Lesson 2

This warm-up prompts students to compare four rectangles that have been partitioned and partially shaded. It gives students a reason to use language precisely (MP6). It gives the teacher an opportunity to hear how students use terminology and talk about the characteristics of the items and the quantities they represent. During the synthesis, ask students to explain the meaning of any terminology they use, such as partition, equal parts, halves, and thirds.

• Groups of 2
• Display the image.
• “Escojan una que sea diferente. Prepárense para explicar por qué es diferente” // “Pick one that doesn’t belong. Be ready to share why it doesn’t belong.”
• 1 minute: quiet think time

• “Discutan con su pareja cómo pensaron” // “Discuss your thinking with your partner.”
• 2–3 minutes: partner discussion
• Share and record responses.

• “¿Podemos marcar las partes con fracciones? ¿Por qué sí o por qué no?” // “Can we label the parts with fractions? Why or why not?” (We can label the parts in A, B, and D with fractions because they are equal in size, but not in C because the parts aren’t the same size.)
• “¿Cómo se llaman las partes de las figuras A, B y D?” // “What do we call the parts in A, B, and D?” (“Halves” in A and D, and “thirds” in B.)
• “¿Qué fracciones usamos para marcar las partes de las figuras A, B y D?” // “What fractions do we use to label the parts in A, B, and D?” (\(\frac{1}{2}\) in A and D, and \(\frac{1}{3}\) in B.)
• Consider asking: “Encontremos al menos una razón por la que cada una es diferente” // “Let’s find at least one reason why each one doesn’t belong.”

The purpose of this activity is for students to practice partitioning and labeling equal-sized parts with unit fractions. This provides students a physical tool they can use throughout the unit to make sense of fractions.

Have students keep their fractions strips to use in future lessons. Consider having students glue the fraction strips in their workbook.

When students make halves, fourths, and eighths they observe regularity in repeated reasoning as each piece is subdivided into 2 equal pieces. They observe the same relationship between thirds and sixths (MP8).

• Use the blackline master to create one set of 6 equal-sized strips for each student.

• Groups of 2
• Give each student one set of 6 equal-sized strips.
• “Hoy vamos a hacer tiras de fracciones” // “Today we are going to make fraction strips.”
• Demonstrate how to fold a strip into two halves. Emphasize that all the strips should be folded to make vertical partitions as shown in student responses.

• “Tómense unos minutos para doblar cada tira de forma que las partes representen medios, tercios, cuartos, sextos u octavos. Usen una tira para cada fracción” // “Take a few minutes to fold each strip so that the parts represent halves, thirds, fourths, sixths, or eighths. Use one strip for each fraction.”
• “Tracen rectas sobre los dobleces con un lápiz y después marquen cada parte con la fracción que le corresponde” // “Mark your folding lines with a pencil, and then label each part with the correct fraction.”
• 5–7 minutes: independent work time
• Monitor for students who fold their strips into fourths, sixths, and eighths by folding halves, thirds, and fourths, respectively, in half.
• “Compartan con su compañero cómo partieron sus tiras y cómo marcaron las partes” // “Share how you partitioned your strips and how you labeled the parts with your partner.”
• 2–3 minutes: partner discussion

• Invite students to display their partitioned strips. Keep a full set of fraction strips displayed.
• Ask previously identified students to share how they fold their strips to get 4, 6, and 8 equal parts.
• If not apparent from students' explanations, highlight that fourths, sixths, and eighths can be found by partitioning each half, third, and fourth, respectively, into two equal parts.

Previously, students partitioned rectangular pieces of paper into 2, 3, 4, 6, and 8 equal parts by folding. The purpose of this activity is for students to partition rectangles by drawing and continue to practice naming the parts with the unit fractions \(\frac{1}{2}\), \(\frac{1}{3}\), \(\frac{1}{4}\), \(\frac{1}{6}\), and \(\frac{1}{8}\). It’s important that students try to make the parts as close to equal-sized as they can, but student drawings do not need to be exact. After they practice partitioning, students partition and shade, but don’t label, a fraction on a rectangle, then trade with a partner to determine the fraction their partner has shaded. The synthesis focuses on how to name a single equal part, such as one sixth, rather than talking about all the equal parts in a shape, such as sixths. This will be helpful as students use non-unit fractions to name multiple equal parts in the next lesson.

• Groups of 2

• “Trabajen en el primer problema con su compañero. Partan cada rectángulo y marquen cada parte” // “Work with your partner to complete the first problem. Partition each rectangle and label each part.”
• 5–7 minutes: partner work time
• For each rectangle, have a group share how they partitioned the rectangle into equal-sized parts and what fraction they used to label each part.
• “Completen la parte a del siguiente problema individualmente. Partan el rectángulo y coloreen una parte para mostrar una fracción, pero no la marquen. No le digan a su compañero cómo partieron ni qué número están mostrando” // “Complete part a of the next problem on your own. Partition the rectangle and shade to show a fraction, but don’t label it. Don’t tell your partner how you are partitioning or what number you are showing.”
• 2 minutes: independent work time
• “Ahora, intercambien los rectángulos con su compañero y respondan la siguiente parte del problema usando el rectángulo de su compañero. Cuando ambos terminen, compartan cómo razonaron” // “Now, trade rectangles with your partner and answer the next part of the problem using their rectangle. When you are both finished, share your reasoning.”
• 1–2 minutes: independent work time
• 1–2 minutes: partner work time

• Have 2–3 students display their shaded rectangles.
• For each rectangle, ask, “¿Cómo supieron qué fracción del rectángulo coloreó su compañero?” // “How did you know what fraction of the rectangle your partner shaded?” (I counted the equal parts in the rectangle. There were four equal parts, so I knew my partner shaded a fourth.)