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School City of Hobart
School City of Hobart Mathematics
Mathematics - Algebra I

Algebraic Concepts
Operations with Real Numbers
The learner will be able to simplify and compare expressions. They use rational exponents, and simplify square roots.
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Expressions Master IDOE
  
A1.1.1
The learner will be able to compare real number expressions.
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Expressions Master IDOE
  
A1.1.2
The learner will be able to simplify square roots using factors.
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Factoring Master IDOE
  
A1.1.3
The learner will be able to understand and use the distributive, associative, and commutative properties. Example: Simplify (6x2 - 5x+1) - 2(x2 + 3x - 4) by removing the parentheses and rearranging. Explain why you can carry out each step. .
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Properties Master IDOE
  
A1.1.4
The learner will be able to use the laws of exponents for rational exponents.
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Exponents Master IDOE
  
A1.1.5
The learner will be able to use dimensional (unit) analysis to organize conversions and computations. Example: Convert 5 miles per hour to feet per second. .
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Computation Master IDOE
  
Linear Equations and Inequalities
The learner will be able to solve linear equations and inequalities in one variable. They solve word problems that involve linear equations, inequalities, or formulas.
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Linear Equations/Inequalities Master IDOE
  
A1.2.1
The learner will be able to solve equations and formulas for a specified variable. Example: Solve the equation q = 4p - 11 for p. .
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Equations Master IDOE
  
A1.2.3
The learner will be able to find solution sets of linear inequalities when possible numbers are given for the variable. Example: Solve the inequality 6x - 3 > 10 for x in the set {0, 1, 2, 3, 4}. .
Strand Scope Source
Linear Inequalities Master IDOE
  
A1.2.4
The learner will be able to solve linear inequalities using properties of order. Example: Solve the inequality 8x - 7 <= 2x + 5, explaining each step in your solution. .
Strand Scope Source
Linear Inequalities Master IDOE
  
A1.2.5
The learner will be able to solve combined linear inequalities. Example: Solve the inequalities -7 < 3x + 5 < 11. .
Strand Scope Source
Linear Inequalities Master IDOE
  
A1.2.6
The learner will be able to solve word problems that involve linear equations, formulas, and inequalities. Example: You are selling tickets for a play that cost $3 each. You want to sell at least $50 worth. Write and solve an inequality for the number of tickets you must sell. .
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Linear Equations/Inequalities Master IDOE
  
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Functions
Relations and Functions
The learner will be able to sketch and interpret graphs representing given situations. They understand the concept of a function and analyze the graphs of functions.
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Functions/Relations Master IDOE
  
A1.3.1
The learner will be able to sketch a reasonable graph for a given relationship. Example: Sketch a reasonable graph for a person's height from age 0 to 25. .
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Relations Master IDOE
  
A1.3.2
The learner will be able to interpret a graph representing a given situation. .
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Graphing Functions Master IDOE
  
A1.3.3
The learner will be able to understand the concept of a function, decide if a given relation is a function, and link equations to functions. Example: Use either paper or a spreadsheet to generate a list of values for x and y in y = x2. Based on your data, make a conjecture about whether or not this relation is a function. Explain your reasoning. .
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Functions/Relations Master IDOE
  
A1.3.4
The learner will be able to find the domain and range of a relation. Example: Based on the list of values from the last example, what do the domain and range of y = x2 appear to be? How can you decide whether you are correct? .
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Relations Master IDOE
  
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Algebraic Concepts
Graphing Linear Equations, Inequalities
The learner will be able to graph linear equations and inequalities in two variables. They write equations of lines and find and use the slope and y-intercept of lines. They use linear equations to model real data.
Strand Scope Source
Linear Equations Master IDOE
  
A1.4.1
The learner will be able to graph a linear equation. Example: Draw the graph of the line with slope 3 and y-intercept -2. .
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Linear Equations Master IDOE
  
A1.4.2
The learner will be able to find the slope, x-intercept and y-intercept of a line given its graph, its equation, or two points on the line. Example: Find the slope and y-intercept of the line 4x + 6y = 12. .
Strand Scope Source
Linear Equations Master IDOE
  
