Embedded Files
Slicing Through 3D Shapes
Slicing Through 3D Shapes
Overview: Every object on the planet can be reduced to simple cylinders, cubes, and spheres. Can these three-dimensional objects be reduced further? Any 3D object is essentially a series of 2D shapes stacked together. This was a grounding concept for our lesson study lesson.
As part of a broader project on building 3D models out of 2D cross-sections of cardboard, we sought to allow the class to discover that every 3D shape is made up of 2D shapes through discovering what happens when they are sliced. Each group was given a tube of Play-Doh to construct four 3D shapes. Once the building was completed, students then sliced into their creations to see what shape the slices would reveal. This led to a rich discussion around what shapes to anticipate depending on the 3D figure and the direction of the slice made. Students were at the center of the discovery, building off of each others' ideas instead of waiting for teachers to step in with the "right" answers.
To welcome the assets of the class, this lesson study had an equity goal of supporting Emergent Multilingual (EML) students in participating in mathematical discourse. The visual aid of the Play-Doh intended to give common ground in discussion. Further, each activity within the lesson had built-in language supports that allow all students to share their ideas confidently with their peers and the class.
Human figures are first drawn using only cylinders, cubes, and spheres.
Bringing Equity into the Math Classroom
Bringing Equity into the Math Classroom
Central Question of Equity: How do we support emergent bilingual students with feeling comfortable to express their mathematical ideas publicly and have those ideas valued by their peers?
Grounding Research
Grounding Research
To learn more about the works consulted to make this lesson possible, read on in my Literature Synthesis and Annotated Bibliography.
Theory of Action: If we include visual tools to connect to students’ own mental models of their environment, we will give linguistic access to students that need it most.
The Lesson
The Lesson
Content Goal: Students will understand that every 3D shape is made up of 2D shapes, allowing them to justify volume formulas that they have already had exposure to.
Structure: Our lesson began with an exciting and active Launch of assigning students a 3D shape to make out of imaginary "clay." There were examples of objects with each of these shapes around the room so that students could make something that they were already seeing in their environment. For example, if a student was assigned a cone, they might see the picture of a birthday hat and make that with their clay. To foster connection and empathy, this was done in groups, and once a student built their object, they would share about it with their peers and then pass the "clay." Next, we moved into using the Play-Doh to Explore slicing geometric shapes. Students built four three-dimensional objects - a cylinder, cube, cone, and pyramid - out of the Play-Doh and then had the opportunity to slice these objects in order to see what shapes the slices would be. Finally, we were able to Discuss as a class what the slices looked like depending on the shape and the direction of the slice. Students took turns sharing out their ideas so that others could build off of them. We concluded with an exit ticket to allow the class to voice their key learnings and thoughts on the lesson.
Student Impact
Student Impact
Focus Student #1
Focus Student #1
This student is very helpful, kind, and diligent.
Although she always understands the mathematical content and goes above and beyond in her work, her voice is often not heard in class. She will share great answers if called on, but will not volunteer her ideas.
Our Hope: Encourage her to share her ideas to the class based on her own agency.
Focus Student #2
Focus Student #2
This student is a great friend to all and is very brave.
He grapples with the mathematics in his own way, showing that he is not afraid of "wrong" answers or getting stuck. Mathematical language is still a barrier for him accessing the content fully.
Our Hope: Create an activity that allows him to access the content goals in a meaningful way.
Focus Student #3
Focus Student #3
This student is caring, detail-oriented, and driven.
Despite understanding the mathematical content and being able to explain it to others, this student struggles to trust her own work. She wants all of her answers to be "right" and seeks validation in knowing that her answers are correct.
Our Hope: Foster an environment that welcomes "wrong" answers and incomplete thoughts.
Lesson Highlights
Lesson Highlights
Focal students' voices were heard in table discussions and the class share-out
The average on the question, "On a scale of 1-5, how confident do you feel about this concept?" was a 4.08 and the median was a 4.
Overall engagement and energy around the task was high.
Missed Opportunities
Missed Opportunities
It would have been helpful for students to talk with an elbow partner about what object they were going to create for the warm-up activity so that they would not feel put on the spot.
Group roles could have been helpful to reduce idleness of some table members.
Meet the Team
Julie Rea - Host - 8th grade Math/Science teacher at HTMNC
Morgan Philips - 10th and 11th grade Math teacher at HTHMA
Freddy Miranda - 10th grade Education Specialist at HTHNC
Sam Pawlikowski - 6-8th Grade Social Studies teacher at King Chavez Middle School
Yekaterina Milvidskaia - Knowledgable Other, Math Specialist, and Improvement Coach for HTH GSE
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