Galactic Exchange Teacher Support

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Galactic Exchange Archived PoW || Student Version

Galactic Exchange is no longer the current ESCOT Problem of the Week. The student version allows teachers to use the problem with their students without giving the students access to the archived answers. Teachers can use the link to the archived problem to get ideas of student thinking.

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The Galactic Exchange problem requires students to determine coin values and product prices from an alien vending machine. Since the American money system, a decimal system, is a familiar experience, the complication of a non-decimal system becomes clear as soon as one tries to understand a system where 12 pennies make a shilling and 20 shillings make a pound, but 2 shillings 6 pence make half a crown.

This problem came out of the real-life situation in math where students have been expected to sort out related unknown quantities on standardized tests (Both ITAS and SAT-9 have balance problems where gray, white, and black cubes have to be balanced against each other and values determined.) The relations between coins in the old English non-decimal system (used until 1971) provides a different approach from the balance scale.

Exercises in this field can provide pre-algebra practice in the area of variable substitutions.

If you have something to share with us as you use any of the links or suggestions on this page (something you tried and changed or a new idea), we would love to hear from you. Please email us.

Alignment to the NCTM Standards - Grades 6-8

    Number and Operations
    - develop meaning for integers and represent and compare quantities with them.
    - understand the meaning and effects of arithmetic operations with fractions, decimals, and integers.

    Algebra
    - relate and compare different forms of representation for a relationship.
    - develop an initial conceptual understanding of different uses of variables.

    Data Analysis & Probability
    -develop and evaluate inferences and predictions that are based on data

    Problem Solving
    - solve problems that arise in mathematics and in other contexts

    Reasoning and Proof
    - make and investigate mathematical conjectures

    Communication
    - communicate their mathematical thinking coherently and clearly to peers, teachers, and others.
    - use the language of mathematics to express mathematical ideas precisely.

    Connections
    - recognize and apply mathematics in contexts outside of mathematics.

Possible Activities:

    Pre-Activity
    - Read the poem "Smart" by Shel Silverstein to your students just as an introduction to money exchange. If you haven't the book you can find it here in this response written by a Teacher2Teacher Associate:   Equivalence of Coins

    - Money Practice -- A difficult concept to grasp is that you must subtract the change to get the cost of the zoogs, etc. The first inclination for most students would be to add the change to the inserted coins. To practice, have some fake money. Have a student give you a five dollar bill, and you give them $1.20 in change. Ask them the cost of the imaginary item that they just purchased. Have them practice with each other. Since we don't usually operate backward when we buy things, this would be a good exercise.

    Post-Activity
    - The Algebra Connection - Student Movie Showcase by Apple


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