# Stretchy™ Calculator

Math teaching aid. The Stretchy™ Calculator is an analog device for teaching multiplication and division, ratios and proportions, squares and square roots.  A batteryless calculator useful for teaching basic math.  Pocket calculators provide answers but no insight into how the answers are derived.  This Stretchy is designed to help the student understand why the answers change in the way they do.

The Stretchy™ calculator has a numerical scale printed on a rubber band which is pulled while holding the calculator by the large hole.  The “1” and arrow on the rubber band is the index, and is important in almost every calculation.

Like a slide rule, the calculator’s accuracy is within 2-3 decimal places by the user mentally keeping track of the decimal place.

 Stretchy™ calculator operation: MULTIPLICATION:  To multiply X times Y (or X x Y), pull the rubber band until the index is next to the X value on the fixed scale.  Opposite the Y value on the rubber band, read the answer.  The animation illustrates two examples, 2 x 4 = 8, and 3 x 2 = 6. DIVISION:  To divide X by Y (or X/Y), set the Y value on the rubber band next to the X value on the fixed scale.  Read the answer, on the fixed scale, next to the index.  Example: 8 ÷ 4.  Set the 4 on the rubber band next to the 8 on the fixed scale.  The index on the rubber band is pointing to the answer, 2, on the fixed scale. RATIOS: X/Y:  Example, to set up a ratio of 2/5, stretch the rubber band until the 2 on the rubber band is adjacent to the 5 on the fixed scale, then adjacent to the 1 on the fixed scale, read 4/10 on the rubber band (or for more accuracy, adjacent to the 10 on the fixed scale, read 4 on the rubber band, and mentally shift the decimal to yield 0.4). PROPORTIONS:  (X/Y) x N: Example: (2/3) x N.  Stretch the rubber band to make the 2 on the rubber band line up with the 3 on the fixed scale.  Then, using the numbers on the fixed scale, read to the right to find 2/3 the value of any number on the fixed scale.  Ex.: (2/3)2 = 1-1/3;  (2/3)3 = 2;  (2/3)4 = 2-2/3;  (2/3)6 = 4;  (2/3)9 = 6. SQUARES:  X2:  To square X, set the index (“1”) on the rubber band adjacent to the value of X on the fixed scale.  Adjacent to the value of X on the rubber band, read the answer on the fixed scale.  Example: 3 squared: set the index on the rubber band adjacent to 3 on the fixed scale, and adjacent to the 3 on the rubber band, read the answer 9 on the fixed scale. SQUARE ROOTS:  To take the square root of X, stretch the rubber band until the same value on the fixed scale (adjacent to the index on the rubber band), and which is on the rubber band, lines up adjacent to the value of X on the fixed scale.  Example: to find the square root of 9, stretch the rubber band until you find that the value on the fixed scale lines up with the index on the rubber band at the same time the same value, 3 on the rubber band, lines up with the 9 on the fixed scale.  Only when the rubber band is stretched so that the 3 on the fixed scale lines up with the index on the rubber band, will the same value (3) on the rubber band line up with the 9 on the fixed scale.  Therefore, the square root of 9 = 3. DECIMAL EQUIVALENTS:  To convert X/Y, set X on the rubber band adjacent to Y on the fixed scale, then adjacent to “1” on the fixed scale read the decimal equivalent on the rubber band.  Example: 2/3: set the 2 on the rubber band adjacent to 3 on the fixed scale.  Adjacent to 1 on the fixed scale (or 10 for more accuracy) read 0.66 on the rubber band. FRACTIONAL EQUIVALENTS:  To convert a number in decimal form, set the number on the rubber band adjacent the 1 or 10 on the fixed scale, and find the pair of numbers that most nearly align with each other.  Notice, for example, that when calculating the fractional equivalent of 0.333, the answers of 3/9, 2/6 and 1/3 are all equivalent.

HinesLab is actively seeking licensees to commercialize this technology.  This is not a product being offered for sale to end users.  To discuss licensing, please contact Steve Hines at:

HinesLab

Glendale, California, USA

phone:  818-507-5812

email: Steve@HinesLab.com