Math in Our World: The Shrink-O-Matic

Cameron just invented The Shrink-O-Matic. It shrinks objects for 1 hour! You look through it like a camera, press one of the red fraction buttons, then press the X button to multiply, and —BOOM! — whatever you had it aimed at shrinks!

The Shrink-O-Matic has a viewing screen, an X button, and 9 fraction buttons. 1-half. 1-third. 2-thirds. 1-fourth. 3-fourths. 1-fifth. 2-fifths. 3-fifths. 4-fifths.

The fraction you push determines the new size of the object.

Cameron said, “If you aimed the Shrink-O-Matic at a 12-foot tall ladder and pushed the ⅓ button, it would shrink to ⅓ of its original size. Because ⅓ of 12 is 4, you’d now have a 4-foot tall ladder.”

He is excited to try out his new invention, and he started a list of things he might shrink.

ObjectApproximate Original Size
Swingset10 feet tall
Fire truck35 feet long
Apple tree30 feet tall
Skyscraper300 feet tall
His house24 feet tall
Airplane180 feet long
  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!
  • You can shrink an object to ½ of its original size by dividing by 2. How can this information help you figure out the size of an object shrunk to ⅓, ¼, or ⅕, of its size?
  • How does knowing ⅓ of the size help you figure out ⅔ of the size?
  • Show your work to someone else, and explain your thinking. Did they understand?
  • Ask if they have any other questions you can answer!

If you shrink your whole family to ⅕ their original sizes, how big will each of you be? Sketch your mini-family and cut out the sketches. What sorts of adventures would you have?