Search the California Content Standards

Cluster:
Investigate chance processes and develop, use, and evaluate probability models.

Standard:
Develop a probability model and use it to find probabilities of events. Compare probabilities from a model to observed frequencies; if the agreement is not good, explain possible sources of the discrepancy. Develop a uniform probability model by assigning equal probability to all outcomes, and use the model to determine probabilities of events. For example, if a student is selected at random from a class, find the probability that Jane will be selected and the probability that a girl will be selected.

Cluster:
Investigate chance processes and develop, use, and evaluate probability models.

Standard:
Develop a probability model and use it to find probabilities of events. Compare probabilities from a model to observed frequencies; if the agreement is not good, explain possible sources of the discrepancy. Develop a probability model (which may not be uniform) by observing frequencies in data generated from a chance process. For example, find the approximate probability that a spinning penny will land heads up or that a tossed paper cup will land open-end down. Do the outcomes for the spinning penny appear to be equally likely based on the observed frequencies?

Cluster:
Investigate chance processes and develop, use, and evaluate probability models.

Standard:
Find probabilities of compound events using organized lists, tables, tree diagrams, and simulation. Understand that, just as with simple events, the probability of a compound event is the fraction of outcomes in the sample space for which the compound event occurs.

Cluster:
Investigate chance processes and develop, use, and evaluate probability models.

Standard:
Find probabilities of compound events using organized lists, tables, tree diagrams, and simulation. Represent sample spaces for compound events using methods such as organized lists, tables and tree diagrams. For an event described in everyday language (e.g., “rolling double sixes”), identify the outcomes in the sample space which compose the event.

Cluster:
Investigate chance processes and develop, use, and evaluate probability models.

Standard:
Find probabilities of compound events using organized lists, tables, tree diagrams, and simulation. Design and use a simulation to generate frequencies for compound events. For example, use random digits as a simulation tool to approximate the answer to the question: If 40% of donors have type A blood, what is the probability that it will take at least 4 donors to find one with type A blood?

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:
Interpret the structure of expressions. [Linear, exponential, and quadratic]

Standard:
Interpret expressions that represent a quantity in terms of its context.* Interpret parts of an expression, such as terms, factors, and coefficients.*

Cluster:
Interpret the structure of expressions. [Linear expressions and exponential expressions with integer exponents]

Standard:
Interpret expressions that represent a quantity in terms of its context. * Interpret parts of an expression, such as terms, factors, and coefficients. *

Cluster:
Interpret the structure of expressions. [Linear expressions and exponential expressions with integer exponents]

Standard:
Interpret expressions that represent a quantity in terms of its context. * Interpret complicated expressions by viewing one or more of their parts as a single entity. For example, interpret P(1 + r)^n as the product of P and a factor not depending on P. *

Cluster:
Interpret the structure of expressions. [Linear, exponential, and quadratic]

Standard:
Interpret expressions that represent a quantity in terms of its context.* Interpret complicated expressions by viewing one or more of their parts as a single entity. For example, interpret P(1 + r)^n as the product of P and a factor not depending on P.*