Search the California Content Standards

Cluster:
Apply and extend previous understandings of numbers to the system of rational numbers.

Standard:
Understand ordering and absolute value of rational numbers. Understand the absolute value of a rational number as its distance from 0 on the number line; interpret absolute value as magnitude for a positive or negative quantity in a real-world situation. For example, for an account balance of –30 dollars, write |–30| = 30 to describe the size of the debt in dollars.

Cluster:
Apply and extend previous understandings of numbers to the system of rational numbers.

Standard:
Understand ordering and absolute value of rational numbers. Distinguish comparisons of absolute value from statements about order. For example, recognize that an account balance less than –30 dollars represents a debt greater than 30 dollars.

Cluster:
Apply and extend previous understandings of numbers to the system of rational numbers.

Standard:
Solve real-world and mathematical problems by graphing points in all four quadrants of the coordinate plane. Include use of coordinates and absolute value to find distances between points with the same first coordinate or the same second coordinate.

Cluster:
Apply and extend previous understandings of operations with fractions to add, subtract, multiply, and divide rational numbers.

Standard:
Apply and extend previous understandings of addition and subtraction to add and subtract rational numbers; represent addition and subtraction on a horizontal or vertical number line diagram. Describe situations in which opposite quantities combine to make 0. For example, a hydrogen atom has 0 charge because its two constituents are oppositely charged.

Cluster:
Apply and extend previous understandings of operations with fractions to add, subtract, multiply, and divide rational numbers.

Standard:
Apply and extend previous understandings of addition and subtraction to add and subtract rational numbers; represent addition and subtraction on a horizontal or vertical number line diagram. Understand p + q as the number located a distance |q| from p, in the positive or negative direction depending on whether q is positive or negative. Show that a number and its opposite have a sum of 0 (are additive inverses). Interpret sums of rational numbers by describing real-world contexts.

Cluster:
Apply and extend previous understandings of operations with fractions to add, subtract, multiply, and divide rational numbers.

Standard:
Apply and extend previous understandings of addition and subtraction to add and subtract rational numbers; represent addition and subtraction on a horizontal or vertical number line diagram. Understand subtraction of rational numbers as adding the additive inverse, p – q = p + (–q). Show that the distance between two rational numbers on the number line is the absolute value of their difference, and apply this principle in real-world contexts.

Cluster:
Apply and extend previous understandings of operations with fractions to add, subtract, multiply, and divide rational numbers.

Standard:
Apply and extend previous understandings of addition and subtraction to add and subtract rational numbers; represent addition and subtraction on a horizontal or vertical number line diagram. Apply properties of operations as strategies to add and subtract rational numbers.

Cluster:
Apply and extend previous understandings of operations with fractions to add, subtract, multiply, and divide rational numbers.

Standard:
Apply and extend previous understandings of multiplication and division and of fractions to multiply and divide rational numbers. Understand that multiplication is extended from fractions to rational numbers by requiring that operations continue to satisfy the properties of operations, particularly the distributive property, leading to products such as (–1)(–1) = 1 and the rules for multiplying signed numbers. Interpret products of rational numbers by describing real-world contexts.

Cluster:
Apply and extend previous understandings of operations with fractions to add, subtract, multiply, and divide rational numbers.

Standard:
Apply and extend previous understandings of multiplication and division and of fractions to multiply and divide rational numbers. Understand that integers can be divided, provided that the divisor is not zero, and every quotient of integers (with non-zero divisor) is a rational number. If p and q are integers, then –(p/q) = (–p)/q = p/(–q). Interpret quotients of rational numbers by describing real-world contexts.

Cluster:
Apply and extend previous understandings of operations with fractions to add, subtract, multiply, and divide rational numbers.

Standard:
Apply and extend previous understandings of multiplication and division and of fractions to multiply and divide rational numbers. Apply properties of operations as strategies to multiply and divide rational numbers.