Posted: Tue, 05/15/2018 - 1:10pm Updated: Tue, 05/15/2018 - 1:29pm

This Teacher Resource Guide has been developed to provide supporting materials to help educators successfully implement the Indiana Academic Standards for Algebra 1. These resources are provided to help you in your work to ensure all students meet the rigorous learning expectations set by the Indiana Academic Standards. Use of these resources are optional; teachers should decide which resources will work best in their classroom for their students.

The resources on this webpage are for illustrative purposes only, to promote a base of clarity and common understanding. Each item illustrates a standard but please note that the resources are not intended to limit interpretation or classroom applications of the standards.

The links compiled and posted on this webpage have been provided by classroom teachers, the Department of Education, and other sources. The IDOE has not attempted to evaluate any posted materials. They are offered as samples for your reference only and are not intended to represent the best or only approach to any particular issue. The IDOE does not control or guarantee the accuracy, relevance, timeliness, or completeness of information contained on a linked website; does not endorse the views expressed or services offered by the sponsor of a linked website; and cannot authorize the use of copyrighted materials contained in linked websites. Users must request such authorization from the sponsor of the linked website.

REAL NUMBERS AND EXPRESSIONS

2014 Indiana Academic Standards

Activities, Examples, or Resources

AI.RNE.1: Understand the hierarchy and relationships of numbers and sets of numbers within the real number system.

Fractions

Classifying Numbers

AI.RNE.2: Explain why the sum or product of two rational numbers is rational; that the sum of a rational number and an irrational number is irrational; and that the product of a nonzero rational number and an irrational number is irrational.

Predict the Result of Adding and Subtracting Rational and Irrational Numbers

AI.RNE.3: Rewrite and evaluate numeric expressions with positive rational exponents using the properties of exponents.

Complex Examples

AI.RNE.4: Simplify square roots of non-perfect square integers and algebraic monomials.

 

AI.RNE.5: Simplify algebraic rational expressions, with numerators and denominators containing monomial bases with integer exponents, to equivalent forms

 

AI.RNE.6: Factor common terms from polynomials and factor polynomials completely.  Factor the difference of two squares, perfect square trinomials, and other quadratic expressions.

 

AI.RNE.7: Understand polynomials are closed under the operations of addition, subtraction, and multiplication with integers; add, subtract, and multiply polynomials and divide polynomials by monomials.

Multiplying and Factoring Polynomials

 

FUNCTIONS

2014 Indiana Academic Standards

Activities, Examples, or Resources

AI.F.1: Understand that a function from one set (called the domain) to another set (called the range) assigns to each element of the domain exactly one element of the range.  Understand that if f is a function and x is an element of its domain, then f(x) denotes the output of f corresponding to the input x. Understand the graph of f is the graph of the equation y = f(x).

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AI.F.2: Describe qualitatively the functional relationship between two quantities by analyzing a graph (e.g., where the function is increasing or decreasing, linear or nonlinear, has a maximum or minimum value).  Sketch a graph that exhibits the qualitative features of a function that has been verbally described.  Identify independent and dependent variables and make predictions about the relationship.

Influenza Epidemic

Warming and Cooling

How is the Weather?

AI.F.3: Identify the domain and range of relations represented in tables, graphs, verbal descriptions, and equations.

 

AI.F.4: Understand and interpret statements that use function notation in terms of a context; relate the domain of the function to its graph and to the quantitative relationship it describes.

Cell Phones

Yam in the Oven

Using Function Notation I

The Random Walk

 

LINEAR EQUATIONS, INEQUALITIES, AND FUNCTIONS

2014 Indiana Academic Standards

Activities, Examples, or Resources

AI.L.1: Understand that the steps taken when solving linear equations create new equations that have the same solution as the original.  Solve fluently linear equations and inequalities in one variable with integers, fractions, and decimals as coefficients.  Explain and justify each step in solving an equation, starting from the assumption that the original equation has a solution.  Justify the choice of a solution method.

Relationships Between Quantities and Reasoning with Equations and Their Graphs

AI.L.2: Represent real-world problems using linear equations and inequalities in one variable and solve such problems. Interpret the solution and determine whether it is reasonable.

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Bernardo and Sylvia Play a Game

AI.L.3: Represent real-world and other mathematical problems using an algebraic proportion that leads to a linear equation and solve such problems.

 

AI.L.4: Represent linear functions as graphs from equations (with and without technology), equations from graphs, and equations from tables and other given information (e.g., from a given point on a line and the slope of the line).

 

AI.L.5: Represent real-world problems that can be modeled with a linear function using equations, graphs, and tables; translate fluently among these representations, and interpret the slope and intercepts.

 

AI.L.6: Translate among equivalent forms of equations for linear functions, including slope-intercept, point-slope, and standard. Recognize that different forms reveal more or less information about a given situation.

