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Make Math Moments Academy › Forums › Mini-Course Reflections › The Concept Holding Your Students Back › Lesson 6-3: Digging Into Thinking Of Ratios As A Multiplicative Comparison and Composed Units – Discussion › Reply To: Lesson 6-3: Digging Into Thinking Of Ratios As A Multiplicative Comparison and Composed Units – Discussion

  • Kyle Pearce

    Administrator
    October 8, 2021 at 6:46 am

    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 hour

    Both 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!

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