Unit 3: Expressions & Equations with Geometry

The big ideas for Unit 3 are generating equivalent expressions with rational coefficients and solving equations & inequalities before applying those skills to work with geometric equations like area, surface area, volume, and finding missing angle measures.  Algebra tiles are highly encouraged for expressions & equations in order to develop procedural fluency from conceptual understanding and to prepare students for their use in Algebra 1.  Time spent in this endeavor is also rewarded when moving to inequalities where although the solutions are dramatically different the solution pathways are not.  See slides 117-146  & See slides.  Alternate methods for sequencing this unit are suggested in the FAQs.  Geometry formulas can be a further chance to learn and apply skills from the unit, including when area, surface area or volume is provided and students solve for a missing side length.  Finding missing angle measures is an even more direct application.  Finally, depth can be explored by examining the supporting ideas of rewriting expressions in problem solving, using variables, and taking multiple learning goals to a “level four” understanding.

Work with zero pairs in the last unit is extended to algebra tiles.  Work with rational numbers should continue to be emphasized in this unit as 8th grade assumes fluency with these concepts.  Angle relations can include an unknown to reinforce the meaning of equality visually.  Other geometric formulas are a chance to apply what has been learned about equations in a new context to ensure transfer.  See also the Distributive Property.