##
* *Reflection: Developing a Conceptual Understanding
Nets and Surface Area - Section 4: Building and Measuring

The polydrons were a wonderful way for students to practice building figures and finding their surface area. I asked students at the end of the lesson about whether or not they were helpful. Most of them expressed that they found the polydrons helpful. Some students said looking at flat, paper nets and imagining what they will create when you fold them is difficult, but the polydrons helped them understand the connection between the net and the 3D figure. Students also used their “Naming 3D Figures” sheet as a resource. A student in this group used the sheet to explain why their figure was a rectangular prism.

Many groups struggled a bit to build use all their pieces to build a 3D figure. Triangular prisms seemed to be difficult for groups, especially the isosceles triangular prisms. This group worked together to connect the pieces, but struggled to figure out a way to create a 3D figure. After a few minutes, I returned to this group and they had created this net for a triangular prism. When I asked them how they did it, they shared that they had kept trying different possibilities until they figured it out.

*Developing a Conceptual Understanding: Group Struggles and Successes*

# Nets and Surface Area

Lesson 10 of 19

## 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.

#### Do Now

*5 min*

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.**

*expand content*

#### Problem

*5 min*

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*.

#### Resources

*expand content*

#### Surface Area Notes

*5 min*

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.**

#### Resources

*expand content*

#### Building and Measuring

*15 min*

**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.

#### Resources

*expand content*

#### Practice

*10 min*

**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.

*expand content*

#### Closure and Ticket to Go

*10 min*

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.**

*expand content*

*Responding to Chamarla Brame*

Hi Chamarla. Â No, I don't post answer keys.

| one year ago | Reply*Responding to Joe Laskowski*

Thanks for your feedback, Joe! Glad I could help!

| 2 years ago | Reply

Andrea,

Â

Thank you for being a part of this.Â I really like the way you structure your lessons and they have been a big help for me.Â I did notice on Example 2 of your notes sheet for this lesson you ask the students to find the surface area of a cube and the net you supply is actually a rectangular prism.Â You may want to correct this.Â Thanks.

Â

Joe Laskowski

| 3 years ago | Reply*expand comments*

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- UNIT 1: Intro to 6th Grade Math & Number Characteristics
- UNIT 2: The College Project - Working with Decimals
- UNIT 3: Integers and Rational Numbers
- UNIT 4: Fraction Operations
- UNIT 5: Proportional Reasoning: Ratios and Rates
- UNIT 6: Expressions, Equations, & Inequalities
- UNIT 7: Geometry
- UNIT 8: Geometry
- UNIT 9: Statistics
- UNIT 10: Review Unit

- LESSON 1: Unit 7 Pretest
- LESSON 2: Perimeter vs. Area
- LESSON 3: Area of Triangles
- LESSON 4: Area of Composite Shapes
- LESSON 5: Exploring Circumference
- LESSON 6: Area vs. Circumference
- LESSON 7: Area, Perimeter, and Circumference
- LESSON 8: Classifying 3D Figures
- LESSON 9: 3D Figures and Nets
- LESSON 10: Nets and Surface Area
- LESSON 11: Show What You Know About Perimeter, Area, and Surface Area
- LESSON 12: Unit Cubes and Volume
- LESSON 13: Filling and Measuring
- LESSON 14: Designing Boxes
- LESSON 15: Geometry Jeopardy
- LESSON 16: Unit Closure
- LESSON 17: Unit Test
- LESSON 18: Quadrilaterals and the Coordinate Plane
- LESSON 19: Covering and Filling: Surface Area and Volume of Rectangular Prisms