Site US and Canada

Algebra

Course Outline

The course outline below is intended for a 9 day institute. Local needs, number of days and participant levels will be taken into consideration by the instructor when choosing the activities.

The materials are broken up into modules however leadership training is incorporated throughout the entire 9 day course. In addition instructors continually model presentation styles and approaches that will be studied in this course.

 Title of Activity Overview and Objectives Math Concepts Pre-TLC Technology Skills Self-Assessment and Algebra Content Assessment These assessments establish a participant’s current level of competence in the use of technology and algebraic content knowledge. Examining the Layout of the TI-84 Plus This activity provides an opportunity to explore the layout of the TI-84 and to perform basic operations Order of operations Scientific notation One-variable Statistics This activity provides an opportunity to collect and analyze one-variable data. One-variable data Measures of central tendency Measures of variability Box plots Histograms Pass the Ball In this activity, participants will collect data on the time it takes different numbers of people to pass a ball and use the data to make predictions. A scatter plot will be graphed and a line of best fit found for the data set. Creating a scatter plot Finding a line of best fit Proportional relationship Exploring the Coordinate Plane In this activity, participants will explore the coordinate plane by graphing a square using an x-y line plot. Entering ordered pairs in lists Coordinate graphing “Standard” window “Decimal” window Picture Graphing – Transformations In this activity, participants will explore transformations in the coordinate plane by graphing a triangle using an x-y line plot. Entering ordered pairs in lists Coordinate graphing Transformations Reflections Managing the Stat Editor This activity gives participants an overview of managing the Stat Editor including naming lists, clearing versus deleting lists, SetUpEditor, operations with lists, and sorting grouped lists. McCalories In this activity, participants will find the relationship between fat grams and calories from fat and between fat grams and total calories for various fast food items. Representing data numerically and graphically Finding the equation of a line Catch Me on the Rebound In this activity, participants will collect data by dropping a ball from various heights and recording bounce heights. The data will be analyzed and used to make predictions. Finding a line of best fit Interpreting the meaning of the slope and y-intercept Using a line of best fit for prediction Memory Management on the TI-84 Plus This activity features ways that memory can be managed on the TI-84 Plus. This will include working with memory in RAM and archive memory. Participants will also learn about grouping files, lists, and variables for later retrieval. What Can Go Wrong and How to Fix It This activity examines possible problems that teachers may encounter when working with calculators. Recursion and Tables on the Home Screen In this activity, participants will use the recursive procedure on the home screen to numerically explore a savings account problem. Number sense Recursion Patterns Guess My Rule – Looking at Tables In this activity, participants will practice determining the rule for a function after seeing several ordered pairs. Patterns and functions Guess My Rule – Looking at Graphs In this activity, participants will practice determining the rule for a function by matching graphs. Graphs and Functions Linear Activities with the CBR2TM Part One In this activity, the participants will use the TI-84 Plus and the CBRTM or CBR2TM to graph and analyze motion data. Interpreting distance-time graphs Comparing different types of motion to increasing, decreasing, and horizontal motion graphs Finding the slope of a distance versus time graph and interpreting that slope as velocity Interpreting the y-intercept of a distance versus time graph as the starting point of the walker Predicting the effect of increasing or decreasing speed on a motion graph Walk the Line: Straight Line Distance Graphs Participants will use the CBR™ or CBR2™ with the EasyData App to collect and analyze linear motion data Interpreting distance-time graphs Finding the slope of a distance versus time graph and interpreting that slope as velocity Interpreting the y-intercept of a distance versus time graph as the starting point of the walker Match the Graph In this activity, participants will walk in front of a CBR2TM to match distance versus time graphs displayed on the calculator. Interpreting distance-time graphs Comparing different types of motion to increasing, decreasing, and horizontal motion graphs Predicting the effect of increasing or decreasing speed on a motion graph Topics in Algebra 1 Application: “Slope with Grid” In this activity, participants use the Topics in Algebra I App to explore slope. Coordinate graphing Proportional reasoning Rate of Change Slope Topics in Algebra 1 Application – Match It! In this activity, participants use the Topics in Algebra I App to explore the connections among linear functions, tables, and graphs. Linear equations Tables Graphs Linear Activities with the CBR2TM Part