# Lesson 8

¿Todas las partes son creadas iguales?

## Warm-up: Conversación numérica: 5 unidades (10 minutes)

### Narrative

The purpose of this Number Talk is to elicit strategies and understandings students have for subtracting multiples of 5 from 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. Monitor for the different ways students use the relationship between the numbers in each expression to choose their strategy. For example, students may subtract by place when both numbers have a 5 in the ones place or look for ways to count on by 5 and 10 (MP7).

### Launch

• 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

### Activity

• Keep expressions and work displayed.
• Repeat with each expression.

### Student Facing

Encuentra mentalmente el valor de cada expresión.

• $$25 - 15$$
• $$40 - 15$$
• $$65 - 25$$
• $$60 - 35$$

### Activity Synthesis

• “¿Qué patrones observaron cuando encontraban el valor de estas expresiones?” // “What patterns did you notice when finding the value of these expressions?” (All the expressions were subtracting a number that had a 5 in the ones place. All the numbers are numbers we say when we count by 5, so we can count by 5 and 10 to find the values. When both numbers had a 5 in the ones place, I just subtracted the tens and knew there would be 0 ones. When only one number had a 5 in the ones place, I thought about adding on to make it easier.)

## Activity 1: Hagamos cuartos y medios (20 minutes)

### Narrative

The purpose of this activity is for students to explore different ways to partition rectangles into halves and fourths. They notice that when they partition two equal-size rectangles into fourths or halves in different ways the resulting pieces may have different attributes. In the synthesis, students explain why the equal pieces of the same whole could look very different even though they have the same size, so long as the original shape was split into the same number of equal pieces (MP3, MP7).

MLR2 Collect and Display. Synthesis: Direct attention to words collected and displayed from the previous lesson. Invite students to borrow language from the display as needed, and update it throughout the lesson.

### Launch

• Groups of 2
• “Lin quería partir este cuadrado en cuartos. Ella empezó por partir el cuadrado en medios” // “Lin wanted to partition this square into quarters. She started by splitting the square into halves.”
• Display the square partitioned into halves.
• “Después de dibujar la primera línea, ella intentó hacer cuartos de 3 maneras distintas” // “After she drew the first line, she tried 3 different ways to make fourths.”
• Display the 3 squares split into 4 pieces.
• “¿Cuál de estos muestra cuartas partes o cuartos? Expliquen” // “Which of these shows fourths or quarters? Explain.” (B is the only one that shows four equal pieces, so they are fourths. The other 2 show 4 parts, but they are not equal.)
• 30 seconds: quiet think time
• 1 minute: partner discussion
• Share and record responses.

### Activity

• “Ahora van a tener la oportunidad de explorar distintas maneras de partir figuras para hacer cuartas partes o cuartos y medios” // “Now you will have a chance to explore different ways to partition shapes to make fourths or quarters and halves.”
• “Individualmente, partan sus figuras y respondan las preguntas sobre las partes. Después, comparen su trabajo con el de su compañero” // “Work on your own to partition your shapes and answer the questions about the pieces. Then compare your work with your partner.”
• 6 minutes: independent work time
• 4 minutes: partner discussion
• Monitor for students who show different ways to partition the rectangle into fourths (see Student Responses).

### Student Facing

Después de dibujar la primera línea, ella intentó hacer cuartos de 3 maneras distintas.

1. ¿Cuál de estos muestra cuartas partes o cuartos? Explica y comparte con tu compañero.
2. Escribe el nombre de la parte coloreada.

La figura A tiene un ________________ coloreado.

La figura B tiene un ________________ coloreado.

3. Muestra 2 maneras distintas de partir el rectángulo en cuartos o cuartas partes. Colorea un cuarto del rectángulo.

### Activity Synthesis

• Invite previously identified students to share their rectangles partitioned to make fourths.
• Display students’ work.
• “Cada uno de estos estudiantes cree que ha partido el rectángulo en cuartas partes o cuartos. ¿Con quién están de acuerdo? Expliquen” // “Each of these students believe they have split the rectangle into fourths or quarters. Who do you agree with? Explain.” (The pieces look different in each rectangle, but they all show fourths because each rectangle is split into 4 equal pieces.)

