MTH148: Integrated Mathematics I

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

This first-year high school integrated math course focuses on linear and simple exponential models. The course contrasts linear behavior with exponential behavior, and it uses both linear and simple exponential equations as models. Students learn about and work extensively with functions—analyzing function properties and behavior, creating new functions from known functions, and applying functions to various continuous and discrete situations. The statistics in the course focus on modeling. Topics in geometry include constructions, transformations, similarity, and congruence, and students use the Pythagorean theorem in analytic geometry contexts.

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Course Length

Two Semesters

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Prerequisites

K12 Intermediate Mathematics C, MTH113: Pre-Algebra (or equivalent)

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Course Outline

SEMESTER 1

Semester A, Unit 1: Expressions and Problem Solving

This unit focuses on variables and measurement. Students practice translating real-world situations into mathematical expressions and equations, and they use units to understand problems. In addition, students look at what the structure of a mathematical expression can say about the relationships between quantities in a real-world context it models.

  • Semester 1 Introduction
  • Foundations for Unit 1
  • Expressions
  • Variables
  • Translating Words into Variable Expressions
  • Equations
  • Translating Words into Equations
  • Problem Solving
  • Dimensional Analysis
  • Precision and Accuracy
  • Core Focus: Structure and Meaning
  • Unit Review
  • Unit Test

Semester A, Unit 2: Solving Linear Equations and Inequalities

This unit is all about equations and inequalities. Students see how to solve equations, and they extend this skill to solving inequalities and real-world applications involving inequalities. Students also use mathematical reasoning to justify each step when solving an equation or inequality.

  • Foundations for Unit 2
  • Addition and Subtraction Equations
  • Multiplication and Division Equations 1
  • Multiplication and Division Equations 2
  • Multiple Transformations
  • Variables on Both Sides of an Equation
  • Discuss: Linear Equations
  • Transforming Formulas
  • Inequalities
  • Solving Inequalities
  • Applications of Inequalities
  • Core Focus: Reasoning
  • Unit Review
  • Unit Test

Semester A, Unit 3: Linear Equations and Inequalities

In this unit, students graph linear equations in two variables and use graphs to solve real-world problems. Students also graph linear inequalities in two variables and use inequalities to model constraints in real-world contexts.

  • Foundations for Unit 3
  • Graphs of Lines
  • Forms of Linear Equations
  • Writing Equations of Lines
  • Applications: Linear Equations
  • Graphing Linear Inequalities
  • Systems of Linear Inequalities
  • Constraints
  • Core Focus: Linear Modeling
  • Unit Review
  • Unit Test

Semester A, Unit 4: Introduction to Functions

In this unit, students learn about mathematical relations, functions, and function notation. They will work with function equations and find intercepts and average rate of change for functions. In addition, they’ll learn how the domain and range of a function can relate to the situation the function models.

  • Foundations for Unit 4
  • Relations
  • Functions
  • Function Equations 1
  • Function Equations 2
  • Discuss: Function Applications
  • Linear Functions
  • Intercepts
  • Average Rate of Change
  • Core Focus: Thinking About Domain and Range
  • Unit Review
  • Unit Test

Semester A, Unit 5: Exponential Equations and Functions

This unit is all about exponents. Students start with reviewing properties of exponents, and then they move on to solving simple exponential equations and graphing exponential functions. Then, students see how exponential models can fit situations involving growth and decay.

  • Foundations for Unit 5
  • Properties of Exponents
  • Exponential Expressions and Equations I
  • Exponential Expressions and Equations II
  • Graphing Exponential Functions
  • Applications: Growth and Decay  
  • Features of Exponential Functions
  • Core Focus: Multiple Representations
  • Unit Review
  • Unit Test

Semester A, Unit 6: Sequences and Modeling with Functions

A sequence is a function with integer domain. In this unit, students learn about arithmetic, geometric, and other types of sequences. Then, students work with other types of functions as models for real-world situations.

