## Nets, Surface Area & Desmos

Before explaining the lesson, I’d like to thank Monica, Allison and Peytra for allowing me to field test this Desmos Activity Builder with their students. If it wasn’t for their flexibility, I wouldn’t have the opportunity to refine the activity. I value their innovative spirit and feedback.

The initial purpose in creating the interactive rectangular prism net on Desmos was for students to investigate nets & surface area by first creating a net on the computer and then recreate it as a 3-d model.  Embedded in the process was a discussion of surface area.

My initial plan was successful. Monica’s students were able to recreate their prism and turn it into a 3-d model. Although, we agreed the surface area discussion required more attention.  I went back to work and built in a few challenges.

The challenges uncovered a new deficit – Spacial reasoning.

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## Day 1:  Exploring Nets

For the day 1 challenges, I suggest the student to computer ratio be 2:1

Slide 1:  This slide was challenging for some of the 6th grade students.  The reason? Students counted the small boxes instead of looking at the number lines.  Many students stated the length and width of the red rectangle as 8 by 4 units.  This lead to a whole class discussion on reading the axes/number lines.

I had tried multiple ways to format the grid.

1. Since the zoom buttons cause the grid squares to change size, I turned off the Desmos grid and used lists to establish a set grid.  Students could determine dimensions easily but the list generated grid lines slowed the movements of the prism.  Students and teachers were frustrated.  My gratitude goes out to Allison who could see the merit of the activity through the computer glitches.
2. For the next day, I used the number line.  No delays. Yay!   Students ignored them. Boo!

Slide 2:  Interacting with the Net.

Figure 1                                                          Figure 2

Figure 1:  You can’t force the conversation.  For the earlier classes, my plan was to emphasize how the sides connected to each other.  My words fell on deaf ears. Conversations within groups were non-existent without multiple prompts. Clearly students weren’t ready for this discussion.

Figure 2:  By the time I ran the lesson in Peytra’s class, I simply asked students to describe how the dots moved.  This request worked.

Slide 3:  Stop Sign.  This is when all the discussions occurred.

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Slides 4 – 8:  Challenges 1 – 5

Students progressed through 5 challenges.  When they created the desired net, a little congratulations guy pops up.

Student reflection:  At first, I wasn’t sure what to do.  But once the little guy popped up, I studied the picture to figure out what I did right.

In the works:  My colleague, J.J., threw out the idea of programming the net to fold into its respective 3-d prism. Since those programming commands currently escape me, I programmed the folded cube to pop up once the challenge was met.

At the moment, only 1 challenge has the 3-d image.  The others are in the works.

My aha moment: As the students moved through the challenges, discussions increased. Peytra and I noticed 2, 3 and occasionally 4 students standing around a computer discussing their strategies. The vibe in the room was upbeat and academic.

The challenges uncovered and addressed a deficit in student learning. Their need to explore spatial relationships of 2-d nets was apparent . I turned to Peytra and said, “This is what day 1 needs to focus on – Exploring interactive nets and nothing else!” Finally, the progression of the concepts, to best serve students, became evident.

• Day 1:  Investigating 2-d nets (Desmos)
• Day 2:  Discussing Surface Area (Desmos)
• Day 3:  2-d nets to 3-d models

### Oh, they went there….

While computers were shutting down, students were given 30 seconds to compose a response to the following prompt:  What did you learn today?  Discussion starters spoke first. The others shared going in a clockwise direction.  Then, the sharing turned whole group.  The results are pictured below.

First I heard:

• I learned how to use the number line to find the length size
• I learned how to move the dots.

Then I heard:

• It was difficult.
• I solved challenge #2 – Mind Blown!!
• It was hard to match up the sides.
• The challenges made me think.  There was more to it than just moving the dots up and down
• I had to create a plan.

My intent from the beginning was to discuss how one side of a prism effects another.  Before exploring the challenges, students weren’t ready for this conversation. I tried forcing it without luck. I dropped the conversation and moved on.

After navigating through the challenges, interacting with nets and observing the patterns, students not only were ready but they started the conversation.    Students were able to explain which sides effected another and how. 🙂

This experience inspired me to create slide 9:

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## Days 2 & 3- Discussing Area & Creating 3-d Models

Slide 10:  Starting the discussion of area

Slides 11 & 12:  Expanding the area discussion to include surface area

Slides 13 & 14:  Challenge 8 & 9 reverses the area conversation.

Slide 15:  Time to transition from computer work to partner/group/whole class discussion. This is the teacher’s opportunity to discuss the intricacies of surface area and clarify misconceptions.

