The purpose of this activity is for students to learn that when you partition a shape into two, three, or four equal pieces, the whole shape can be named as “2 halves,” “3 thirds,” and “4 fourths,” respectively. This activity uses the context of sharing fractional pieces of a circle for a craft project to intentionally elicit from students the use of “whole” to describe the situation. They will continue to deepen their understanding of “whole” as a mathematical term, during their study of fractions in grade 3. Students observe regularity in repeated reasoning (MP8) when they see that no matter the number of equal pieces into which the whole circle is cut, that number of pieces makes the whole.

Students begin the activity by looking at the problem displayed, rather than in their books. At the end of the Launch, students open their books and work on the problem.

This activity uses MLR5 Co-Craft Questions. Advances: writing, reading, representing.

If students disagree that two halves, three thirds, or four fourths is the same as the whole circle, consider asking:

• “If Jada took this piece (a half) and Mai took this piece (a half), how much of the circle is left?”
• “How could you show how much of the circle each student took?”

• Invite students to share how much of the circle each group of friends took, using “2 halves,” “3 thirds,” “4 fourths,” and “4 quarters.”
• Record responses.
• “What is the same about these phrases? What is different?” (The first number is how many of that kind of equal piece it takes to make a whole. They all are the same as the whole circle. They use different numbers and different kinds of equal pieces.)
• If connections between the “whole” and 2 halves, 3 thirds, and 4 fourths, do not come up, consider:
  • “We noticed that 3 thirds of the circle were the same as the whole circle. What are other ways we can use a number and the names of equal pieces to describe the whole circle?”

The purpose of this activity is for students to recognize and describe pieces of circles, using the words “half of,” “a third of,” and “a quarter of.” Students match shapes partitioned into halves and quarters to stories, and partition shapes into quarters and halves, based on directions. Students can continue to use “fourth” when describing a piece, but encourage the use of “quarter” as a way to describe the same piece.

• Invite previously selected students to display their partitioned circles. Share at least one example of a circle partitioned into halves and one example of a circle partitioned into fourths.
• “How are the circles you partitioned and shaded the same? How are they different?” (Both are circles. They are shaded with different colors. They are partitioned differently. The whole circle is shaded in both. All of the pieces are shaded in both.)
• “How much of each circle is shaded?” (4 fourths, 2 halves, the whole circle)