Download Decimal Equivalents

SCMP
Summer 2009
Tri-Square Dartboards
Part 1:
Building the Dart Boards
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decompressor
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Choose any 3 sizes of squares. It is OK to repeat one or more
sizes.
Arrange your three squares so that corners touch and you form a
triangle in the center, like these:
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decompressor
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If you cannot arrange your squares to form such a figure, try a
different set of squares.
Tape the squares together as in the diagram.
You have just created a tri-square dartboard. Now, build some
more of these dart boards.
SCMP
Summer 2009
Dartboards
Jack and Maggie are avid dart players. They compete regularly to
see who is best. They’ve thrown so many darts, that they’ve
become tired of the traditional round target.
They experimented with other shapes, but none was as interesting
to them as a triangular target made by combining three squares.
Here are some samples of what they’ve invented:
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decompressor
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They decided that they would get a point each for hitting their
“home” areas. Since there were three areas on the target, they
agreed that Jack should take the two smaller squares and Maggie
should take the one larger square.
They quickly realized that this scheme wasn’t always fair. Some
targets favored Jack while other targets favored Maggie.
Your task is to explore possibilities. Build triangular targets.
Which targets favor Jack? Which targets favor Maggie? Try to
find at least two fair targets that don’t favor either player.
For all of your targets, be sure to label the length of the sides so
you can share your results with the class.
SCMP
Summer 2009
Using Diagrams to Solve Problems
1. The beautiful young princess of Polygonia is very upset. Her father,
the king, has chosen a husband for her but she is in love with someone
else. In order to ensure that the princess will not escape and elope
with her prince charming, the king has locked her in the tower until
the marriage ceremony. The princess could escape through the
window, but it is 50 feet above the ground. An alligator-infested
moat, which is 10 feet wide, surrounds the tower. Naturally her
prince charming is planning to rescue her but he is not too bright. He
wants to use an arrow to shoot a rope up to her window. She can slide
down the rope to the other side of the moat into his waiting arms. He
has tried to rescue the princess every night but each time his rope
has been too short. The wedding is tomorrow and the prince needs
your help. With your partner, find the minimum length of rope the
prince needs. Assume they need an extra, 1.5 feet at each end to tie
off the rope. Write a complete explanation for the prince that shows
how to determine the minimum length of rope needed. Include a
diagram.
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2. On a baseball diamond, the bases are 90 feet apart. (Every baseball
diamond is a square.) How far is it from home plate to second base?
Sketch and label a diagram. Use the diagram to write an equation to
solve the problem.
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decompressor
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SCMP
Summer 2009
3. A 10-foot ladder is leaning against a tree. The foot of the ladder is
3.5 feet away from the base of the tree trunk. How high on the tree
does the ladder touch? Draw and label a diagram. Write an equation
to solve the problem.
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dec ompres sor
are needed to s ee this pic ture.
4. A careless construction worker drove a tractor into a telephone pole,
cracking the pole. The top of the pole fell as if hinged at the crack.
The tip of the pole hit the ground 24 feet from its base. The stump
of the pole stood seven feet above the ground. If an additional five
feet of the pole extends into the ground to anchor it, how long should
the replacement pole be? Draw a diagram and write an equation to
solve the problem. Show all sub-problems.
SCMP
Summer 2009
Pythagorean
Society
Pythagorean
Society
Pythagorean
Society
Pythagorean
Society
Pythagorean
Society
Pythagorean
Society
Pythagorean
Society
Pythagorean
Society
Pythagorean
Society
Pythagorean
Society
Pythagorean
Society
Pythagorean
Society