MTH348: Integrated Mathematics III

This list is representative of the materials provided or used in this course. Keep in mind that the actual materials used may vary, depending on the school in which you are enrolled, and whether you are taking the course as Independent Study.

For a complete list of the materials to be used in this course by your enrolled student, please visit MyInfo. All lists are subject to change at any time.

Scope & Sequence : Scope & Sequence documents describe what is covered in a course (the scope) and also the order in which topics are covered (the sequence). These documents list instructional objectives and skills to be mastered. K12 Scope & Sequence documents for each course include:

Course Overview

In this third-year high school math course, students encounter unified instruction reviewing and expanding all previous high school math topics.  First, they extend their work on polynomials beyond quadratics to graphing, problem solving, and working with rational expressions. Next, they use statistical and probability tools, such as the standard normal distribution, to understand data. Students make inferences using simulations, experiments, and surveys. In geometry, they extend trigonometric concepts to general triangles and use trigonometric functions to model periodic processes. Finally, students substantially use mathematical modeling by making use of well-developed skills with various mathematical tools.

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Course Length

Two Semesters

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Prerequisites

MTH247: Integrated Mathematics II (or equivalent)

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Course Outline

SEMESTER 1

Semester A, Unit 1: Randomness and Probability

In this unit, students explore different kinds of random variables. Discrete binomial distributions as well as the continuous normal distribution will be used to analyze and compare data.

  • Semester 1 Introduction
  • Foundations for Unit 1
  • Creating Probability Distributions
  • Interpreting Probability Distributions
  • Binomial Distributions
  • Discuss: Model vs. Experiment
  • Continuous Random Variables
  • The Normal Distribution
  • Standardizing Data
  • Comparing Scores
  • The Standard Normal Curve
  • Finding Standard Scores
  • Core Focus: What Data Are Normal?
  • Unit Review
  • Unit Test

Semester A, Unit 2: Sampling, Surveys, and Experiments

Collecting and interpreting samples is the groundwork of statistics. In this unit, students focus on how the sampling process is improved by random selection, and how samples can be used to make estimations and predictions. Particular attention will be paid to the Central Limit Theorem and using samples to evaluate statistical claims.

  • Foundations for Unit 2
  • Sample and Population
  • Statistics and Parameters
  • Discuss: Data Gathering with Uncertainty
  • Interval Estimates
  • The Central Limit Theorem
  • Estimating Means
  • Mean Differences
  • Estimating Proportions
  • Core Focus: Evaluating Reports
  • Unit Review
  • Unit Test

Semester A, Unit 3: Polynomials and Series

This unit focuses on polynomials and geometric series. By looking closely at polynomials, polynomial operations, and factoring patterns, students discover the connections between polynomials and series.

  • Foundations for Unit 3
  • Working with Polynomials
  • Multiplying Polynomials
  • Factoring Patterns
  • Solving Polynomial Equations
  • Geometric Sequences
  • Series and Sigma Notation
  • Geometric Series
  • Applications: Series
  • Core Focus: Calculating Mortgage Payments
  • Unit Review
  • Unit Test

Semester A, Unit 4: Rational and Radical Equations

In this unit, students explore operations with rational expressions as well as solving rational equations. Students also cover square roots in more depth as well as higher roots and rational exponent expressions. Radical equations are solved, and the concept of extraneous solutions is introduced.

  • Foundations for Unit 4
  • Dividing Monomials and Polynomials
  • Operations with Rational Expressions 1
  • Operations with Rational Expressions 2
  • Solving Rational Equations
  • Simplifying Radical Expressions
  • Fractional Exponents and Higher Roots
  • Solving Radical Equations
  • Discuss: Extraneous Solutions
  • Core Focus: Using Technology to Solve Equations
  • Unit Review
  • Unit Test

Semester A, Unit 5: Operations with Polynomials

Polynomials are like real numbers. In fact, polynomials can be divided in the same way that real numbers can be divided. In this unit, students learn different ways to divide polynomials and how that process leads to factoring.

  • Foundations for Unit 5
  • Polynomial Long Division
  • Synthetic Division
  • The Polynomial Remainder Theorem
  • Factors and Rational Roots
  • Graphing Polynomials
  • Factoring Polynomials Completely
  • Factoring with Complex Numbers
  • Core Focus: Polynomials and Arithmetic
  • Unit Review
  • Unit Test

Semester A, Unit 6: Graphing Functions

The emphasis of this unit is on graphing functions. Students explore special functions such as absolute value functions, power functions, reciprocal power functions, rational functions, and radical functions. Students also use the structure of these functions to identify characteristics of their graphs.

