## Ultimate Stem

## Bio

## About the lesson

A major philosophical belief that I hold is that students be allowed time to experiment and "play around" with numbers, shapes, etc. in order to construct their conceptual understanding. The 7th grade geometry lesson "Gold Rush" provides such an opportunity. In this lesson students are asked to determine the maximum possible area of a rectangle given a fixed perimeter. Through multiple trials and/or representations and after a hopefully successful result, they are then asked to validate the statement that increasing the perimeter by a factor of 2 or 3 or more, that the new area would result in a proportionally greater area. Essentially , they are answering the questions, "Does doubling the perimeter of a square result in twice the area?" Or "What is the effect of increasing the perimeter of a square on its area?"

Students are then asked to share their approaches and solutions to the problem in small groups. After determining the best approach, students then create a group solution and display their solution/explanation on a poster. Finally, groups are asked to evaluate other students' (non-classmates) solutions to the problem by addressing the misconceptions as well the work that was done correctly.

While this lesson was gratifying for me and the students in itself, the subsequent discussions and work was equally, if not more, rewarding. The question arose about what if there were no limitations on the number of corners? "What would be the area of a regular pentagon with the same perimeter? What about a hexagon? An octagon? What is the relationship of these new shapes and the resulting areas?

These conversations and exploration demonstrated a direct application of the studied concepts in new ways. Furthermore, students using this type of questioning and mathematical inquiry will benefit in future lessons, especially those dealing with shapes, area and three-dimensional objects.

Students are then asked to share their approaches and solutions to the problem in small groups. After determining the best approach, students then create a group solution and display their solution/explanation on a poster. Finally, groups are asked to evaluate other students' (non-classmates) solutions to the problem by addressing the misconceptions as well the work that was done correctly.

While this lesson was gratifying for me and the students in itself, the subsequent discussions and work was equally, if not more, rewarding. The question arose about what if there were no limitations on the number of corners? "What would be the area of a regular pentagon with the same perimeter? What about a hexagon? An octagon? What is the relationship of these new shapes and the resulting areas?

These conversations and exploration demonstrated a direct application of the studied concepts in new ways. Furthermore, students using this type of questioning and mathematical inquiry will benefit in future lessons, especially those dealing with shapes, area and three-dimensional objects.

TOP 5 - Common Themes for a STEM lesson

Through discussion and collaboration, our team identified the following five themes present in all our STEM lessons.

Through discussion and collaboration, our team identified the following five themes present in all our STEM lessons.

**Gradual Release of Responsibility/Scaffolding**- “I do, we do, you do together, you do alone” in STEM lessons ensures students receive support and scaffolding while learning skills and content.**Accountable Student Talk**- Students have opportunities to discuss lesson concepts with each other; this can prove to be invaluable with clearing up misconceptions and reaffirming any understandings.**Technology as a Tool**- Technologies are tools that aid in concept clarity. There are many levels of technology; each activity can evolve based on technology accessibility and teacher TPACK.**Cross Curricular Opportunities/Literacy**- In addition to STEM, lessons include literacy, writing, and arts components that could be developed in collaboration with other teachers to reinforce STEM’s interdisciplinary nature.**Student Centered Activity**- Students feel comfortable in collaborating when analyzing informational texts. Students feel valued, respected, and part of the group. Students show ownership of their learning.
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