A1.4.3
The learner will be able to write the equation of a line in slope-intercept form. Understand how the slope and y-intercept of the graph are related to the equation. Example: Write the equation of the line 4x + 6y = 12 in slope-intercept form. What is the slope of this line? Explain your answer. .
Strand Scope Source
Linear Equations Master IDOE
  
A1.4.4
The learner will be able to write the equation of a line given appropriate information. Example: Find an equation of the line through the points (1, 4) and (3, 10), then find an equation of the line through the point (1, 4) perpendicular to the first line. .
Strand Scope Source
Linear Equations Master IDOE
  
A1.4.5
The learner will be able to write the equation of a line that models a data set and use the equation (or the graph of the equation) to make predictions. Describe the slope of the line in terms of the data, recognizing that the slope is the rate of change. Example: As your family is traveling along an interstate, you note the distance traveled every 5 minutes. A graph of time and distance shows that the relation is approximately linear. Write the equation of the line that fits your data. Predict the time for a journey of 50 miles. What does the slope represent? .
Strand Scope Source
Linear Equations Master IDOE
  
A1.4.6
The learner will be able to graph a linear inequality in two variables. Example: Draw the graph of the inequality 6x + 8y >= 24. .
Strand Scope Source
Linear Inequalities Master IDOE
  
Pairs of Linear Equations, Inequalities
The learner will be able to solve pairs of linear equations using graphs and using algebra. They solve pairs of linear inequalities using graphs. They solve word problems involving pairs of linear equations.
Strand Scope Source
Linear Equations/Inequalities Master IDOE
  
A1.5.1
The learner will be able to use a graph to estimate the solution of a pair of linear equations in two variables. Example: Graph the equations 3y - x = 0 and 2x + 4y = 15 to find where the lines intersect. .
Strand Scope Source
Linear Equations Master IDOE
  
A1.5.2
The learner will be able to use a graph to find the solution set of a pair of linear inequalities in two variables. Example: Graph the inequalities y <= 4 and x + y <= 5. Shade the region where both inequalities are true. .
Strand Scope Source
Linear Inequalities Master IDOE
  
A1.5.3
The learner will be able to understand and use the substitution method to solve a pair of linear equations in two variables. Example: Solve the equations y = 2x and 2x + 3y = 12 by substitution. .
Strand Scope Source
Linear Equations Master IDOE
  
A1.5.4
The learner will be able to understand and use the addition or subtraction method to solve a pair of linear equations in two variables. Example: Use subtraction to solve the equations: 3x + 4y = 11, 3x + 2y = 7. .
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Linear Equations Master IDOE
  
A1.5.5
The learner will be able to understand and use multiplication with the addition or subtraction method to solve a pair of linear equations in two variables. Example: Use multiplication with the subtraction method to solve the equations: x + 4y = 16, 3x - 2y = -3. .
Strand Scope Source
Linear Equations Master IDOE
  
A1.5.6
The learner will be able to use pairs of linear equations to solve word problems. Example: The income a company makes from a certain product can be represented by the equation y = 10.5x and the expenses for that product can be represented by the equation y = 5.25x + 10,000, where x is the amount of the product sold and y is the number of dollars. How much of the product must be sold for the company to reach the break-even point? .
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Linear Equations Master IDOE
  
Polynomials
The learner will be able to add, subtract, multiply, and divide polynomials. They factor quadratics.
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Polynomials Master IDOE
  
A1.6.1
The learner will be able to add and subtract polynomials. .
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Polynomials Master IDOE
  
A1.6.2
The learner will be able to multiply and divide monomials.
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Polynomials Master IDOE
  
A1.6.3
The learner will be able to find powers and roots of monomials (only when the answer has an integer exponent).
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Polynomials Master IDOE
  
A1.6.4
The learner will be able to multiply polynomials. Example: Multiply (n + 2)(4n - 5). .
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Polynomials Master IDOE
  
A1.6.5
The learner will be able to divide polynomials by monomials.
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Polynomials Master IDOE
  
A1.6.6
The learner will be able to find a common monomial factor in a polynomial.
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Polynomials Master IDOE
  
A1.6.7
The learner will be able to factor the difference of two squares and other quadratics.
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Quadratic Equations/Formula Master IDOE
  
