Lesson Title: Surface Area__________________________ Course: _Common Core 6___________________
Date: _____________ Teacher(s): ____________________ 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?
MP2: Reason abstractly and quantitatively.
MP6: Attend to precision.
Lesson Launch Notes: Exactly how will you use the first five minutes of the lesson?
1.
Ask, “Knowing what you do now about nets, how would you approach this problem now? Would it be the same or different than your first approach?”
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?
2.
Ask, “How would creating a net for the launch problem help you to answer the question?”
Students should discuss that they would know the dimensions of each side of the package so they can find the area of each side of the rectangular prism to know how much wrapping paper would be needed to cover it.
Lesson Closure Notes: Exactly what summary activity, questions, and discussion will close the lesson and provide a foreshadowing of tomorrow? List the questions.

What is surface area and how is it similar to/different from area?

How is surface area different from volume? Why do you think some people might mix these up?

What are some strategies that can be used for finding the surface area of problems 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.
Day 1:
1.
After re-reading the lesson launch problem, allow students to work in groups to solve the problem using a net and finding the area of each side. Ask them, “How will you know whether or not the wrapping paper will cover the total area you found?” Lead students to discuss the shape of wrapping paper when it is unfolded to determine it is rectangular. Ask, “How can you find the area of the piece of wrapping paper you are given?
How will you know if it will cover the package? At this point, students will be fully equipped to finish the lesson launch problem and have it represented as a net. You may choose to finish answering it as a whole class discussion or allot a few more minutes for groups to finish and then share.
2.
Provide different boxes that would be found at the grocery store that are shaped like rectangular prisms (cereal box) and triangular prisms (Toblerone box or an individual pizza slice box). Pre-cut boxes so that they can be laid out as nets or folded up as boxes. Also pre-label the sides so that the dimensions are readily available. You can use integers, decimals, or fractional sides depending on what students are comfortable with. Have the
HCPSS Secondary Mathematics Office (v2); adapted from: Leinwand , S. (2009).
Accessible mathematics : 10 instructional shifts that raise student achievement. Portsmouth , NH : Heinemann .

Lesson Title: Surface Area__________________________ Course: _Common Core 6___________________
Date: _____________ Teacher(s): ____________________ Start/end times: _________________________ students travel in pairs to calculate the surface areas of each box. Each student should be responsible for recording work and answers on their own paper. They should make sketches as well as show work because this will serve as example problems to put in their notes. (Look for evidence of MP2 and MP6.)
Day 2:
3.
Set up stations around the room at which students will find real-world problems that involve finding surface area of rectangular and triangular prisms. Stations should include word problems written for available objects (for example, “Find how much cardboard is needed for a Cheerios box.”). Objects can include everyday furniture like filing cabinets (rectangular prism), objects found at the grocery store, vases (both triangular and rectangular—would you calculate the area of the open part?), blocks, gift packages, etc. Have students work either in pairs or independently. Have students complete their work on their own paper regardless of whether or not they work in pairs. This should be turned in at the end of the activity. To offer options, students can be strategically sent to specific stations or be given the choice to visit a minimum number of stations. Students may work individually or in small groups for the stations’ activities. (Look for evidence of MP2 and MP6.)
4.
If time permits, provide practice problems that are real-world problems, which require students to calculate surface areas of triangular and rectangular prisms. Put individual problems on index cards and have them available on an empty desk. (See Practice Problems—Index Cards ). Allow students to choose problems to solve from those available, and instruct them to solve problems on their own paper. Most students should be working independently by this point, allowing you to help individuals who may need more direct teaching at this point. Encourage students to use graph paper to draw the net of the figures to make finding the surface area more clear.
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 break an image into its net in order to calculate the surface area.
Students will analyze problems and determine if all sides need to be included in the calculation of the surface area.
Students understand a word problem and how to draw a net to represent the shape to find the surface area.
Notes and Nuances: Vocabulary, connections, common mistakes, typical misconceptions, etc.
Vocabulary: surface area
Common mistakes: not calculating all sides, not adding all areas together, calculating the area of an unnecessary side (like a vase has no top surface)
Resources: activities?
What materials or resources are essential for students to successfully complete the lesson tasks or
Boxes from grocery store that can be unfolded into nets
Examples for stations
Index cards prepared with problems for practice (see
Practice Problems—Index Cards, attached)
Homework: Tissue Box Problem (Student Resource, attached)
Homework: Exactly what follow-up homework tasks, problems, and/or exercises will be assigned upon the completion of the lesson?
Tissue Box Problem (attached)
Glencoe Mathematics Applications and Connections
Course 2 Chapter 12 Section 4
Glencoe Pre-Algebra Chapter 11 Section 4
Lesson Reflections: 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.
HCPSS Secondary Mathematics Office (v2); adapted from: Leinwand , S. (2009).
Accessible mathematics : 10 instructional shifts that raise student achievement. Portsmouth , NH : Heinemann .

