The purpose of this activity is for students to partition rectangles into halves, thirds, and fourths. Students fold paper shapes to guide their partitioning. Like the previous lesson with pattern blocks, students may determine that the pieces formed by the creases of their folds are equal by visual inspection. They also are encouraged to cut out the equal pieces to check whether they are close to being equal.

Most students likely will lay the pieces on top of each other to compare them. The expectation is that they may not be exact, but will be very close. Monitor as students fold the paper, and if students’ partitions are noticeably inaccurate, have them fold a new piece of paper before they cut.

• Invite students to share examples of the rectangle split into fourths.
• “When you cut a rectangle into 4 equal pieces, what are the pieces called?” (fourths)
• “Do you know another name for these pieces?” (quarters)
• Invite students to share examples of their rectangle split into thirds.
• “What do you think each piece may be called?”
• Share and record responses.
• “When a shape is split into 3 equal pieces, each piece is called a third.”
• Fold a rectangle to create a nonexample of thirds, in which the pieces are not equal.
• Display the nonexample.
• “What went wrong when I tried to partition this rectangle into thirds?” (It was hard to fold thirds because you can’t just fold it in the middle.)
• “When making thirds, I know the pieces are smaller than halves. I can check to see if I am on the right track before I make the crease.”
• Fold a rectangle to create thirds, and demonstrate testing before making the hard creases. Display the example.
• “Sometimes it will take a few tries.”

The purpose of this activity is to determine whether or not circles are partitioned into halves, thirds, or fourths. Students explain why some circles are not examples of halves, thirds, and fourths, and demonstrate their understanding that it’s not just the number of pieces that help determine whether to use halves, thirds, or fourths, but whether they are equal pieces of the same whole (MP3, MP6).

• Display the images of circles from the row labeled thirds.

  

• “You had to decide which circle is partitioned into thirds. Which of these circles did you think were not showing thirds? Explain.”
• Invite previously identified students to explain their reasoning.
• As time permits, invite students to share their responses for halves and fourths.