## Topic outline

• ### General

Algebra 1

Welcome to Miss Thompson's Algebra 1 course.  My classroom is located in upper Sparta in room B208.

You can access the online textbook at www.flourishkh.com with the username "Thompson" and the password "thompson" and pin "49686".

You can access the online resources at http://math.kendallhunt.com/.

Algebra 1A is chapters 1-5 and Algebra 1B is chapters 6-10.

You will find the weekly plans in box 11 at the bottom of the moodle page.

Algebra 1 Essential Questions:

* How do you use multiple representations to model patterns?

* How do you construct, interpret, and manipulate algebraic expressions and functions?

• ### Chapter 1: Data Exploration

In this chapter you learn how statistical measures and graphs can help you organize and make sense of data.

Chapter 1 Essential Question: How do you summarize and interpret data sets?

• ### Chapter 2: Proportional Reasoning and Variation

You explore and analyze relationships among ratios, proportions, and percents in this chapter.  You use a variable to represent an unknown number, define a proportion using the variable, and then solve the proportion to determine the value of the variable.  You learn the difference between direct variation and inverse variation.  Finally, you explore number tricks and learn how to use an undoing process to find solutions to equations.

Chapter 2 Essential Question: How can you use proportional thinking to solve mathematical problems?

• ### Chapter 3: Linear Equations

In this chapter you start by investigating recursive sequences by using their starting values and rates of change to write recursive routines.  You then transfer that knowledge to plots and learn how to rewrite a sequence as a linear equation in intercept form, given the y-intercept and rate of change.  Finally, you develop your equation-solving skills, using the undoing method, the balancing method, and the intercept method.

Chapter 3 Essential Question: How can you model linear relationships?

• ### Chapter 4: Fitting a Line to Data

You start by learning to calculate the slope of a line and how to write an equation in point-slope form.  You then investigate equivalent forms of expressions and equations and then used the distributive, commutative, and associative properties along with properties of equality to rewrite point-slope equations and standard form equations in intercept form.  Finally, you investigate 3 methods for deriving a line of fit for a set of data.

Chapter 4 Essential Question: How can you use a linear relationship to model real-world data?

• ### Chapter 5: Systems of Equations and Inequalities

You learn to model many situations with a system of equations in this chapter.  You use the interesection of graphs method, substitution method, elimination method, and row operations on a matrix method to solve systems of equations.  Then you analyze situations involving inequalities and discover how to find their solutions using graphs, tables, and symbolic manipulation.  Finally, you discover how to use inequalities to define constraints that limit the solution possibilities in real-world applications and then graph the system of inequalities to find the feasible region.

Chapter 5 Essential Question: How can you use multiple strategies to solve systems of equations and inequalities?

• ### Chapter 6: Exponents and Exponential Models

In this chapter, you discover that exponential equations model sequences that increase or decrease by a constant multiplier.  The constant multiplier is the base and the number of the term in the sequence is the exponent.  Many real-world quantities can be modeled as exponential growth y = A(1 + r)x or exponential decay y = A(1 – r)x.  You also learn properties of exponents and explore their meanings.  Finally, you apply these properties to scientific notation, a way to express numbers with powers of ten.

Chapter 6 Essential Question: How can you model exponential relationships?

• ### Chapter 7: Functions

In this chapter, you investigate functions represented by rules, equations, tables, and graphs.  You then use functions to describe real-world relationships.  In addition, you learn how to use function notation f(x).  You explore the absolute-value function and the squaring function and their graphs.  You also use the square root function to undo the squaring function.  Finally, you discover how to solve all three types of functions both graphically and symbolically and that these two functions can have zero, one, or two solutions.

Chapter 7 Essential Question: How can you identify, interpret, and evaluate functions?

• ### Chapter 8: Transformations

You start this chapter by moving individual points, polygons, and graphs of functions with transformations.  You learn to translate, reflect, stretch, and shrink a parent function to create a family of functions based on it.  You learn that the inverse function, y = 1/x , is one type of rational function.  The graphs of transformations of the parent function have one vertical asymptote and one horizontal asymptote.  Finally, you use matrices to organize the coordinates of points and do transformations.

Chapter 8 Essential Question: How can you use transformations to create and model families of functions?

• ### Chapter 9: Quadratic Models

You learn about quadratic functions in this chapter.  You use quadratic functions to model and solve projectile motion problems.  You also discover how to solve quadratic equations using graphs, tables, and symbolic methods.  In addition, you learn to convert quadratic equations among vertex, factored, and general forms.  Lastly, you transfer your knowledge of quadratic models to cubic functions.

Chapter 9 Essential Question: How can you model and solve quadratic functions?

• ### Chapter 10: Probability

In this chapter, you learn to analyze situations that involve uncertainty.  You look at experimental and theoretical probabilities.  In order to determine some probabilities you learn to visualize and count possible outcomes using a tree diagram.  You are also introduced to the counting principle, permutations, combinations, and multiplication rule, which you use to help find probabilities.  Finally, using what you learned about theoretical probability, you are able to calculate the expected value of an event.

Chapter 10 Essential Question: How can you analyze situations involving uncertainty (random processes)?