Lesson Title: Surface Area__________________________ Course: _Common Core 6___________________
Date: _____________ Teacher(s): ____________________ Start/end times: _________________________
Were students able to find the surface area of a given rectangular or triangular prism?
Did students successfully transfer knowledge to break down real-world problems involving triangular and rectangular prisms?
Did students understand the value of using a net for finding surface area and successfully use this skill?
HCPSS Secondary Mathematics Office (v2); adapted from: Leinwand , S. (2009).
Accessible mathematics : 10 instructional shifts that raise student achievement. Portsmouth , NH : Heinemann .

Lesson Title: Surface Area__________________________ Course: _Common Core 6___________________
Date: _____________ Teacher(s): ____________________ Start/end times: _________________________
Practice Problems—Index Cards
1.
A door that is 30 inches wide, 84 inches high, and 1.5 inches thick is to be decoratively wrapped in gift paper. How many square inches of gift paper are needed? (Glencoe Pre-Algebra Student
Practice reproducible workbook 11-4)
2.
Ms. Frank is going to wallpaper a living room with dimensions 24 feet long, 18 feet wide, and 8 feet high. What surface area does Ms. Frank plan to wallpaper? (Glencoe Pre-Algebra Student
Word Problem reproducible workbook 11-4)
3.
A museum curator needs to order a display case for a small artifact. The case needs to be a rectangular prism and made entirely of clear plastic. The bases must each measure 1
1
2
feet by 1
3
4 and the sides must each measure 3 feet high. Find the cost of the case if the clear plastic costs $10 per square foot. (Glencoe Pre-Algebra Student Word Problem reproducible workbook 11-4)
4.
The Ramirez family is going to put vinyl siding on a shed. They will cover all four walls cost for their shed? (Glencoe Pre-Algebra Student Word Problem reproducible workbook 11-4)
5.
FPS, a shipping company, uses a container in the shape of a triangular prism to pack blueprints, posters, and other items that can be rolled up to fit inside the container. What is the surface area of the box? (Glencoe Pre-Algebra Student Word Problem reproducible workbook 11-4)
HCPSS Secondary Mathematics Office (v2); adapted from: Leinwand , S. (2009).
Accessible mathematics : 10 instructional shifts that raise student achievement. Portsmouth , NH : Heinemann .

Lesson Title: Surface Area__________________________ Course: _Common Core 6___________________
Date: _____________ Teacher(s): ____________________ Start/end times: _________________________
Homework: Tissue Box Problem
Ally sews together pieces of plastic canvas to make tissue box covers. For which tissue box (Box A or
Box B) will she use more plastic canvas to cover the sides and the top?
Box Length
(in.)
Width
(in.)
Height
(in.)
A 9 4 5
B 5 5 6
Source: Microsoft Clip Art
HCPSS Secondary Mathematics Office (v2); adapted from: Leinwand , S. (2009).
Accessible mathematics : 10 instructional shifts that raise student achievement. Portsmouth , NH : Heinemann .