STANDARD COURSE OF STUDY

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

INTEGRATED MATHEMATICS I

High School Grades

Integrated Mathematics 1 provides students the opportunity to study traditional topics from algebra, geometry, probability, and statistics in a problem-centered, connected approach. 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

  • Operate with real numbers to solve problems.
  • Use formulas to solve problems.
  • Find, identify, and interpret the slope and intercepts of a linear relation.
  • Visually determine the line of best fit for a given scatterplot; explain the meaning of the line; and make predictions using the line.
  • Collect, organize, analyze, and display data to solve problems.


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

1.01 Write equivalent forms of algebraic expressions to solve problems.

  1. Apply the laws of exponents.
  2. Operate with polynomials.
  3. Factor polynomials.

1.02 Use algebraic expressions, including iterative and recursive forms, to model and solve problems.
Geometry and Measurement
Competency Goal 2 The learner will use properties of geometric figures to solve problems.
  Objectives

2.01 Use the length, area, and volume of geometric figures to solve problems. Include arc length, area of sectors of circles; lateral area, surface area, and volume of three-dimensional figures; and perimeter, area, and volume of composite figures.

2.02 Develop and apply properties of solids to solve problems.
Data Analysis and Probability
Competency Goal 3 The learner will analyze data and apply probability concepts to solve problems.
  Objectives

3.01 Use graph theory to model relationships and solve problems.

3.02 Use theoretical and experimental probability to model and solve problems.

  1. Use addition and multiplication principles.
  2. Calculate and apply permutations and combinations.
  3. Create and use simulations for probability models.
  4. Find expected values and determine fairness.

3.03 Create linear and exponential models, for sets of data, 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 linear functions or 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.

4.02 Use exponential functions to model and solve problems; justify results.

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

4.03 Use systems of linear equations or inequalities in two variables to model problems and solve graphically.

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