Last week, I got to teach a math lesson using pentominos. In case you are not familiar, pentominos are the various shapes that result when you connect five identical square tiles along the edges. This lesson comes from the Covering and Surrounding workbook from Lappan, Fey, Fitzgerald, Friel, and Phillips. The lesson requires students to draw out all the possible pentomino shapes. To enhance this lesson, I used multicolored square tile manipulatives. The students were very engaged and enjoyed using the tiles, however, many of them quickly became more interested in building 3-D shapes with the tiles.
The point of this lesson was to highlight the differences between area and perimeter, and how the perimeter and area change when a tile is added. I think it was a great hands-on lesson to help students see how area and perimeter are connected, but not identical.
My students were able to notice patterns in how the perimeter changed when a tile was added to a particular area of the pentominos. Depending on the placement of the tile, you could increase the perimeter by 2 units or keep the perimeter the same, but increase the area by one unit.
I think this lesson was enhanced by the use of the tiles. The students could easily move these tiles around to explore the different pentomino shapes. The tiles made it easier to notice when a pentomino shape was a repeat of a previously drawn shape. I also got to see how manipulatives add to the students' understanding or help them make sense of a new concept.
I wish I could have participated in this lesson, Kristen! It sounds like you found a great lesson to dig into the mathematical ideas of area and perimeter. This is a topic that, for learners of all ages, can get messy. Your mind can start flickering back and forth and get confused about what is what. The way you used a manipulative to help students explore area and perimeter sounds really powerful-- especially the way your lesson highlighted the connections between area and perimeter AND moved to discussion about patterns when perimeter changed. This discussion sounds like a particularly rich part of the lesson to leverage. What kinds of things did students notice about the patterns? How did they record the patterns or organize that information?
ReplyDeleteAllison,
ReplyDeleteSome of the kids were quick to notice patterns. They saw that if you added a tile to a cut out corner then the perimeter did not change. I think they just organized the information in their heads. These kids have an amazing memory!