Lesson 11

A Bigger Piece

Warm-up: Choral Count: 10 More, 10 Less (10 minutes)

Narrative

The purpose of this Choral Count is to invite students to practice counting on and counting back from two-digit numbers by 10 and notice patterns in the count. These understandings help students develop fluency with 10 more and 10 less.

Launch

• “Count by 10, starting at 6.”
• Record as students count.
• Stop counting and recording at 116.
• “Count back by 10 starting at 116.”
• Record as students count.
• Stop counting and recording at 6.

Activity

• “What patterns do you see?”
• 1-2 minutes: quiet think time
• Record responses.

Activity Synthesis

• “Who can restate the pattern in different words?”
• “Does anyone want to add an observation on why that pattern is happening here?”

Activity 1: Which is Bigger? (15 minutes)

Narrative

In previous lessons, students identified halves and fourths of rectangles and circles and have partitioned these shapes into halves and fourths. The purpose of this activity is for students to reason about the size of halves and fourths of the same shape. Because 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 fourth of the same-size circle and repeat the comparison with a half and a fourth of the same sized square, they begin to generalize that when you partition the same-size shape into more parts, the size of each part gets smaller (MP8).
MLR7 Compare and Connect. Synthesis: Lead a discussion comparing, contrasting, and connecting the different observations. Ask, “What was shared about folding the squares?” , “What was shared about folding the circles?”, and “How were those observations the same and different?” Advances: Representing, Conversing
Action and Expression: Develop Expression and Communication. Provide students with alternatives to writing on paper: students can share their learning orally.
Supports accessibility for: Language, Conceptual Processing

Required Materials

Materials to Gather

Launch

• Groups of 2
• Give each student a pair of scissors.

Activity

• 10 minutes: partner work time
• Monitor for students who notice that the halves are bigger than the fourths for both shapes.

Student Facing

• Each partner cuts out their circle.
• Decide who will cut into halves and who will cut into fourths.
• Fold your circle into halves or fourths then cut it.
• What do you notice?
• Be ready to explain your thinking in a way that others will understand.

• What do you notice?
• Be ready to explain your thinking in a way that others will understand.

Activity Synthesis

• Invite previously identified students to share.
• “___ noticed that for both same-sized shapes, a half of the shape was bigger than a fourth of the shape. Do you think that will always be true? Why?” (Yes. When you cut a circle into halves, it is two pieces. Then if you cut it into fourths, you get four smaller pieces. Fourths are smaller than halves of the same-size shape.)

Activity 2: Priya and Han Share Roti (10 minutes)

Narrative

The purpose of this activity is to help students generalize that partitioning the same-size shape into fourths creates smaller pieces than partitioning it 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 may also shade in part of a half to show fourths. 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).

Required Materials

Materials to Gather

Launch

• Groups of 2
• “What are some different types of food that you can share with another person?” (pizza, sandwich, papadum, quesadilla, tortilla)
• “This picture shows roti, a flatbread from India.”

Activity

• 5 minutes: partner work time
• Monitor for a student who shows and can explain that a half is bigger than a fourth.

Student Facing

Priya and Han are sharing roti.

• Priya says, “I want half of the roti because halves are bigger than fourths.”

• Han says, “I want a fourth of the roti because fourths are bigger than halves because 4 is bigger than 2.”

Who do you agree with?

Show your thinking using drawings, numbers or words.

Use the circle if it helps you.

Activity Synthesis

• Invite previously identified students to share.

MLR8 Discussion Supports

• “Who can restate what ____ shared in their own words?”
• Consider providing students time to restate what they heard to a partner before selecting one or two students to share with the class.
• Ask the original speaker if their peer was accurately able to restate their thinking.

Activity 3: Introduce Geoblocks, Feel and Guess (15 minutes)

Narrative

The purpose of this activity is for students to learn stage 4 of the Geoblocks center. Students guess which geoblock is inside a bag, without looking at the block.

Required Materials

Materials to Gather

Required Preparation

• Place 4–6 different geoblocks into a bag that is not see-through for each group of 2 students.

Launch

• Groups of 2
• Give each group of students a bag containing 4-6 solid shapes.
• “We are going to learn a new way to play Geoblocks, called Feel and Guess.”
• “One partner will reach into the bag and feel one shape without looking at it. Feel the shape until you can guess which shape it is. Once you guess, remove the shape and show it to your partner. If your partner agrees, put the shape back into the bag, and switch roles.”

Activity

• 10 minutes: partner work time

Activity Synthesis

• “What did you feel that helped you guess the shape?” (I felt if the shape had points or not. I felt the shape of the sides on the shape.)

Lesson Synthesis

Lesson Synthesis

“In this section we learned about splitting shapes into equal pieces. What have you learned?” (I learned that a half is larger than a fourth. I learned that a quarter is another way to say a fourth. I learned that when one piece is shaded it is a fourth or a half, but when the entire shape is shaded it’s called 'two of the halves' or 'four of the fourths'.)

Student Section Summary

Student Facing

We learned that circles and rectangles can be split into two equal pieces which are called halves and four equal pieces which are called fourths or quarters.

A half of the square is shaded.

A fourth or a quarter of the circle is shaded.

Two of the halves are shaded.

Four of the fourths are shaded.