Problem Description Sheet:       Squares of a Checkerboard          

Introduction:You read the rules for playing Checkers. They tell you to move a checker from one square diagonally to another square. That starts you wondering. How many squares are on a checkerboard? You think there are 64 squares on a board with 8 rows and 8 columns. Your friend disagrees.

Problem:

  1. How many squares in total are there on a 2 by 2 checkerboard? The answer is not 4.
  2. How many squares in total are there on a 3 by 3 checkerboard?
  3. How many squares in total are there on a 4 by 4 checkerboard?
  4. How many squares in total are there on an 8 by 8 checkerboard?

Materials: paper, pencil, calculator, ruler, and scissors to make squares if that would be helpful.

Extra Questions:  The floor in a room has square tiles. There are 7 tiles along the width of the room and 11 tiles along the length of the room. How many squares in total are formed by these tiles? Show your work to explain your answer.

Topic(s):

Numbers and Patterns, Geometry, Communication, Independent Learning, Creative and Critical Thinking

  Activity Type:

Group      Individual 

  Assessment:

Scale:    Levels 1-5   
Self     Peer     Teacher 
Include in your portfolio?
Yes     No     Optional 
Toward Your Marks?
Yes     No     Optional 

  Hints: