This box is
the fourth in a series of letterboxes with mathematical clues. The boxes
are intended for both regular letterboxers and my students. This box was
developed by some of my Honors Advanced Algebra students for an extra credit
opportunity, and as an example for future boxes to be created by my students.
Unfortunately, this group of students never got it done, and I waited nearly 200
days for them to get the box back to me so I could plant it myself! I had
just gotten the box back and was brainstorming ideas for it when the freshmen in
my Algebra class asked for a letterbox they could do over Christmas vacation.
So, here's a box for them! In order to find this box, you must solve some
Algebra problems of the type found in the first semester of our Algebra course.
Be sure to read through
all the clues before looking for the box so you know what is expected of you.
Most of the problems could be worked out before arriving at the park,
or can be worked on when suggested in the clues. (Regular letterboxers
please ignore some of the directions for my students.)
Drive to Homestead Hollow County Park in Germantown, WI. (Just east of
County Y on Freistadt Rd.) Park in the lot near the playground and barn.
Start by climbing the large metal slide in the playground. Count the
number of steps you take to the top. Then slide down. Sitting at the
end of the slide, figure out the numbers in the following sequence if the
difference is the number of steps up the slide:
50 _____ _____ _____ _____ ______
The last number in this sequence is the first bearing you need to set on your
compass. From the end of the slide, walk on that bearing through the open
picnic area. You will then come to an opening in the brush where a trail
leads to the woods. Take this trail to the SECOND* intersection. Stop
and simplify the following:
3(37x + 14y) - (26y + 21x)
*Note: The park is adding trails through here, so hopefully these clues are not
too outdated. The intersection you should be at is the one about 120 feet south
down the trail not the new one that is only 10-20 feet down the trail.
The coefficient of the x term will be the bearing of the trail you now need to
take. Head down this trail to the next intersection. Stop and solve
the following equation:
-4.1x - 72 = -6.4x + 43
The value of x is the bearing of the next trail you should take. Head down
that trail. Soon you will come upon a bridge. Count the number of
planks used for the walkway of the bridge. Assign this number to the
variable a: a = ______. Then continue on down the trail to the first
major turn (about a 90 degree turn). Stop and scan the area for a black
and yellow sign with a large number on it and record the number as variable b: b
= ______. (Note: It could be covered with snow in winter.
Otherwise you should be able to easily see it.) Turn around and go back
over the bridge and back to the intersection. Head down the other path now
(the one you haven't been down yet).
After a while, you'll cross another bridge. Again, count the number of
planks used for the walkway of the bridge, and assign this number to variable c:
c = _____. (Note: Count carefully - the last two boards look like
one.) Continue on down the trail to the next intersection. Stop and solve
the following formula for d, using the values you found for a, b, and c:
c = 0.25(d - b + a)
The value of d is the bearing of the trail you should continue on.
At the next intersection, stop and determine what percent of 200 is 566.
This percent is the bearing of the trail you should continue on.
At the next intersection, stop and find the 3rd quartile of the following set of
151 216 360
87 183 2
125 356 176
This will be the bearing of the trail you should continue on.
At the next intersection find the double striped pole and stand there to work
out the next two problems:
If t varies directly as w, and t = 3195 when w =
213, what is the constant of variation (k)?
Find the equation (in slope-intercept form) of the
line that passes through the points (-8, -2) and (3, 42).
BEFORE RETRIEVING THE BOX, BE SURE NO ONE IS AROUND TO
SEE YOU TAKE THE BOX OUT! DO NOT BRING ATTENTION TO YOURSELF OR THE HIDING
LOCATION OF THE BOX!
The bearing of the trail you should continue on is the constant of variation
found above. The number of paces (steps) you should take down that trail
from the pole is the y-intercept of the linear equation you found. There,
to your right, just off the trail is a tree with as many trunks as the slope on
the linear equation you found (although one of the trunks has fallen away and
another is broken). Look in the hole created by the fallen trunk in the
base of the tree for the box! It should be covered with a rock, leaves,
and twigs. Please re-hide the box this way as well. Thanks!
Stamp your personal stamp on the next empty page in the box's log
book and write me a nice note. Read any other comments from
other people who have found the box and enjoy their stamp images.
Stamp an image of each of the box's stamps on this sheet below in the
space provided. Wipe the stamps so they are cleared of extra ink
and return all items back into their baggies and seal them well.
Seal the lid on the box well and re-hide the box. Thanks!
Mathman 4 stamp: Homestead Hollow stamp: