Course Information
Algebra 1B Strategies
Algebra I is organized around the families of functions, with special emphasis on linear and quadratic functions. Students will learn to represent them in multiple ways as verbal descriptions, equations, tables, and graphs. These functions will be applied and used to model real-world situations in order to solve arising problems. Students will also learn data analysis and apply geometric properties in the algebraic realm.
Subject: | Special Education |
State Number: | 115810 |
Course Credits: | Full Credit (1.0) Course |
Course Options: | |
NCAA: |
Unit 6: Descriptive Statistics
Unit Overview: In this unit you will learn how to represent data on a number line and use appropriate measures of center and spread to make conclusions about the data. You will also learn how to use scatter plots and the line of best fit to describe trends of data in real life situations. Lastly, you will learn how to use two-way frequency tables to discover associations between two-variable data.
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)
- 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)
- Interpret relative frequencies in the context of the data.
- Recognize possible associations and trends in the data.
Unit 7: Nonlinear Functions
Unit Overview: In this unit you will write and define piecewise functions. You will rely on your understanding of key features and interpretations of graphs to explore other nonlinear function families, including piecewise, absolute value, and step functions and will explore the effects of vertical and horizontal transformations to the functions. You will use approximations of rational and irrational numbers to solve square root and cube root equations. You will relate the importance of restricted domain and range of the functions to its graph and to the context of the problem. You will extend the properties of rational and irrational numbers, as well as integer exponents, to that of rational exponents. You will learn how to rewrite fractional exponents in radical form and learn two different methods for simplifying radicals. You will rewrite radical expressions using rational exponents. You will use the properties of exponents to write equivalent expressions, providing insight into the structure of the expression.
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
Unit Overview: In this unit you will broaden your understanding of exponential functions to model real-world scenarios. You will learn how to interpret domain, range, and growth factor, and initial value in an exponential context. You will recognize situations that can be represented by exponential functions and will write and graph the equations that model exponential behavior. You will go further into interpreting the parameters of the equations in the context of real-world problems and use laws of exponents to rewrite the functions. You will also see complicated expressions by viewing one or more of their parts as a single entity as they explore compound interest.
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)
- 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
Unit Overview: In this unit you will work with linear expressions and integer exponents as you begin to explore more complex polynomial expressions. You will interpret different parts of polynomials in context and begin to see expressions as sums, products, and factors instead of different entities. You will add, subtract, and multiply polynomials to create equivalent expressions that will allow them to interpret different forms of quadratic functions. You will deepen your knowledge of properties of rational exponents and will use these properties to simplify variable expressions. You will further explore algebraic expressions that can be expressed as products of factors. You will discover patterns to identify factors, leading to the examination of the structure of quadratic equations. You will find different methods for factoring quadratic expressions.
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)
- Find the zeros of a quadratic function by rewriting it in factored form.
- Find the maximum or minimum value of a quadratic function by completing the square.
Unit 10: Quadratic Expressions
Unit Overview: In this unit you will use prior knowledge of functions and equations as you solve quadratic equations. You will use the properties of rational and irrational numbers to solve quadratic equations with rational or irrational solutions. In addition, you will begin to investigate some of the properties of quadratic functions. You will apply the quadratic formula to solve quadratic equations, and you will identify the type and number of real solutions given by the formula. You will continue your exploration of quadratic functions and key features of the functions’ graphs.
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)
- Use the method of completing the square to create an equivalent quadratic equation.
- Derive the quadratic formula.
- 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)
- Find the zeros of a quadratic function by rewriting it in factored form.
- 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)
Concept 2: Analyze Quadratic Equations
- Solve problems involving quadratic equations. (A1.REI.A.2)
- Use the method of completing the square to create an equivalent quadratic equation.
- Derive the quadratic formula.
- Analyze different methods of solving quadratic equations.
- Create equations and inequalities in one variable and use them to model and/or solve problems. (A1.CED.A.1)
- 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)