Mathman 4 -
Homestead Hollow Letterbox
(Algebra 1 Review Sem 1)

Terrain: Easy

Difficulty: Depends on math ability (Algebra I)
Placed by The Dragon (Mathman)
Location: Germantown, Washington County, WI

Materials needed: Rubber stamp, stamp pad, calculator (?), compass, these clues

Dragon's Home Page
Mathman Home Page


Students and parents of students should read my introduction to letterboxing before seeking the boxes.


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.  Enjoy!



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 common 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*Note: The park is adding trails through here, so hopefully these clues are not too outdated.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 data:


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).


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:


Before you set out read the waiver of responsibility and disclaimer.

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