Math in Our World: The Size Transmogrifier P10

The size transmogrifier has a view screen and 9 buttons. 2 white buttons perform operations: multiplication or division. 6 red buttons indicate values: 0.01, 0.1, 1, 10, 100, and 1,000. And a red equals button makes things transmogrify.

This is Cameron’s Size Transmogrifier P10. It works kind of like a camera.
You point. You click.
But it doesn't take a picture.

Choose to multiply or divide and then select a green power-of-ten button. Then with the push of the red Equals button, you can make things shrink or grow!

Cameron is excited to try out this new invention, and started a list of things to shrink or grow. Don’t worry—everything returns to its original size in an hour, no harm done. What would you transmogrify?

A lists objects and their approximate original size. A swing set: 10 feet tall, 18 feet wide. Pet cat: 45.72 cm long. Building blocks: 31.9 mm long by 15.8 mm wide by 9.6 mm tall. Toy car: 8.5 cm long. Cameron's father: 69.5 inches tall. Statue of Liberty: 305 feet tall. Cameron's house: 24 feet tall. Ripe peach: 9.1 cm diameter.
  1. Use pictures, models, or numbers to show what is happening.
  2. What do you notice? What do you wonder?
  3. What mathematical questions can you ask about this situation? Answer all the questions you can!

Pick one object. Start by using the multiplication button only. Try out the different green numbers.

  • What do you notice about the digits in your answers?
  • What’s the difference between multiplying by 10 and multiplying by 0.1?
  • Show your work to someone and explain your thinking. Did they understand?
  • Ask whether they have any other questions you can answer!

If you shrunk your whole family to one-tenth of their original sizes, how big would each of you be? Sketch your mini-family and cut out the sketches. What sorts of adventures would you have? What if you made your family 10 times their original sizes?