### Vocabulary

Addition and subtraction within 5, 10, 20, 100, or 1000. Addition or subtraction of two whole numbers with whole number answers, and with sum or minuend in the range 0-5, 0-10, 0-20, or 0-100, respectively. Example: 8 + 2 = 10 is an addition within 10, 14 – 5 = 9 is a subtraction within 20, and 55 – 18 = 37 is a subtraction within 100.

Additive inverses. Two numbers whose sum is 0 are additive inverses of one another. Example: 3/4 and – 3/4 are additive inverses of one another because 3/4 + (- 3/4) = (- 3/4) + 3/4 = 0.

Associative Property of Addition The problem (3 + 6) + 8 = 3 + (6 + 8)demonstrates the associative property of addition. Observe that the addends are the same on either side of the equal sign: 3 plus 6 plus 8

The associative property of addition says that when we add more than two numbers the grouping of the addends does not change the sum.

In the example above, we can easily observe that:

(3 + 6) + 8 = 3 + (6 + 8)

9 + 8 = 3 + 14

1

7 = 17

Associative Property of Multiplication

The problem (2 � 4) � 3 = 2 � (4 � 3) demonstrates the associative property of multiplication. Observe that the factors are the same on either side of the equal sign: 2 times 4 times 3

Commutative Property
• Commutative Property of Addition: It states that changing the order of addends does not change the sum.
That is, a + b = b + a.
• Commutative Property of Multiplication: It states that changing the order of factors does not change the product.
That is, a × b = b × a.

• Addition and multiplication are commutative over the set of real numbers.
That means, for any two real numbers x and yx + y = y + x and xy = yx.
• Subtraction and Division are not commutative.

### Examples of Commutative Property

• 2 + 3 = 3 + 2. Whether you add 3 to 2 or you add 2 to 3, you get 5 both ways.
• 4 × 7 = 7 × 4, Whether you multiply 4 by 7 or you multiply 7 by 4, the product is the same, 28.

Computation algorithm. A set of predefined steps applicable to a class of problems that gives the correct result in every case when the steps are carried out correctly.

Congruent.  Two plane or solid figures are congruent if one can be obtained from the other by rigid motion (a sequence of rotations, reflections, and translations).

Counting on. A strategy for finding the number of objects in a group without having to count every member of the group. For example, if a stack of books is known to have 8 books and 3 more books are added to the top, it is not necessary to count the stack all over again. One can find the total by counting on—pointing to the top book and saying “eight,” following this with “nine, ten, eleven. There are eleven books now.”

Expanded form. A multi-digit number is expressed in expanded form when it is written as a sum of single-digit multiples of powers of ten. For example, 643 = 600 + 40 + 3.

Fraction. A number expressible in the form a/b where a is a whole number and b is a positive whole number. (The word fraction in these standards always refers to a non-negative number.) See also: rational number.

Definition of Identity Properties of Addition and Multiplication.

• Identity property of addition states that the sum of zero and any number or variable is the number or variable itself. For example, 4 + 0 = 4, - 11 + 0 = - 11, y + 0 = y are few examples illustrating the identity property of addition.

• Identity property of multiplication states that the product of 1 and any number or variable is the number or variable itself. For example, 4 × 1 = 4, - 11 × 1 = - 11, y × 1 = y are few examples illustrating the identity property of multiplication.

Line plot. A method of visually displaying a distribution of data values where each data value is shown as a dot or mark above a number line.

Mean. A measure of center in a set of numerical data, computed by adding the values in a list and then dividing by the number of values in the list.4 Example: For the data set {1, 3, 6, 7, 10, 12, 14, 15, 22, 120}, the mean is 21.

Median. A measure of center in a set of numerical data. The median of a list of values is the value appearing at the center of a sorted version of the list—or the mean of the two central values, if the list contains an even number of values. Example: For the data set {2, 3, 6, 7, 10, 12, 14, 15, 22, 90}, the median is 11.

Multiplicative inverses. Two numbers whose product is 1 are multiplicative inverses of one another. Example: 3/4 and 4/3 are multiplicative inverses of one another because 3/4 Ã— 4/3 = 4/3 Ã— 3/4 = 1.

Number line diagram. A diagram of the number line used to represent numbers and support reasoning about them. In a number line diagram for measurement quantities, the interval from 0 to 1 on the diagram represents the unit of measure for the quantity.

Percent rate of change. A rate of change expressed as a percent. Example: if a population grows from 50 to 55 in a year, it grows by 5/50 = 10% per year.

Probability. A number between 0 and 1 used to quantify likelihood for processes that have uncertain outcomes (such as tossing a coin, selecting a person at random from a group of people, tossing a ball at a target, or testing for a medical condition).

Rectilinear figure. A polygon all angles of which are right angles.

Repeating decimal. The decimal form of a rational number. See also: terminating decimal.

Terminating decimal. A decimal is called terminating if its repeating digit is 0.

Visual fraction model. A tape diagram, number line diagram, or area model.

Whole numbers. The numbers 0, 1, 2, 3, …