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SAMPLER - BORDERLINES 2
What is a borderline?
-- a narrow line or space forming a boundary, edge, border, fringe,
margin, rim, periphery
-- a traditional interval beyond which some new action or state of
affairs is likely to occur (a threshold, brink, point)
-- an uncertainty, a problematic or questionable situation
That's a lot of borderline definitions for us to explore!
PART 1
Let’s start with some questions that are within the math territory -1. What would you rather have your height in (a)stacked nickels or (b)quarters laid end to
end? How do you figure this one out?
Suppose you agree to take a really crummy job for just one cent for the first day of work.
(Sound like prisoner wages?) The next day and every day thereafter for a month of 30 days,
you’ll charge twice as much as the day before.
2. Is this a good deal for you or for the person hiring you? Why or why not?
3. How much will you have at the end of 30 days?
Math isn’t all about calculation. Sometimes it is just about using your head:
4. Some months have 30 days, some have 31. How many have 28 days?
5. How many birthdays does the average person have?
6. Take two apples from three apples and what do you have?
The answers are:
for #3 -- They all do.
for #4 -- Everybody has just one.
for #5 -- You have two apples.
This next one goes from the outer borders of mathematics, almost into geometry…
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7. How many squares do these lines make?
Some only count 24, others 32 or 36, but the correct answer is 40.
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Mathematicians love mazes. The first one below is one of the oldest known mazes; it is called
the Cretan Maze. (Do you know why?)
8. See if you can solve them both --
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A maze is a kind of map. Now it's your turn to be mapmaker.
9. There is a fly on the ceiling -- map your cell from the fly’s perspective.
10. On a map of a city park, what important features would be included if the
mapmaker were:
a butterfly
a picnicker
a dog
a trash collector
a police officer?
Here's what the United States looks like according to most mapmakers --
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11. Print the names of the states you can identify on this map.
12. Which two states border seven others?
13. What states border only two others? Only one other? No others?
14. Where can you stand in four states at the same time?
15. What state is smack in the middle of the USA?
16. Name 5 state capitals.
The biggest town in a state may not be its capital.
17. Name the states in which these big cities belong:
Philadelphia
St Louis
Seattle
New York
Baltimore
Denver
Detroit
Chicago
Minneapolis
Miami
18. List any 10 states -- write the name of another that borders it (and no peeking!)
19. Find these words in the names of other states:
a writing implement
two women’s names
Most of our states [27 in fact] have names that can be traced back to Native American roots.
Some, like Arkansas and Utah, are named for the tribes that lived there. Others are words that
have interesting meanings when translated into English. Kentucky is supposed to mean “Land of
Tomorrow.” We are told that Alabama meant “I clear the thicket.” (Any of you guys from the
south know if that is true?) We do know that a dozen states have names that came from English
sources, nine of which were names of royalty or important government figures of the colonial
period. Six states have Spanish names; Colorado means “colored red,” for example. There are
three states with names that come from France; ours in Maine is one of those.
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20. What's one state name from an English source? Spanish? Native American?
That leaves a grand total of only one state that has a name not related to Native American,
Pacific Island, English, Spanish, or French peoples.
21. Name the one state whose name is tied to American politics.
If you were to fly over the United States, it wouldn’t look like our map. First, the states
wouldn’t be divided by neat lines as they are on the map. The second problem is that the world is
round. Maps are flat and often distort actual sizes of countries and their placement relative to
other countries. World maps always show the north pole at the top.
23. Why would these cause controversy?
Some borderlines are quite visible, like the Great Lakes, the Mississippi River and the Rio
Grande. But borders are usually invisible lines -- they can be between states, countries or
cellmates. [“This is my bunk.”] Invisible lines on the world map may seem unimportant, but
wars have been fought to determine the location of some of them.
24. Name one war fought to determine boundaries.
Fights have also arisen when people crossed invisible lines in prison cells.
25. What is the most common kind of "boundary war" among prisoners?
26. How can such fights be minimized?
27. Why are cultural, ethnic and racial differences so often borderlines?
28. What is the border between Mexico and the United States?
Between the Mexican and U.S. governments?
Between the Mexican and U.S. peoples?
29. The long-standing conflict between Israel and Palestine -- what does it have to do
with borders?
Two men, living almost 300 years apart, wrote poems about boundaries and what they mean.
The first was a guy named Richard Lovelace who was thrown into prison in England in about
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1650. As you will see in his poem, Richard did not believe that he was guilty of any crime. His
girlfriend was named Althea, and this is part of the poem he smuggled out to her:
Stone walls do not a prison make
Nor iron bars a cage
Minds innocent and quiet take
That for an hermitage
If I have freedom in my love
And in my soul am free
Angels alone that soar above
Enjoy such liberty
30. What is the author saying in his poem?
31. Do you agree with him? Why or why not?
Robert Frost also wrote a poem about stone walls. He lived in New England. The land there is
full of stones, and for many years people have piled them into walls -- both to mark boundaries
and to get the stones out of the way. His poem talks about what walls meant to him and to his
neighbor -- read "Mending Wall" in the Appendix.
32. Do you agree with the poet or with his neighbor? Why?
33. Why did the poet decide not to talk to his neighbor about the wall?
34. Write a poem about walls in your own life.
APPENDIX
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MENDING WALL
Something there is that doesn't love a wall,
That sends the frozen-ground-swell under it,
And spills the upper boulders in the sun,
And makes gaps even two can pass abreast.
The work of hunters is another thing:
I have come after them and made repair
Where they have left not one stone on a stone,
But they would have the rabbit out of hiding,
To please the yelping dogs. The gaps I mean,
No one has seen them made or heard them made,
But at spring mending-time we find them there.
I let my neighbor know beyond the hill;
And on a day we meet to walk the line
And set the wall between us once again.
We keep the wall between us as we go.
To each the boulders that have fallen to each.
And some are loaves and some so nearly balls
We have to use a spell to make them balance:
'Stay where you are until our backs are turned!'
We wear our fingers rough with handling them.
Oh, just another kind of out-door game,
One on a side. It comes to little more:
There where it is we do not need the wall:
He is all pine and I am apple orchard.
My apple trees will never get across
And eat the cones under his pines, I tell him.
He only says, 'Good fences make good neighbors'.
Spring is the mischief in me, and I wonder
If I could put a notion in his head:
'Why do they make good neighbors? Isn't it
Where there are cows?
But here there are no cows.
Before I built a wall I'd ask to know
What I was walling in or walling out,
And to whom I was like to give offense.
Something there is that doesn't love a wall,
That wants it down.' I could say 'Elves' to him,
But it's not elves exactly, and I'd rather
He said it for himself. I see him there
Bringing a stone grasped firmly by the top
In each hand, like an old-stone savage armed.
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He moves in darkness as it seems to me~
Not of woods only and the shade of trees.
He will not go behind his father's saying,
And he likes having thought of it so well
He says again, "Good fences make good neighbors."
A Pocket Book of Robert Frost's Poems, Copyright © 1960, Henry Holt & Co. Inc.
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