Algebra I

SEMESTER 1:

Unit 1: Foundations of Algebra

Missouri Learning Standards: You will know you have achieved the learning goal when you can:

Concept 1: Analyze Expressions and Equations

• Use units of measure as a way to understand and solve problems involving quantities. (A1.NQ.B.3)
  1. Identify, label and use appropriate units of measure within a problem.
  2. Convert units and rates.
  3. Use units within problems.
  4. Choose and interpret the scale and the origin in graphs and data displays.
• Define and use appropriate quantities for representing a given context or problem. (A1.NQ.B.4)
• Interpret the contextual meaning of individual terms or factors from a given problem that utilizes formulas or expressions. (A1.SSE.A.1)

Concept 2: Reason with Expressions and Equations

• Use units of measure as a way to understand and solve problems involving quantities. (A1.NQ.B.3)
  1. Identify, label and use appropriate units of measure within a problem.
  2. Convert units and rates.
  3. Use units within problems.
  4. Choose and interpret the scale and the origin in graphs and data displays.
• Define and use appropriate quantities for representing a given context or problem. (A1.NQ.B.4)
• Create equations and inequalities in one variable and use them to model and/or solve problems. (A1.CED.A.1)

Concept 3: Apply and Evaluate Expressions and Equations

• Use units of measure as a way to understand and solve problems involving quantities. (A1.NQ.B.3)
  1. Identify, label and use appropriate units of measure within a problem.
  2. Convert units and rates.
  3. Use units within problems.
  4. Choose and interpret the scale and the origin in graphs and data displays.
• Interpret the contextual meaning of individual terms or factors from a given problem that utilizes formulas or expressions. (A1.SSE.A.1)
• Create equations and inequalities in one variable and use them to model and/or solve problems. (A1.CED.A.1)
• Create and graph linear, quadratic and exponential equations in two variables. (A1.CED.A.2)

 

Unit 2: Equations and Inequalities

Missouri Learning Standards: You will know you have achieved the learning goal when you can:

Concept 1: Solve Equations and Inequalities

• Create equations and inequalities in one variable and use them to model and/or solve problems. (A1.CED.A.1)
• Represent constraints by equations or inequalities and by systems of equations or inequalities, and interpret the data points as a solution or non-solution in a modeling context. (A1.CED.A.3)
• Explain how each step taken when solving an equation or inequality in one variable creates an equivalent equation or inequality that has the same solution(s) as the original. (A1.REI.A.1)
• Explain that the graph of an equation in two variables is the set of all its solutions plotted in the Cartesian coordinate plane. (A1.REI.C.6)

Concept 2: Rewrite Literal Equations

• Use units of measure as a way to understand and solve problems involving quantities. (A1.NQ.B.3)
  1. Identify, label and use appropriate units of measure within a problem.
  2. Convert units and rates.
  3. Use units within problems.
  4. Choose and interpret the scale and the origin in graphs and data displays.
• Define and use appropriate quantities for representing a given context or problem.  (A1.NQ.B.4)
• Interpret the contextual meaning of individual terms or factors from a given problem that utilizes formulas or expressions. (A1.SSE.A.1)
• Represent constraints by equations or inequalities and by systems of equations or inequalities, and interpret the data points as a solution or non-solution in a modeling context. (A1.CED.A.3)
• Create equations and inequalities in one variable and use them to model and/or solve problems. (A1.CED.A.1)

Concept 3: Solve Absolute Value Equations and Inequalities

• Represent constraints by equations or inequalities and by systems of equations or inequalities, and interpret the data points as a solution or non-solution in a modeling context. (A1.CED.A.3)
• Create equations and inequalities in one variable and use them to model and/or solve problems. (A1.CED.A.1)
• Explain that the graph of an equation in two variables is the set of all its solutions plotted in the Cartesian coordinate plane. (A1.REI.C.6)

 

Unit 3: Functions

Missouri Learning Standards: You will know you have achieved the learning goal when you can:

Concept 1: Understand and Interpret Functions

• Understand that a function from one set (domain) to another set (range) assigns to each element of the domain exactly one element of the range. (A1.IF.A.1)
  1. Represent a function using function notation.
  2. Understand that the graph of a function labeled 𝑓 is the set of all ordered pairs (𝑥, y) that satisfy the equation 𝑦=f (𝑥).
• Use function notation to evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context. (A1.IF.A.2)
• Compare the properties of two functions given different representations. (A1.IF.C.9)
• Interpret the parameters of a linear or exponential function in terms of the context. (A1.IF.B.6)

Concept 2: Analyze Arithmetic Sequences and Linear Functions

• Recognize that sequences are functions, sometimes defined recursively, whose domain is a subset of the set of integers. (A1.LQE.B.5)
• Determine the average rate of change of a function over a specified interval and interpret the meaning. (A1.IF.B.5)
• Interpret the parameters of a linear or exponential function in terms of the context. (A1.IF.B.6)
• Compare the properties of two functions given different representations. (A1.IF.C.9)
• Construct linear, quadratic and exponential equations given graphs, verbal descriptions or tables. (A1.LQE.A.3)
• Write arithmetic and geometric sequences in recursive and explicit forms, and use them to model situations and translate between the two forms. (A1.LQE.B.4)
• Distinguish between situations that can be modeled with linear or exponential functions. (A1.LQE.A.1)
  1. Determine that linear functions change by equal differences over equal intervals.
  2. Recognize exponential situations in which a quantity grows or decays by a constant percent rate per unit interval.