A1.6.8
The learner will be able to understand and describe the relationships among the solutions of an equation, the zeros of a function, the x-intercepts of a graph, and the factors of a polynomial expression.
Strand Scope Source
Algebraic Concepts Master IDOE
  
Algebraic Fractions
The learner will be able to simplify algebraic ratios and solve algebraic proportions.
Strand Scope Source
Algebraic Concepts Master IDOE
  
A1.7.1
The learner will be able to simplify algebraic ratios.
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Algebraic Concepts Master IDOE
  
A1.7.2
The learner will be able to solve algebraic proportions.
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Algebraic Concepts Master IDOE
  
Quadratic, Cubic, and Radical Equations
The learner will be able to graph and solve quadratic and radical equations. They graph cubic equations.
Strand Scope Source
Quadratic Equations/Formula Master IDOE
  
A1.8.1
The learner will be able to graph quadratic, cubic, and radical equations.
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Quadratic Equations/Formula Master IDOE
  
A1.8.2
The learner will be able to solve quadratic equations by factoring. .
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Quadratic Equations/Formula Master IDOE
  
A1.8.3
The learner will be able to solve quadratic equations in which a perfect square equals a constant.
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Quadratic Equations/Formula Master IDOE
  
A1.8.4
The learner will be able to complete the square to solve quadratic equations.
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Quadratic Equations/Formula Master IDOE
  
A1.8.5
The learner will be able to derive the quadratic formula by completing the square.
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Quadratic Equations/Formula Master IDOE
  
A1.8.6
The learner will be able to solve quadratic equations by using the quadratic formula.
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Quadratic Equations/Formula Master IDOE
  
A1.8.7
The learner will be able to use quadratic equations to solve word problems.
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Quadratic Equations/Formula Master IDOE
  
A1.8.8
The learner will be able to solve equations that contain radical expressions.
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Radicals Master IDOE
  
A1.8.9
The learner will be able to use graphing technology to find approximate solutions of quadratic and cubic equations.
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Quadratic Equations/Formula Master IDOE
  
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Problem Solving
Mathematical Reasoning, Problem Solving
The learner will be able to use a variety of strategies to solve problems.
Strand Scope Source
Problem Solving Master IDOE
  
A1.9.1
The learner will be able to 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. Example: Fran has scored 16, 23, and 30 points in her last three games. How many points must she score in the next game so that her four game average does not fall below 20 points? .
Strand Scope Source
Strategies Master IDOE
  
A1.9.2
The learner will be able to decide whether a solution is reasonable in the context of the original situation. Example: John says the answer to the problem in the first example is 10 points. Is his answer reasonable? Why or why not? .
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Evaluating Solutions Master IDOE
  
A1.9.3
The learner will be able to use the properties of the real number system and the order of operations to justify the steps of simplifying functions and solving equations. Example: Given an argument (such as 3x + 7 > 5x + 1, and therefore -2x > -6, and therefore x > 3), provide a visual presentation of a step-by-step check, highlighting any errors in the argument. .
Strand Scope Source
Strategies Master IDOE
  
A1.9.4
The learner will be able to 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. Example: Try "solving" the equations x + 3y = 5 and 5x + 15y = 25 simultaneously, and explain what went wrong. .
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Strategies Master IDOE
  
A1.9.5
The learner will be able to decide whether a given algebraic statement is true always, sometimes, or never (statements involving linear or quadratic expressions, equations, or inequalities).
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Strategies Master IDOE
  
A1.9.6
The learner will be able to distinguish between inductive and deductive reasoning, identifying and providing examples of each. Example: What type of reasoning are you using when you look for a pattern? .
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Analyzing Problems Master IDOE
  
A1.9.7
The learner will be able to identify the hypothesis and conclusion in a logical deduction. Example: What is the hypothesis and conclusion in this argument: If there is a number x such that 2x + 1 = 7, then x = 3. .
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Analyzing Problems Master IDOE
  
A1.9.8
The learner will be able to use counterexamples to show that statements are false, recognizing that a single counterexample is sufficient to prove a general statement false. Example: Use the demonstration-graphing calculator on an overhead projector to produce an example showing that this statement is false: all quadratic equations have two different solutions. .
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Analyzing Problems Master IDOE
  
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