Expectations:

Measurement

E1.2 construct three-dimensional objects when given their top, front, and side views

E2.5 create and use nets to demonstrate the relationship between the faces of prisms and pyramids and their surface areas

teacher background

• Math Background: Constructing, Composing and Decomposing 3-D Objects: Misconception Chart

Face to Face Classroom Unit: Investigations in Geometry: Net Quest

Source: Small, M. (2016) Open Questions: For the Three-Part Lesson Grades 4-8 Geometry and Spatial Sense, Data Management and Probability. Pg.92

1. Some people say that isometric sketches of 3-D figures are not very useful because you can’t always see the whole structure? Do you agree? Why or why not?

Sample Response

I agree, If your structure has a lot of arms that stick out in different places, it is not very easy to see them on a an isometric sketch. If you have to build a duplicate of a structure and you have to do so using only an isometric sketch, the sketch will not be very helpful. It would be a lot better to see the full structure that you are going ot make so that you can see all its parts. As another option, it would be better to have images of all the different views of the structure instead of just one isometric sketch of it. OR I think that isometric sketches are very helpful because they allow you to see parts from three different views at the same time. Regular sketches only let you see one view at a time.

2. How is it possible for sketches to the same 3-D figure to look so different from one another?

Sample Response

It is possible because you can look at 3-D figures from many different perspectives: the front, back, sides, top and bottom. OR When you are sketching a 3-D figure using 2-D sketches, it is not possible to show the entire figure in one sketch. So, different views will look a lot different from one another because figures can look a lot different depending on the part you look at.

3. If you could see only three views of a link cube structure to help you build it, which of the following views would you choose? Which views would you not choose? Why?

a)Top, left side b) bottom, front c) right side, back

Sample Response

If I could see only three views, I would want to see either the top or the bottom view. I would also want to see one of the side views and either the front or back view. I think that these views would give me the most information because the top and bottom views will already look a lot alike because they will show the same number of cubes. The same is true fro the side views and for the front and back views. So, I wouldn’t want to see both views from each of those sets of views since I wouldn’t get a lot of extra information about the structure as possible. OR I think that is it best to see both sides and the front. This would allow me to get a good sense of the structures’s shape and I would get to see most of the colours in the structure as well. OR It depends on the shape of the structure because each view could supply either a lot of information or a little information about the structure. It is too hard to choose without knowing more about the structure.