Nets and Surface Area

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Objective

SWBAT: • Build a given 3D figure using manipulatives. • Create and label a net for a prism or pyramid. • Find the surface area of rectangular prisms, cubes, triangular prisms and pyramids.

Big Idea

What is surface area? How can we use nets to help us find surface? Students work with manipulatives to build 3D figures, create nets, and calculate surface area.

Do Now

5 minutes

See my Do Now in my Strategy folder that explains my beginning of class routines.

Often, I create do nows that have problems that connect to the task that students will be working on that day.  Today I want students to start thinking about covering 3D figures.  Some students may realize that there are three sets of matching faces and use these calculations to find the surface area.  Other students may try drawing a net to help them.  A common mistake is that students confuse covering a 3D figure with filling a figure.  Some students may find the volume rather than the surface area. 

I ask students what strategies they are thinking about to answer the questions.  I call on students to share what they think and why.  I have a sample rectangular prism that students can use to explain their thinking.  Students are engaging in MP3: Construct viable arguments and critique the reasoning of others.

Problem

5 minutes

I show students that we can create a net for the rectangular prism.  Some students struggle to use the three labeled dimensions to label the other sides of the net.  I explain that each rectangular prism is composed of three matching faces.  Two faces that fold together to make one edge must share the same measurement. 

Once we have labeled all of the dimensions, I ask students “How can we figure out the least amount of paper it would take to cover this box?”  I want students to realize that they can find the area of the faces and add them together.  Typically you would need more paper to wrap the box, but the question asks for the least amount.  

Surface Area Notes

5 minutes

We fill in the notes and complete the examples together.  I want students to look for patterns when finding the surface area.  For instance, with a cube all of the faces are identical so once we find the area of one face we can multiply it by six to find the surface area.  I do not introduce the formulas for surface area of a cube and rectangular prism.  I want students to continue working with a strategy that works for them.  If students find shortcuts on their own, I have them explain them to the class and emphasize why they work.  Students are engaging in MP8: Look for and express regularity in repeated reasoning.

Building and Measuring

15 minutes

Notes:

  • I use polydrons as manipulatives for this part of the lesson. I have a prism set and a pyramid set.
  • I take the pieces that create rectangular prisms, cubes, triangular prisms, and pyramids and put them in their own separate plastic bag.  I label each bag with a number. I measure the base and height of each figure in centimeters and label it using sharpie on the pieces.
  • Before the lesson I Create Heterogeneous Groups of 3-4 students.
  • I tell students that they can use their Naming 3D Figures sheet from the previous lesson.

We go over directions and expectations.  As students work I walk around to monitor student progress and behavior.  Students are engaging in MP5: Use appropriate tools strategically, MP6: Attend to precision, and MP8: Look for and express regularity in repeated reasoning.

 If students are struggling, I may ask them one or more of the following questions:

  • What 3D figure can you build?  How do you know?
  • How can you create a net for this figure?
  • Is this the only net that works?  Why or why not?
  • How can you find the surface area?  What do you need to know?

When a group has completed a prism or pyramid, I quick scan their work.  If they are on track, I give them a different figure.  My goal is for each group to work with a triangular prism and a pyramid.  If students complete both pages, they can answering questions for another figure.

Practice

10 minutes

Note:

  • I Post a Key for these problems around the room.

As students work I walk around to monitor student progress and behavior.  If students are struggling, I may ask them one or more of the following questions:

  • What do you know? What are you trying to figure out?
  • How many faces does that 3D figure have?  What shape is each face?
  • How can you find the surface area?  Why does that work?

When students complete their work, they raise their hands.  I quickly scan their work.  If they are on track, I send them to check with the key.  If there are problems, I tell students what they need to revise.  If students successfully complete the problems they can move onto the challenge problems. 

Closure and Ticket to Go

10 minutes

For the Closure, I have students turn to the closure problem.  I give students time to work on it.  Students participate in a Think Pair Share.  I call on students to share their answer and explain their thinking.  Students are engaging with MP3: Construct viable arguments and critique the reasoning of others and MP8: Look for and make sense of repeated reasoning.

I pass out the Ticket to Go and the Homework.