Search the California Content Standards

Cluster:
Understand ratio concepts and use ratio reasoning to solve problems.

Standard:
Use ratio and rate reasoning to solve real-world and mathematical problems, e.g., by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations. Use ratio reasoning to convert measurement units; manipulate and transform units appropriately when multiplying or dividing quantities.

Cluster:
Analyze proportional relationships and use them to solve real-world and mathematical problems.

Standard:
Compute unit rates associated with ratios of fractions, including ratios of lengths, areas and other quantities measured in like or different units. For example, if a person walks 1/2 mile in each 1/4 hour, compute the unit rate as the complex fraction ½/¼ miles per hour, equivalently 2 miles per hour.

Cluster:
Analyze proportional relationships and use them to solve real-world and mathematical problems.

Standard:
Recognize and represent proportional relationships between quantities. Decide whether two quantities are in a proportional relationship, e.g., by testing for equivalent ratios in a table or graphing on a coordinate plane and observing whether the graph is a straight line through the origin.

Cluster:
Analyze proportional relationships and use them to solve real-world and mathematical problems.

Standard:
Recognize and represent proportional relationships between quantities. Identify the constant of proportionality (unit rate) in tables, graphs, equations, diagrams, and verbal descriptions of proportional relationships.

Cluster:
Analyze proportional relationships and use them to solve real-world and mathematical problems.

Standard:
Recognize and represent proportional relationships between quantities. Represent proportional relationships by equations. For example, if total cost t is proportional to the number n of items purchased at a constant price p, the relationship between the total cost and the number of items can be expressed as t = pn.

Cluster:
Analyze proportional relationships and use them to solve real-world and mathematical problems.

Standard:
Recognize and represent proportional relationships between quantities. Explain what a point (x, y) on the graph of a proportional relationship means in terms of the situation, with special attention to the points (0, 0) and (1, r) where r is the unit rate.

Cluster:
Analyze proportional relationships and use them to solve real-world and mathematical problems.

Standard:
Use proportional relationships to solve multistep ratio and percent problems. Examples: simple interest, tax, markups and markdowns, gratuities and commissions, fees, percent increase and decrease, percent error.

Cluster:
Prove and apply trigonometric identities.

Standard:
Prove the Pythagorean identity sin^2(θ ) + cos^2(θ ) = 1 and use it to find sin(θ ), cos(θ ), or tan(θ ) given sin(θ ), cos(θ ), or tan(θ ) and the quadrant of the angle.

Cluster:
Extend the domain of trigonometric functions using the unit circle.

Standard:
Understand radian measure of an angle as the length of the arc on the unit circle subtended by the angle.

Cluster:
Extend the domain of trigonometric functions using the unit circle.

Standard:
Understand radian measure of an angle as the length of the arc on the unit circle subtended by the angle.