# Geometry: Simple 3D Objects

Time Required: Two 60-minute sessions
Skill Level: Beginner
Recommended Grades: 9th to 12th

In this activity, students will work with a partner to build three separate models of 3D simple objects. They will create models of a cube, a rectangular prism, and a square based pyramid. The students will then calculate the surface area, volume, total number of vertices, and sum of internal angles. They will apply these ideas to concepts of 3D geometry.

Note: Any links outside of the3doodler.com are optional resources. We can’t ensure their upkeep or accuracy. ### Knowledge

Students have
• had an introduction to geometry in 3D

• prior instruction on how to calculate surface area, volume, total number of vertices, and sum of internal angles

### Objectives

Students will
• work together in pairs to build the 3D object models

• compare and contrast the differences between the objects

• use 3Doodler pens to build 3D models of a cube, rectangular prism, and square based pyramid

• better understand how to picture or imagine simple objects in 3D

### Materials

Students will need
• 3Doodler pen

• Scissors

• At least 2 different colors and 4 strands of ABS 3Doodler Plastic

### Lesson Plan

#### Instructions

Step 1

Begin the lesson by handing out the Geometry: 3D Simple Objects Worksheet. This will guide the lesson for the students. The students are expected to fill out the “concept” and “questions to aid in calculations” on the worksheet during the lesson.

Step 2

Give the students instructions on the length of each side (in centimeters) of the cube, rectangular prism, and the square based pyramid. Write the lengths on the board at the front of the class so all of the students can refer to it actively.

Step 3

Discuss how the final units are determined for surface area (cm2) and volume (cm3).

Step 4

Discuss the differences between 2D and 3D objects. Encourage the students to ask questions and compare objects. Ask them how many spatial dimensions are in the real world. Give the example of the 3D object of the room in which they are sitting.

Step 5

Ask the students, “What is a vertex?” and discuss.

Step 6

Give the students all of the equations in the “questions to aid in the calculations” section of the worksheet. Give them the equations in a discussion format, whether comparing the equations to one another, or having them look it up in their textbooks.

Step 7

Instruct the students to review diagrams of 3D simple objects in their textbooks or online.

Step 8

Discuss the applications of geometry in real life and engineering. Refer them to read the article, “How is Geometry Used in Real Life?” by Laurie Brenner in the possible extensions section of this lesson plan. Give the example of CAD (computer aided design) models for engineering. Refer them to classes they may take at their school that use CAD modeling as well as the other link in possible extensions for Tinkercad.

Step 9

If the students are not familiar with the 3Doodler pen, then give them a demonstration on how to build the cube. *See Appendix. If they are familiar with how to use the 3Doodler pen then continue to step 9.

Step 10

Given that the students are familiar with the 3Doodler pen, divide the students into pairs and handout the 3Doodler pens and ABS plastics with at least 2 colors. *See Appendix.

Step 11

Circle to assist students and ask them questions about their models. Encourage the students to work together to calculate the worksheet problems.

#### Wrap Up

Students will build the models of their three simple 3D objects and fill out the worksheet. Students will share on Twitter. @3Doodler #3DoodlerEDU

#### Assessment

The teacher will assess students’ work based on their 3D models, written responses on the worksheet, as well as verbal responses.

#### Possible Extensions

• Answer the question students often ask, “When will I have to use this in real life?” by having them read this article: “How is Geometry Used in Real Life?” by Laurie Brenner

• Tinkercad: 100% free 3D modeling software meant for students. It introduces students to the concepts of CAD, 3D printing, and laser cutting. Note: the creators of Tinkercard is Autodesk, a popular and well-known CAD software used by professional engineers. tinkercad.com

#### Vocabulary

• cube - a regular three-dimensional shape composed of six square faces.

• geometry - a branch of mathematics that deals with the measurement, properties, and relationships of points, lines, angles, surfaces, and solids; broadly : the study of properties of given elements that remain invariant under specified transformations.

• rectangular prism - In geometry, a rectangular prism can be defined as a 3-dimensional solid shape which has six faces that are rectangles. A rectangular prism is also a cuboid.

• square based pyramid - A three-dimensional geometric figure with a square base and four triangular sides that connect at one point. An example is the Great Pyramid of Giza.

• sum of internal angles - The sum of the angles on the inside of a polygon formed by each pair of adjacent sides.

• surface area - The total area of the surface of a three-dimensional object. Example: the surface area of a cube is the area of all 6 faces added together.

• vertices - each angular point of a polygon, polyhedron, or other figure. A meeting point of two lines that form an angle. The point at which an axis meets a curve or surface.

• volume - Volume is the measure of the amount of space inside of a solid figure, like a cube, ball, cylinder or pyramid. It's units are always "cubic", that is, the number of little element cubes that fit inside the figure.

#### Educational Standards

Common Core
CCSS.ELA-LITERACY.WHST.9-10.9

Draw evidence from informational texts to support analysis, reflection, and research.

In This Lesson

Students will base models of 3D simple objects on their textbooks and in-class reflections.

Common Core
CCSS.ELA-LITERACY.WHST.9-10.4

Produce clear and coherent writing in which the development, organization, and style are appropriate to task, purpose, and audience.

In This Lesson

Students will compare and contrast different 3D objects on a worksheet and together based upon their prior learning of the subject.

ISTE
1C

Use technology to seek feedback that informs and improves their practice and to demonstrate their learning in a variety of ways.

In This Lesson

Students will use the 3Doodler pens to visually demonstrate three simple objects in three dimensions..

ISTE
4C

Students develop, test and refine prototypes as part of a cyclical design process.

In This Lesson

Students build models of 3D objects and can refine those models if determined that it is incorrect.

ISTE
4D

Exhibit a tolerance for ambiguity, perseverance and the capacity to work with open-ended problems.

In This Lesson

Students will work to answer concept questions related to geometry and work to build 3D models of three simple objects.

ISTE
5C

Students break problems into component parts, extract key information, and develop descriptive models to understand complex systems or facilitate problem-solving.

In This Lesson

Students build their 3D objects edge by edge and identify their vertices. Then they will calculate the surface area, volume, total number of vertices, and sum of interior angles for each object and compare.

ISTE
6C

Students communicate complex ideas clearly and effectively by creating or using a variety of digital objects such as visualizations, models or simulations.

In This Lesson

Students create models of 3D simple objects using 3Doodler pens and discuss those ideas via a worksheet and with a partner.

ISTE
7C

Students contribute constructively to project teams, assuming various roles and responsibilities to work effectively toward a common goal.

In This Lesson

Students will work together to answer questions and build the 3D objects.

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