Creating and Graphing Linear Equations in Two Variables

This Creating and Graphing Linear Equations in Two Variables presentation also includes:

This detailed presentation starts with a review of using key components to graph a line. It then quickly moves into new territory of taking these important parts and teasing them out of a word problem. Special care is taken to discuss scale and graphing strategies, along with common phrases that identify slopes and constants. Keystroke instructions for TI graphing calculators are also included, with one example at the end worked by hand and one by calculator. A bonus inclusion in both worked examples is a link to an online graphing applet that is pre-filled with information from the problem for easy demonstration and manipulation.

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CCSS: Adaptable
Instructional Ideas

  • Post online for young algebrists to view before class in a flipped classroom model or for remediation and review during homework time 
  • Link with a physical science or physics lab on falling objects to give abstract variables real-life context
  • Prior to the lesson, have learners brainstorm possible pairs of related variables. These could link to other units of study or current events and provide a place to emphasize cause vs. correlation
  • Consider having some learners work the examples by hand, some with a graphing calculator, and some with the interactive applet, then teach one another how to obtain results
Classroom Considerations

  • Accessing this lesson PowerPoint file requires ability to open a *.pptx file
  • Linked applet in the presentation for working examples requires Internet access and updated Java player
  • Step-by-step graphing calculator instructions are given for the TI-83/84 and Nspire within the presentation and on one of the worked examples. Using a presentation version of one of these calculators to work the steps might help the class follow the instructions
  • Slides are very word-dense, printing those slides with key points to fill in might assist with IEP accommodations or ESL learners
Pros

  • Exceptionally thorough presentation of graphing mechanics
  • Seamless integration of technology in multiple ways
  • Identification and explanation of common misunderstandings and mistakes
  • Multiple attack strategies identified and demonstrated
Cons

  • No independent or guided practice problems provided
  • Explanation of vertical slope as "no slope" in the same paragraph as the zero slope of a horizontal line is misleading
  • Examples labeled 4 and 7 instead of 1 and 2