# Relationships Between Quantities and Reasoning with Equations and Their Graphs

##### This Relationships Between Quantities and Reasoning with Equations and Their Graphs unit also includes:

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.

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
##### Pros

• 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
##### Cons

• 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