Lesson 10

Una de las partes, todas las partes

Warm-up: Cuál es diferente: Figuras partidas (10 minutes)

Narrative

This warm-up prompts students to compare four shapes split into pieces. It gives the teacher an opportunity to hear how students use geometric vocabulary and talk about the characteristics of the shapes in comparison to one another (MP6).

Launch

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

Activity

• “Discutan con su compañero lo que pensaron” // “Discuss your thinking with your partner.”
• 2-3 minutes: partner discussion
• Share and record responses.

Student Facing

¿Cuál es diferente?

Activity Synthesis

• “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.”

Activity 1: Colorea una parte (10 minutes)

Narrative

The purpose of this activity is to introduce the language of a half of and a fourth of a shape. Students begin by applying the language of halves and fourths, or quarters, to partition each shape. Students are asked to describe “cuánto” // “how much” of each shape is shaded to elicit a variety of responses that include half, fourth, or quarter, including the phrases “del cuadrado” // “of the square” or “del círculo” // “of the circle.” Monitor for a variety of words and phrases to share in the synthesis including:

• phrases that reference the pieces only (“un pedazo (o una parte)” // “one piece”).
• phrases that reference that some, but not all of the shape is shaded (“parte de ella”, “un poco” // “part of it,” “a little bit”)
• phrases that name the pieces (“un medio (o una mitad)”, “un cuarto”, “una cuarta parte” // “a half,” “a fourth,” “a quarter”)
• phrases that name the pieces in reference to the whole shape (“un medio del cuadrado (o una mitad del cuadrado)”, “un cuarto del círculo” // “a half of the square,” “a fourth of the circle”)

All responses should be shared and compared in the synthesis to help build students understanding of the new vocabulary and the concept of fractional pieces of a whole (MP6).

Required Materials

Materials to Gather

Launch

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

Activity

• 2 minutes: independent work time.
• 2 minutes: partner discussion
• Monitor for a range of ways to describe the amount shaded such as “some is shaded,” “one piece of the square is shaded,” “one out of two pieces is shaded,” or “a half is shaded.”

Student Facing

Colorea una de las mitades.
2. Parte el círculo en cuartos.

Colorea uno de los cuartos.
¿Cuánto del círculo esta coloreado?

Activity Synthesis

• Invite previously identified students to share for each problem. Sequence the students in the order described in the narrative.
• “Cada una de las partes de una figura que se ha partido en dos partes del mismo tamaño se llama una mitad. Cada una de las partes de una figura que se ha partido en cuatro partes del mismo tamaño se llama un cuarto” // “One piece of a shape split into two pieces that are the same size is called a half. One piece of a shape split into four pieces that are the same size is called a fourth.”
• For each shape, invite students to describe how much is colored in. (A half of the square is colored in. A fourth of the circle is colored in.)

Activity 2: Clasificación de tarjetas: Partes sombreadas (15 minutes)

Narrative

The purpose of this card sort is for students to connect words and phrases to visual representations of partitioned shapes. Students begin by sorting the cards in a way that makes sense to them, and then are invited to sort the shapes based on the language that can be used to describe them. In the activity synthesis, the phrases “two of the halves” and “four of the fourths” are introduced to describe shapes where all pieces are shaded in.

Keep cards D and N available to use during the lesson synthesis.

As students sort the shape cards they look for structure, namely the number of pieces making up each shape, whether or not the pieces are equal, and the number of those pieces that are shaded (MP7).

MLR2 Collect and Display. Circulate, listen for and collect the language students use as they describe the shapes. On a visible display, record words and phrases such as: “sombreada”, “mitad”, “cuarta parte”, “cuarto”, “iguales”, “no iguales”, “todo”, “figura” // “shaded,” “half,” “fourth,” “quarter,” “equal,” “not equal,” “whole,” “shape.” Invite students to borrow language from the display as needed, and update it throughout the lesson.

Required Materials

Materials to Copy

• Shaded Parts Cards

Required Preparation

• Create a set of Shaded Parts Cards for each group of 2.

Launch

• Groups of 2
• Give each group a set of cards.
• “Clasifiquen sus tarjetas de una manera que tenga sentido para ustedes. Luego, expliquen cómo las clasificaron” // “Sort your cards in a way that makes sense to you. Then explain how you sorted them.”
• 3 minutes: partner work time
• Share responses.

Activity

• “Ahora clasifiquen las tarjetas en las categorías que se muestran en su hoja. Piensen en palabras que pueden usar para describir las figuras de las tarjetas. Escriban la letra de cada tarjeta en el espacio de su categoría” // “Now, sort the cards into the categories shown on your paper. Think about what words you can use to describe the shape on each card. Write the letter of each card in the space for it's category.”
• 5 minutes: partner work time

Student Facing

1. Clasifica las tarjetas en categorías de una manera que tenga sentido para ti. Explica cómo agrupaste las tarjetas.

2. Clasifica tus tarjetas en estas categorías.
Escribe la letra de cada tarjeta en el espacio de su categoría.

Un cuarto está sombreado

Toda la figura está sombreada

No son partes iguales

Activity Synthesis

• Display card J.
• “¿Cómo podemos describir esta figura?” // “How can we describe this shape?” (It is a square. It is cut into halves. The whole shape is shaded.)
• “Cuando una figura está partida en mitades y ambas mitades están sombreadas, decimos que la figura entera está sombreada o que dos de las mitades están sombreadas” // “When a shape is split into halves and they are both shaded, we say the whole shape is shaded or two of the halves are shaded.”
• Repeat with card E.
• “Cuando una figura está partida en cuartos y todos están sombreados, decimos que toda la figura está sombreada o que cuatro de los cuartos están sombreados” // “When a shape is split into fourths and they are all shaded, we say the whole shape is shaded or four of the fourths are shaded.”

Activity 3: Describamos partes iguales (10 minutes)

Narrative

The purpose of this activity is for students to match language to visual representations of rectangles and circles partitioned and shaded in different ways.

Representation: Access for Perception. Read each of the phrases aloud. Students who both listen to and read the information will benefit from extra processing time.
Supports accessibility for: Language, Conceptual Processing

• Groups of 2

Activity

• “Pueden usar las frases más de una vez” // “You may use the phrases more than once.”
• 6 minutes: partner work time

Student Facing

Estas son algunas maneras de describir las figuras.
• partida en cuartas partes
• partida en mitades
• partida en cuartos
• un cuarto sombreado
• una cuarta parte sombreada
• cuatro de los cuartos sombreados

Para cada figura, escribe por lo menos una de las frases de la lista para describirla.

1.

2.

3.

4.

5.

6.

7.

Activity Synthesis

• Display the circle with four of the fourths shaded.
• “Hagamos una lista de todas las maneras en las que podríamos describir esta figura” // “Let’s list all the ways we could describe this shape.” (It’s split into fourths. It is split into quarters. Four of the fourths are shaded.)
• Repeat with other shapes as time permits.

Lesson Synthesis

Lesson Synthesis

Display cards D and N.

¿En qué se parecen las figuras? ¿En qué son diferentes?” // “How are the shapes the same? How are they different?” (They are both rectangles. They are both split into halves. They are split differently. One has a half shaded and one has two of the halves shaded.)