Illuminations: Soda Cans

Soda Cans
Soda cans are placed on their side, in a box—four in the bottom row, three in the second row, four in the third row, and three in the top row. When the cans are shifted, some interesting things happen. What do you notice?

Instructions
 
Drag points A and B to move either of the middle cans on the bottom row. (The other cans in the arrangement will shift as a result.)

Click Show Line XZ to draw a line that passes through points X and Z.

Exploration
 
When you move the cans in the bottom row, what happens to the cans in the top row? For a major hint, click Show Line XZ.
  • Can you explain why this happens?
  • Will it work for arrangements with more cans in the bottom row? What if the width of the box is changed?
   Sorry, you must have a java-enabled browser to use this tool.

NCTM Resources

Principles and Standards for School Mathematics

Lessons
National Council of Teachers of Mathematics Thinkfinity
More and Better Mathematics for All Students
© 2000 National Council of Teachers of Mathematics
Use of this Web site constitutes acceptance of the Terms of Use

The National Council of Teachers of Mathematics is a public voice of mathematics education, providing vision, leadership, and professional development to support teachers in ensuring mathematics learning of the highest quality for all students. The views expressed or implied, unless otherwise noted, should not be interpreted as official positions of the Council.