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 to talk about the characteristics of the items and the quantities they represent. During the Activity Synthesis, ask students to explain the meaning of any terms they use, such as “partition,” “equal parts,” “halves,” and “thirds.”
Launch
Groups of 2
Display the image.
“Escojan 3 rectángulos que vayan juntos. Prepárense para compartir por qué van juntos” // “Pick 3 rectangles that go together. Be ready to share why they go together.”
1 minute: quiet think time
Activity
“Discutan con su pareja cómo pensaron” // “Discuss your thinking with your partner.”
2–3 minutes: partner discussion
Share and record responses.
¿Cuáles 3 van juntos?
A
B
C
D
Student Response
Loading...
Advancing Student Thinking
Activity Synthesis
“¿Podemos marcar las partes de cada rectángulo con la misma fracción? ¿Por qué sí o por qué no?” // “Can we label the parts of each rectangle with the same fraction? Why or why not?” (We can label the parts in A, B, and D with the same fraction 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?” ( in A and D, and in B.)
Activity 1
Standards Alignment
Building On
Addressing
3.NF.A.1
Understand a fraction as the quantity formed by 1 part when a whole is partitioned into equal parts; understand a fraction as the quantity formed by parts of size .
The purpose of this activity is for students to practice partitioning and labeling equal-size 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 for reference in future lessons. They also will need the fraction strips for activities in Section C. Consider having them glue the fraction strips in their student book.
When students make halves, fourths, and eighths, they observe regularity in repeated reasoning as each piece is subdivided into two equal pieces. They observe the same relationship between thirds and sixths (MP8).
Engagement: Develop Effort and Persistence. Chunk this task into more manageable parts. Check in with students to provide feedback and encouragement after each chunk. Check in after students fold and label each fraction strip. Supports accessibility for: Organization, Attention
Launch
Groups of 2
Give each student one set of 6 equal-size 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.
Activity
“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
Tu profesor te va a dar algunas tiras de papel. Cada tira representa 1.
Dobla cada tira de forma que las partes representen una de las siguientes fracciones. Usa una tira para cada fracción.
medios
cuartos
octavos
tercios
sextos
Cuando termines de doblar las tiras, traza rectas sobre los dobleces con un lápiz, y luego marca cada parte con la fracción que le corresponde.
Student Response
Loading...
Advancing Student Thinking
Activity Synthesis
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.
Activity 2
Standards Alignment
Building On
Addressing
3.NF.A.1
Understand a fraction as the quantity formed by 1 part when a whole is partitioned into equal parts; understand a fraction as the quantity formed by parts of size .
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 to continue to practice naming the parts with the unit fractions , , , , and . It’s important that students try to make the parts as close to equal in size as they can, but students’ drawings do not need to be exact. After they practice partitioning, students partition and shade—but do not label—a fraction on a rectangle, and then they trade with a partner to determine the fraction their partner has shaded. The Activity 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.
MLR8 Discussion Supports. At the appropriate time, give students 2–3 minutes to make sure that everyone in their group can explain their process for partitioning their rectangles and for determining how to label each part. Invite groups to rehearse what they will say when they share with the whole class. Advances: Speaking, Representing
Launch
Groups of 2
Activity
“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-size parts and what fraction they used to label each part.
“Completen la primera parte 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 the first part 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 both are finished, share your reasoning.”
1–2 minutes: independent work time
1–2 minutes: partner work time
Parte cada rectángulo en medios, tercios, cuartos, sextos y octavos. Después, marca cada parte con la fracción que le corresponde.
medios
tercios
cuartos
sextos
octavos
Haz una partición del rectángulo en partes de igual tamaño. Colorea una de esas partes.
Intercambia el rectángulo con el de un compañero. Si el rectángulo completo representa 1, ¿qué número representa la parte coloreada? Explica tu razonamiento.
Activity Synthesis
Have 2 or 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 4 equal parts, so I knew my partner shaded one-fourth.)
Lesson Synthesis
Display a rectangle with each part labeled as a unit fraction and a rectangle shaded to show the unit fraction, such as:
sextos
un sexto o
“¿Cómo saben que el primer diagrama muestra sextos?” // “How do you know the first diagram shows sixths?” (It has 6 equal parts.)
“¿Por qué creen que el segundo diagrama está marcado con un sexto?” // “Why do you think the second diagram is labeled one-sixth?” (Only 1 of the six parts is shaded, so it’s just 1 of the sixths. We are focusing on 1 of the sixths.)
“El primer diagrama muestra sextos porque el rectángulo está partido en seis partes iguales. Cada parte es un sexto. El segundo diagrama muestra un sexto porque hay seis partes iguales y describimos cuántas partes están sombreadas. En este caso, una de las partes está sombreada” // “The first diagram shows sixths because the rectangle is partitioned into six equal parts. Each part is one-sixth. The second diagram shows one-sixth because there are six equal parts and we are describing how many parts are shaded. In this case, one of the parts is shaded.”
Standards Alignment
Building On
2.G.A.3
Partition circles and rectangles into two, three, or four equal shares, describe the shares using the words halves, thirds, half of, a third of, etc., and describe the whole as two halves, three thirds, four fourths. Recognize that equal shares of identical wholes need not have the same shape.
Understand a fraction as the quantity formed by 1 part when a whole is partitioned into equal parts; understand a fraction as the quantity formed by parts of size .