Two In this activity, participants will used the TI-84 Plus and the CBR™ or CBR2™ to graph and analyze motion data Interpreting distance-time graphs Computing the area “under” a velocity graph over a restricted domain to determine the distance traveled Comparing the area under a velocity graph to distance traveled Walk this Way: Definition of Rate In this activity, participants will record distance versus time data for a person walking at a uniform rate, analyze the data to determine the slope and y-intercept, and interpret the physical meaning of the slope and y-intercept Interpreting distance-time graphs Computing the area “under” a velocity graph over a restricted domain to determine the distance traveled Comparing the area under a velocity graph to distance traveled TI ConnectTM Quick-Start Guide This activity outlines the use of TI Connect™ computer software. Downloading and Installing Calculator Software Applications (Apps) This activity describes the process for downloading and installing Calculator Software Applications (Apps). Preparing Handouts This document provides tips and tricks for developing appropriate and effective handouts. Internet Exploration This document outlines the goals of an Internet exploration: Explore the education part of the Texas Instruments website, Locate and examine content-area specific websites, Acquire research documents on working with the adult learner What’s the Voltage? This activity investigates the voltage of different numbers of batteries when the batteries are connected in series. Scatter plot Linear function Proportional relationship Equations of Lines In this activity, participants will use the Cabri?Jr 2.0 APP to make a direct link between the equation of a line, its graph, and the geometric properties of linear equations in the coordinate plane. Coordinates in the Plane Slope of a Line Y-intercept Equation of a Line Algebraic and Geometric connections Parallel Lines and Slope Perpendicular Lines and Slope Reasoning and Proof Exploring Diameter and Circumference In this activity, participants will use the Cabri?Jr 2.0 APP to explore the relationship between the diameter and circumference of a circle. Diameter Circumference Proportional relation The Celsius to Fahrenheit Connection In this activity, participants will use the Calculator Based Laboratory (CBL2) and two temperature probes to collect temperature readings in degrees Celsius and degrees Fahrenheit. They will then develop the Celsius to Fahrenheit and Fahrenheit to Celsius conversion equations. Units of Measure Finding a Line of Best Fit Inverse Functions Strategies for Solving Linear and Absolute Value Equations and Inequalities In this activity, participants will explore numerical, algebraic, and graphical strategies for solving linear and absolute value equations and inequalities Solving linear and absolute value equations and inequalities numerically, algebraically, and graphically Transformations of Absolute Value Functions Using the Transformation Graphing Application In this activity, participants will use the Transformation Graphing Application to explore transformations of functions. Transformations of absolute value functions Parametrics and Linear Functions In this activity, participants will explore parametric equations of points and lines and simulate and solve motion problems graphically and numerically. Representation of points and lines parametrically Modeling motion parametrically Interpreting speed in parametric motion graphs in dot mode Converting equations in Cartesian form to parametric form Solving motion problems algebraically and graphically Maximizing Your Efforts In this activity, participants will use the Inequalities app to solve a linear programming problem related to manufacturing. Defining variables Developing a system of inequalities to describe a problem situation Graphing and solving a system of inequalities Paper Folding In this activity, participants will use paper folding to explore a “doubling” pattern and to find an exponential model for the paper folding data. Exponential functions Using Recursion for Exponential Functions In this activity, participants will use recursion on the Home Screen to model the height of a bouncing ball on successive bounces and to compare linear and exponential relationships. Representing exponential functions recursively Comparing linear and exponential relationships Double Your Pleasure Participants will collect and analyze population growth data and find the relationship between the "year" and the "population" of candies. Exponential functions Data collection and analysis Bounce Back: The Exponential Pattern of Rebound Heights In this activity, participants will use a CBR2TM to collect data on the height of a bouncing ball. The data will be analyzed to find the relationship between the height of the ball at different bounces and the bounce number. Modeling data with an exponential function Transformations of Exponential Functions In this activity, participants will use the TI-84 Plus to explore transformations of exponential functions. Characteristics of exponential functions Exploring transformations of exponential functions Chill Out: How Hot Objects Cool In this activity, participants will collect temperature versus time cooling data and find an exponential model for