  • Foundations for Unit 6
  • Sequences and Patterns
  • Arithmetic Sequences
  • Geometric Sequences
  • Discuss: Sequences
  • Applications: Sequences
  • Function Parameters
  • Combining Functions
  • Core Focus: Comparing Models
  • Unit Review
  • Unit Test

Semester A, Unit 7: Semester Review and Test

  • Semester Review
  • Semester Test

SEMESTER 2

Semester B, Unit 1: Systems of Equations

When two equations have to be true same at the same time, they are called a system of equations. In this unit, students use graphs, substitution, and linear combination to solve systems of equations. Students also use systems to solve real-world problems.

  • Semester 2 Introduction
  • Foundations for Unit 1
  • Systems of Equations
  • Approximating Solutions with Graphs
  • Substitution Method
  • Linear Combination
  • Linear Combination with Multiplication
  • Applications: Systems of Linear Equations
  • Core Focus: Justifying Linear Combination
  • Unit Review
  • Unit Test

Semester B, Unit 2: Describing Data

This unit focuses on data. First, students calculate measures of center (mean, media, and mode) and variability (variance and standard deviation). Then, students use graphs and tables to make sense of data and identify outliers.

  • Foundations for Unit 2
  • Measures of Center
  • Variability
  • Graphs of Univariate Data
  • Selecting Measures of Center
  • Frequency Distributions
  • Discuss: Comparing Data Sets
  • Core Focus: Outliers
  • Unit Review
  • Unit Test

Semester B, Unit 3: Linear Models for Data

Sometimes, data come in ordered pairs. Ordered pairs can be plotted on a graph, and then you can start to see patterns. In this unit, students graph two-dimensional data and describe how the input values (the x-values) are related to the output values (the y-values). Then, students use correlation and linear regression to describe the relationship between the values.

  • Foundations for Unit 3
  • Two-Way Tables
  • Scatterplots
  • Association
  • The Correlation Coefficient
  • Fitting a Line to Data
  • Least Squares Regression
  • Core Focus: Parameters and Residuals
  • Unit Review
  • Unit Test

Semester B, Unit 4: Transformations

This unit covers essential geometric terms such as point, line, plane, and angle. Once students have mastered those definitions, they’ll be ready to learn about polygons, transformations, and symmetry. Then, students will see how to use coordinates for transformations.

  • Foundations for Unit 4
  • Basic Geometric Terms and Definitions 1
  • Basic Geometric Terms and Definitions 2
  • Measuring Length
  • Measuring Angles
  • Transformations 1
  • Transformations 2
  • Discuss: Transformations
  • Using Algebra to Describe Geometry 1
  • Using Algebra to Describe Geometry 2
  • Polygons and Symmetry 1
  • Polygons and Symmetry 2
  • Core Focus: Looking at Transformations
  • Unit Review
  • Unit Test

Semester B, Unit 5: Constructions and Congruence

In this unit, students learn about congruence, with a focus on reasoning about the congruence of polygons and triangles. Then, students see how to perform geometric constructions including segment bisectors and simple regular polygons. Finally, they see how congruence and transformations are related to each other.

  • Foundations for Unit 5
  • Congruent Polygons and Their Corresponding Parts 1
  • Congruent Polygons and Their Corresponding Parts 2
  • Triangle Congruence: SSS, SAS, and ASA 1
  • Triangle Congruence: SSS, SAS, and ASA 2
  • Bisectors and Line Relationships 1
  • Bisectors and Line Relationships 2
  • Constructions with Polygons 1
  • Constructions with Polygons 2
  • Core Focus: Congruence and Rigid Motions
  • Unit Review
  • Unit Test

Semester B, Unit 6: Analytic Geometry

When the tools of algebra are applied to geometry, the result is called analytic geometry. In this unit, students see how to use coordinates and algebra to solve geometric problems, prove theorems, and describe geometric relationships.

  • Foundations for Unit 6
  • Using the Distance Formula
  • Computing Area with Coordinates
  • Discuss: Applications of Coordinates
  • Your Choice
  • Proofs and Coordinate Geometry 1
  • Proofs and Coordinate Geometry 2
  • Your Choice
  • Slope 1
  • Slope 2
  • Core Focus: Coordinate Proofs
  • 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