1. Topic-
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2. Content-
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Emphasis will be
on graphing systems of equations and finding their solutions. Students
will draw lines with different information. They will solve equations
to find slope and explore the relation of parallel and perpendicular
lines.
Explanation of Math Involved: The primary math involved in solving
systems by graphing is graphing. By graphing these linear equations,
the
solution needs to be common to both equations. By graphing these linear
equations, students in addition will have to perform substitution
to verify
the solution is valid for both equations. |
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3. Goals: Aims/Outcomes-
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Demonstrate, with use of technology, understanding of slope with
respect to:
- line segments and lines
- rate of change
- ratio of rise to run
- parallel lines
- perpendicular lines.
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4. Objectives-
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-Determine the slope of a line segment by using rise and run.
-Explain why the slope of a straight line can be determined by using
any two distinct points on that line.
-Draw a line given its slope and a point on the line.
-Determine another point on a line, given the slope and a point on
the line.
-Apply strategies for determining whether two lines are parallel or
perpendicular. |
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5. Materials and Aids-
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-Graph paper
-Computers with GeoGebra program
-Work sheet with questions |
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6. Procedures/Methods-
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A. Introduction-
Students will learn how to find 1 solution, no unique
solution, or no solution by graphing and mathematically solving system
of equations. After graphing these linear equations, students will
have to perform substitution to verify the solution is valid for both
equations. |
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B. Development-
1. Graph both equations using slope- intercept format.
a. Plot y intercept (b).
b. Count- out slope by rise and run, plot 2nd point.
c. Connect 2 points with straight line.
2. Determine the solution, if it exists:
a. One solution- point of intersection.
b. Infinite solution- coincident, equivalent equations.
c. No solution- parallel lines, slopes of both lines are equal.
3. Validate solution, by performing check.
a. Substitute x and y coordinates found (if exists) back into
original equations.
Solve equations to ensure correctness, that equations balance properly. |
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C. Practice-
Students will do the first 6 questions on work sheet on graph paper.
2 questions will be to analyze a graph and find slope by rise over
run.
2 questions will be to graph two equations (either in slope-point
formula or slope-intercept) that are parallel and compare their slopes.
2 questions will be to find solutions to a system of equations mathematically
with out a graph. |
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D. Independent Practice-
Students will do the last 6 questions on GeoGebra.
Students will do an interactive exercise, exploring linear solutions
by
changing slope and y-intercept values using sliders. |
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Checking for understanding-
Last 3 questions on assignment.
Students explain the relationship of the slope between different lines,
parallel lines, and perpendicular lines. |
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Closure-
I will assign 10 questions for homework that include questions that
have students construct equations finding slopes from parallel or
perpendicular lines to deepen the students understanding of slopes. |
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7. Evaluation-
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For classwork activity and intro, the
feedback will be interactive as student's progress through the
assignment. I will be walking around the classroom interacting with
students and providing direct feedback on my observations. |
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