Concept 3: Analyze Geometric Sequence and Exponential Functions

• Recognize that sequences are functions, sometimes defined recursively, whose domain is a subset of the set of integers. (A1.LQE.B.5)
• Determine the average rate of change of a function over a specified interval and interpret the meaning. (A1.IF.B.5)
• Interpret the parameters of a linear or exponential function in terms of the context. (A1.IF.B.6)
• Distinguish between situations that can be modeled with linear or exponential functions. (A1.LQE.A.1)
  1. Recognize exponential situations in which a quantity grows or decays by a constant percent rate per unit interval.
• Describe, using graphs and tables, that a quantity increasing exponentially eventually exceeds a quantity increasing linearly or quadratically. (A1.LQE.A.2)
• Interpret the parameters of a linear or exponential function in terms of the context. (A1.IF.B.6)

 

Unit 4: Graphs of Functions

Missouri Learning Standards: You will know you have achieved the learning goal when you can:

Concept 1: Analyze Graphs of Functions

• Explain that the graph of an equation in two variables is the set of all its solutions plotted in the Cartesian coordinate plane. (A1.REI.C.6)
• Use function notation to evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context. (A1.IF.A.2)
• Using tables, graphs and verbal descriptions, interpret key characteristics of a function that models the relationship between two quantities. (A1.IF.B.3)
• Relate the domain and range of a function to its graph and, where applicable, to the quantitative relationship it describes. (A1.IF.B.4)
• Determine the average rate of change of a function over a specified interval and interpret the meaning. (A1.IF.B.5)
• Graph functions expressed symbolically and identify and interpret key features of the graph. (A1.IF.C.7)
• Construct linear, quadratic and exponential equations given graphs, verbal descriptions or tables. (A1.LQE.A.3)

Concept 2: Compare Graphs of Linear and Exponential Functions

• Using tables, graphs and verbal descriptions, interpret key characteristics of a function that models the relationship between two quantities. (A1.IF.B.3)
• Graph functions expressed symbolically and identify and interpret key features of the graph. (A1.IF.C.7)
• Compare the properties of two functions given different representations. (A1.IF.C.9)
• Distinguish between situations that can be modeled with linear or exponential functions. (A1.LQE.A.1)
  1. Determine that linear functions change by equal differences over equal intervals.
  2. Recognize exponential situations in which a quantity grows or decays by a constant percent rate per unit interval.
• Describe, using graphs and tables, that a quantity increasing exponentially eventually exceeds a quantity increasing linearly or quadratically. (A1.LQE.A.2)
• Interpret the parameters of a linear or exponential function in terms of the context. (A1.IF.B.6)

 

Unit 5: Systems of Equations and Inequalities

Missouri Learning Standards: You will know you have achieved the learning goal when you can:

Concept 1: Solve Systems of Equations and Inequalities

• Create equations and inequalities in one variable and use them to model and/or solve problems. (A1.CED.A.1)
• Create and graph linear, quadratic and exponential equations in two variables. (A1.CED.A.2)
• Represent constraints by equations or inequalities and by systems of equations or inequalities, and interpret the data points as a solution or non-solution in a modeling context. (A1.CED.A.3)
• Solve literal equations and formulas for a specified variable that highlights a quantity of interest. (A1.CED.A.4)
• Justify that the technique of linear combination produces an equivalent system of equations. (A1.REI.B.5)
• Solve a system of linear equations algebraically and/or graphically. (A1.REI.B.3)
• Explain that the graph of an equation in two variables is the set of all its solutions plotted in the Cartesian coordinate plane. (A1.REI.C.6)
• Solve problems involving a system of linear inequalities. (A1.REI.C.8)

 

SEMESTER 2:

 

Unit 6: Descriptive Statistics

Missouri Learning Standards: You will know you have achieved the learning goal when you can:

Concept 1: Represent and Analyze Data

• Analyze and interpret graphical displays of data. (A1.DS.A.1)
• Use statistics appropriate to the shape of the data distribution to compare center and spread of two or more different data sets. (A1.DS.A.2)
• Interpret differences in shape, center, and spreads in the context of the data sets, accounting for possible effects of outliers. (A1.DS.A.3)

Concept 2: Analyze Scatter Plots

• Construct a scatterplot of bivariate quantitative data describing how the variables are related; determine and use a function that models the relationship.  (A1.DS.A.5)
  1. Construct a linear function to model bivariate data represented on a scatterplot that minimizes residuals.
• Interpret slope (rate of change) and the y-intercept (constant term) of a linear model in the context of the data. (A1.DS.A.6)
• Determine and interpret the correlation coefficient for a linear association. (A1.DS.A.7)
• Distinguish between correlation and causation. (A1.DS.A.8)

Concept 3: Interpret Two-Way Frequency Tables

• Summarize data in two-way frequency tables. (A1.DS.A.4)
  1. Interpret relative frequencies in the context of the data.
  2. Recognize possible associations and trends in the data.

