Tag Archives: Spatial Reasoning

Shrinking Square Challenge

Shrinking Square Challenge

This week’s Puzzle Corner activity is a seemingly simple one that may prove more difficult than one might expect. In it, students place four pennies on the corners of the square pictured. They are then challenged to move only two of the coins to create a new square that is smaller than the original. Most students will need to exercise their spatial reasoning to solve this puzzle. Persistence will also help.

This activity is one that should be done individually and the solutions not shared until all the students have had ample time to try solving it on their own. Therefore, it is important to caution students not to share their solutions with other students –doing so will rob these other students of the joy of discovery.

I hope that you and your students enjoy this challenge.

Place four pennies at the vertices (corners) of the square below. The sides of this square are about 10 cm long, when measured from the centers of the coins. Your challenge in this puzzle is to move only two coins so that you form another square that is smaller. This new square has sides that are about 7 cm long. Sketch your solution on the back of your worksheet. Click here or on the picture to download. (Note: if the dimension don’t match the stated ones above on your print out, don’t worry the puzzle is still solvable.)

Shrinking Square

Solution

Click the arrow below to view the solution.

Students were presented with a 10-cm square and asked to place four pennies on the vertices of the square. Then, they were challenged to move only two pennies to create a square that was smaller than the original square. One solution to this puzzle is shown below.

Shrinking Square Solution