Unit 4: Ratios, Rates & Percents

The big ideas for Unit 4 are ratio concepts and ratio reasoning and how they apply to unit rates, percentages, unit conversions, and problem solving.  In sixth grade, this is a unit on equivalent ratios & their representations; not a unit on analyzing proportional relationships, proportionality is saved for seventh grade as are complex fractions (a ratio of one fraction to another).  Both of the latter can be explored for depth at the end, time permitting.  Ratio language & unit rates have been embedded in the lone essential standard of 6.RP.3, using ratio and rate reasoning to solve real-world and mathematical problems.  They too can be explored for their own merit for depth, time permitting.  Care should be taken not to jump right into the sub-standards of completing ratio tables, solving unit rate problems, solving percent problems and using unit conversion.  6.RP.3 itself stipulates the instructional models/representations of: reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, and equations.  One way to build understanding of ratio concepts & reasoning is by comparing representations on a Frayer Model providing all students multiple points of access with the chance to make connections to the others.  Care should also be taken to illustrate the distinctions between a fraction and a ratio and a ratio and a rate.  Namely, all fractions are ratios while not all ratios are fractions even though they might appear to be written that way.  Likewise, all rates are ratios, but not all ratios are rates.  SMP #6, Attention to Precision will be important in understanding these distinctions.

Don't let the single target fool you; besides being foundational for future courses - ratios, unit rates, percents & unit conversions are also Widely Applicable Prerequistes for college, careers & life.  Multiple representations are the key to building procedural proficiency from conceptual understanding in every unit & this one in particular.