A Wrinkle in Time

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.