Lesson Title: Cross Sections of 3-D Objects
Date: _____________ Teacher(s): ____________________
Course: Common Core Geometry, Unit 4
Start/end times: _________________________
Lesson Standards/Objective(s): What mathematical skill(s) and understanding(s) will be developed? Which
Mathematical Practices do you expect students to engage in during the lesson?
G.GMD.4 Identify the shapes of two-dimensional cross-sections of three-dimensional objects.
MP1:
MP3:
MP5:
MP7:
Make sense of problems and persevere in solving them.
Construct viable arguments and critique the reasoning of others.
Use appropriate tools strategically.
Look for and make use of structure.
Common Core Geometry, Unit 4
Lesson Launch Notes: Exactly how will you use the
first five minutes of the lesson?
Have students work in pairs to build a threedimensional figure of their choosing out of Katy cubes.
Instruct them to sketch a view from the top, bottom,
and the two sides of their figure. Have partners share
their figure and explain their sketches using the
document camera. Give the class an opportunity to
critique the views of each figure. (Look for evidence of
MP3.) Discuss what information the views give you
about the figure and what information is not visible.
Lesson Closure Notes: Exactly what summary activity,
questions, and discussion will close the lesson and
connect big ideas? List the questions. Provide a
foreshadowing of tomorrow.
1. What Standards for Mathematical Practice did you use
today? Explain.
2. Where can you find two-dimensional cross-sections of
three-dimensional figures in the real world?
Lesson Tasks, Problems, and Activities (attach resource sheets): What specific activities, investigations,
problems, questions, or tasks will students be working on during the lesson? Be sure to indicate strategic
connections to appropriate mathematical practices.
1. As a class, discuss the term cross-section. Have students attempt to sketch a cross-section of the figure using
what they know about the term. (Note: Cross-sections will be taught in Common Core 7 and may or may not
need review at this point.) Discuss the different cross-sections created by students. Based on the level of prior
knowledge of the students, you can either specify how and where the cross-section can be cut or you can allow
students to choose how and where to cut the figure. If the cross-section is specified, come to a consensus as a
group as to what it should look like. If students are given a choice, allow a few to present and justify their
sketch. (Look for evidence of MP1 and MP3.)
2. Divide students into small groups and have them work through each of the Cross-Section Stations. Give groups
a time limit at each station to do as much as they possibly can. Each group will need a device that can digitally
record photographs as evidence of their work at each station (iPads, digital cameras, computers, flip cameras,
etc.) This can be modified to allow students to film and justify their work or to use the document camera to
create podcasts. (Look for evidence of MP1, MP3, MP5, and MP7.)
3. If there is time, allow groups to edit and order their photographic evidence of the work done at each station. You
may wish to give them time to create a PowerPoint presentation or other multimedia portfolio of their work.
Evidence of Success: What exactly do I expect students to be able to do by the end of the lesson, and how will I
measure student success? That is, deliberate consideration of what performances will convince you (and any outside
observer) that your students have developed a deepened and conceptual understanding.
Students should be able to sketch cross-sections given various three-dimensional figures. In addition, students
should be able to use cross-sections in order to generate possible three-dimensional figures with those cross-sections.
HCPSS Secondary Mathematics Office (v2.1); adapted from: Leinwand, S. (2009). Accessible mathematics: 10 instructional shifts that raise student
achievement. Portsmouth, NH: Heinemann.
Lesson Title: Cross Sections of 3-D Objects
Course: Common Core Geometry, Unit 4
Date: _____________ Teacher(s): ____________________
Start/end times: _________________________
Notes and Nuances: Vocabulary, connections, anticipated misconceptions (and how they will be addressed), etc.
Vocabulary: cross-section
Misconceptions: Students may struggle to visualize three-dimensional figures and their cross-sections.
Manipulatives should be used extensively to give students physical representations of three-dimensional objects
being described.
Resources: What materials or resources are essential
for students to successfully complete the lesson tasks or
activities?
Homework: Exactly what follow-up homework tasks,
problems, and/or exercises will be assigned upon the
completion of the lesson?
Digital recording devices for each group
Cross-Section Stations
Katy Cubes
Plastic knife
Grid printed onto transparency
Laptop(s)
Computer paper and tape
Document camera
Have students research topographical maps and bring in
the following:
1. Three facts about topography or topographical
maps that they can explain to the class.
2. The relationship between topography and what
was done in class today.
3. A printed example or a link to an example of a
topographical map.
Lesson Reflections: How do you know that you were effective? What questions, connected to the lesson
standards/objectives and evidence of success, will you use to reflect on the effectiveness of this lesson?
Were students able to sketch cross-sections of given figures, whether presented in three-dimensions or described?
Could students create feasible three-dimensional figures given cross-sections of those figures?
Were students able to explain where and how each cross-section was cut from its three-dimensional figure?
Howard County Public Schools Office of Secondary Mathematics Curricular Projects has licensed this
product under a Creative Commons Attribution-NonCommercial-NoDerivs 3.0 Unported License.
HCPSS Secondary Mathematics Office (v2.1); adapted from: Leinwand, S. (2009). Accessible mathematics: 10 instructional shifts that raise student
achievement. Portsmouth, NH: Heinemann.