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NAME DATE BAND

PILES OF SALT

ADV GEOMETRY |PACKER COLLEGIATE INSTITUTE

Today were going to be looking at piles of salt to illustrate geometric ideas.

1.

To begin, please google the term angleofreposeand define it: _______________________________

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2.

Like we demonstrated before, prop up a rectangular piece of cardboard/cardstock in the tin containe

Determine the angle of repose of salt: _________

At the back of this packet will be copies of the shapes you are going to use as templatesto cut out the

proper shape/size cardboard/cardstock. Onto each shape, you are going to (a) first guess what will happe

to the salt when you pour it onto the figure, (b) pour the salt onto the figure, and then (c) record what

actually happens when you pour the salt onto the figure.

3.

(a) The first shape youre going to pour salt on is this triangle.

What I think I will see when I look directly down on this figure, after pouring salt on it, is:

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What I actually see when I look directly down on this figure, after pouring salt on it, is:

(b) Now lets try to understand what is happening. Dump the salt off and start over with a clean slate.

Pour a lot of salt down near point A, and continue to pour until approximately youve filled the part of

the triangle below. What do you notice about the ridge formed?

Do this again, but filling a region near point B. And

again, filling a region near point C.

What do you notice about the ridges that get

formed?

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4. Try your hand with another triangle.

What I think I will see when I look directly down on this figure, after pouring salt on it, is:

What I actually see when I look directly down on this figure, after pouring salt on it, is:

What do you think is happening? Given any triangle, can you figure out beforehandwhat the salt will look like

If not, before you move on, cut out a few more random triangles and see what you discover. Before moving o

be sure to call Mr. Shah/Mr. Kinnell over to share what youve discovered.

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An illustration of the piles of salt!

5.

Now do the salt thing, but with a square:

What I think I will see when I look directly down on this figure, after pouring salt on it, is:

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What I actually see when I look directly down on this figure, after pouring salt on it, is:

6. And again, but with a rectangle:

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What I think I will see when I look directly down on this figure, after pouring salt on it, is:

What I actually see when I look directly down on this figure, after pouring salt on it, is:

7.

And again, but with a parallelogram:

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What I think I will see when I look directly down on this figure, after pouring salt on it, is:

What I actually see when I look directly down on this figure, after pouring salt on it, is:

8. And again, but with a trapezoid:

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What I think I will see when I look directly down on this figure, after pouring salt on it, is:

What I actually see when I look directly down on this figure, after pouring salt on it, is:

9.

And again, but with a random looking quadrilateral:

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What I think I will see when I look directly down on this figure, after pouring salt on it, is:

What I actually see when I look directly down on this figure, after pouring salt on it, is:

10.And again, but with a circle:

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What I think I will see when I look directly down on this figure, after pouring salt on it, is:

What I actually see when I look directly down on this figure, after pouring salt on it, is:

11.

And again, but with a circle with a circle cut out of it:

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What I think I will see when I look directly down on this figure, after pouring salt on it, is:

What I actually see when I look directly down on this figure, after pouring salt on it, is:

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Now cut out any shape figure youre curious about but created only with straight lines. Trace it belo

and (a) make a guess, (b) pour salt, and (c) record what you see.

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What I think I will see when I look directly down on this figure, after pouring salt on it, is:

What I actually see when I look directly down on this figure, after pouring salt on it, is:

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Now cut out any shape figure youre curious about you can use straight lines, curved lines, blobby,

holes in it, whatever! As complex as you like. Trace it below and (a) make a guess, (b) pour salt, and (c

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record what you see.

What I think I will see when I look directly down on this figure, after pouring salt on it, is:

What I actually see when I look directly down on this figure, after pouring salt on it, is:

Cardboard Cardstock figures:

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