Lesson 9

The purpose of this Number Talk is to elicit strategies and understandings students have for adding multiples of 5 to multiples of 5. These understandings help students develop fluency and will be helpful later in this unit when students will learn to tell time to the nearest 5 minutes.

• Display one expression.
• “Give me a signal when you have an answer and can explain how you got it.”
• 1 minute: quiet think time

• Record answers and strategies.
• Keep expressions and work displayed.
• Repeat with each expression.

• “What patterns did you notice working with these numbers?”
• “How could the second problem help you think about the last one?” (I know that \(15 + 15 = 30\), so it was the same problem.)

The purpose of this activity is for students to learn that when you partition a shape into 2, 3, or 4 equal pieces, the whole shape can be named as 2 halves, 3 thirds, 4 fourths respectively. This activity uses the context of pizza to intentionally elicit “whole” from students to describe the situation. They will continue to deepen their understanding of a whole as a mathematical term during their study of fractions in grade 3. Students observe regularity in repeated reasoning (MP8) when they see that however many equal pieces the whole pizza is cut into, 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.

• Groups of 2

MLR5 Co-Craft Questions

• Display only the problem stem and image for Clare’s pizza, without revealing the questions. 
• “Clare’s friends were going to share a pizza. The image shows how they cut the pizza.”
• “Write a list of mathematical questions that could be asked about this situation.” (How many friends does she have? How much pizza can each friend get? Can they slice the pizza a different way? What would be a fair way to share the pizza with her friends?)
• 2 minutes: independent work time
• 2–3 minutes: partner discussion
• Invite several students to share one question with the class. Record responses.
• “What do these questions have in common? How are they different?”
• Reveal the additional context and questions for Clare’s pizza (students open books), and invite additional connections. 
• “Why do you believe her friends are upset?” (The pizza is cut into thirds, so 3 slices would be the whole pizza. 3 thirds is the same as the whole thing.)

• “Now you and your partner will discuss what happened in each problem when students share a pizza.”
• 10 minutes: partner work time

If students disagree that 2 halves, 3 thirds, or 4 fourths is the same as the whole pizza, consider asking:

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

• Invite students to share how much of the pizza each group of friends ate using halves, thirds, fourths, and quarters.
• Record responses.
• “Each group had the same-size pizza. Of all the students, which group of students will have the largest slices? Why do you think that is?” (Jada and Mai only have to share the pizza with 2 people, so they have the largest pieces.)
• “What do you notice about the size of the slices and the number of students?” (The slices get smaller if there are more students.)
• Share and record responses.

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 one fourth when describing a piece, but encourage the use of a quarter as a way to describe the same piece.

• Groups of 2
• Give students access to colored pencils.

• “You are going to read some stories with a partner about students sharing pies.”
• “Then you will partition and color shapes on your own.”
• 5 minutes: partner work time
• As students work, encourage them to use precise language when talking with their partners.
• Consider asking: “Is there another way you could say how much of the circle is shaded?"
• 10 minutes: independent work time
• Monitor for students who accurately shade the circles to share in the synthesis.

• 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?” (They are both 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)