Lesson Title: Nets___________________________________
Date: _____________ Teacher(s): ____________________
Course: _Common Core 6___________________
Start/end times: _________________________
Lesson Objective(s): What mathematical skill(s) and understanding(s) will be developed?
Solve real-world and mathematical problems involving area, surface area, and volume.
6.G.4 Represent three-dimensional figures using nets made up of rectangles and triangles, and use the nets to find
the surface area of these figures. Apply these techniques in the context of solving real-world and mathematical
problems.
Which Mathematical Practices do you expect students to engage in during the lesson?
MP1: Make sense of problems and persevere in solving them.
MP3: Construct viable arguments and critique the reasoning of others.
MP5: Use appropriate tools strategically.
Lesson Launch Notes: Exactly how will you use the first
five minutes of the lesson?
Present the following problem to the class:
Nana is wrapping a birthday present that is 8 inches long,
3 inches wide, and 10 inches high. If Nana bought a roll
of wrapping paper that is 1 foot wide and 2 feet long,
does she have enough wrapping paper to wrap the
birthday present?
Lesson Closure Notes: Exactly what summary activity,
questions, and discussion will close the lesson and
provide a foreshadowing of tomorrow? List the
questions.
How do nets relate to surface area? Why do we use
them?
Why do some nets not form the 3-D figure that we
expect? What did you do to make sure your net does
work?
Have the students brainstorm ways they think they can
answer this question and after a few minutes, start putting
student responses on the board. Do not guide students to
favor any one way at this point, but allow students to
share why they think each method will/will not be
effective in solving the problem.
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.
Days 1-2:
1. After students finish brainstorming the lesson launch, they will explore various ways to answer this question in
order to come up with a solution. Students will work in groups of 3 or 4 to do this. Provide any supplies you
think will help such as graph paper, tape, scissors, boxes, wrapping paper, etc. Have students organize their
work on poster paper or set up presentations at the table they are working at so students can view solutions
during a presentation at the end of the activity. (Look for evidence of MP1 and MP5.)
2. During presentations, students should be able to explain the method that they used to answer the question,
explain what they know that leads them to believe the approach they used is valid and leads to a reasonable
answer, and make connections to the previous topic of area. Students should also be able to explain why this is
not a volume problem. (Look for evidence of MP3.)
3. At the end of the presentations, have students share the methods that they saw as the presentations were given.
Have them analyze answers and approaches using what they already know. In breaking this problem up into
different area problems students were really analyzing a two-dimensional representation of the three-dimensional
box. Discuss this as the students realize it and refer to the 2-D representation as a “net.” Make sure students
understand that the 2-D figure is the same as the 3-D figure because a box is formed from 6 sides being folded
HCPSS Secondary Mathematics Office (v2); adapted from: Leinwand, S. (2009). Accessible mathematics: 10 instructional shifts that raise student
achievement. Portsmouth, NH: Heinemann.
Lesson Title: Nets___________________________________
Course: _Common Core 6___________________
Date: _____________ Teacher(s): ____________________
Start/end times: _________________________
up. Explain that every 3-D figure has a net, and the net is how we analyze the area of its surfaces or “surface
area.” Explain that students will be learning how to find the surface area of 3-D shapes (polyhedron) that are
made up of squares, rectangles, and triangles by analyzing the net for each type of figure.
4. Have students complete activities in the NCTM Illuminations “Building a Box” Lesson, available at
http://illuminations.nctm.org/LessonDetail.aspx?ID=L570 to explore different nets that make cubes and nets that
do not make cubes. Give the “cube nets” tool as a resource sheet at the end of the lesson, and let students
determine which nets would/would not form cubes. Collect and grade.
Day 3:
5. Display rectangular and triangular prisms and have them classify these shapes. Have the students discuss the
classification of each and why they have the names that they do. As students analyze the parts of each shape,
have them begin to discuss how they could represent each one using a net like we did in the previous exercises.
Say, “A rectangular prism would be made up of 6 different rectangles. What relationship would the rectangles
have to each other? What shapes make up a triangular prism? When we completed the “Building a Box” lesson
we found that not every net would fold to make a cube.” Ask students, “Do you think that will be an issue as we
break rectangular and triangular prisms into nets? Why or why not?”
6. Display the Prism Examples resource sheet. Pair students and distribute graph paper, scissors and tape.
7. Allow them to create nets that, when folded, will make rectangular and triangular prisms. Have the students
create as many as they can and analyze the ones that do not work.
8. At the end of the class, give students several nets drawn on grid paper that have dimensions labeled on them.
Have them determine whether or not they could use these nets to make the 3-dimensional object desired. Collect
this activity to analyze student understanding of nets. (Look for evidence of MP3.)
Note: As new vocabulary is added throughout the lesson, consider adding it to a word wall for the unit.
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 mastery? 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 will make nets to represent rectangular and triangular prisms as well as determine whether a given net will
fold to make the desired shape. Student mastery will be measured by class discussion, teacher monitoring of student
work, and through collecting student work during on the end of day 2 and 3.
Notes and Nuances: Vocabulary, connections, common mistakes, typical misconceptions, etc.
Vocabulary: nets, two-dimensional, three-dimensional, surface area, rectangular prism, triangular prism,
polyhedron
Typical misconceptions: thinking that a three-dimensional figure is always a volume problem since it’s not “flat”
Connections: area, two-dimensions, three-dimensions
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?
Illuminations “Building a Box” Lesson, available at
http://illuminations.nctm.org/LessonDetail.aspx?ID=L570
Graph paper
Tape
Scissors
Boxes for lesson launch
Find 6 examples of rectangular and triangular prisms in
real life. Why would it ever be useful to make nets of
these?
Have students go to the website for the 3-D paper
models and have them choose one that has rectangles
HCPSS Secondary Mathematics Office (v2); adapted from: Leinwand, S. (2009). Accessible mathematics: 10 instructional shifts that raise student
achievement. Portsmouth, NH: Heinemann.
Lesson Title: Nets___________________________________
Course: _Common Core 6___________________
Date: _____________ Teacher(s): ____________________
Start/end times: _________________________
Wrapping paper for lesson launch
and/or triangles in it. Have them print it and construct it
Poster paper
to bring to class and share with the class. Have them
Rectangular and triangular prisms around the room
make note of the name of the type of solid they choose.
Resource for paper models of 3-D figures
http://www.korthalsaltes.com/
Prism Examples (Student Resource 1)
Does the Net Work? (Student Resource 2)
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 create a net for a given rectangular or triangular prism?
Were students able to understand that a 3-D figure can be decomposed into a net?
Were students able to find surface area of a given rectangular or triangular prism?
Are students understanding and using appropriate vocabulary throughout the lesson?
Did students successfully transfer knowledge to break down real-world problems involving triangular and
rectangular prisms?
HCPSS Secondary Mathematics Office (v2); adapted from: Leinwand, S. (2009). Accessible mathematics: 10 instructional shifts that raise student
achievement. Portsmouth, NH: Heinemann.