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Learning the Jargon
Frequently, one of the most difficult things for students to grasp is proper terminology for familiar ideas. Learning the terms associated with line segment slope relationships is no exception. These lesson plans for teaching parallel, perpendicular and intersecting lines should help students understand these new terms by attaching them to familiar real-life examples.
- The official definition for parallel lines is two lines with the same slope which never intersect.
- The definition for perpendicular lines is two lines with negative reciprocal slopes which form right angles when they intersect.
- Intersecting lines are two lines with negative reciprocal slopes which may or may not create right angles at their points of intersection.
While these definitions may not be troublesome for most adults, students hearing this for the first time might feel overwhelmed and be easliy lost in the terminology. Drawing a picture to support each term is a good place to start, but may not help students remember the information as each subsequent line slope relationship is explained.
While slope relationship information should be easy for students to grasp because examples of it are all around them, it can easily be made difficult because too much information is given in a short period of time. To avoid this problem, teachers should spread out the use of their lesson plans for teaching parallel, perpendicular, and intersecting lines over a period of days to help break down the data and provide time for students to process the new information. Reviewing the previous days concepts is also key to making sure that students understand each part before going on to the next.
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It is helpful to start with parallel lines as the definition is technically the simplest. Begin by describing the definition and then drawing an example where students can see. If students use journals or notebooks, it is useful to have them copy both the definition and the image.
After the definition has been explained, give students time to brainstorm a list of possible parallel lines that are common in their life. A wipe-off board is useful for this exercise. Allow students to throw out answers and write each one on the wipe-off board. A key point to remember is that nothing is wrong in brainstorming until the brainstorming session is over. If students make a suggestion that is not in fact a parallel line situation, write it down and when the list is complete go over each one individually. Here are some suggestions that might be useful prompts for a list of familiar real-life parallel lines.
- a row of lockers
- a street full of houses and driveways
- the side lines of any rectangular object (a book, a placemat, a computer screen, a door, a smart board, etc.)
- the painted lines on a road
- lanes on a highway
- wooden or aluminum siding on a house
- venetian blinds
- railroad tracks
- lines on a ruler
- lines on a football field
For homework, students might be asked to find three sets of parallel lines in their home.
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Perpendicular lines and Intersecting lines
Since perpendicular lines are themselves intersecting lines, it might be useful to first teach intersecting lines and then describe the particular uniqueness of perpendicular lines. It is important that students understand the nature of a right angle before they are expected to understand perpendicular lines. For intersecting and perpendicular lines, the same approach can be taken as for parallel lines. The terminology should be explained and drawn where students can see a visual example. After students have copied this information into their notebooks, students should be given time to offer examples.
Here are a few ideas for a list of intersecting lines which are not perpendicular:
- noodles crossing one another in a pot of boiling water
- many of the sticks in a game of pick-up sticks
- logs situated in a fireplace
Here are some intersecting lines which are perpendicular:
- a four way stop can be perpendicular, but is not always
- the relationship between a sign post and the ground
- a standard driveway and it's relationship to a house
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A Note For Tactile Learners
While most students will master these ideas through the information already given in these lesson plans on teaching parallel, perpendicular and intersecting lines, kinesthetic, or tactile, learners will grasp this information best by building these lines themselves. Wooden or paper blocks, toothpicks, sticks, straws, or even pencils or markers can be used for students to set up examples of each slope line relationship. While this kind of hands-on learning may seem a bit more time consuming, a teacher's efforts will pay off when the whole class grasps this foundational concept in geometry.