# A Very Improbable Story

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Purpose

This is an activity based on the picture book A Very Improbable Story

Achievement Objectives
S3-3: Investigate simple situations that involve elements of chance by comparing experimental results with expectations from models of all the outcomes, acknowledging that samples vary.
Specific Learning Outcomes
• Students will be able to construct a model of the possible outcomes of a situation.
• Students will be able to identify and evaluate probability within real life contexts.
Description of Mathematics

The probability of an event occurring is dependent on the number of possible outcomes.

Models of possible outcomes can be represented in numerical terms using fractions.

Required Resource Materials
• A Very Improbable Story by Edward Einhorn
• Pairs of socks (paper cutouts or real ones)
Activity

Sock it to me!
This activity is based on the picture book: A Very Improbable Story

Author: Edward Einhorn
Publisher: Charlesbridge (2008)
ISBN: 978-1-57091-872-8

Summary:
Ethan wakes up one morning to find the improbable has happened- there is a cat stuck on his head. The cat, named Odds, will not detach itself until Ethan wins a game of probability with it. They play several games and explore several situations involving chance until Ethan is finally successful. He then applies his new understanding to his goal shooting outcomes and makes a strategic decision.

Lesson Sequence:

1. Prior to reading, explore the students’ understanding of chance and probability by working through a few scenarios with marbles or counters or unifix blocks of different colours. Model the language used to express chances of an outcome occurring.
If this jar is filled with only red lollies what is our chance of taking out a red one?
If there is 1 green lolly and 11 red what is the probability of getting the green one? A red one? Can we express that as a fraction?
If there are 3 blue, 3 green and 6 red what are the chances of getting each colour? Let’s test that a few times. Why was our result different from the “odds”?
Discuss places in our lives where we have to consider probability when we make decisions. Record some of these to refer to later
2. Share the book with your students. As you read discuss some of the scenarios (or games) Ethan and Odds play. Discuss the concepts of fairness, chance, and impossibility.
3. Go back to the sock game in the story (pp. 11-13). Discuss how the odds get better after each withdrawal of a sock. Ask students to work in several small groups and model this situation using a set number of different pairs of socks (or paper cutouts of socks). For example 5 pairs = 10 socks. As they work through their model ask them to record each new possible outcome as a fraction. Withdraw one and now chance of getting a pair is 1/9, then 1/8 etc. As them to play the game until they get a pair. Bring the class back together and look at the results for the groups.
How do we account for the variance in the number of times it took to get a pair?
How would we make this an impossible game? Better odds or worse odds?
4. In conclusion go back to the ideas from the introduction about places in our lives where we have to consider probability.
What role does chance play in our lives?
What kind of things do we do to improve odds or when do we decide it is worth taking a chance when the odds are “bad”?
5. For further investigation, students could design a game of chance and record the outcomes over several trials or evaluate games of chance played at school galas or investigate odds in lotteries and raffles.