Need help with this word problem

[jtpieters]

How do I help my second grade daughter solve a homework problem like this??

Problem: Kyle and Joey were building a tower out of 3D solids during Math centers. They used three different shapes. When they looked at their tower, it had 24 edges, 13 faces and 17 vertices altogether. What three shapes did Kyle and Joey use?

 

[tkhunny]

Hokey smokes! Well, let's just try it.

1 cube

12 edges
6 faces
8 vertices

That leaves

12 edges
7 faces
9 vertices

Another cube

That leaves

0 edges
1 faces
1 vertices

Tricky. We're down to a sphere (attach it any way you like!), leaving

0 edges
0 faces
1 vertices

Pretty close. Poke around some more.

 

[soroban]

Hello, jtpieters!

Do they use the word "vertex" with second-graders? . . . Wow!

Kyle and Joey were building a tower out of 3D solids during Math centers.
They used three different shapes.
When they looked at their tower, it had 24 edges, 13 faces and 17 vertices altogether.
What three shapes did Kyle and Joey use?

Here's my lame attempt . . .

A cube on the bottom with edges, say, 2 inches long.

Then a triangular prism.
The base is an equilateral triangle of side 1 inch.
The height doesn't matter, say, 2 inches.

Then a regular tetrahedron of side 1 inch.
(Its triangular base is matched to the triangular top of the prism.)

I counted: 24 edges, 13 faces, and 15 vertices.

Oh, well . . .

 

[Denis]

How do I help my second grade daughter solve a homework problem like this??

Phone the teacher...

 

[lookagain]

They used three different shapes. ... / / ... What three shapes did Kyle and Joey use?

jtpieters, "shape" is not the word you want to use here. You are intending three solids
(specifally with plane faces) that have different shapes.

But you could have been stating that at least three solids are to be used, as long as there
are three different shapes among them.\

"Shape" is not the same as a solid when used in "different shapes," It is one of the qualities
of a solid.

You should state the equivalent to:

There are three solids (which are polyhedra), all having different shapes from each other,
that are used to build a tower.

Even then, you have not given rules as to how the pieces can be touching/connected.

I am showing two examples (to explain where the solids might be adjoined). However,
the following is different from the intended problem's set-up. The following is where
the two solids are the same shape, and more specifically, I am using two cubes of the
same size), but of different orientations:

1) A cube has a face joined flush with a face of the other cube.
There are still 6 faces, 12 edges, and 8 vertices, when compared
to just one cube.

2) The cubes' faces are set against each other with all of their edges either parallel or
perpendicular to each other (allowing for edges to be extended), respectively.
But this time, their centers are off. A cube is "pushed in" with respect to another.

 

[soroban]

Hello, everyone!

Kyle and Joey were building a tower out of 3D solids during Math centers.
They used three different shapes.
When they looked at their tower, it had 24 edges, 13 faces and 17 vertices altogether.
What three shapes did Kyle and Joey use?

I was inspired by lookagain's ideas ... and found a solution.

A cube on the bottom with edges, say, 2 inches long.

A corner is cut off so it looks like this:

              * - - - - - - *
            *             * |
          *           ..*   |
        *         ..*::*    |
      * - - - - *:::::*     |
      |           *::*     |
      |             *       *
      |             |     *
      |             |   *
      |             | *
      * - - - - - - *

Then a triangular prism.
The base is an equilateral triangle of side 1 inch.
The height doesn't matter, say, 2 inches.

Then a regular tetrahedron of side 1 inch.
(Its triangular base is matched to the triangular top of the prism.)


I counted: 24 edges, 13 faces, and 17 vertices.

 

[JeffM]

Congratulations soroban. YOU passed 2nd grade. I on the other hand failed.

 

[mmm4444bot]

A corner is cut off so it looks like this:

              * - - - - - - *
            *             * |
          *           ..*   |
        *         ..*::*    |
      * - - - - *:::::*     |
      |           *::*      |
      |             *       *
      |             |     *
      |             |   *
      |             | *
      * - - - - - - *

Where do you come up with these? Do you hold an AA degree (ASCII Arts)?