Linear Equations in Three Forms

AI.L.7: Represent real-world problems using linear inequalities in two variables and solve such problems; interpret the solution set and determine whether it is reasonable.  Solve other linear inequalities in two variables by graphing.

 

AI.L.8: Solve compound linear inequalities in one variable, and represent and interpret the solution on a number line. Write a compound linear inequality given its number line representation.

Compound Inequalities

AI.L.9: Solve absolute value linear equations in one variable.

Intro to Absolute Value Equations and Graphs

AI.L.10: Graph absolute value linear equations in two variables.

 

AI.L.11: Solve equations and formulas for a specified variable, including equations with coefficients represented by variables.

Solving Literal Equations

 

SYSTEMS OF EQUATIONS AND INEQUALITIES

2014 Indiana Academic Standards

Activities, Examples, or Resources

AI.SEI.1: Understand the relationship between a solution of a pair of linear equations in two variables and the graphs of the corresponding lines.  Solve pairs of linear equations in two variables by graphing; approximate solutions when the coordinates of the solution are non-integer numbers.

 

AI.SEI.2: Understand that, given a system of two equations in two variables, replacing one equation by the sum of that equation and a multiple of the other produces a system with the same solutions. Solve pairs of linear equations in two variables using substitution and elimination.

Systems of Linear Equations: Solving by Addition/Elimination

AI.SEI.3: Write a system of two linear equations in two variables that represents a real-world problem and solve the problem with and without technology.  Interpret the solution and determine whether the solution is reasonable.

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AI.SEI.4: Represent real-world problems using a system of two linear inequalities in two variables and solve such problems; interpret the solution set and determine whether it is reasonable. Solve other pairs of linear inequalities by graphing with and without technology.

Modeling Real-World Situations Using Systems of Linear Inequalities

 

QUADRATIC AND EXPONENTIAL EQUATIONS AND FUNCTIONS

2014 Indiana Academic Standards

Activities, Examples, or Resources

AI.QE.1: Distinguish between situations that can be modeled with linear functions and with exponential functions.  Understand that linear functions grow by equal differences over equal intervals, and that exponential functions grow by equal factors over equal intervals.  Compare linear functions and exponential functions that model real-world situations using tables, graphs, and equations.

Equal Differences over Equal Intervals 1

In the Billions and Linear Modeling

Exponential Growth versus Linear Growth I

Exponential Growth versus Linear Growth II

Linear or Exponential?

AI.QE.2: Represent real-world and other mathematical problems that can be modeled with exponential functions using tables, graphs, and equations of the form y = ab^x (for integer values of x > 1, rational values of b > 0 and b ≠ 1 ); translate fluently among these representations and interpret the values of a and b.

Compound Interest

A1.QE.3: Graph exponential and quadratic equations in two variables with and without technology.

How to Determine…

AI.QE.4: Solve quadratic equations in one variable by inspection (e.g., for x^2 = 49), finding square roots, using the quadratic formula, and factoring, as appropriate to the initial form of the equation.

 

AI.QE.5: Represent real-world problems using quadratic equations in one or two variables and solve such problems with and without technology.  Interpret the solution and determine whether it is reasonable.

Real World Examples of Quadratic Equations

AI.QE.6: Use the process of factoring to determine zeros, lines of symmetry, and extreme values in real-world and other mathematical problems involving quadratic functions; interpret the results in the real-world contexts.

 

AI.QE.7: Describe the relationships among the solutions of a quadratic equation, the zeros of the function, the x-intercepts of the graph, and the factors of the expression.

 

 

DATA ANALYSIS AND STATISTICS

2014 Indiana Academic Standards

Activities, Examples, or Resources

AI.DS.1: Distinguish between random and non-random sampling methods, identify possible sources of bias in sampling, describe how such bias can be controlled and reduced, evaluate the characteristics of a good survey and well-designed experiment, design simple experiments or investigations to collect data to answer questions of interest, and make inferences from sample results.

Why Randomize?

AI.DS.2: Graph bivariate data on a scatter plot and describe the relationship between the variables.

 

AI.DS.3: Use technology to find a linear function that models a relationship for a bivariate data set to make predictions; interpret the slope and y-intercept, and compute (using technology) and interpret the correlation coefficient.

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AI.DS.4: Distinguish between correlation and causation.

Differentiate between Correlation and Causation

Golf and Divorce

AI.DS.5: Understand that patterns of association can also be seen in bivariate categorical data by displaying frequencies and relative frequencies in a two-way table.  Construct and interpret a two-way table summarizing data on two categorical variables collected from the same subjects.  Use relative frequencies calculated for rows or columns (including joint, marginal, and conditional relative frequencies) to describe possible associations and trends in the data.

Two-Way Frequency Tables

Musical Preferences

AI.DS.6: Understand that statistics and data are non-neutral and designed to serve a particular interest.  Analyze the possibilities for whose interest might be served and how the representations might be misleading.

The Average Switcheroo