Search the California Content Standards

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:
Prove geometric theorems. [Focus on validity of underlying reasoning while using variety of ways of writing proofs.]

Standard:
Prove theorems about triangles. Theorems include: measures of interior angles of a triangle sum to 180°; base angles of isosceles triangles are congruent; the segment joining midpoints of two sides of a triangle is parallel to the third side and half the length; the medians of a triangle meet at a point.

Cluster:
Prove geometric theorems. [Focus on validity of underlying reasoning while using variety of ways of writing proofs.]

Standard:
Prove theorems about parallelograms. Theorems include: opposite sides are congruent, opposite angles are congruent, the diagonals of a parallelogram bisect each other, and conversely, rectangles are parallelograms with congruent diagonals.

Cluster:
Prove geometric theorems. [Focus on validity of underlying reasoning while using variety of ways of writing proofs.]

Standard:
Prove theorems about lines and angles. Theorems include: vertical angles are congruent; when a transversal crosses parallel lines, alternate interior angles are congruent and corresponding angles are congruent; points on a perpendicular bisector of a line segment are exactly those equidistant from the segment’s endpoints.

Cluster:
Understand independence and conditional probability and use them to interpret data. [Link to data from simulations or experiments.]

Standard:
Describe events as subsets of a sample space (the set of outcomes) using characteristics (or categories) of the outcomes, or as unions, intersections, or complements of other events (“or,” “and,” “not”). *

Cluster:
Understand independence and conditional probability and use them to interpret data. [Link to data from simulations or experiments.]

Standard:
Understand that two events A and B are independent if the probability of A and B occurring together is the product of their probabilities, and use this characterization to determine if they are independent. *

Cluster:
Understand independence and conditional probability and use them to interpret data. [Link to data from simulations or experiments.]

Standard:
Understand the conditional probability of A given B as P(A and B)/P(B), and interpret independence of A and B as saying that the conditional probability of A given B is the same as the probability of A, and the conditional probability of B given A is the same as the probability of B. *

Cluster:
Understand independence and conditional probability and use them to interpret data. [Link to data from simulations or experiments.]

Standard:
Construct and interpret two-way frequency tables of data when two categories are associated with each object being classified. Use the two-way table as a sample space to decide if events are independent and to approximate conditional probabilities. For example, collect data from a random sample of students in your school on their favorite subject among math, science, and English. Estimate the probability that a randomly selected student from your school will favor science given that the student is in tenth grade. Do the same for other subjects and compare the results. *

Cluster:
Understand independence and conditional probability and use them to interpret data. [Link to data from simulations or experiments.]

Standard:
Recognize and explain the concepts of conditional probability and independence in everyday language and everyday situations. *

Cluster:
Use the rules of probability to compute probabilities of compound events in a uniform probability model.

Standard:
Find the conditional probability of A given B as the fraction of B’s outcomes that also belong to A, and interpret the answer in terms of the model. *