## Reflection: Student Led Inquiry Making Sense of Surface Area (day 1 of 2) - Section 2: Warm up exploration

When I taught this lesson again it went in a completely different direction. The students immediately figured out what surface area was and how to calculate it so there was less grappling with meaning. I taught it with a different population who were already familiar with the term "surface", but with a high ELL or low socioeconomic population I would want to spend the time developing this definition first. As I circulated, one of the students twisted the figure and claimed that he had increased the surface area by exposing more faces.

I had him show the class and asked if they could rearrange the 12 cubes so that it had a different surface area. One student took all the cubes apart and said it was the largest possible surface area, because all the faces of each cube were exposed. Other groups put the cubes together in different orientations to create different surface areas. For homework they were asked to figure out the shape that would produce the greatest possible surface area. Most of them came up with one long tower, some said this was the only possible way, while one student came up with other possible orientations that was slightly different. Because not all the students came up with clear explainations and I wanted to make sure they understood the distinction that surface area included all the exposed areas I further asked them to explain in small groups why both of these last two figures showed the greatest surface area possible. They concluded in a whole group discussion that it was because each of the 'inside' cubes had 2 hidden sides that were covered and the outer two cubes had two extra showing.

Other possible ideas we could have pursued were:

• how could we connect 12 cubes to form the smallest possible surface area
• how does this relate to area & perimeter

Student Led Inquiry: Following student ideas

# Making Sense of Surface Area (day 1 of 2)

Unit 9: Exploring Surface Area
Lesson 3 of 6

## Big Idea: Surface area is a two dimensional measurement of a three dimensional object.

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Standards:
Subject(s):
Math, surface area, Geometry, multiple methods, collaborative groups, manipulatives, visual representation
54 minutes

### Erica Burnison

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