 

Unit 7: Nonlinear Functions

Missouri Learning Standards: You will know you have achieved the learning goal when you can:

Concept 1: Create and Analyze Piecewise Functions

• Create and graph linear, quadratic and exponential equations in two variables. (A1.CED.A.2)
• Graph functions expressed symbolically and identify and interpret key features of the graph. (A1.IF.C.7)
• Compare the properties of two functions given different representations. (A1.IF.C.9)

Concept 2: Investigate Square Root and Cube Root Functions

• Analyze the effect of translations and scale changes on functions. (A1.BF.A.1)
• Relate the domain and range of a function to its graph and, where applicable, to the quantitative relationship it describes. (A1.BF.A.4)
• Graph functions expressed symbolically and identify and interpret key features of the graph. (A1.IF.C.7)

Concept 3: Investigate Rational Exponents

• Explain how the meaning of rational exponents extends from the properties of integer exponents. (A1.NQ.A.1)
• Rewrite expressions involving radicals and rational exponents using the properties of exponents. Limit to rational exponents with a numerator of 1. (A1.NQ.A.2)

 

Unit 8: Exponential Functions

Missouri Learning Standards: You will know you have achieved the learning goal when you can:

Concept 1: Represent Exponential Functions

• Construct linear, quadratic and exponential equations given graphs, verbal descriptions or tables. (A1.LQE.3)
• Analyze the effect of translations and scale changes on functions. (A1.BF.A.1)
• Relate the domain and range of a function to its graph and, where applicable, to the quantitative relationship it describes. (A1.IF.B.4)
• Determine the average rate of change of a function over a specified interval and interpret the meaning. (A1.IF.B.5)
• Graph functions expressed symbolically and identify and interpret key features of the graph. (A1.IF.C.7)

Concept 2: Analyze Exponential Growth and Decay Models

• Create and graph linear, quadratic and exponential equations in two variables. (A1.CED.A.2)
• Interpret the contextual meaning of individual terms or factors from a given problem that utilizes formulas or expressions. (A1.SSE.A.1)
• Explain that the graph of an equation in two variables is the set of all its solutions plotted in the Cartesian coordinate plane. (A1.REI.C.6)
• Graph functions expressed symbolically and identify and interpret key features of the graph. (A1.IF.C.7)
• Translate between different but equivalent forms of a function to reveal and explain properties of the function and interpret these in terms of a context. (A1.IF.C.8)
• Distinguish between situations that can be modeled with linear or exponential functions. (A1.LQE.A.1)
  1. Recognize exponential situations in which a quantity grows or decays by a constant percent rate per unit interval.
• Interpret the parameters of a linear or exponential function in terms of the context. (A1.IF.B.6)

 

Unit 9: Polynomials

Missouri Learning Standards: You will know you have achieved the learning goal when you can:

Concept 1: Perform Operations on Polynomials

• Rewrite expressions involving radicals and rational exponents using the properties of exponents. Limit to rational exponents with a numerator of 1. (A1.NQ.A.2)
• Interpret the contextual meaning of individual terms or factors from a given problem that utilizes formulas or expressions. (A1.SSE.A.1)
• Add, subtract and multiply polynomials, and understand that polynomials follow the same general rules of arithmetic and are closed under these operations. (A1.APR.A.1)

Concept 2: Factor Polynomials

• Interpret the contextual meaning of individual terms or factors from a given problem that utilizes formulas or expressions. (A1.SSE.A.1)
• Analyze the structure of polynomials to create equivalent expressions or equations. (A1.SSE.A.2)
• Choose and produce equivalent forms of a quadratic expression or equations to reveal and explain properties. (A1.SSE.A.3)
  1. Find the zeros of a quadratic function by rewriting it in factored form.
  2. Find the maximum or minimum value of a quadratic function by completing the square.

 

Unit 10: Quadratic Expressions

Missouri Learning Standards: You will know you have achieved the learning goal when you can:

Concept 1: Solve Quadratics

• • Solve problems involving quadratic equations. (A1.REI.A.2)
    1. Use the method of completing the square to create an equivalent quadratic equation.
    2. Derive the quadratic formula.
    3. Analyze different methods of solving quadratic equations.
  • Translate between different but equivalent forms of a function to reveal and explain properties of the function and interpret these in terms of a context. (A1.IF.C.8)
  • Choose and produce equivalent forms of a quadratic expression or equations to reveal and explain properties. (A1.SSE.A.3)
    1. Find the zeros of a quadratic function by rewriting it in factored form.
    2. Find the maximum or minimum value of a quadratic function by completing the square.
  • Graph functions expressed symbolically and identify and interpret key features of the graph. (A1.IF.C.7)