Student Solution:
After finding out that this shape didn't fit the rules of a cylinder, we started trying names. We said that it looked like a half a leaning cylinder which we put into Pig Latin to form: Alfhayahayeaninglayylindercay. I bet you can guess why we didn't choose that one. We started brainstorming what it looked like and finally decided that it looked most like a volcano, a barnicle and that it was a polyhedron. So we threw them into the boiling cauldron and after stirring for a while, we came up with our answer: Barnicvolichedron, a nasty mix.

Being as there was no right answer to this problem, it was my favorite. This is a very good problem because it makes people use their mathematical creativity to make a geometrical shape.

The Yield Sign
In Boulder I saw a triangular yield sign that was on Broadway. When I saw it I heard Ms. Koenig say that someone could figure out the percent of red in the sign and the percent of white. I asked a tall person if they could give me the base of the white triangle which was 32 cm and the height is 39 cm. I multiplied those two numbers then divided them in half (base X height /2). I used the same formula for the r3ed triangle, but I used different numbers for the red triangle. I got 3066 sq. cm for the red triangle.

The next step I took was to figure out the space inside the red triangle. I figured this out by subtracting the white area from the red area which is 2442. I estimated that each letter in Yield was about 2 sq. cm, so I got 2450. I also estimated that around the edges was about 10 sq. cm of white so I added on to 634. Then I found out the percent by adding up 634 with 2450 and got 3084. The I divided 634 and 2450 by 3084 (part/whole) to find the percents.

The answer I got was red = about 79% of the sign and white = about 21% of the yield sign. I am pretty sure I got this right because it looks like it is correct and I checked that I added up everything correctly. But the only way I could get this answer wrong is by not having the correct measurements. I learned that some things can really be mathematically interesting. I also learned a little more about percent which might help me in the future.

The Handrails -
There are three sets of handrails on the outside of the Boulder Public Library on Arapahoe near 9th. When I saw them I instantly knew that they would make a great Math Trail problem. The problem I decided to write was "How much material (surface area) is in one handrail".

I happened to have a tape measure, so I measured the circumference. C = 5.25 in.
Then I measured the length or height of each pole:
H1 = 36.5 in.
H2 = 6.75 in.
H3 = 23.5 in.
H4 = 36.5 in.
The I added each height to get 103.25 in. Then I multiplied that by the circumference to get 542 sq. in. of surface area.

Math Trail Problem #1

I: There is a metal statue of a lady sitting in a swing on Pearl Street Mall (on Broadway, right across from Haagen Daz). The problem is the following: If you wanted to ship the statue in a crate, what size dimentions (height, length and width) should the crate have (using the least amount of wood possible)? Do not include the cement pedistal that the statue is on, just the lady and the swing.

II: We planned to take a metric tape down to the statue and have one person hold one end at the base of the statue (the top of the stone pedestal). Then another person would take the other end of the measuring tape and hold it up straight. We would see where the top of the statue came up to on the measuring tape and write it down in centimeters. This would be the height of the statue. To find the length, we planned to measure the distance in centimeters from one side of the swing to the other (the length of the swing). For the width, we planned to hold the tape measure above the statue and kind of eyeball it. We would approximately where the statue stuck out the furthest in the front, and hold the beginning of the tape measure above it. Then we would see where the statue stuck out the furthest back, and hold the other end of the tape measure above it. Then we would measure the distance between these two points in centimeters. This would give us the three dimensions, solving the problem.

III: We did exactly what we had planned to do, and got the following dimensions: Height: 110 cm., Length: 120 cm., Width: 110 cm.

IV: The answer we got are the following dimensions:
110 cm. Height - 120 cm. Length - 110 cm. Width

V: I don't think that this is an incredibly hard problem, because the only thing you have to do is math measure (though the measuring is harder than it looks).

More Student Problems

There is a steeple on top of Sacred Heart Church. On the steeple there are a number of angels sticking out of the side. They go around the circumference of the steeple. You have to find out how many degrees apart each angel is.

To solve this problem I counted the number of angles going around the steeple. Then I divided that number I chose 360 degrees because that is how far around a whole circle is. Then whatever the answer of that is that's what the answer to the problem is. I used the number of degrees in a full circle to find what to divide by. I had no assistance in this problem, but I did discuss it with Brian Zapp.

The answer that I got was 30 degrees apart is each angel. I am sure that this is the correct answer because I double checked the number of angles and I checked with my Dad that a circle is 360 degrees.

In this problem I learned that if you want to know how far apart things are you divide the number of things there are by the distance of all of them.

• The objective of this investigation is to find the area of a stop sign by finding how many congruent triangles make up the shape of then using measurements and formulas to find the area.
• The first thing that I did to solve this problem was I thought about what measurements I needed. I found that the measurements I needed were the height of the entire sign, the width of one side of the sign and the height of half the sign. My group and I found that the height of the entire sign was about 70 cm. I then divided 70 by 2 because when I split the sign into triangles I found that there were 8 and I needed to find the height of just one. I then found the base of the triangle and found that it was 32 cm. To find the area on one triangle I took the formula A=1/2 bh and turned it into A=1/2 * 37.5 * 32. I now knew that the area of one triangle was 600 cm., so I multiplied it by 8 since there were eight triangles in the sign.
• The answer that I got was that the area of the stop sign was 4,800 cm2. My answer is correct because if you work backwards you end up with a height of 70 cm and a base of 32 cm, which is what I started with.
• While doing this problem I learned that you can find shapes within another shape and use other shapes formulas in order to find something for your original shape. I think that this is a worthwhile problem for other people to solve because it teaches them to use other problems to solve one original problem.