1. Exploring “Purpleness”
Mix drops of white and purple paints (extensive) in different ratios on blank index cards with q-tips; the third quantity (intensive) is purpleness
Maria: Do the ‘purpleness’ activity here –It is a good way to focus on what is ‘measured’ – definite amounts of purple and white paint (extensive) quantities, AND, when they are combined in a cup, two quantities both change from their original colors (which is covariation), and ‘Seeing’ this ‘third’ thing of ‘purpleness’ (invariance) as the new 3rd quantity. This will also come out in our discussions of ‘extensive’ versus ‘intensive’ quantities.
Another “big idea’ here – Is it easier to see this new ‘3rd quantity’ when we use continuous items and see a ‘blend’ (purpleness) as opposed to the discrete items, compared to the earlier problem of having candy kisses and marshmallows together. We can make a composite unit with discrete objects, but the continuous items seem to better build the 3rd quantity as a new, distinct quantity.

2. Revisiting the “Purpleness” Activity
Let’s go back and look at all of our cards from the “Purpleness” activity yesterday. Which ratios do you think are equivalent?
Maria: Need to create some ratio cards ahead of time to do activity.
Leah: Go back to Purpleness Activity from Day #1, add ORDERING by purpleness.
Create different ratio cards (no more than 6 per group)—be sure to include SOME ratios that are equivalent!

3. Revisiting the “Purpleness” Activity
Let’s go back and look at all of our cards from the “Purpleness” activity yesterday.
Do you think we can ORDER these by “purpleness”?
Maria: Need to create some ratio cards ahead of time to do activity.
Leah: Go back to Purpleness Activity from Day #1, add ORDERING by purpleness.
Create different ratio cards (no more than 6 per group)—be sure to include SOME ratios that are equivalent!