Visualizing Geometry
Lesson Objective: Use properties of similarity and build 3D models and cross-sections
Grade 7 / Math / Geometry

#### Thought starters

1. How is tracing paper used to increase understanding of similar figures?
2. See how Ms. Whicker uses blocks and drawing to help students visualize three-dimensional objects How do students create cross sectional views from 3-D objects?
6 Comments
This video was awesome. I am studying to be a teacher, and I used this as a mock up lesson plan. Thank you for providing this resource.
Recommended (2)
I would like to teach similar polygons on my smart board. Could you forward me that part of your lesson? I teach 6th grade. I think I might try surface areas with blocks. Thanks, Barbara
Recommended (0)
Hi Barbara, If you look to the right of this discussion thread you will see all of the supporting materials for this lesson. Thanks!
Recommended (0)
This lesson gave me an awesome view of how to teach this lesson.
Recommended (2)
I am a new teacher and I have a self contained class with 3 5th graders, 3 6th graders and 1 7th grader. I know I will be using the Teaching channel to help me through the next 6 months. Thank you
Recommended (0)

#### Transcripts

• Great Lesson Ideas: Visualizing Geometry with Amy Whicker

Whicker: [00:00:08] My name is Amy Whicker. I teach seventh grade math, and

Great Lesson Ideas: Visualizing Geometry with Amy Whicker

Whicker: [00:00:08] My name is Amy Whicker. I teach seventh grade math, and I have a great lesson to share with you today about visualizing geometry. [00:00:15]

[00:00:15] All right, today guys, we’re going to be looking at visualizing geometry. [00:00:19]

[00:00:19] My lesson has three different components of similar figures; three-dimensional views and cross sectional views. By the end of the lesson, I want my students to be able to set up proportions and solve for missing sides on the similar figures. I want them also to be able to take a three-dimensional figure and be able to go to the two-dimensional views by setting up manipulatives. Also I want them to be able to go from 3-D objects like cylinders and prisms and cones and create the cross sectional views. [00:00:51]

[00:00:53] We first did similar figures. The students had some figures on their desk and instead of them trying to visualize rotating it in their minds—which sometimes works, sometimes doesn’t—we had them take tracing paper and trace over the figures. Then move the tracing paper, flip it, rotate it, slide it around on their desks and then be able to figure out what matches with what. We did the same thing on the smart board using the flip and rotate features and have them do some color coding so they can see what goes with what, and therefore, they can set their proportion a whole lot more accurately. [00:01:28]

[00:01:28] Sixteen, there we go. [00:01:31]

[00:01:33] The second phase was doing two and three-dimensional views of things. [00:01:37]

[00:01:37] So what I want you to do now is with the blocks that are in your bag, I want you to build a figure that you see in the next slides. [00:01:44]

[00:01:45] I love using the manipulative for geometry because it gives the student something hands on, and it gives them a better understanding of the overall geometry concepts. [00:01:54]

[00:01:55] If we describe the figure, it’s kind of like stair steps going in two different directions. [00:02:00]

[00:02:00] I think it’s better to have the student actually build the figure with real blocks and actually have it there in front of them. [00:02:06]

Child: [00:02:06] Because I’m a visual learner, and I like to see things and do something with my hands. You get to use the blocks, just makes it easier for me instead of me writing it or reading it. [00:02:17]

Whicker: [00:02:17] Okay and you build from there. How many are going to be inside of that? [00:02:21]

[00:02:22] The other thing we did was kind of a challenge with that, where they had to go from the two dimensions to the three-dimensional. [00:02:29]

[00:02:29] All right, this is what we need to do now. If you look at the next slide that you have, you’ve got a picture of three different views. You want to build that three-dimensional figure based on those views. [00:02:39]

[00:02:39] That’s what we were doing on the document camera, having the kids actually build the figure. [00:02:44]

[00:02:44] Can you build the top view for us first using those blocks? [00:02:47]

[00:02:48] So that’s kind of the challenge for students, and, if they don’t have any blocks in front of them for them to use, it just doesn’t work. Then the third phase was cross-sectional views which is taking like cylinders and prisms and cones and pyramids, and cutting them up into different slices and then figuring out what it looks like when we open it up. [00:03:08]

[00:03:08] We’re going to take this cylinder made of Play-Doh, and you can see that I’ve kind of cut it up a little bit. We’re going to be cutting it two different ways. We need to see what shapes result when I cut it and I open it up. If I cut it parallel to the base, that’s cutting it this way, so I’m going to open it up this way. What shapes do we think is going to result when I open it up that way? Brandon what do you think? [00:03:30]

[00:03:31] Yeah if I open it up this way, I’m going to have two circles there. [00:03:35]

[00:03:36] Then had them see if they got the idea with some remotes. So the remotes kind of help me see what they’re really thinking. [00:03:43]

[00:03:43] Okay looks like some chose A, most chose B. Now guys the correct answer on this one is actually A. Because if you look at it from above and you slice this cone, you’re going to see a circle, but underneath that circle you’re going to see another circle which is your base. So it’s circle on top of circle. That’s why it’s two circles. [00:04:08]

Child: [00:04:09] I like this class cause we get to get up and move around and learn about geometry, and geometry is fun, and it’s not as hard as other problems in math. [00:04:17]

Whicker: [00:04:18] So this is a great lesson. It’s a foundation for all geometric type concepts. I’m going to hook you up with lesson plans, manipulatives and visuals that can help you make this one of your lesson plans. [00:04:30]

#### School Details

Northwest Middle
5501 Murray Rd
Winston Salem NC 27106
Population: 957

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Amy Whicker
Math / 7 / Teacher

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