Relationships Between Quantities and Reasoning with Equations and Their Graphs

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Graphing all kinds of situations in one and two variables is the focus of this detailed unit of daily lessons, teaching notes, and assessments. Learners start with piece-wise functions and work their way through setting up and solving quadratic equations, systems of linear equations, and systems of inequalities. Throughout the unit, a high importance is placed on describing and interpreting results, not just reporting numerical answers. The level of detail in the daily teaching notes and answer keys makes this extensive unit a nearly turn-key addition to any curriculum.

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CCSS: Designed
Instructional Ideas

  • Consider breaking up the unit and using individual parts as remediation or supplements to existing curriculum
  • Have pairs of students time each other traveling a path in different ways then graphing the piecewise function
  • Use systems of equations and inequalities to develop a mock business model by accounting for overhead, taxes, supply, and demand of a product, etc.
  • Great unit for a long-term substitute situation or homebound learners
Classroom Considerations

  • Teaching notes contain remediation and accommodation suggestions for tricky parts throughout the individual lessons
  • Student worksheets are attached in the resources section, matching the daily homework answer keys in the teaching references
  • Each day's assignments depend highly on the prior days, perhaps requiring out-of-class remediation for absent students to catch back up

  • Detailed plans, remediation, and assignments included for every day of the multi-week unit
  • Clear emphasis on analyzing and interpreting results
  • Daily lessons gradually build math skills and develop math intuition based on previous work
  • Multiple situations and topics covered in the problem sets appeal to a wide variety of interests

  • Work on piece-wise functions, setting up polynomials, and solving quadratics is not spiraled into later work on solving equations/inequalities and systems of equations/inequalities