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^c 02d505 19 9(1222291>,!$'W5W5Z!ZActivity: Catch Me If You Can
Concepts
Linear systems
Rate of Change  Slope
Yintercept
Materials
TI83 or TI84 Plus
Graph paper
Straight edge
Stopwatch or timer
TINavigator
StudyCard APP
LearnCheck APP
APP Vars
Florida Benchmarks
MA.D.2.4.2
MA.D.2.3.1
MA.D.2.3.2
MA.D.2.4.1Overview:
In this activity, students will model a situation with a system of equations to find the time and distance when one student catches up to another. The TINavigator system will be used to send the StudyCard APP, a vocabulary and concept stack of study cards  Solving Systems (SOLVSYS.8xv), a self check to use with this activity (CatchMeIfYouCan.edc), and an assessment (FCATMAD242.edc).
Sunshine State Standard and FCAT alignment:
Strand D: Algebraic Thinking
Standard D2: The student uses expressions, equations, inequalities, graphs, and formulas to represent and interpret situations.
Benchmarks: MA.D.2.4.2 uses systems of equations and inequalities to solve real world problems graphically, algebraically, and with matrices. This benchmark also assesses:
D.2.3.1 represents and solves realworld problems graphically, with algebraic expressions, equations, and inequalities
D.2.3.2 uses algebraic problemsolving strategies to solve realworld problems involving linear equations and inequalities
D.2.4.1 represents realworld problem situations using finite graphs, matrices, sequences, series, and recursive relations (italicized not assessed on FCAT)
Problem
Two students, Sarah and Jeff, arrive at the school parking lot at about the same time. They both park in the gym area; however they are about 30 yards from each other. Jeffs car is parked even with the gym; Sarahs parking place is 30 yards closer to the main building where they attend class. She starts walking toward the building to go to class at a rate of 1.5 ft/sec. Jeff realizes that Sarah left her books in his car when he gave her a ride home yesterday. He needs to catch up to her so that she will have her books for class. If he starts walking towards her at a rate of 3 ft/sec about 5 seconds after she heads in, how far will they be from the gym when Jeff catches up to Sarah?
Exploration
Before tackling this problem, students are going to explore a similar problem within the walls of their classroom.
Students will work in groups of 5 and choose one of the following roles:
Recorder: Marks off a distance of about 20 feet in increments of 1 foot from a wall in the classroom, Serves as the spotter for student S and notes and records distance from the wall for each second.
Student S: Represents Sarah walking away from the wall at a constant rate, starting 3 ft from the wall.
Student J: Represents Jeff walking away from the wall at a constant rate, starting at the wall 5 seconds after Student S begins walking. This student will need to walk faster than student S.
Spotter J: Serves as the spotter for student J and notes and records distance from the wall for each second.
Timekeeper: Starts timer when student S begins walking. Reads the time out loud each second. Runs the timer for 10 to 15 seconds.
A CBL could be used to collect the data, if available.
Complete the data tables for each student:
Student SStudent JTime (seconds)Distance from Wall (feet)Time (seconds)Distance from Wall (feet)0350
Create a distance verses time graph by labeling the xaxis with Time (seconds) and the yaxis as Distance (feet) and plot the points on graph paper. Does it look like a linear equation could model each of the scatter plots?
Describe the conditions under which each of the scenarios listed below would occur?
The scatter plots for Student S and Student J do not look linear.
Two lines drawn through the points are parallel to each other.
Two lines drawn through the points intersect each other.
The two line segments drawn do not intersect, however, if the lines are extended, the two lines drawn through the points look like they will intersect each other.
The two lines overlap and appear to be the same line.
Use two of the points that are representative of the line and find the slope of each
line, and then write an equation for each line.
Equation for Student S: _______________________________
Equation for Student J:________________________________
Explain the realworld meaning for the slope:____________________________
Explain the realworld meaning of the yintercept:_________________________
These two equations form a system of linear equations. Graph the system on your
graphing calculator and find the solution to the system. Your calculator
solution should match the solution on your paper and pencil graph?
Solution:______________. Explain the realworld meaning of the coordinates to
the solution.
Solve the system algebraically, using substitution or linear combination(elimination): Solution: __________________
Reread the original problem. Set up a system of two equations in two variables
representing the problem. Please note that you will want to change the yard units
to feet before you get started.
Solve the system:
By graphing
By substitution or linear combination (elimination)
Give the solution.
Explain the realworld meaning of the solution.
Is this system dependent or independent?
Is this system consistent or inconsistent?
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