(10/01/96)
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MathMagic Cycle 22: Level K3 Regular
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LET ME COUNT THE WAYS
1) Tina has 3 shirtsred, blue, and yellow. She also has 2 skirts
black and white. Each day, she wears a different shirt with a
different skirt.
A) For how many days can she do this before she must repeat and
Draw pictures of Tina and color if you wish.
There is also a chart called a TREE that can help Tina to know
which outfit is next to wear. It looks like this:
Black
Red
 White


 Black
Blue
 White


 Black
Yellow
White
So, you can see all the possibilities and even count them.
C) Uh oh, Tina accidentally ripped her yellow shirt and cannot wear
it anymore. How many outfits does she have now? Draw a tree.
2) When Billy comes home from school each day, he gets a snack
and a drink. His Mom lets him choose either a piece of fruit, a
cookie, or a peanut butter sandwich. He can drink juice,
milk, or a soda.
A) Can you make a TREE that explains all the possibilities of
snacks and sodas? How many snack and drink combinations are there?
B) How many combinations are there if the drink is MILK?
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MathMagic Cycle 22: Level K3 Advanced
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BALANCING ACT
A scale can be used to measure the weight of various items, by
comparing the item to a known weight. This cycle's problem will
require you to do some empirical work (empirical is a scienttific
term that means you will experiment and observe and then
report what you see). First you will need to make a scale using a
ruler (the kind with 3 holes), 3 pieces of string (all the same
length) and 2 baskets (like for strawberries, milk , etc that are
the same size). Tie the 3 pieces of string to the ruler through the
3 holes. Attach the two end pieces to the baskets and tie the middle
string to a support. Hopefully, the scale will be balancedif not, attach weights (paper clips, clay) to one side or the other until the scale is balanced.
Before you begin, explain the differences (if any) between
weight and mass.
Experiment 1) Place 4 or 5 common items that are identical (pencils,
erasers, etc) in basket #1. Decide on another, different item
(marbles are good or paper clips) that can be used to balance
them in basket #2. Then try to balance basket #1 with basket #2.
Did it work right offIf not, add more to basket #1. Explain your
results. Use your results to estimate the weight of 1 basket #1
item in terms of the basket #2 item. Check your results.
Experiment 2) How much does one piece of paper weigh, compared to
a paper clip or a pencil? Explain how you did this experiment? Which
weighs more500 sheets of paper or 500 paper clips?
Experiment 3) You don't necesarilly need your scale for this. Suppose
6 oranges balance with 4 apples. And suppose 4 apples balance with
8 bananas. How many bananas will be needed to balance 9 oranges?
Experiment 4) Suppose now that 12 pencils balance with 4 erasers,
and that 6 erasers balance with 12 sharpeners. How many pencils would
be needed to balance 6 sharpeners?
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Good luck
MrH