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.

Engagement: Provide Access by Recruiting Interest. Invite students to generate a list of food items that can be cut and shared with multiple people (sandwich, candy bar, brownie, cake, etc.) and that connect to their personal backgrounds and interests. Let the paper rectangles represent one of the items they could share. Discuss that halves are when two people share the item, thirds are for three people sharing, and fourths/quarters are when four people share the item.
Supports accessibility for: Conceptual Processing, Memory, Attention

• Invite students to share examples of the rectangle split into fourths.
• “Cuando se corta un rectángulo en 4 partes iguales, ¿cómo se llaman las partes?” // “When you cut a rectangle into 4 equal pieces, what are the pieces called?” (fourths)
• “¿Conocen algún otro nombre para estas partes?” // “Do you know another name for these pieces?” (quarters)
• Invite students to share examples of their rectangle split into thirds.
• “¿Cómo piensan que puede llamarse cada parte?” // “What do you think each piece may be called?”
• Share and record responses.
• “Cuando una figura se parte en 3 partes iguales, cada parte se llama un tercio” // “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.
• “¿Qué salió mal cuando intenté partir este rectángulo en tercios?” // “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.)
• “Al formar tercios, sé que las partes son más pequeñas que los medios. Antes de hacer el pliegue, puedo comprobar eso para ver si voy por buen camino” // “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.
• “Algunas veces se necesitarán varios intentos” // “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.

  

• “Tenían que decidir cuál círculo está partido en tercios. ¿Cuáles de estos círculos piensan que no muestran tercios? Expliquen” // “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.