STANDARD COURSE OF STUDY

MATHEMATICS :: 2003 :: TO BE IMPLEMENTED 9-12 :: INTEGRATED MATHEMATICS III

INTEGRATED MATHEMATICS III

High School Grades

Integrated Mathematics 3 continues students’ study of topics from algebra, geometry, and statistics in a problem-centered, connected approach. Functions and the deductive methods of proof with geometric concepts are the principle topics of study. Students will be expected to describe and translate among graphic, algebraic, numeric, tabular, and verbal representations of relationships and use those representations to solve problems. Appropriate technology, from manipulatives to calculators and application software, should be used regularly for instruction and assessment.

Prerequisites

  • Use the trigonometric ratios to model and solve problems.
  • Apply geometric properties and relationships to solve problems.
  • Use systems of linear equations or inequalities to model and solve problems.
  • Define and use linear and exponential functions to model and solve problems.


Number and Operations
Competency Goal 1 The learner will perform operations with numbers and algebraic expressions to solve problems.
  Objectives

1.01 Write equivalent forms of algebraic expressions to solve problems.

1.02 Use algebraic expressions, including iterative and recursive forms, to model and solve problems.

1.03 Simplify and perform operations with rational exponents and logarithms to solve problems.

1.04 Model and solve problems using direct, inverse, combined and joint variation.
Geometry and Measurement
Competency Goal 2 The learner will use properties of geometric figures to solve problems.
  Objectives

2.01 Use logic and deductive reasoning to draw conclusions and solve problems.

2.02 Apply the properties, definitions, and theorems of angles and lines to solve problems and write proofs.

2.03 Apply the properties, definitions, and theorems of two-dimensional figures to solve problems and write proofs:

  1. Triangles.
  2. Quadrilaterals.
  3. Other polygons.
  4. Circles.

2.04 Use the law of sines and law of cosines to solve problems.
Algebra
Competency Goal 3 The learner will use relations and functions to solve problems.
  Objectives

3.01 Use systems of two or more equations or inequalities to model and solve problems; justify results. Solve using tables, graphs, matrix operations, and algebraic properties.

3.02 Use quadratic functions and inequalities to model and solve problems; justify results.

  1. Solve using tables, graphs, and algebraic properties.
  2. Interpret the constants and coefficients in the context of the problem.

3.03 Use rational equations to model and solve problems; justify results.

  1. Solve using tables, graphs, and algebraic properties.
  2. Interpret the constants and coefficients in the context of the problem.
  3. Identify the asymptotes and intercepts graphically and algebraically.

3.04 Use equations and inequalities with absolute value to model and solve problems; justify results.

  1. Solve using tables, graphs, and algebraic properties.
  2. Interpret the constants and coefficients in the context of the problem.

3.05 Transform functions in two dimensions; describe the results algebraically and geometrically.

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