possible whole-number numerator and denominator, such as 2/3 instead of 8/12. This happens when 1 is the only common factor of the two numbers.

A number that is a multiple of the denominators of two or more fractions, letting them be added or compared. For 1/3 and 1/4, 12 is a common denominator.

A number made of a whole number and a fraction, such as 2 3/4, meaning 2 + 3/4. It can be rewritten as an improper fraction, here 11/4.

A fraction whose numerator is greater than or equal to its denominator, such as 7/4. Its value is 1 or more, and it can be rewritten as a mixed number.

To multiply fractions, multiply the numerators together and the denominators together: 2/3 × 4/5 = 8/15. The product of two fractions less than 1 is smaller than either factor.

Sharing a whole number among pieces of size 1/n. Dividing by 1/n is the same as multiplying by n, so 4 ÷ 1/3 = 12 because four wholes contain twelve thirds.

A rectangle diagram whose side lengths represent factors and whose area represents the product. It shows visually why 1/2 × 1/3 = 1/6, since one sixth of the whole rectangle is shaded twice.

The amount of space a solid figure occupies, measured in cubic units. A rectangular prism's volume equals length × width × height, or base area × height.

A cube with edges one unit long, used as the measuring unit for volume. Filling a prism with unit cubes shows how many cubic units it holds.

The units used to report volume, such as cubic centimeters or cubic inches. They record that three dimensions were multiplied together.

A flat surface marked by a horizontal x-axis and a vertical y-axis that cross at the origin. Points are named by ordered pairs and located by moving right or left, then up or down.

The point (0, 0) where the x-axis and y-axis of a coordinate plane meet. It is the starting point from which all other points are located.

The two number lines that form a coordinate plane. The horizontal x-axis measures left and right, and the vertical y-axis measures up and down.

A number line marked with data values, where each X above a value stands for one item. It shows how data cluster and helps find the median and range.

The middle value of a data set put in order; if there are two middle values, it is their mean. Half the data lie at or below it.

The difference between the greatest and least values in a data set. It describes how spread out the data are, not how large a typical value is.

The measurement system used in the United States, including inches, feet, yards, ounces, pounds, cups, quarts, and gallons. Converting within it uses factors such as 12 inches = 1 foot.

A decimal-based measurement system including millimeters, centimeters, meters, grams, kilograms, and liters. Converting within it means multiplying or dividing by powers of ten.

Changing a measurement from one unit to another without changing the amount, such as 3 feet to 36 inches. Multiply or divide by the known relationship between the units.

A closed flat figure made of straight line segments that meet only at their endpoints. Triangles, quadrilaterals, pentagons, and hexagons are polygons.

A polygon with exactly four sides and four angles. Squares, rectangles, parallelograms, rhombuses, and trapezoids are all quadrilaterals.

A quadrilateral with two pairs of parallel sides, where opposite sides are equal and opposite angles are equal. A rectangle is a special parallelogram with right angles.

A quadrilateral with four right angles, whose opposite sides are equal and parallel. Its area is length × width and its perimeter is twice the sum of length and width.

A point where two sides of a figure meet or where two edges of a solid meet. Its plural is vertices, and a triangle has three of them.

A line segment where two faces of a solid figure meet. A rectangular prism has twelve edges, and the number of edges helps identify a solid.

A flat polygon surface of a solid figure. A cube has six square faces, and the shapes of its faces help classify the solid.

A solid with six rectangular faces, where opposite faces are equal and parallel. Its volume is length × width × height, and it is also called a box.

The number of square units needed to cover a flat figure. For a rectangle it equals length × width, and for other polygons it can be found by decomposing the figure.

The total distance around the outside of a flat figure, found by adding its side lengths. It is measured in linear units such as centimeters, not square units.