Search the California Content Standards

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. Convert a rational number to a decimal using long division; know that the decimal form of a rational number terminates in 0s or eventually repeats.

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

Standard:
Solve real-world and mathematical problems involving the four operations with rational numbers.

Footnote:
Computations with rational numbers extend the rules for manipulating fractions to complex fractions.

Cluster:
Perform arithmetic operations on polynomials. [Linear and quadratic]

Standard:
Understand that polynomials form a system analogous to the integers, namely, they are closed under the operations of addition, subtraction, and multiplication; add, subtract, and multiply polynomials.

Cluster:
Know that there are numbers that are not rational, and approximate them by rational numbers.

Standard:
Know that numbers that are not rational are called irrational. Understand informally that every number has a decimal expansion; for rational numbers show that the decimal expansion repeats eventually, and convert a decimal expansion which repeats eventually into a rational number.

Cluster:
Know that there are numbers that are not rational, and approximate them by rational numbers.

Standard:
Use rational approximations of irrational numbers to compare the size of irrational numbers, locate them approximately on a number line diagram, and estimate the value of expressions (e.g.,π^2). For example, by truncating the decimal expansion of √2, show that √2 is between 1 and 2, then between 1.4 and 1.5, and explain how to continue on to get better approximations.

Cluster:
Perform arithmetic operations on polynomials. [Polynomials that simplify to quadratics]

Standard:
Understand that polynomials form a system analogous to the integers, namely, they are closed under the operations of addition, subtraction, and multiplication; add, subtract, and multiply polynomials.

Cluster:
Perform arithmetic operations on polynomials. [Beyond quadratic]

Standard:
Understand that polynomials form a system analogous to the integers, namely, they are closed under the operations of addition, subtraction, and multiplication; add, subtract, and multiply polynomials.

Cluster:
Perform arithmetic operations on polynomials. [Beyond quadratic]

Standard:
Understand that polynomials form a system analogous to the integers, namely, they are closed under the operations of addition, subtraction, and multiplication; add, subtract, and multiply polynomials.

Cluster:
Understand the relationship between zeros and factors of polynomials.

Standard:
Know and apply the Remainder Theorem: For a polynomial p(x) and a number a, the remainder on division by x – a is p(a), so p(a) = 0 if and only if (x – a) is a factor of p(x).

Cluster:
Understand the relationship between zeros and factors of polynomials.

Standard:
Know and apply the Remainder Theorem: For a polynomial p(x) and a number a, the remainder on division by x – a is p(a), so p(a) = 0 if and only if (x – a) is a factor of p(x).