# Integrated Math I Online Credit Recovery

This first-year high school integrated math course focuses on linear and simple exponential models. The course contrasts linear behavior with exponential behavior and uses both linear and simple exponential equations as models. Students learn about and work extensively with functions—analyzing function properties and behavior, creating and transforming functions, and applying functions to various continuous and discrete situations. The statistics in the course cover both univariate and bivariate data. For univariate data, students learn about measures of center and spread. For bivariate data, they learn about correlation and fitting data to a line. The topics in geometry include transformations, reasoning, congruence, construction, and analytic geometry.

Diagnostic tests assess students’ current knowledge and generate individualized study plans, so students can focus on topics that need review.

Semester 1

Unit 1: Expressions and Problem Solving

This unit focuses on variables and algebraic expressions. Students practice translating real-world situations into mathematical expressions and equations, and use units to understand problems. In addition, students learn how the structure of a mathematical expression explains the relationships between the quantities in the real-world context it models.

• Foundations

• Expressions

• Variables

• Equations

• Translate Words into Variable Expressions

• Translate Words into Equations

• Problem Solving

• Dimensional Analysis

• Structure and Meaning

Unit 2: One-Variable Linear Equations and Inequalities

This unit is about single variable equations and inequalities. Students learn how to solve equations and 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

• One-Step Equations

• Multiple Transformations

• Variables on Both Sides of an Equation

• Applications of Linear Equations

• Solve Literal Equations

• Solve Inequalities

• Applications of Inequalities

• Reasoning

Unit 3: Two-Variable 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

• Graphs of Lines

• Forms of Linear Equations

• Write Equations of Lines

• Graph Linear Inequalities

• Systems of Linear Inequalities

• Constraints

Unit 4: Working with Functions

In this unit, students learn about functions, use function notation to write function equations, and learn how to transform linear functions. The transformations include translations, reflections, stretches, and compressions. Students will find and interpret intercepts and learn how the domain and range of a function relate to the real-world situation it models. In addition, students will work with absolute value functions.

• Foundations

• Relations and Functions

• Function Equations

• Linear Functions

• Transform Linear Functions 1

• Transform Linear Functions 2

• Intercepts

• Domain and Range

• Absolute Value Functions

Unit 5: Radicals and Exponents

This unit is about radical expressions and exponents. Students learn about the properties of rational and irrational numbers and simplify radical expressions. Students also learn how exponential models can fit situations involving growth and decay and use the properties of exponents to interpret and transform exponential expressions.

• Foundations

• Irrational Numbers

• Simplify Radical Expressions

• Operations with Radical Expressions

• Properties of Rational and Irrational Numbers

• Properties of Exponents

• Growth and Decay Equations

• Rewrite Exponential Expressions

Unit 6: Exponential Functions

This unit begins with graphs of exponential functions. Students graph and transform exponential functions and interpret key features of graphs, including intercepts and end behavior. Students also learn how to determine an average rate of change for a given interval. Finally, students compare linear and exponential functions and work with multiple representations of both types of functions.

• Foundations

• Graph Exponential Functions

• Features of Exponential Functions

• Transform Exponential Functions

• Interpret Exponential Graphs

• Average Rate of Change

• Identify Linear and Exponential Functions

• Multiple Representations

Unit 7: Sequences and Modeling with Functions

A sequence is a function with integer domain. In this unit, students learn about sequences, with a focus on arithmetic and geometric sequences. Students model real-world situations with linear and exponential equations, using function or sequence notation as needed.

• Foundations

• Sequences and Patterns

• Arithmetic Sequences

• Geometric Sequences

• Function Parameters

• Model Linear Relationships

• Model Exponential Relationships

Semester 2

Unit 1: Systems of Equations

When two equations must 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.

• Foundations

• Graphs of Systems

• Approximate Solutions with Graphs

• Graph Systems to Solve Equations

• Substitution Method

• Linear Combination

• Linear Combination with Multiplication

• Applications: Systems of Linear Equations

Unit 2: Univariate Data

This unit covers graphs and statistics used with univariate data. Students create and interpret dot plots, histograms, and box-and-whisker plots, and calculate measures of center and spread. Students also learn how to choose the most appropriate measure(s) for a situation and how to identify outliers.

• Foundations

• Measures of Center

• Frequency Distributions

• Box-and-Whisker Plots

• Measures of Spread

• Appropriate Measures

• Fences and Outliers

Unit 3: Bivariate Data

Sometimes, data come in ordered pairs. When these ordered pairs are graphed, patterns may emerge. 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). Students use correlation and linear regression to describe the relationship between the values.

• Foundations

• Make Two-Way Tables

• Interpret Two-Way Tables

• Scatter Plots

• Association

• The Correlation Coefficient

• Correlation and Causation

• Fit a Line to Data

• Least Squares Regression

• Residuals

Unit 4: Basic Tools and Transformations

This unit reviews essential geometric terms and concepts, including the segment and angle addition postulates, before moving onto transformations. Students will learn how to use mapping rules for transformations on the coordinate plane. Students will also learn about polygons and symmetry.

• Foundations

• Basic Geometric Terms and Definitions

• Measure Length

• Measure Angles

• Transformations 1

• Transformations 2

• Use Algebra to Describe Geometry 1

• Use Algebra to Describe Geometry 2

• Polygons and Symmetry 1

• Polygons and Symmetry 2

• Dilations

Unit 5: Proof, Congruence, and Construction

In this unit, students learn about reasoning and proof before performing geometric constructions, including segment and angle bisectors and simple regular polygons. Students also learn about triangle congruence and proving triangle congruence, with either congruence postulates and theorems or through a series of rigid motions.

• Foundations

• Reasoning 1

• Reasoning 2

• Reasoning 3

• Styles of Proofs

• Algebraic Proof

• Geometric Two-Column Proof

• Constructions of Segments, Angles, and Bisectors

• Vertical Angle Relationships

• Congruent Polygons 1

• Congruent Polygons 2

• Triangle Congruence 1

• Triangle Congruence 2

• Constructions with Polygons 1

• Constructions with Polygons 2

• Congruence and Rigid Motions

Unit 6: Analytic Geometry

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

• Foundations

• Compute Area and Perimeter with Coordinates

• Applications of Coordinates

• Parallel and Perpendicular Lines

• Use Slope

• Coordinate Proofs