Search the California Content Standards

Cluster:
Solve real-life and mathematical problems using numerical and algebraic expressions and equations.

Standard:
Use variables to represent quantities in a real-world or mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities. Solve word problems leading to inequalities of the form px + q > r or px + q < r, where p, q, and r are specific rational numbers. Graph the solution set of the inequality and interpret it in the context of the problem. For example: As a salesperson, you are paid $50 per week plus $3 per sale. This week you want your pay to be at least $100. Write an inequality for the number of sales you need to make, and describe the solutions.

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:
Understand solving equations as a process of reasoning and explain the reasoning. [Master linear; learn as general principle.]

Standard:
Explain each step in solving a simple equation as following from the equality of numbers asserted at the previous step, starting from the assumption that the original equation has a solution. Construct a viable argument to justify a solution method.

Cluster:
Understand solving equations as a process of reasoning and explain the reasoning. [Master linear; learn as general principle.]

Standard:
Explain each step in solving a simple equation as following from the equality of numbers asserted at the previous step, starting from the assumption that the original equation has a solution. Construct a viable argument to justify a solution method.

Cluster:
Represent and solve equations and inequalities graphically. [Linear and exponential; learn as general principle.]

Standard:
Understand that the graph of an equation in two variables is the set of all its solutions plotted in the coordinate plane, often forming a curve (which could be a line).