21st Century Lesson Plan: Surface Area & Volume of 3-D Figures

PowerPoint for Lesson:


Lesson Plan:


(Rationale & Connections to Reading are included in the Lesson Choice & Technology Paragraphs)

Lesson Choice: I chose to create a lesson for my Geometry Support class. The curriculum we use for our Geometry classes doesn’t allow for much implementation outside of the program and the pacing is already pretty fast, so I opted to go with the course that allowed me the most flexibility. The common core standards are aligned to grade 8; however, the 8th grade standards provide a foundation for the high school standards, which address more complex ideas using 3-D figures. This lesson will help the students consolidate their learning, prepare them for the geometry lessons to come, and provide them with a real-world problem finding/solving scenario.

About the Lesson: I chose to do a three-act math lesson plan. Dan Meyer (2013), one of my all time favorite math bloggers, created the curriculum idea. His rationale is that math is a lot like storytelling, and most stories divide into three acts, each of which maps onto a mathematical task. This is how it works:

  • Act 1: Introduce the central conflict of your story/task clearly, visually, viscerally, using as few words as possible. Students will become problem finders. They will be curious and pose a question about what they are wondering.
  • Act 2: The protagonist/student overcomes obstacles, looks for resources, and develops new tools. Act 2 is not the teacher’s job; the student takes control. However, the teacher may become one of many resources or tools students choose to utilize.
  • Act 3: Resolve the conflict and set up the sequel. The third act must answer the motivating question in act 1 and pay off the hard work in act two.

Dan also talks about the importance of extension problems and the “what’s next” in terms of a sequel (Meyer, 2013). I think the sequel is really the best part of this lesson. I came up with an extension activity where students would create a new package for a product to present to a company; however, students may also come up with great extension activities. There are endless opportunities for the sequel, which opens the door for great classroom discussions.

The ideas behind three-act math lessons were the building blocks, or driving forces if you will, for my lesson plan on surface area and volume. Bransford, Brown and Cocking (2000) address the importance of providing learning opportunities that spark learners’ curiosity in such a way that they want to further explore the ideas (p.18). I believe that act one of this curriculum design does just that. It captures the students’ attention and naturally allows for them to wonder about the problem at hand. They are not handed over the problem; they identify what the problem is. They become innovative thinkers and problem finders. Act two requires learners to be aware of what they know and how they may use it. It also scaffolds learning in such a way that they know when more information is needed and how to find (Vygotsky, 1978; Palinscar & Brown, 1984).

The best part about three-act math is that the video does much more than a textbook problem can. Even the greatest textbook problems have to provide or pose a question at some point. By using a video, I can provide a concrete scenario that forces students to inquire about something or establish a problem. Textbooks, at best, could provide a problem about volume and pop cans where the problem has already been abstracted, which robs students of the skills needed to formulate and solve problems. Traditional textbook problems don’t really even ask students to solve a problem at all. Generally, they provide a question and scenario where all of the information is given, it just has to be plugged into a formula (found two pages back) and computed. The trouble with this approach is it doesn’t require learners to think critically. Really, can you think back to a time where you solved a meaningful, worthwhile problem where you knew all of the necessary information beforehand? Probably not, because in most meaningful problems we encounter, identifying what the actual problem is is half of the battle (Meyer, 2013).  For these reasons, I believe this three-act math lesson encompasses each of Renee Hobbs’ five core competencies as fundamental literacy practices (Hobbs, 2011, p.12).

Three-act math also aligns with the learning environments discussed by Douglas Thomas and John Seely Brown (2011). Specifically, in act two, the students are generating content that represents their learning. Then, in the sequel, students are using play and creation to explore packaging efficiency and costs. Ideally, they would go on to create a package for a company (p.91-99). They are being innovative and creative. In the article, Need a Job? Invent It, Thomas L. Friedman (2013) interviewed Tony Waggoner, a Harvard education specialist. Waggoner discussed the idea solving problems or bringing new possibilities to life and/or companies as what will bring new generation employees from the disappearing middle-class job to the high-wage, high-skilled job of the 21st century (Friedman, 2013). I believe that the mathematical tasks within each act contain the skills needed to successfully live and thrive in an ever-changing world.

Technology Incorporation: Although I didn’t plan for it, this lesson uses several of the digital technologies listed on The Center for Learning and Performance Technologies list of the 100 Best Tools for Learning. I used iMovie to create Act 1 & Act 3. iMovie is something I have worked with before, so it wasn’t new. However, I felt like it was the best option for combining short video clips, pictures, and sounds to create the videos I needed for my lesson plan. I used PowerPoint, SlideShare, and SlideRocket to create and embed this presentation into this post. I used PPT to create the presentation; however, since I had videos in the presentation, the online uploading and sharing became difficult. I initially was going to use SlideRocket, but it told me my account and files would be deleted in 80 days because they were upgrading, so I decided to create a SlideShare. Creating a SlideShare was easy and quick, I just had to upload my PPT file. After previewing the presentation on SlideShare I noticed it didn’t preserve the video properties, it turned them into pictures. I read that SlideShare didn’t have video capabilities, so I went back to SlideRocket. At least I have 80 days to find an alternative. SlideRocket is great for uploading presentations that have sound, videos, and other forms of multimedia. It is something I used once in the past and it worked great for this presentation. I am sad to see the site go away. Within the presentation, I used Google Conversions to provide content necessary for the students to complete the task. Douglas Thomas and John Seely Brown (2011) suggest that students must focus on knowing where to find information rather than knowing the information (p.91-99). While planning my lesson, I reflected on what information I should give my students, information that is widely available, and what information I wanted them to know and build on. This forced me to identify what the real purpose for the lesson was. Did I want my students to memorize or recall formulas? Or did I want my students to know when and how to apply formulas. Going with the latter of the two, I decided to give them the conversions and formulas they needed, but only after they realized the need for them. That is, I didn’t tell them this is the formula you need to use now, but instead, when they realized they needed to make a conversion or use a formula, I provided the information for them.  The last piece of technology I used was Scribd. Since most websites do not preserve formulas, I saved my lesson plan as a PDF and uploaded it to Scribd, which was easy to embed right on my site.


Bransford, J.D., Brown , A.L., & Cocking, R.R. (Eds.). (2000). How people learn: Brain, mind, experience, and school. Washington, D.C.: National Academy Press.

Friedman, T. L. (2013, March 30). Need a job? invent it. New York Times. Retrieved from http://www.nytimes.com/

Hobbs, R. (2011). Digital and media literacy: Connecting culture and classroom. Thousand, Oaks, CA: Corwin/Sage.

Meyer, D. (2013). The three acts of a mathematical story [Blog Post]. Retrieved from http://blog.mrmeyer.com/?p=10285/

Thomas, D., & Brown, J. S. (2011). A new culture of learning: Cultivating the imagination for a world of constant change. Lexington, Ky: CreateSpace.


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