Exploring Volume

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This week my third grade class explored volume and surface area concepts. Last week they used centimeter cubes to build a number of structures. Students transitioned from counting centimeter cubes to using a formula to find the volume of a rectangular prism.

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The next few math sessions in the week revolved around the concepts of identifying faces, edges, vertices, nets, and how all of those characteristics play a role in the volume of prisms. During the next day I asked students to create a net of a rectangular prism using 1cm grid paper. This was a struggle for some students. Being able to visualize the net, cutting it out and creating a prism was challenging. My class went through a LOT of grid paper during this process.  Students started out using trial-and-error and moved closer to a formula method.  After multiple attempts and some major perseverence, I decided to frame the next few lessons with a project.

I decided to dig into my Evernote account and combined a few projects that I’ve used or found through my PLN. I also spoke with a few colleagues in my school for feedback.  The project was going to take some time. I decided that although the project may take more time than individual lessons it was worth the time and gave students opportunities to learn more about the math concepts that were scheduled to be explored.

The project is called volume city. Students were given directions, a model map, 1 cm grid paper and a rubric. You can find the files that I used here. Essentially, students were asked to create a model city using rectangular prisms as buildings. The city had to have at least four basic buildings and students could add more if they desired. Students were required to write the dimensions of the buildings: length, width, height and volume.

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Students then used the grid paper to draw and cut out the net for that particular building.

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This was probably one of the more challenging aspects of the project, especially when the building wasn’t shaped like a cube.  Students had trouble drawing nets with different heights. Students were given more grid paper as needed. I think every group had to redraw or recut their nets two or more times. This was good in my mind, because it demonstrated that they made a mistake, but were trying again in an attempt to make improvements. The concept of visualizing the net and the action of creating them accurately started to combine as the project continued. I even had a few students decide to create the largest possible net using the entire grid paper.

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So after students created the nets they decorated them and glued/taped them on the map sheet. Students filled out the dimension sheet as they created their prisms. Here’s one that’s almost complete.

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Not all of projects are complete, but the next phase of the project is for students to find the total volume of their model city. This will most likely take place as students will start taking the PARCC test next week and our math block is shortened. At some point we’ll also be exploring rates in the next unit. During that time we might use some type of stop-motion video of our model cities to look at the frames-per-second in our film.

“Aligned” to the Common Core

Image by:  Felixico


Now more than ever it seems that educational leaders are being encouraged to align their curriculum to the Common Core. Currently, 45 states and 3 territories have signed the Common Core initiative.  National tests are now being developed to evaluate how well students understand the math and reading Common Core standards.  Seeing that the majority of the United States supports the Core, new “Common Core Aligned” products seem to be popping up everywhere. Workshops, seminars, webinars, and PD sessions are dedicated to communicating how the Common Core standards impact curriculum.  In general, I believe that the workshops mostly benefit teachers. I also believe that the Core will give opportunities for educators to positively change the way that they deliver math and reading instruction. What I’m concerned about though is how the “aligned” resources are being utilized.  I in no way endorse/oppose the products below, but the images & links contribute to the notion of how publishers (McGraw Hill, ASCD, Pearson, etc.) are marketing Common Core resources to educators and administrators.

I’m finding that teachers are being pressured into purchasing these “aligned” materials to prepare their students for the upcoming accountability testing.  I’m not against the Common Core materials being produced or used in the classroom.  I’ve actually read many “aligned” resources and have found them most beneficial.  To be honest, most educators that I know have already viewed a number of the Common Core materials.

Don’t get me wrong, educators should be aware of the new standards and adjust their instruction accordingly.  The over reliance on “aligned” published materials can cause teachers to take less risks as they focus only on items located in specific published books.  In these cases differentiation may occur less as the teacher uses whole group Common Core instructional techniques to cover specific content that’s found on future standardized assessments.  I view the “aligned” resources as important and another tool in an educators tool belt.

“Aligned” materials and other supplemental materials should not be viewed as a magic bullet in raising test scores or in teaching in general.  Instead of impulsively purchasing “aligned” materials, school districts around the country should collaborate with each other to share resources that will benefit all stakeholders involved.  I believe some states are attempting to use this model and I applaud their efforts.

Utilizing teaching strategies that work for educators and their students instill an appreciation for learning and give students an opportunity to show their learning in new settings.  Using solid pedagogy along with supplemental resources allows teachers to differentiate their instruction to meet the needs of all students.