Portfolio - Yvonne V. Richardson

MATHEMATICS 2

COMPETENCY GOALS and OBJECTIVES

This course contains 6 core content areas and 42 objectives. Instruction is organized to maximize student participation in the learning experience, as suggested in the Washington State K-12 Mathematics Learning Standards. The overall framework for the course is as follows.

When the components for a competency goal are developed, the number for the objective within the goal will become a hyperlink.

M2.1. Core Content: Modeling situations and solving problems

M2.1.A
Select and justify functions and equations to model and solve problems.
M2.1.B
Solve problems that can be represented by systems of equations and inequalities.
M2.1.C
Solve problems that can be represented by quadratic functions, equations, and inequalities.
M2.1.D
Solve problems that can be represented by exponential functions and equations.
M2.1.E
Solve problems involving combinations and permutations.

M2.3. Core Content: Conjectures and proofs, part I

M2.3.A
Use deductive reasoning to prove that a valid geometric statement is true.
M2.3.B
Identify errors or gaps in a mathematical argument and develop counterexamples to refute invalid statements about geometric relationships.
M2.3.C
Write the converse, inverse, and contrapositive of a valid proposition and determine their validity.
M2.3.D
Distinguish between definitions and undefined geometric terms and explain the role of definitions, undefined terms, postulates (axioms), and theorems.

M2.2. Core Content: Quadratic functions, equations, and relationships

M2.2.A
Represent a quadratic function with a symbolic expression, as a graph, in a table, and with a description, and make connections among the representations.
M2.2.B
Sketch the graph of a quadratic function, describe the effects that changes in the parameters have on the graph, and interpret the x-intercepts as solutions to a quadratic equation.
M2.2.C
Translate between the standard form of a quadratic function, the vertex form, and the factored form; graph and interpret the meaning of each form.
M2.2.D
Solve quadratic equations that can be factored as (ax + b)(cx + d) where a, b, c, and d are integers.
M2.2.E
Determine the number and nature of the roots of a quadratic function.
M2.2.F
Solve quadratic equations that have real roots by completing the square and by using the quadratic formula.
M2.2.G
Solve quadratic equations and inequalities, including equations with complex roots.
M2.2.H
Determine if a bivariate data set can be better modeled with an exponential or a quadratic function and use the model to make predictions.

M2.3. Core Content: Conjectures and proofs, part II

M2.3.E
Know, explain, and apply basic postulates and theorems about triangles and the special lines, line segments, and rays associated with a triangle.
M2.3.F
Determine and prove triangle congruence and other properties of triangles.
M2.3.G
Know, prove, and apply the Pythagorean Theorem and its converse.
M2.3.H
Solve problems involving the basic trigonometric ratios of sine, cosine, and tangent.
M2.3.I
Use the properties of special right triangles (30°–60°–90° and 45°–45°–90°) to solve problems.
M2.3.J
Know, prove, and apply basic theorems about parallelograms.
M2.3.K
Know, prove, and apply theorems about properties of quadrilaterals and other polygons.
M2.3.L
Determine the coordinates of a point that is described geometrically.
M2.3.M
Verify and apply properties of triangles and quadrilaterals in the coordinate plane.

M2.4 Core Content: Probability

M2.4.A Apply the fundamental counting principle and the ideas of order and replacement to calculate probabilities in situations arising from two-stage experiments (compound events).

M2.4.B
Given a finite sample space consisting of equally likely outcomes and containing events A and B, determine whether A and B are independent or dependent, and find the conditional probability of A given B.
M2.4.C Compute permutations and combinations, and use the results to calculate probabilities.
M2.4.D
Apply the binomial theorem to solve problems involving probability.

M2.5. Additional Key Content

M2.5.A
Use algebraic properties to factor and combine like terms in polynomials.
M2.5.B
Use different degrees of precision in measurement, explain the reason for using a certain degree of precision, and apply estimation strategies to obtain reasonable measurements with appropriate precision for a given purpose.
M2.5.C
Solve problems involving measurement conversions within and between systems, including those involving derived units, and analyze solutions in terms of reasonableness of solutions and appropriate units.
M2.5.D
Find the terms and partial sums of arithmetic and geometric series and the infinite sum for geometric series.

M2.6. Core Processes: Reasoning, problem solving, and communication

M2.6.A
Analyze a problem situation and represent it mathematically.
M2.6.B
Select and apply strategies to solve problems.
M2.6.C
Evaluate a solution for reasonableness, verify its accuracy, and interpret the solution in the context of the original problem.
M2.6.D
Generalize a solution strategy for a single problem to a class of related problems, and apply a strategy for a class of related problems to solve specific problems.
M2.6.E
Read and interpret diagrams, graphs, and text containing the symbols, language, and conventions of mathematics.
M2.6.F
Summarize mathematical ideas with precision and efficiency for a given audience and purpose.
M2.6.G
Synthesize information to draw conclusions and evaluate the arguments and conclusions of others.
M2.6.H
Use inductive reasoning to make conjectures, and use deductive reasoning to prove or disprove conjectures.

If you have questions or comments, please contact me at yvonne.richardson@comcast.net, leave comments on the Guest Blog, or use the form on the Contact Us page.