# Integrated Math 1

## Course Summary

Use patterns, modeling, and conjectures to build an understanding of and attain competency in mathematics. Develop mathematical skills through collaboration, data collection, experimentation, and conjectures. In this course, students engage in mathematical sense-making, make and test conjectures and justify conclusions, use mathematical models to represent real-world data, learn to provide clear and concise answers, and gain computational and symbolic fluency.

This course is the first of a three-year Integrated Math series.

**Course Prerequisite(s):**Students should have successfully completed middle school mathematics through grade 7.

## Curriculum

This is a 2-semester course. We do not recommend taking both semesters simultaneously.

##### Unit 1: Solving Equations and Inequalities

- The Distributive Property
- Solving Multi-Step Equations Part 1
- Solving Multi-Step Equations Part 2
- Solving Equations with Variables on Both Sides
- Literal Equations and Formulas
- Ratios, Rates, and Conversions
- Solving Proportions
- Solving Multi-Step Inequalities
- Compound Inequalities
- Absolute Value Equations
- Absolute Value Inequalities

##### Unit 2: An Introduction to Functions

- Using Graphs to Relate Two Quantities
- Patterns and Linear Functions
- Patterns and Nonlinear Functions
- Graphing a Function Rule
- Writing a Function Rule
- Formalizing Relations and Functions
- Arithmetic Sequences

##### Unit 3: Linear Functions

- Rate of Change and Slope
- Slope and Graphs
- Slope-Intercept Form
- Point-Slope Form
- Standard Form
- Slopes of Parallel and Perpendicular Lines
- Graphing Absolute Value Functions

##### Unit 4: Systems of Equations and Inequalities

- Solving Systems by Graphing
- Solving Systems Using Substitution
- Solving Systems Using Elimination
- Applications of Linear Systems
- Linear Inequalities
- Systems of Linear Inequalities

##### Unit 5: Exponential and Radical Functions

- Zero and Negative Exponents
- Exponential Functions
- Comparing Linear and Exponential Functions
- Exponential Growth and Decay
- Solving Exponential Equations
- Geometric Sequences
- Combining Functions
- Simplifying Radicals

##### Unit 6: Data Analysis

- Frequency and Histograms
- Measures of Central Tendency and Dispersion
- Box-and-Whisker Plots
- Scatter Plots and Trend Lines
- Two-Way Frequency Tables

##### Unit 7: Tools of Geometry

- Nets and Drawings for Visualizing Geometry
- Points, Lines, and Planes
- Measuring Segments
- Measuring Angles
- Exploring Angle Pairs
- Midpoint and Distance in the Coordinate Plane

##### Unit 8: Transformations

- Translations
- Reflections
- Rotations
- Compositions of Isometries

##### Unit 9: Congruent Triangles

- Congruent Figures
- Triangle Congruence by SSS and SAS
- Triangle Congruence by ASA and AAS
- Using Corresponding Parts of Congruent Triangles
- Isosceles and Equilateral Triangles
- Congruence in Right Triangles
- Congruence in Overlapping Triangles
- Congruence Transformations

##### Unit 10: Connecting Algebra and Geometry

- Perimeter and Area in the Coordinate Plane
- Areas of Parallelograms and Triangles
- Areas of Trapezoids, Rhombuses, and Kites
- Polygons in the Coordinate Plane

##### Unit 11: Reasoning and Proof

- Basic Constructions
- Patterns and Inductive Reasoning
- Conditional Statements
- Biconditionals and Definitions
- Deductive Reasoning
- Reasoning in Algebra and Geometry
- Proving Angles Congruent