IM1.1: Students simplify and compare expressions. They use rational exponents and simplify square roots.

IM1.1.1: Compare real number expressions.

Comparing and Ordering Decimals
Rational Numbers, Opposites, and Absolute Values

IM1.1.2: Simplify square roots using factors.

Operations with Radical Expressions

IM1.1.3: Understand and use the distributive, associative, and commutative properties.

Equivalent Algebraic Expressions I
Equivalent Algebraic Expressions II
Square Roots
Using Algebraic Equations

IM1.1.5: Use dimensional (unit) analysis to organize conversions and computations.

Unit Conversions

IM1.2: Students solve linear equations and inequalities in one variable. They write equations of lines and find and use the slope and y-intercept of lines. Students solve pairs of linear equations using graphs and algebra. Students add, subtract, multiply, and divide polynomials and solve word problems using exponential functions.

IM1.2.1: Solve linear equations.

Modeling One-Step Equations
Modeling and Solving Two-Step Equations
Solving Algebraic Equations II
Solving Equations by Graphing Each Side
Solving Two-Step Equations

IM1.2.2: Solve equations and formulas for a specific variable.

Solving Formulas for any Variable

IM1.2.3: Find solution sets of linear inequalities when possible numbers are given for the variable.

Systems of Linear Inequalities (Slope-intercept form)

IM1.2.4: Solve linear inequalities using properties of order.

Compound Inequalities
Linear Inequalities in Two Variables
Solving Linear Inequalities in One Variable

IM1.2.5: Solve word problems that involve linear equations, formulas, and inequalities.

Point-Slope Form of a Line
Standard Form of a Line

IM1.2.6: Sketch a reasonable graph for a given relationship.

Absolute Value with Linear Functions
Distance-Time Graphs
Quadratics in Polynomial Form

IM1.2.8: Understand the concept of a function, decide if a given relation is a function and link equations to functions.

Absolute Value Equations and Inequalities
Function Machines 1 (Functions and Tables)
Function Machines 2 (Functions, Tables, and Graphs)
Function Machines 3 (Functions and Problem Solving)
Introduction to Functions
Linear Functions
Points, Lines, and Equations

IM1.2.9: Find the domain and range of a relation.

Introduction to Functions

IM1.2.10: Graph a linear equation.

Absolute Value with Linear Functions
Linear Functions
Point-Slope Form of a Line
Points, Lines, and Equations
Solving Equations by Graphing Each Side
Standard Form of a Line

IM1.2.11: Find the slope, x-intercept and y-intercept of a line given its graph, its equation, or two points on the line.

Cat and Mouse (Modeling with Linear Systems)
Function Machines 2 (Functions, Tables, and Graphs)
Function Machines 3 (Functions and Problem Solving)
Point-Slope Form of a Line
Points, Lines, and Equations
Slope
Slope-Intercept Form of a Line
Standard Form of a Line

IM1.2.12: Write the equation of a line in slope-intercept form. Understand how the slope and y-intercept are related to the equation.

Linear Inequalities in Two Variables
Point-Slope Form of a Line
Points, Lines, and Equations
Slope-Intercept Form of a Line
Standard Form of a Line

IM1.2.13: Write the equation of a line given appropriate information.

Linear Inequalities in Two Variables
Point-Slope Form of a Line
Points, Lines, and Equations
Slope-Intercept Form of a Line
Solving Equations on the Number Line
Standard Form of a Line

IM1.2.16: Understand and use the substitution method to solve a pair of linear equations in two variables.

Solving Equations by Graphing Each Side
Solving Linear Systems (Slope-Intercept Form)
Solving Linear Systems (Standard Form)

IM1.2.17: Understand and use the addition or subtraction method to solve a pair of linear equations in two variables.

Solving Linear Systems (Standard Form)

IM1.2.18: Understand and use multiplication with the addition or subtraction method to solve a pair of linear equations in two variables.

Solving Equations by Graphing Each Side
Solving Linear Systems (Slope-Intercept Form)
Solving Linear Systems (Standard Form)

IM1.2.19: Use pairs of linear equations to solve word problems.

Cat and Mouse (Modeling with Linear Systems)
Solving Linear Systems (Matrices and Special Solutions)
Solving Linear Systems (Standard Form)

IM1.2.20: Add and subtract polynomials.

Addition and Subtraction of Functions
Addition of Polynomials

IM1.2.21: Multiple and divide monomials.

Dividing Exponential Expressions
Multiplying Exponential Expressions

IM1.2.23: Multiply polynomials.

Modeling the Factorization of x²+bx+c

IM1.2.24: Divide polynomials by monomials.

Dividing Polynomials Using Synthetic Division

IM1.2.26: Graph quadratic, cubic, and radical equations.

Parabolas
Quadratics in Polynomial Form
Radical Functions
Roots of a Quadratic

IM1.2.27: Solve quadratic equations by using the quadratic formula.

Roots of a Quadratic

IM1.2.30: Graph exponential functions.

