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Author:
Madeleine L'Engle
Publisher/Date: Farrar,
Straus & Giroux, 1962
ISBN: LCN 336103
Grade Levels Recommended
for Use: 6-9
Brief Summary: Meg Murry
and her small brother, Charles Wallace search for their father, a physicist
who disappeared while studying a tesseract.
Topics: probability;
compound events; equally likely
Suggested Activities:
Activity One
Mrs. Whatsit is introduced to us at the end of chapter one. It
is a stormy night and her boots are soaked. She asks for help in removing
her boots because her feet are damp and cold. On one foot, she has a red-and
white-striped sock and on the other she has an argyle sock. Ask students,
How many individual socks must be drawn from a drawer to guarantee that
you have a matched pair?" Tell them that a second sock does not guarantee
a match because finding a match depends both on what was drawn first and
on what was available in the drawer.
Then ask them. "What are the chances that Mrs. Whatsit would get
a matched pair if she drew only two socks from the drawer?" They will
have a picture of Mrs. Whatsit's socks. The book does not tell you the
number of each type of sock that she owns so students will apply a what
if strategy, analyzing her chances of getting a matched pair if she has
two kinds of socks and three pairs of each kind, five pairs of each kind,
and even unequal numbers of pairs of each kind.
Have students use bags to represent Mrs. Whatsit's sock drawer
and put a given number of each kind of sock into the bag. Students will
experiment to find the results empirically and to infer the probability
of getting a matched pair by drawing two socks, recording whether they
matched, and returning them to the bag for another draw.
We will choose a team "puller", team recorder and a team facilitator.
They will have a sheet provided for their use.
Activity Two
Introduce an attribute set based on Mrs. Whatsit's socks.
What is an attribute set?
Show an example of what an attribute set looks like: color, design,
and state of repair.
Each group of three or four students needs its own attribute set.
Students will explore the sets and determine how the socks are alike or
different.
Identify the three distinguishing characteristics (may need help
with vocabulary, such as argyle).
The discussion should focus on characteristics that help distinguish
among the socks or help explain why two socks are more like each other
than a third is.
The situation of "socks in the drawer" can be used to investigate
probability, either theoretically (by charting all the possible combinations)
or empirically (by performing an experiment of pulling socks).
To introduce the notion that probability is the likelihood that
an event will occur, have students place all 20 sock pieces in a bag,
shake the bag, draw a sock, record the sock's state of repair, and return
the piece to the bag.
After performing this procedure ten times, students should discuss
their results and predict the probability of pulling a sock with a hole.
Activities involving attribute sets such as this one may help avoid
the misconception that equally likely and fifty-fifty are synonymous.
Activity Three
An extension of the previous activity has students investigate
the chance of pulling a sock with two given attributes.
When determining
the chance of drawing an argyle sock with a hole, students could spread
the pieces out face up and note that three socks are argyles with holes;
therefore, the probability should be 3 out of 18, or 1/6.
Discuss with students: By referring to previously identified simple
probabilities (i.e., the probability of choosing an argyle sock is 1/3
and the probability of choosing a sock with a hole is 1/2), students may
develop an informal understanding of the logical connective.
Discuss with students: Some students may even notice that the probability
for a sock that is argyle and has a hole is the same as the product of
the probability for argyle and the probability for a sock with a hole.
Activity Four
To help students perceive the meaning of the logical connective.
Using the sock set, students note that 1/3 of the socks are argyle
and 1/2 of the socks have holes, but some socks, 1/6 of the set, are counted
twice because they both are argyle and have holes.
By adding the probabilities for each attribute and subtracting
the probability of the combined attributes, the double-counted items are
accounted for.
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