Make Math Moments Academy › Forums › MiniCourse Reflections › The Concept Holding Your Students Back › Lesson 63: Digging Into Thinking Of Ratios As A Multiplicative Comparison and Composed Units – Discussion › Reply To: Lesson 63: Digging Into Thinking Of Ratios As A Multiplicative Comparison and Composed Units – Discussion

You’re not alone on that one!
First off – in our eyes (and van de Walls’s) a rate is a single quantity (doesn’t need a denominator of 1…) with a compound unit (pounds per inch, km per hour, etc)
A rate could be:
100 km per hour
But also
98/3 km per hourBoth are rates: a single quantity with a compound unit. One is not a unit rate and the other is not… they are both just rates.
As for partitive and quotative:
Partitive is dividing by number of parts to find how many per part (to find the rate)
“12 cookies divided by 4 kids”Quotative is dividing by how many per part (the rate) to determine how many parts/groups
“12 cookies divided by 3 cookies per kid”Crazy stuff – I know! I got a math degree without ever knowing there were two types of division. Crazy!