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This lesson provided by:
Author: Kenneth Webb
System:Tuscaloosa City
School:Tuscaloosa City Board Of Education
Lesson Plan ID: 33163
Title:

PER - PIN - TIC - YOU - LER!

(Part 2 to Take the Stairs Lesson)

Overview/Annotation:

This lesson allows students to investigate the slope criteria and characteristics of perpendicular lines using graphing calculators and rectangle/square tiles.  Students will also use equations and graphs.  Students will work cooperatively to develop and justify ideas/conjectures.

This is a College- and Career-Ready Standards showcase lesson plan.

Content Standard(s):
MA2013(9-12) Geometry31. Prove the slope criteria for parallel and perpendicular lines, and use them to solve geometric problems (e.g., find the equation of a line parallel or perpendicular to a given line that passes through a given point). [G-GPE5]
Local/National Standards:

  • Standard 1: Make sense of problems and persevere in solving them
  • Standard 2: Reason abstractly and quantitatively
  • Standard 3: Construct viable arguments and critique the reasoning of others
  • Standard 4: Model with mathematics
  • Standard 5: Use appropriate tools strategically
  • Standard 6: Attend to precision
  • Standard 7: Look for and make use of structure
  • Standard 8: Look for and express regularity in repeated reasoning
Primary Learning Objective(s):

Students will discover and use the properties of perpendicular lines.  Students will find equations of perpendicular lines given other equations of lines passing through other points.   Students will use slope definitions with rise over run and slope/distance formulas to solve problems and justify reasoning for developed discoveries.

Additional Learning Objective(s):

Students will work cooperatively to discover patterns in the graph table of values while problem solving. Students will verify conclusions by finding slope/distance and understanding properties of perpendicular lines.  Students will measure and document lengths of the L shape of a rectangle/square traced on a coordinate grid or a triangle verified with pythagorean triples verified and compare values to determine perpendicular slopes.

Approximate Duration of the Lesson: Greater than 120 Minutes
Materials and Equipment:

Poster Paper or Poster with grid lines, sticky notes of different types, straight edge, markers, rectangle/square tiles or rectangular/square objects, student may use their own devices or teacher issued graphing calculators.

Technology Resources Needed:

Computer with Internet access, LCD Projector and Document camera to share student work (helpful but not necessary.) Smartview with calculator is needed.

Background/Preparation:

Teacher:

  • Have rectangle/square tiles or shaped objects available for students.
  • Have graphing calculator ready to be assigned.

Students:

  • Geometry students should be able to graph coordinates on Cartesian plane and measure the lengths of models with ruler. 
  • Students should be able to find slope algebraically and graphically, use slope intercept form to solve problems, know/understand the pythgorean theroem/distance formula and have some knowledge of using the graphing calculators.
Procedures/Activities:

ENGAGE

As students enter the classroom, they should receive a group that tells where to sit with all needed materials available.  Students should be informed that their mission today is to determine whether a pair of equations of lines is perpendicular. 

EXPLORE

Student groups should trace the rectangular/square tile/object on a coordinate plane.  Each group can decide to use a L shape from the graph to receive coordinate pairs to input into graphing calculator to generate equations of lines and graphs. Each group can also decide to use a triangle from the traced shape, use distance formula to calculate length values and then verify values as a Pythagorean triple.

The students should key their information into their graphing calculators (using the list key on the graphing calculator) to determine if the L shape of the traced object makes perpendicular lines and have perpendicular slopes. They should look for patterns, develop equations based on data and list slope conclusions based on data.  The groups must agree on findings and be able to justify. 

If students do not understand perpendicular lines and slopes, provide necessary feedback to move them forward with their thinking.  Refer to :  http://www.youtube.com/watch?v=VVvErpLG2EQ(if your school system does not allow youtube access, you may download the video using http://www.keepvid.com/)

Refer to https://www.khanacademy.org/math/trigonometry/graphs/parallel_perpendicular/v/perpendicular-line-slope

EXPLAIN

The teacher should be sure that students are using slope/distance or pythagorean theorem correctly to verify perpendicular lines. 

Groups will discuss properties discovered and begin justifying their ideas; along with creating equations and graphs to match their tables in the calculator.

Allow students time to prepare attractive posters to share with class to begin discussions about perpendicular, along with having the groups share their findings using the Smartview function of the calculator.

  


Attachments:**Some files will display in a new window. Others will prompt you to download. Rubric.docx
Assessment Strategies:

EVALUATE

Use the rubric provided to assess student work individually and as a group. Students should justify all reasoning stated on poster.  The Assessment Process is on-going. The teacher should visit each group and ask questions to make sure students apply the properties of perpendicular line definitions.  Post the posters in the classroom and have students present conclusions.  As students present posters and graphing calculator finds, they should compare posters for other information not listed on their group's poster.

Extension:

Extensions can be to include formal proofs in geometry or have students justify the properties of perpendicular lines using more coordinate  and two column proofs.

 

 

 Groups can be random or you can select groups to allow struggling students to find slopes using formulas or inputing information into calculator for graphs.

Remediation:
Each area below is a direct link to general teaching strategies/classroom accommodations for students with identified learning and/or behavior problems such as: reading or math performance below grade level; test or classroom assignments/quizzes at a failing level; failure to complete assignments independently; difficulty with short-term memory, abstract concepts, staying on task, or following directions; poor peer interaction or temper tantrums, and other learning or behavior problems.

Presentation of Material Environment
Time Demands Materials
Attention Using Groups and Peers
Assisting the Reluctant Starter Dealing with Inappropriate Behavior

Be sure to check the student's IEP for specific accommodations.
Variations Submitted by ALEX Users:
Alabama Virtual Library
Alabama Virtual Library

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The University of Alabama at Birmingham
The University of Alabama at Birmingham
The Malone Family Foundation
The Malone Family Foundation
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Thinkfinity
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