the data. Modeling data with an exponential function Using the Finance Application for Compound Interest, Annuities, and Loans In this activity, participants will use the Finance Application on the TI-84 Plus to calculate values and solve problems involving compound interest, annuities, and loans. Calculating present and future values for compound interest, annuities and loans Finding total interest paid over the life of a loan Creating a balance of payments table Count or Fit In this activity, participants will collect data on the number of diagonals in a polygon and find a quadratic model for the data. Developing a quadratic function to model data Making connections between geometric formulas and algebraic functions Using finite differences to justify a quadratic model Using combinations Transformations, Domain, and Range of Quadratic Functions In this activity, participants will explore transformations of quadratic functions and connect their algebraic and graphical representations. Determining domain and range from a graph Describing the changes in the graph of a quadratic parent function when one or more parameters are changed Determining the equation of a quadratic function when transformations are described Completing the square to convert a quadratic function from standard form to vertex form What Goes Up: Position and Time for a Cart on a Ramp In this activity, position and time data for a cart rolling up a ramp are collected and a parabolic model for position versus time is developed. Quadratic functions x-intercepts y-intercepts Zeros and Factors In this activity, participants will find real and complex zeros of quadratic functions algebraically, numerically, graphically, and by using the PolySmlt Application. They will check factors, make the connection between zeros and factors, and perform operations with complex numbers. Finding real and complex zeros of quadratic functions Connecting zeros and functions Factoring quadratic expressions Red Meat Consumption Continues to Drop In this activity, data on the annual per capita consumption of red meat and poultry for the years 1997 through 2001 are analyzed and used to make predictions. Solving a system of equations graphically Developing scatter plots for two data sets Independent and dependent variables Identifying the best-fit models (linear and quadratic) for a scatter plot Making reasonable estimates and predictions Don’t Fence Me In In this activity, participants will use numerical, graphical, and algebraic techniques to maximize the area of a rectangular garden with a fixed total length for three sides. Other similar problems will also be solved. Solving application problems using linear and quadratic functions Fitting linear and quadratic regression equations to data Finding maximum function values numerically and graphically Composition and Inverses Involving Quadratic Functions In this activity, participants will explore composite functions and inverse relations and functions. Finding inverse functions and relations algebraically and graphically Exploring composition of functions, including domain and range Graphing a function with a restricted domain and graphically confirming its inverse Graphing inverses parametrically Exploring Matrices In this activity, participants will enter matrices in the TI-84 Plus and use the calculator to perform scalar multiplication and the addition, subtraction, and multiplication of matrices. Additionally, matrices will be used to solve systems of linear equations. Matrices Operations with matrices Using matrices to solve systems of linear equations Solving Systems with Matrices and PolySmlt In this activity, participants will use the TI-84 Plus to solve systems with matrix operations. Additionally, systems of equations will be solved using the PolySmlt Application. Solving a system of equations by using an inverse matrix Solving systems with a single matrix and reduced-row echelon form computation Solving systems using the PolySmlt Application Eye Spy In this activity, participants will collect data on the distance from a wall a person must stand to view a certain height on the wall reflected in a mirror. The data will be analyzed to find the relationship between the height viewed on the wall and the person’s distance from the mirror. Proportional reasoning Patterns Similar figures Rational functions The Period of a Pendulum This activity investigates the relationship between the length of a pendulum and its period. Periodic motion Period of a function Square root function Swinging Ellipses with the CBR2TM In this activity, participants will use a motion detector to plot the motion of a swinging pendulum and develop an equation that models the pendulum's velocity versus position data. Investigating the relationship between the velocity of a swinging pendulum and its position Developing a mathematical model for a data set Determining lengths of the major and minor axes of an ellipse Determining the center of an ellipse Writing the equation of an ellipse Programming on the TI-84 Plus This is a programming activity appropriate for Algebra teachers. Calculator programming Post-TLC Technology Skills Self-Assessment and Algebra Content Assessment These assessments evaluate a participant’s growth in the use of technology and algebraic content knowledge.