"Scale 'n Pop" Teacher Support

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Scale 'n Pop Archived PoW || Student Version

Scale 'n Pop 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.
[Standards]  [Activities]  [Lessons]  [Student Resources]   [Other Resources]

The Scale 'n Pop problem challenges students to find a fraction that will inflate or deflate a balloon such that it will pass through a barrier wall and get "popped" by a pair of nails. The goal is for students to investigate the effect of multiplying an integer by a fraction to scale the size of a balloon's diameter. The students are also exploring the effect of the numerator and denominator on the magnitude of a fraction.

Depending on the students' ability to understand the idea of scaling the diameter of the balloon by a ratio, it may be helpful to explore the first carnival booth as a whole group, or in small groups. The pre-activity should also be useful in helping students understand how changing the numerator or denominator affects the magnitude of a fraction.

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
    - work flexibly with fractions, decimals, and percents to solve problems
    - understand the meaning and effects of arithmetic operations with fractions, decimals, and integers
    - develop and use strategies to estimate the results of rational-number computations, and judge the reasonableness of the results
    - develop, analyze, and explain methods for solving problems involving proportions, such as scaling and finding equivalent ratios

    Measurement
    - solve problems involving scale factors, using ratio and proportion

    Problem Solving
    - solve problems that arise in mathematics and in other contexts
    - monitor and reflect on the process of mathematical problem solving

    Communication
    - communicate 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-Activities
    1. Here are some suggested activities to help students think about the value of fractions and comparing two fractional values.
      - Play a "guess my fraction" game with the class. For example, "I am a fraction greater than 1/2 but less than 3/4; what could I be?" or "I am a fraction less than 4/5 but greater than 2/3; what could I be?
      - Play the Find Grammy game at the Visual Fractions website.
      - Use the Compare Fractions activity at the Visual Fractions website.
    2. Discuss the concept of scaling factors used in building models and architecture drawings.

    Post-Activity

    Use the FractPie Excel spreadsheet to explore the effect of changing a numerator or denominator in the magnitude of the fraction, decimal, percent, and parts-of-a-pie representations. The FractPie.xls spreadsheet file can be downloaded for free, but to use it you need Microsoft Excel 5.0 or higher installed on your local machine (PC or MAC). When opening the file, you may be given a warning prompt about "macros." Choose the option to "Enable Macros" so the file will run correctly.

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Related Lessons Online:

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Resources to Help Students:

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Possible Geometry Extensions (suggested by Susan Socha)

    The Scale 'n Pop problem could be extended for teaching or introducing
    1. dilation and scale factor
    2. similarity of circles or spheres
    3. using a scale factor as a scalar in matrices to transform a geometric object on a cartesian plane
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Other Resources
- History of Fractions
- Balloon Games (just for fun!)

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