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Math Tourist: Capacity in Italy

**Essential Questions for students (objectives):** How would define and calculate capacity?

**Supplies:** video (length 1:55), note-maker

**CCSS:** 7.G.6 & 7.G.4, G-MG-2,3, Mathematical modeling

**Instructional Format:** Video, student problem-solving, group work

**Time needed:** 10 minutes - full class period

**Vocabulary for a Word Wall:** capacity, area, volume

**Description:** There are many ways to use this video in your math class. I filmed it with the express purpose of modeling a concept, capacity, which is a word most of us hear and believe but don’t know how it is determined. This type of problem is incredibly rich because the variables and constants are not flushed out and must be researched and agreed upon. This video may be an interesting start for 7th graders, but could be too difficult for them in the long run; however, it may start a conversation about the need for higher levels of math in order to determine such calculations. This video has two parts and each could be done separately. I do feel that it leads to great discussion about capacity is a concept that changes once you determine the object that is supposed to fit in the container.

1) You can show this video (1:55) at the beginning of a unit on area/volume as a hook that will keep the students interested in learning about formulas for area/volume. You can have them work on the problem at the end of daily lessons (or once a week) armed with new knowledge that they are exploring in class. Or you could revisit the video at the end of the unit as a formative check to see what the students have learned about area/volume and whether they can apply that knowledge.

2) You could show this video as a warm-up activity after the students have learned some basic area/volume applications and calculations. It is a great way to show context to geometry that isn’t the same old find home improvement examples.

**Extensions: ** How do we determine capacity at zoos – what sizes do the cages or enclosures need to be? What about the capacity of raising cattle and how does that play into concentrated animal feeding operations (CAFOs)? How do architects create spaces to help them look larger/smaller and fool the eye?