Activity Set #6: "Multiplication" and Proportional Reasoning

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Start notebook reference page on: quantity and metric units.

• operational definitions of length, area, volume, weight, mass
• a top of the page banner on metric prefixes.
• MKS and cgs basic units
• Units for volume and weight 
  

 Small group whiteboarding task w/ student led discussion circle:
 
 •Picture/Explain algebraically and geometrically on a whiteboard how many cc's and liters fit in a meter-sized cube?

Note: It is very helpful to hold up cc, dc and create a meter cube with meter sticks for students to be able to get a proper handle on this activity. In addition sufficient props, i.e. "powers of ten" sets of yellow plastic small cubes, sticks, plates and large cubes and meter sticks for the groups are essential.

 

 glossary entrees/ words to discuss meaning:
dimension (as in spatial dimension)*
point, edge, perimeter, face, surface, boundary, 3D shape, enclosed region,
string theory and higher dimensions
replication and regrouping
zooming in/out
scaling, rescaling
whole/part relations*
"multiplication" - number by quantity, number by number, quanity by quantity
 formula
 algorithm
 meaning of LxWxH=V
 meaning of unit1*unit2 = new unit
"derived units"
"multiplication by squeegy".
 increasing and decreasing dimension.

  Think/Pair/Share:
 
 •How many kinds of reasoning did we use to solve the cube problem?  

 glossary entrees/ words to discuss meaning:
algorithmic reasoning, proportional reasoning, dimensional reasoning, quantitative reasoning, scaling.
  Think/Pair/Share:

 
 •What is the basic algebraic process used to combine related two whole/part relations to determine a new whole/part. If the whole/part relations are numbers or conversion factors, how do the original whole/part relations need to be related for it to make sense to combine them through multiplication?  How is this related to proportional reasoning?

 glossary entrees/ words to discuss meaning:
 number***
 conversion factor
 chain rule