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# ALGEBRA 1A TASKS

 UNIT 1: THE SPEEDING PROBLEM Action Item 1.1: Introduction to Functions TEKS TAKS Activity 1: Describing Fines with Algebra Algebra provides us with ways to show and discuss the relationships between quantities. For instance, in algebra, we would say that fines, in dollars, and speed, in miles per hour, are examples of quantities. The relationship between these quantities is known as a function. Use this Activity to see an example of a speeding fine described as a function. 111.32(a)(3) 111.32(b)(1)(C) A(b)(1)(C) Activity 2: Using Independent and Dependent Variables to Make Predictions Each question describes a problem situation. In each situation, there is a pair of quantities that may be related by a function.Use the given viewpoint of each pair to determine if the quantities are related by a function. 111.32(a)(3) 111.32(b)(1)(A) 111.32(b)(1)(B) A(b)(1)(A) A(b)(1)(B) A(b)(1)(C) Activity 3: Domain and Range Each unknown quantity has a possible set of values. You should be able to think about reasonable values for quantities in problem situations.Use this Activity to learn about the domain and the range of values in different problem situations. 111.32(b)(1)(B) 111.32(b)(2)(B) A(b)(2)(B) Action Item 1.2: Tables and Graphs of Data TEKS TAKS Activity 4: Using Functions to Make Predictions Functions can be used to make predictions of unknown values.Use this Activity to explore the relationship between a car’s speed and the time it takes the car to stop. Understanding this relationship and how it is presented may be useful in communicating mathematics. 111.32(b)(2)(D) A(b)(2)(D) Activity 5: Graphing Function Data Graphing functions is useful for obtaining information about a relationship.Use this activity to learn how to draw scatterplots of data with your TI-83 Plus and with pencil and paper. Then use these graphs to make predictions about data sets. 111.32(a)(5) 111.32(b)(1)(D) 111.32(b)(2)(C) 111.32(b)(2)(D) A(b)(2)(C) A(b)(2)(D) Activity 6: Graphs of Functions and the Two-Second Rule Graphs are useful for describing relationships.Use this Activity to continue exploring the functional relationship between a car’s speed and the time it takes that car to stop. This activity also introduces the idea of using an algebraic rule (symbols) for estimating a safe following distance. 111.32(b)(1)(B) 111.32(b)(2)(C) 111.32(b)(3)(A) 111.32(b)(4)(A) A(b)(1)(B) A(b)(2)(C) A(b)(3)(A) A(b)(4)(A) Activity 7: Function Graphs and Speeding Drivers Different kinds of graphs can help you answer questions about functions, such as what are the dependent and independent variables.Use this activity to learn how different graphs and tables represent functions and help answer questions. 111.32(b)(1)(B) 111.32(b)(2)(C) A(b)(1)(B) A(b)(2)(C) Activity 8: Functions and Insurance Rates People buy automobile insurance by paying monthly or yearly premiums. The insurance company uses this money to pay claims, such as when someone has a car accident and claims repair costs.Use this Activity to explore functions further by considering automobile insurance rates. 111.32(b)(1)(A) 111.32(b)(1)(C) 111.32(b)(1)(E) A(b)(1)(A) A(b)(1)(C) A(b)(1)(E) Action Item 1.3: Multiple Representations of Functions TEKS TAKS Activity 9: Using tables to think about speeding fines Use this Activity to learn about the process column and write algebraic rules. 111.32(b)(3)(B) 111.32(b)(4)(A) A(b)(3)(B) A(b)(4)(A) Activity 10: Analyzing speeding fine functions in other communities Use this Activity to learn how functions are represented in tables using a graphing calculator and making predictions based on those tables. 111.32(b)(1)(C) 111.32(b)(1)(D) 111.32(b)(1)(E) 111.32(b)(3)(B) 111.32(b)(4)(A) A(b)(1)(C) A(b)(1)(D) A(b)(1)(E) A(b)(3)(B) A(b)(4)(A) Activity 11: Interpreting your graphs and your data Use this Activity to continue to learn how functions are represented in scatterplots and how comparing shapes of different scatterplots can help you predict unknown values. 111.32(b)(2)(C) 111.32(b)(1)(E) A(b)(2)(C) A(b)(1)(E)