Compound Interest
Exponential Functions
Introduction to Exponential Functions
Logarithmic Functions

IM1.3: Students identify and describe polygons, including finding measures of sides, perimeters, and areas. They use congruence, similarity, symmetry, tessellations, and transformations. Students understand the Pythagorean Theorem and use it to solve problems. They describe relationships and symmetries in geometric solids.

IM1.3.1: Identify and describe convex, concave, and regular polygons.

Polygon Angle Sum

IM1.3.3: Find and use measures of sides, perimeter, and areas of polygons, and relate these measures to each other using formulas.

Area of Parallelograms
Area of Triangles
Perimeter and Area of Rectangles
Perimeters and Areas of Similar Figures

IM1.3.4: Use properties of congruent and similar quadrilaterals to solve problems involving lengths and areas.

Perimeters and Areas of Similar Figures
Similar Figures

IM1.3.5: Find and use measures of sides, perimeters, and areas of quadrilaterals, and relate these measures to each other using formulas.

Area of Parallelograms
Area of Triangles
Perimeter and Area of Rectangles

IM1.3.6: Prove and use the Pythagorean Theorem.

Circles
Cosine Function
Distance Formula
Pythagorean Theorem
Pythagorean Theorem with a Geoboard
Sine Function
Surface and Lateral Areas of Pyramids and Cones
Tangent Function

IM1.4: Students find measures of the center and variability of a set of data, as well as construct and analyze data displays and plot least square regression lines.

IM1.4.1: Construct a line plot.

Mean, Median, and Mode
Stem-and-Leaf Plots

IM1.4.2: Find measures of central tendency for a set of data.

Box-and-Whisker Plots
Describing Data Using Statistics
Mean, Median, and Mode
Reaction Time 1 (Graphs and Statistics)
Stem-and-Leaf Plots

IM1.4.3: Find skewness and symmetry from a graph of data.

Mean, Median, and Mode

IM1.4.5: Identify clusters, gaps, and outliers for a set of data.

Describing Data Using Statistics
Least-Squares Best Fit Lines
Mean, Median, and Mode

IM1.4.6: Find a linear transformation.

Absolute Value with Linear Functions
Exponential Functions

IM1.4.8: Find the mean absolute deviation for a set of data.

Polling: City
Populations and Samples
Real-Time Histogram
Sight vs. Sound Reactions

IM1.4.9: Find the standard deviation and describe its properties.

Polling: City
Real-Time Histogram
Sight vs. Sound Reactions

IM1.4.10: Construct a frequency table for a set of data.

Histograms

IM1.4.11: Summarize and interpret sets of data using center and variability.

Box-and-Whisker Plots
Describing Data Using Statistics
Mean, Median, and Mode
Reaction Time 1 (Graphs and Statistics)
Stem-and-Leaf Plots

IM1.4.12: Construct a scatterplot from a set of data.

Correlation
Least-Squares Best Fit Lines
Solving Using Trend Lines
Trends in Scatter Plots

IM1.4.13: Calculate the sum of squared differences for a set of data.

Correlation
Least-Squares Best Fit Lines
Solving Using Trend Lines

IM1.4.14: Plot the least square regression line from a set of data.

Correlation
Least-Squares Best Fit Lines
Solving Using Trend Lines

IM1.4.15: Compare sets of data using scatterplots and the line y = x, and interpret these comparisons for real-world data.

Correlation
Trends in Scatter Plots

IM1.4.16: Recognize patterns in tables and graphs that are modeled by linear equations.

Function Machines 2 (Functions, Tables, and Graphs)

IM1.5: Students use simulations, find probabilities, and use the Law of Large Numbers.

IM1.5.2: Use empirical (experimental) and theoretical probabilities.

Binomial Probabilities
Geometric Probability
Independent and Dependent Events
Probability Simulations
Theoretical and Experimental Probability

IM1.5.3: Understand independent events.

Independent and Dependent Events

IM1.5.4: Use the Law of Large Numbers to understand situations involving chance.

Theoretical and Experimental Probability

IM1.5.5: Understand the concept of a probability distribution. Understand how an approximate probability can be constructed using simulation involving chance.

Polling: City

IM1.6: Students construct graphs, explore algorithms, and use recursion equations and matrices.

IM1.6.6: Use a variety of recursion equations to describe a function.

Arithmetic Sequences
Geometric Sequences

IM1.7: Students use a variety of strategies to solve problems and develop and evaluate mathematical arguments and proofs.

IM1.7.1: Use a variety of problem solving strategies, such as drawing a diagram, making a chart, guess-and-check, solving a simpler problem, writing an equation, and working backwards.

Estimating Population Size
Linear Inequalities in Two Variables
Modeling One-Step Equations
Solving Equations on the Number Line
Using Algebraic Equations

IM1.7.3: Use the properties of the real number system and the order of operations to justify the steps of simplifying functions and solving equations.

Solving Algebraic Equations II
Solving Equations on the Number Line

IM1.7.4: Understand that the logic of equation solving begins with the assumption that the variable is a number that satisfies the equation, and that the steps taken when solving equations create new equations that have, in most cases, the same solution set as the original. Understand that similar logic applies to solving systems of equations simultaneously.

Solving Linear Systems (Standard Form)