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| Background: |
This Project was done with Mrs. Horazy's Algebra class. They had just
finished the section on solving equations. This project was meant to reinforce
the concept and make them see how it was applicable to their lives. The
project was presented twice. The Algebra class had thirty students so the
class was broken up into two groups one that went the first day and those
in the other group went the second day. It was presented on the RCHS stage
because it provided ample space and so Mrs. Horazy could teach the
other group. The point of the project is to show the point of intersection.
The students use the motion detectors to find the point of intersection.
They also create the equation of two lines and find their point of intersection.
They then compare the two answers for the point of intersection which should
be very close and then draw conclusions and make connections from the fact
that they are similar answers.
| Materials: |
4 meter sticks
4 voyage calculators
4 Lab Pros
student worksheets
8 motion detectors
dataview
batteries
tape
stopwatch
8 desks
Datamate
4 workstations worksheets
| Objectives: Students should be able to... |
- explain slope in terms of x and y ( the change in y over the change in x) and in terms of distance and time
- write their own story problem using slope, distance, and time
- explain the solution of two equations
- explain the point of intersection
- record motion data for two walkers
- graph both motions on a common axis and find their intersection
- find linear equations to the model the motions
- solve the system of two linear equations to determine the intersect
- compare the algebraic solution to the graphical solution
| Indiana's Academic Mathematics Standards |
A1.2.1 Solve linear equations.
A1.2.2 Solve equations and formulas for a specific variable.
A1.2.6 Solve word problems that involve linear equations, formulas,
and inequalities.
A1.3.2 Interpret a graph representing a given situation.
A1.4.1 Graph a linear equation.
A1.4.4 Write the equation of a line given appropriate information.
A1.4.5 Write the equation of the line that models data set and use
the equation ( or the graph of the equation) to make predictions. Describe
the slope of the line in terms of the data, recognizing that slope is the
rate of change.
A1.5.3 Understand and use the substitution method to solve a pair of
linear equations in two variables.
A1.5.4 Understand and use the addition or subtraction method to solve
a pair of linear equations in two variables.
A1.5.5 Understand and use multiplication with the addition or subtraction
method to solve a pair of linear equations in two variables.
A1.5.6 Use pairs of linear equations to solve word problems.
A1.9.1 Use a variety of problem solving strategies.
| Procedures: |
Set up stations
- Two parallel motion detectors waist level two meters apart.
- Connect the motion detectors to the LabPro one detector in sonic port one and the other in sonic port two.
- Using tape, mark the starting point for the walkers. 5 meters in front of one the motion detectors place a piece of tape. In front of the other the tape should be half a meter away from the detector.
Introduction
Have students give four random points.
~from these, find the equation of two lines through them using point-slope
form,
~using these points find the point of intersection using elimination
Body
Collect one set of data in front of class. Using one of the groups.
Workstations
worksheet.
- One person walks toward the motion detector as the other one walks way as the motion detector starts collecting data.
- Another person is timing the walkers until they cross.
- Then the students measure the distance from the motion detectors.
- View the two graphs by lining the cursor up with the Dig-Distance line and hitting enter.
~~What unit does the y-axis represent?
~~What unit does the x-axis represent?
~~What does this mean in terms of slope?
Does anyone have any questions???
Explain what will be happening:
- Groups of 4
- the 4 data-collecting stations throughout the room
- once in groups, quickly find a spot where you can work and each member choose a different number, 1-4.
- You have 2 minutes to do this, then please be quiet so we can further instruct you.
Number 2: Walker/Calculator Operator
Number 3: Walker
Number 4: Marker/Measurer
Pass out worksheets and calculators
Groups collect data and then complete the worksheet
Conclusion
Have the students create a story problem that is
applicable in daily life and then have them find the answer.
| Projected Time Schedule: |