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.
• “Hagan una señal cuando tengan una respuesta y puedan explicar cómo la obtuvieron” // “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.

• “¿Qué patrones observaron al trabajar con estos números?” // “What patterns did you notice working with these numbers?”
• “¿Cómo les puede ayudar el segundo problema a pensar en el último?” // “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. 
• “Los amigos de Clare iban a compartir una pizza. La imagen muestra cómo cortaron la pizza” // “Clare’s friends were going to share a pizza. The image shows how they cut the pizza.”
• “Escriban una lista de preguntas matemáticas que se pueden hacer sobre esta situación” // “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.
• “¿Qué tienen en común estas preguntas? ¿En qué son diferentes?” // “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. 
• “¿Por qué creen que los amigos de Clare están enojados?” // “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.)

• “Ahora ustedes y su compañero van a discutir sobre lo que ocurrió en cada problema cuando los estudiantes compartieron una pizza” // “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:

• “Si Jada se comió esta parte (un medio) y Mai se comió esta parte (un medio), ¿cuánta pizza queda?” // “If Jada ate this piece (one half) and Mai ate this piece (one half), how much of the pizza is left?” 
• “¿Cómo podrías mostrar cuánto de la pizza se comió cada estudiante?” // “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.
• “Cada grupo tenía una pizza del mismo tamaño. ¿En cuál grupo los estudiantes obtendrán las tajadas más grandes? ¿Por qué piensan que ocurre esto?” // “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.)
• “¿Qué observan sobre el tamaño de las tajadas y el número de estudiantes?” // “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.

• “Con un compañero, van a leer algunas historias sobre estudiantes que comparten tartas” // “You are going to read some stories with a partner about students sharing pies.”
• “Después, individualmente, van a partir y a colorear figuras” // “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: “¿Hay alguna otra manera en la que podrían decir cuánto del círculo está sombreado?” // “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.
• “¿En qué se parecen los círculos que partiste y sombreaste? ¿En qué son diferentes?” // “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.)
• “En cada caso, ¿cuánto del círculo está sombreado?” // “How much of each circle is shaded?” (4 fourths, 2 halves, the whole circle)