  • Foundations for Unit 6
  • Absolute Value Functions
  • Power Functions
  • Reciprocal Power Functions
  • Graphing Rational Functions
  • Radical Functions
  • Intersections of Graphs
  • Core Focus: Using Technology for Graphs
  • Unit Review
  • Unit Test

Semester A, Unit 7: Semester Review and Test

  • Semester Review
  • Semester Test

SEMESTER 2

Semester B, Unit 1: Exponential and Logarithmic Functions

In this unit, students extend their knowledge of exponents to more complicated exponential equations. They see that logarithms arise naturally as inverses of exponential functions. Then, they use logarithms to solve many mathematical and real-world problems, including problems involving growth.

  • Semester 2 Introduction
  • Foundations for Unit 1
  • Exponential Equations
  • Exponential Graphs
  • Inverse Functions
  • Logarithms
  • Using Logs to Solve Exponential Equations
  • Graphing Logarithmic Functions
  • Systems with Exponents and Logs
  • Applications: Logarithms
  • Core Focus: Logarithmic Growth
  • Unit Review
  • Unit Test

Semester B, Unit 2: Radians and Trigonometric Functions

In this unit, students use the unit circle to understand trigonometric ratios, and they use radian measure to define trigonometric functions that are no longer bound by angles in a triangle.

  • Foundations for Unit 2
  • Right Triangle Trigonometry
  • Special Right Triangles
  • Angles, Arcs, and Radian Measure
  • The Unit Circle
  • More Trig Ratios on the Unit Circle
  • Basic Trigonometric Functions
  • More Trigonometric Functions
  • Core Focus: Properties of Trig Functions
  • Unit Review
  • Unit Test

Semester B, Unit 3: Graphs of Trigonometric Functions

In this unit, students see how the graphs of the sine and cosine functions are waves that can be shifted, amplified, and compressed to model many periodic phenomena.

  • Foundations for Unit 3
  • Sine and Cosine Graphs
  • Sinusoidal Graphs: Amplitude
  • Sinusoidal Graphs: Vertical Shift
  • Sinusoidal Graphs: Period
  • Sinusoidal Family of Functions
  • Interpreting Trigonometric Models
  • Creating Trigonometric Models
  • Core Focus: Properties of Sinusoidal Graphs
  • Unit Review
  • Unit Test

Semester B, Unit 4: Selecting and Modeling with Functions

Functions can be used to model many different real-world situations and phenomena. In this unit, students learn how to evaluate, combine, compare, and adjust functions that model a situation.

  • Foundations for Unit 4
  • Working with Function Models
  • Combining Function Types
  • Logistic Growth
  • Comparing Models
  • Adjusting Function Parameters
  • Core Focus: Expressions and Models
  • Unit Review
  • Unit Test

Semester B, Unit 5: Optimization

Every company wants to maximize profit and minimize costs. Finding these maximum or minimum values is called optimizing. In this unit, students learn how to use equations and inequalities to solve several real-world optimization problems.

  • Foundations for Unit 5
  • Inequalities in One Variable
  • Compound Inequalities
  • Inequalities in Two Variables
  • Systems of Linear Inequalities
  • Linear Programming
  • More Linear Programming
  • Applications of Linear Programming
  • Core Focus: Domain in Linear Programming
  • Unit Review
  • Unit Test

Semester B, Unit 6: Modeling with Geometry

The tools of geometry can help solve problems in outer space and around the corner. In this unit, students use angles, distances, surface area, volume, and density to solve many kinds of problems.

  • Foundations for Unit 6
  • Geometry in Space
  • Geometry on Earth
  • Manufacturing Problems: Design
  • Manufacturing Problems: Optimization
  • Density in Two Dimensions
  • Density in Three Dimensions
  • Core Focus: Fermi Problems
  • Geometry in Space
  • Unit Review
  • Unit Test

Semester B, Unit 7: End-of-Year Project

  • Project Day 1
  • Project Day 2
  • Project Day 3
  • Project Day 4
  • Project Day 5

Semester B, Unit 8: Semester Review and Test

  • Semester Review
  • Semester Test
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K12 Scope & Sequence documents for each course include:

  • Course Overview (as seen above)
  • Course Outline
  • Lesson Time and Scheduling