Slide 16 & 17:

1. Students create their own rectangular prism on the last slide and then recreate the net on the design worksheet. Students may use the same or different color combination
2. Students complete the math calculations
3. Once the surface area has been calculated, students are to recreate their net one
last time on graph paper.
4. This last net is then cut out, folded and taped together.
5. Students, happily, take home the 3-d model.

Instructional Technology Coach. Desmos Fellow. Google Level 1 Certified. SoCal transplant. New Englander at heart. Lover of yoga, dogs, green smoothies and coffee creamer
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### 13 Responses to Nets, Surface Area & Desmos

1. ekabekeko says:

Hi Jenn. I find your blog very interesting and very useful. I like your commitment as you support students and ways looking to better understand, learn and transmit their knowledge.
It made me very happy that challenges worked well (Nets, Surface Area and Desmos) and students have begun discussions. In the end they were even happy and have brought 3D models home 🙂
As a future teacher, I’m worried and I interested in how teachers handle it when challenges burdening students and they have no joy?
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Liked by 1 person

• Kathrin says:

I thought about the same problem. So would it be an option to build in something like the little congratulations guy for help if they are close to solve the problem but need help for the last step. So he could say “Did you think on the right dimension”, “You are close to solve the problem try on” and somethin like that. Would it be a motivaton and help or demotivating? What else could be done?

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• CathiVd says:

I thought about the same problem. So would it be an option to build in something like the little congratulations guy for help if they are close to solve the problem but need help for the last step. So he could say “Did you think on the right dimension”, “You are close to solve the problem try on” and somethin like that. Would it be a motivaton and help or demotivating? What else could be done?

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• cathyvd says:

I thought about the same problem… So would it be an option to build in something like the little congratulations guy for help if they are close to solve the problem but need help for the last step. So he could say “Did you think on the right dimension”, “You are close to solve the problem try on” and somethin like that. Would it be a motivaton and help or demotivating? What else could be done?

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Thank you for reading – I appreciate your reflective comment! During the challenges, many students enjoyed figuring out the solution whereas a couple kiddos were almost paralyzed. These students sat staring at their computer not sure of what to do. For those students, I paired them up with a peer who understood the process.

Let’s say “John” was confused and “Mark” knew what to do. I would ask Mark to explain challenge #1 to John. Mark was not allowed to touch John’s computer. His job was to talk John through the process and explain the choices he made. I would periodically follow up by asking John about the information that Mark shared.

It’s imperative that Mark let John manipulate the net. If he swooped in and finished the challenge both students would miss out on a learning opportunity. By requiring Mark to talk John through the challenge, both students are now active participants in their learning. John learns how to work with the net. He gains the confidence and skill needed to tackle the next challenge. On the other hand, Mark verbalizes his mathematical and strategic process – another skill that our students need to develop. Their time together strengthens the model of a student centered classroom.

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2. Kathrin says:

I thought about the same problem. So would it be an option to build in something like the little congratulations guy for help if they are close to solve the problem but need help for the last step. So he could say “Did you think on the right dimension”, “You are close to solve the problem try on” and somethin like that. Would it be a motivaton and help or demotivating? What else could be done?

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3. cathyvd says:

Sorry! I just wanted to write it only one time. But there was a technical problem… ^^”

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No worries! You pose a thoughtful suggestion. Some students may benefit from encouraging prompts informing them of their progress. It is possible to program another “guy” stating that the dimensions of their black, blue or red rectangle are correct. This information can be stored in a folder and turned “on” when needed.

What do I mean? Let’s say I programmed encouraging comments. I would store all these commands in a folder to be used when necessary. At the start of the challenges, the folder is turned off. There’s a circle to the left of the folder. If the circle is empty, then the folder is turned off and nothing inside the folder can be seen. When the folder is activated, the circle displays a small picture of a folder. At this point, the contents can be seen. Therefore when a student creates a rectangle with the correct dimensions, one of the encouraging messages will pop up.

First, I’d pair up a struggling student with a classmate as mentioned in the above comment (in response to Ekabekeko. John struggles and Mark helps). It’s important to create a classroom culture where students learn how to work together and support one another. Once the two students complete challenge #1, Mark could return to his computer and the teacher could turn on the folder for John. The support folder provides a nice scaffold for John to find individual success.

Liked by 1 person

• cathyvd says:

Thank you very much for your fast replay. It is very detailed and that helped a lot to understand everything. ^^
I hab another question. How did the Students glued the models together, with tape? Or is it a good idea to expand the models to have an adhesive edge?

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1. We used clear tape.
2. We didn’t expand the models.

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4. cathyvd says:

Thank you very much for the info ^^

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