 UNIT 2: THE TRASH PROBLEM Action Item 2.1: Exploring Linear Functions TEKS TAKS Activity 1: Reviewing the Four-Corner Model Use the Four-Corner Model to describe functional relationships in different problem situations. 111.32(b)(1)(C) 111.32(b)(1)(D) 111.32(b)(3)(B) A(b)(1)(C) A(b)(1)(D) A(b)(3)(B) Activity 2: Defining Linear Functions A variety of function types can represent problem situations. In this activity you will learn that functions whose graphs are (straight) lines are called linear functions.You will also be able to recognize the graphs of linear and non-linear functions. 111.32(c)(1)(A) A(c)(1)(A) Action Item 2.2: Rate of Change TEKS TAKS Activity 3: Introduction to Motion In this activity, we use motion detectors to study the functional relationship between time and distance. Since the distance traveled is directly related to the time spent traveling, we say that distance is a function of time or that there is a functional relationship between time and distance. 111.32(b)(2)(C) A(b)(2)(C) Activity 4: Rate of Change I The rate of change of a function can determine if it is linear. Use this activity to explore constant rates of change and how to write algebraic rules that describe linear functions. 111.32(b)(1)(C) 111.32(b)(3)(A) 111.32(b)(3)(B) 111.32(c)(1)(A) 111.32(c)(1)(C) 111.32(c)(2)(A) 111.32(c)(2)(B) A(b)(1)(C) A(b)(3)(A) A(b)(3)(B) A(c)(1)(A) A(c)(1)(C) A(c)(2)(A) A(c)(2)(B) Activity 5: Rate of Change II The rate of change of a function can be determined in several ways, from the data in a table, from a graph, or directly from the algebraic rule. In this activity, you will continue to use verbal descriptions, tables, graphs, and rules to describe rate of change. 111.32(c)(1)(C) 111.32(c)(2)(A) 111.32(c)(2)(B) 111.32(c)(3)(A) A(c)(1)(C) A(c)(2)(A) A(c)(2)(B) A(c)(3)(A) Action Item 2.3: The Parent Function TEKS TAKS Activity 6: The Linear Parent Function In this activity, you will learn about the linear parent function, y = x, and begin to explore variations of this function. 111.32(b)(3)(B) 111.32(c)(1)(B) 111.32(c)(1)(C) 111.32(c)(2)(A) 111.32(c)(2)(B) 111.32(c)(2)(C) 111.32(c)(2)(E) A(b)(3)(B) A(c)(1)(B) A(c)(1)(C) A(c)(2)(A) A(c)(2)(B) A(c)(2)(C) A(c)(2)(E) Activity 7: A Variation of the Linear Parent Function: y = mx Use this activity to investigate a variation of the linear parent function and to review proportional relationships and learn to identify the constant of proportionality and the constant of variation. 111.32(b)(3)(B) 111.32(c)(2)(C) 111.32(c)(2)(G) A(b)(3)(B) A(c)(2)(C) A(c)(2)(G) Activity 8: Another Variation of the Linear Parent Function: y = mx + b In this activity, you will continue to explore variations of the linear parent function in the form y = mx + b. 111.32(b)(3)(B) 111.32(c)(2)(C) A(b)(3)(B) A(c)(2)(C) Action Item 2.4: Writing Rules TEKS TAKS Activity 9: Writing Rules Given the Slope and y-intercept Use this activity to practice writing the algebraic rules for linear functions given the slope and y-intercept. 111.32(c)(1)(C) 111.32(c)(2)(D) A(c)(1)(C) A(c)(2)(D) Activity 10: Writing Rules Given Points on the Line Use this activity to practice writing the algebraic rules for linear functions given the slope and a point, or given two points. 111.32(b)(3)(B) 111.32(c)(1)(C) 111.32(c)(2)(D) A(b)(3)(B) A(c)(1)(C) A(c)(2)(D) Activity 11: Using Function Notation Use this activity to look at situations you have already explored and learn how to use function notation to describe the algebraic rules. 111.32(b)(1)(C) 111.32(b)(4)(A) A(b)(1)(C) A(b)(4)(A) A(b)(2)(C) Activity 12: Practice Writing Rules This activity gives you experience with a variety of situations that can be modeled by linear functions. Some of the questions also ask you to generalize the methods you use. 111.32(a)(3) 111.32(a)(6) 111.32(b)(1)(C) 111.32(c)(2)(D) A(b)(1)(C) A(c)(2)(D) Activity 13: Practicing Linear and Non-Linear Functions Use this activity to compare linear and non-linear functions. 111.32(c)(1)(A)