## Activity 2: Hagamos partes iguales (15 minutes)

### Narrative

The purpose of this activity is for students to consider different ways to partition a circle or rectangle into thirds. They continue to deepen their understanding that equal pieces of the same whole can look different. Monitor for the ways students reason that the equal pieces of the same whole may look different, but they are the same size to share in the lesson synthesis (MP3, MP7).

Representation: Develop Language and Symbols. Synthesis: Maintain a visible display to record images of ways to make thirds (also add fourths and halves) to reiterate that fractions have equal parts and can be made in certain ways. Invite students to suggest details (words or pictures) that will help them remember the meaning of the fractions.
Supports accessibility for: Memory, Language, Organization

• Groups of 2

### Activity

• “A Lin, Mai y Andre se les pidió que colorearan un tercio de una figura. Observen las imágenes y escojan las que muestran un tercio coloreado. Expliquen cómo lo saben o si están en desacuerdo” // “Lin, Mai, and Andre were asked to shade in one third of a shape. Look at their images and choose the ones that show one third shaded. Explain how you know or if you disagree.”
• 2 minutes: partner discussion
• “Ahora, individualmente, completen los 2 últimos problemas” // “Now work independently to complete the last 2 problems.”
• 6 minutes: independent work time
• Monitor for students who have a clear explanation for Diego’s brother to share in the lesson synthesis.

### Student Facing

1. A Lin, Mai y Andre se les pidió que colorearan un tercio de una figura.

Lin

Mai

Andre

¿Todas las figuras muestran un tercio coloreado? Explica y comparte con un compañero.

2. Parte el rectángulo en tercios y colorea un tercio de la figura.
3. El papá de Diego hizo 2 panes de maíz en sartenes cuadradas y los cortó en rebanadas para la familia.

Para el hermano de Diego

Para Diego

El hermano menor de Diego estaba enojado porque él pensó que su parte de pan de maíz era más pequeña que la de Diego. ¿Qué le dirías?

### Student Response

If students agree that both Diego and Diego’s brother each got a fourth, but disagree that they got the same amount because the shape of their pieces is different, consider asking:

• “¿En qué se parecen y en qué son diferentes las partes de pan de maíz de Diego y su hermano?” // “How are the pieces of cornbread Diego and his brother have the same and different?”
• “¿Ven alguna manera en la que podrían separar y volver a juntar la parte del hermano de Diego para que tenga la misma forma que la parte de Diego?” // “Do you see a way you could break apart Diego's brother's piece and put it back together so it's the same shape as Diego's piece?”

### Activity Synthesis

• Invite previously selected students to share.
• “¿Cómo puede ser que ambos estudiantes hayan coloreado un tercio si sus partes no se ven iguales?” // “How is it possible that both students have shaded a third if they don’t look the same?” (Their thirds might not look the same when compared to each other, but they each partitioned the rectangle into 3 equal parts and shaded one part.)

## Lesson Synthesis

### Lesson Synthesis

“Hoy aprendieron que si una figura se parte en el mismo número de partes iguales, pero de maneras distintas, las partes de las figuras tienen el mismo nombre, aunque se vean diferentes” // “Today, you learned that if a shape is partitioned into the same number of equal pieces, but in different ways, the pieces of the shapes will have the same name, even though they look different.”

Display or draw:

“El hermano de Diego estaba enojado por su parte de pan de maíz. ¿Cómo podríamos ayudar al hermano de Diego?” // “Diego's brother was upset about his piece of cornbread. How could we help Diego’s little brother?”

Invite previously selected students to share their reasoning.

“Como ambas sartenes tienen el mismo tamaño, sabemos que los dos hermanos recibieron un cuarto de lo que había en la sartén, aunque las partes se vean distintas. Las partes se ven diferentes, pero es la misma cantidad” // “Since both pans are the same size, we know that both brothers got a fourth of the pan even though it looks different. The pieces look different, but it's the same amount.”