Scale 'n' Bowl 4
posted November 22, 1999 as a Math Forum EPoW

Introduction: In the Scale 'n' Bowl puzzle series, students were given instructions to find a scaling ratio that will enlarge or reduce the blue ball to fit through the green bowling alley and move the two red pins. For each of the alleys, they were asked to explain the scaling ratios tried, why they tried them, and which one worked. After bowling all alleys, students put the scaling ratios which worked in order from smallest to largest, describing how they chose this order. In this part of the series, students used fractions, decimals, and percents as scaling ratios.

Where's the Math: The four-part problem maintains the same graphical representation in each section, but requires the use of first decimal, then percentage and fractional notation to manipulate the size of the bowling ball. Students may start with trial and error guessing, but soon discover strategies to narrow the input values to get the necessary ratio. In this part of the problem series, students review each of the previous notations for scaling ratios, but also convert between numerical representations. Each of the problems in the series requires that students place the ratios in ascending order, encouraging them to revisit their problem-solving strategy and solidify their developing understanding of numerical representations of the concept of scale. Standards: Number & operations, measurement, geometry Role of Components: The Scale 'n' Bowl problem series uses Geometer's Sketchpad to animate scaling and bowling actions based on values inputted into number entry fields (labeled with ESCOT labels) and triggered by a button panel. Instructions are displayed via the HTML viewer, and solutions are entered in a text entry box. Users reset the alley with an Action menu. Javascript handles communication among components.

(The applet for this problem is currently unavailable)

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Sample submitted solution:

From:  Wil, age 13
Jeanette, age 13
School:  School of the Arts, San Francisco, California

1. For alley 1: Find the correct decimal scaling ratio. Put it into percent and fraction forms.
.5, 50%, 1/2-too small
.8, 80%, 4/5-too big
.6, 60%, 3/5-too small
.7, 70%, 7/10-too small
.75, 75%, 3/4- CORRECT!

2. For alley 2: Find the correct decimal scaling ratio. Put it into percent and fraction forms.
50%, .5, 1/2-too small
55%, .55, 11/20-too small
60%, .6, 3/5-CORRECT!

3. For alley 3: Find the correct decimal scaling ratio. Put it into percent and fraction forms.
2/1, 2, 200%-too big
1/1, 1, 100%-too small
7/5, 1.4, 140%-too big
6/5, 1.2, 120%-CORRECT!

4. Put your solutions in order from largest to smallest.
Largest-#3 (120%, 6/5, 1.2)
Next largest-#1 (75%, 3/4, .75)
Smallest-#2 (60%, 3/5, .6)

Bonus: Which of the three scaling ratio forms was hardest to use? Which was easiest to use? Why?
The easiest scaling ratio to use is percent because it is the most clear to read and you can instantly see how they compare. The fractions were hardest because of the x/y form. It is unclear what the value of the fraction is.

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