Friday, April 4, 2014

The Sticky, The Woodsicle, The Leg, and The Dogoala

Let's not bury the lede: yes, those are chocolate-filled blueberries and cheese-filled raspberries. A kid brought them in, we ate them, and they're gross.

OK but why? That's a slightly longer story, and I recommend that you start it over at Danielson's place. Basically, I gave kids an object to build a measurement system around. They named it, created a "made-up-of" (e.g. an inch) and a "made-out-of" unit (e.g. a yard). They made a measuring tape, they measured stuff with their units. 

Then we made square units to measure area with, and then cubic units to measure volume. Along the way a ton of good math happened -- fractions, scaling area, units, multiplication, measurement, volume concepts -- and a good time was definitely had by all.

Important questions for us were:
  • How should we make a helpful tape measure?
  • What's the best way to create a unit of area?
  • How come so many of the square small units fit into the square major units?
  • Ditto with cubes.
Important observations for me:
  • There was a strong desire to measure area in terms of the physical objects that were their measures of length.
  • Pretty much everyone had a moment while they were making a square or cubic unit where they went "Wait this is totally way too big." 
  • The kids couldn't keep "square" and "cubic" straight. That's a distinction they don't really make in their regular language, and I've seen the same thing with older kids calling a sphere a circle.
  • Measurement is simply a great context for fraction work.


  1. Michael, this is really great; so much math happening all at once. I've been carrying around "Measurement, Explored" all year and really want to try it out. What grade level? How many days did you spend on the project?

    1. 4th Grade, a mathematically courageous group of kids. I think the whole project took eight 45-minute periods.

      I made modifications from Christopher's outline. We didn't swap units to do conversions. After the conversation posted in that video we spent a day where I gave them different shaped rulers for a unit of my own to directly engage with the idea of constructing a unit of area from the physical, linear unit. And we added a few days for volume because that was important to me.

      Basically, slightly less depth than what Christopher's students went through, a slightly faster clip than what he describes to match their little tiny person attentions.