STANDARD COURSE OF STUDY

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

INTEGRATED MATHEMATICS II

High School Grades

Integrated Mathematics 2 continues students’ study of topics from algebra, geometry, and statistics in a problem-centered, connected approach. Functions, matrix operations, and algebraic representations of 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

  • Create linear and exponential models, for sets of data, to solve problems.
  • Use linear expressions to model and solve problems.
  • Collect, organize, analyze, and display data to solve problems.
  • Apply geometric properties and relationships to solve problems.
  • Apply the Pythagorean Theorem to solve problems.


Number and Operations
Competency Goal 1 The learner will perform operations with numbers, algebraic expressions, and matrices 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 Model and solve problems using direct variation.

1.04 Operate with matrices to model and solve problems.
Geometry and Measurement
Competency Goal 2 The learner will describe geometric figures in the coordinate plane algebraically.
  Objectives

2.01 Find the lengths and midpoints of segments to solve problems.

2.02 Use the parallelism or perpendicularity of lines and segments to solve problems.

2.03 Use the trigonometric ratios to model and solve problems.

2.04 Describe the transformation (translation, reflection, rotation, dilation) of polygons in the coordinate plane in simple algebraic terms.
Data Analysis and Probability
Competency Goal 3 The learner will collect, organize, and interpret data to solve problems.
  Objectives

3.01 Describe data to solve problems.

  1. Apply and compare methods of data collection.
  2. Apply statistical principles and methods in sample surveys.
  3. Determine measures of central tendency and spread.
  4. Recognize, define, and use the normal distribution curve.
  5. Interpret graphical displays of data.
  6. Compare distributions of data.

3.02 Create and use, for sets of data, calculator-generated models of linear, exponential, and quadratic functions to solve problems.

  1. Interpret the constants, coefficients, and bases in the context of the data.
  2. Check the model for goodness-of-fit and use the model, where appropriate, to draw conclusions or make predictions..
Algebra
Competency Goal 4 The learner will use relations and functions to solve problems.
  Objectives

4.01 Use systems of linear equations or inequalities in two variables to model and solve problems. Solve using tables, graphs, and algebraic properties; justify steps used.

4.02 Use quadratic functions 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.

4.03 Use power models to solve problems.

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

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