3D Figures and Nets

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.  For this lesson I want students to review their work with 3D figures from the previous two lessons.  This knowledge will help them to identify patterns and properties of successful nets.  Common mistakes are that students confuse the vocabulary terms for each other.  If students are still struggling, encourage them to use their Naming 3D Figures Reference Sheet.  Some students will still struggle to count the edges, faces, and vertices from a drawing.  Feel free to give these students the 3D figures used in the previous lesson so they can check their work.

When checking answers, I am sure that students are using accurate vocabulary.  I do not accept “prism” or “pyramid” as adequate answers.  I push students to give the most specific names for the 3D figures. Mathematical Practice 6: Attend to precision.

After the Do Now, I have a student read the objectives for the day.   I have a volunteer read about Syria and the dice.  I ask students to make predictions of which designs will form dice just by looking.  See the video Exploring Cube Designs in the resource section for more details.

Video: http://learnzillion.com/lessons/1219-represent-threedimensional-figures-with-nets

I play the video and pause it frequently for students to take notes and ask any questions they have.  I want students to make the connection between the number and type of faces a 3D figure has and its net. 

For the guided practice, students can draw nets on the Designing Nets Paper if they prefer.  It is important that students recognize that the rectangular prism as two square faces, which means that all of the rectangles must have the same dimensions.  If students are struggling to name the prism in #3, I encourage them to use their Naming 3D Figures Reference Sheet.

Polydons are another type of manipulative that students can use to investigate different nets that will create a cube (among other prisms).  http://illuminations.nctm.org/LessonDetail.aspx?id=L793

Here are some questions I may ask before moving on:

• What is a net?  How does it relate to a 3D figure?  How is it different?
• Can a 3D figure have more than one net?  Why or why not? (Prove it)
• Why are nets helpful?  What can we use them for?

If students understand the concepts in the video and practice and need extension, here are a couple tasks I may give students:

• Design 3 different nets for the rectangular prism in the guided practice: 2 that work and 1 that do not.  Show the designs to your partner and ask them to figure out which nets match and which one does not.
• Design 3 different nets for the triangular prism in the guided practice: 2 that work and 1 that do not.  Show the designs to your partner and ask them to figure out which nets match and which one does not.

I have students work on these problems independently.  They check in with their partner if they are stuck, before asking me a question.  If students finish a page, they raise their hand and I quickly scan their work.  If they are on the right track, I tell them to check the key.  See Posting A Key video in my Strategy Folder for more details.

Some students will struggle to determine appropriate nets just by looking at designs.  Here are some actions I might take:

• Have extras copies of these problems (copied single-sided) so that students can cut them out and test them.  For example, I had a student who said that none of the triangular prism nets on page 2 would work.  I told her to cut them out and test them.  She then revised her answer to say that design B worked.  She previously thought that they triangle bases had to be directly across from each other in order to for the net to work.
• Have students build each design using other manipulatives, like polydrons.
• Ask students what kind of 3D figure they must make.  How many faces does that 3D figure need to have?  What shapes are those faces?

If students successfully complete these problems and have extra time I may ask students to:

• Complete the Extra Practice Problems
• Serve as a tutor for another student
• Design as many different nets that would successfully create a square pyramid (problem 3).

Before moving on I have students stop working and look at problem 1.  I want students to explain which nets work and why they work, as well as which net does not work.   I want students to recognize:

• These nets are creating a rectangular prism that has a rectangle as its base (unlike the guided practice problem that had squares).
• Each rectangle (there are 2 distinct rectangles) has a matching face.  To demonstrate this I have students label corresponding faces with numbers (1, 1, 2, 2, 3, 3)
• Some students will explain how they “fold” the net in their mind to see if it works.  Other students may have cut them out and can prove that they work.
• Net E has all of the correct faces, but it has the matching faces next to each other which will not work.  (I have this net cut out so that I can prove it does not work by folding.)

We return to Syria and her cube nets.  I have students conduct a think-write-pair-share in partners. I want students to write their predictions and their strategies for creating their predictions.  See my Think Write Pair Share video in my Strategy Folder for more details. 

Possible strategies students may share (I will share strategies that students don’t bring up):

• Counting faces and making sure they match the number of faces for that 3D figure
• Choosing one face as the base or bottom and imagining you fold the other faces around it (some students may even make a gesture with their hands as they are doing this)
• Cutting the designs out and folding them (This is okay as a last resort, or to settle a dispute, but I encourage my students to use other strategies to replace this one)
• Using other manipulatives (like polydrons) to create the net and test it (Again this is okay as a last resort, or for a student who continues to struggle, but the goal is to transition to using visual strategies)

Revisiting Syria’s cube nets served as a closure for this lesson.  I use the last five minutes for students to complete the ticket-to-go and self-reflection independently.  See my Ticket to Go video in my Strategy Folder for more details.