In previous lessons, students identified and partitioned halves and fourths of rectangles and circles. The purpose of this activity is for students to reason about the sizes of halves and fourths of the same shape. As a result of their prior work with comparing quantities of objects, students may reason that because four pieces are more than two pieces, a fourth should be larger than a half. When students compare the sizes of a half and a fourth of the same circle and repeat the comparison with a half and a fourth of the same square, they begin to generalize that when you partition a shape into more parts, the size of each part gets smaller (MP8).

• Invite previously identified students to share.
• “___ observó que en ambas figuras, una mitad era más grande que un cuarto. ¿Creen que esto siempre será verdadero? ¿Por qué?” // “___ noticed that for both shapes, a half was bigger than a fourth. Do you think that will always be true? Why?” (Yes, when you cut a circle into halves, it is 2 pieces. And when you cut it into fourths, you get 4 smaller pieces. Fourths are smaller than halves of the same shape.)

The purpose of this activity is to help students generalize that partitioning a shape into fourths creates smaller pieces than partitioning the same shape into halves. This builds on work from a previous activity in which students compare halves and fourths of circles and squares. Students generalize that for halves and fourths of the same circle, a half is larger than a fourth (and a fourth is smaller than a half). As students explain how they know, some may show or color half of the circle and label it “Priya,” then show or color a fourth that is not shaded and label it “Han.” Some students also may shade in half of a half to show a fourth. When students decide whether they agree with Priya's or Han's statement and justify their choice with diagrams and words, they construct viable arguments and critique the reasoning of others (MP3).

• Invite previously identified students to share.

MLR8 Discussion Supports

• “¿Alguien puede expresar con sus propias palabras lo que compartió _____?” // “Who can restate what ____ shared in their own words?”
• Consider providing students time to restate what they heard to their partner before selecting one or two students to share with the class.
• Ask the original speaker if their partner accurately restated their thinking.

The purpose of this activity is for students to learn Stage 4 of the Geoblocks center. Students take turns reaching into a bag and feeling a solid shape, without looking. They guess the shape and show it to their partner. Together, they check to see if the shape from the bag matches the guess.

• “De lo que sintieron, ¿qué les ayudó a adivinar cuál era la figura?” // “What did you feel that helped you guess the shape?” (I felt that the shape had points. I felt the sides of the shape.)