# Lesson 9

Partes iguales

## Warm-up: Cuál es diferente: Pedazos de figuras (10 minutes)

### Narrative

This warm-up prompts students to carefully analyze and compare images. In making comparisons, students have a reason to use language precisely (MP6). The activity also enables the teacher to hear the terminologies students know and how they talk about characteristics of shapes and pieces of shapes. To help all students distinguish the composite shapes from the smaller shapes they are made up of, invite students to clarify or show what they mean when they describe attributes of the shapes they see in each image.

### 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: Construyamos un círculo (10 minutes)

### Narrative

The purpose of this activity is for students to recognize the difference between equal-size pieces and unequal-size pieces. Students work together to make circles from the pieces they are given. After some circles have been made, students discuss what they notice about each circle. Both circles have four pieces, however one has equal-size pieces and the other doesn't.
MLR8 Discussion Supports. Synthesis. Display sentence frames to support whole-class discussion: “Estas piezas son / no son iguales porque . . .” // “These pieces are/are not equal because…” and “Con estas piezas se forma / no se forma un círculo porque . . .” // “These pieces do/do not make a circle because…”

### Required Materials

Materials to Copy

• Pieces of Circles

### Required Preparation

• Cut out the pieces of the circles on the blackline master. Each copy has enough pieces for 8 students.

### Launch

• Give each student one piece of a circle.
• “Hoy vamos a hacer círculos. Cada círculo estará formado por cuatro piezas. Van a recorrer el salón y a buscar tres personas que tengan piezas que encajen con la suya para formar un círculo” // “Today we are going to make circles. Each circle will be made up of four pieces. You will walk around and find three other people who have pieces that fit with yours to make a circle.”
• “Si intentan juntar su pieza con las otras tres y no forman un círculo, busquen otras personas que tengan otras piezas e intenten de nuevo” // “If you try to put your piece together with three other pieces and they don’t make a circle, find other people with different pieces and try again.”
• “Cuando hayan hecho un círculo, déjenlo sobre la mesa y siéntense. Así sabremos que ya terminaron” // “When you have made a circle, leave it on the table, and sit down so we know you are done.”

### Activity

• 5 minutes: whole-class work time
• Monitor for a group that makes a circle with equal-size pieces and one that makes a circle with unequal-size pieces.

### Student Facing

Síntesis:

¿En cuál se muestran piezas iguales que forman un círculo?

### Activity Synthesis

• Display the two different circles that were made, or the images in the student book.
• “Hicimos estos dos círculos. ¿Qué observan acerca de ellos?” // “We made these two circles. What do you notice about them?” (One of them has pieces that all look the same. One has a tiny piece and some bigger pieces. They both have four pieces but the pieces are different sizes.)

## Activity 2: Doblemos en partes iguales (15 minutes)

### Narrative

The purpose of this activity is for students to fold circles and squares into two or four equal pieces. To make equal pieces, some students may partition the shape by folding it down the middle (and folding again for fourths) and matching up the edges of the shapes. There are several ways students may fold their square into equal pieces--vertically, horizontally, or diagonally--although each way gives different shaped pieces, they all result in four equal pieces. There are many ways to fold the circle but the size and shape of the pieces when it is folded are all the same (MP8).

### Required Materials

Materials to Gather

Materials to Copy

• Circles and Squares

### Required Preparation

• Consider having extra shapes cut from the blackline masters for students who may need more than one of each shape.

### Launch

• Give each student a copy of the blackline master and scissors.

### Activity

• 10 minutes: independent work time
• Monitor for students who line up the edges and fold the square horizontally, vertically, or diagonally, and a student who folds the circle.

### Student Facing

Dobla cada figura de manera que queden 2 partes iguales.

Prepárate para explicar cómo sabes que tu figura tiene 2 partes iguales.

Dobla cada figura de manera que queden 4 partes iguales.

Prepárate para explicar cómo sabes que tu figura tiene 4 partes iguales.

### Activity Synthesis

• Invite previously identified students to share.
• “¿Su papel está doblado de una manera en la que cada parte tiene el mismo tamaño? ¿Cómo lo saben?” // “Is your paper folded so that each piece is the same size? How do you know?” (Yes, the pieces line up perfectly. No. when I fold it on the line, one piece is bigger.)
• Consider cutting out the pieces and laying them on top of one another to show whether or not they are the same size.

## Activity 3: Mitades y cuartos (10 minutes)

### Narrative

The purpose of this activity is for students to be introduced to the terms halves and fourths. In the launch, students explore examples and non-examples of shapes split into halves and fourths and develop a shared understanding of what these terms mean (MP6). Students then draw lines to partition shapes into halves or fourths. During the synthesis students learn that the term 'quarters' means the same as fourths. Fourths and quarters will be used interchangeably throughout this section.

Action and Expression: Develop Expression and Communication. Give students access to a straight edge or ruler.
Supports accessibility for: Fine Motor Skills, Visual-Spatial Processing

### Launch

• Groups of 2
• Display the categories of shapes from the student workbook.
• “Estas son algunas figuras que están partidas en varias partes” // “Here are some shapes split into pieces.”
• “¿Qué observan?” // “What do you notice?” (One table shows shapes split into two pieces and the other table shows shapes split into four pieces. The pieces are equal in the first group.)
• 1 minute quiet think time
• 2 minutes: partner discussion
• Record responses.
• “Teniendo en cuenta lo que observaron, ¿qué piensan que significa ‘partir en mitades’? ¿Qué piensan que significa ‘partir en cuartos’?” // “Based on what you observed, what do you think split into halves means? What do you think split into fourths means?”
• 1 minute quiet think time
• Record responses.
• “Las mitades son las partes que se crean cuando una figura se parte en dos partes que tienen el mismo tamaño. Los cuartos son las partes que se crean cuando una figura se parte en cuatro partes que tienen el mismo tamaño” // Halves are the pieces created when a shape is split into two pieces that are the same size. Fourths are the pieces created when a shape is split into four pieces that are the same size.”

### Activity

• 4 minutes: independent work time
• Monitor for students who accurately partition the shapes into fourths in different ways.

### Student Facing

2. Parte cada figura en cuartos.
3. Parte cada figura en cuartos.
6. Parte cada figura en cuartos.

### Student Response

Students may split the shapes into halves accurately by drawing a vertical or horizontal line down the middle of each shape. These students may attempt to create fourths, for the rectangles and circles, using the same technique by guessing-and-checking. Ask these students to explain their method and what they hope to achieve. Consider asking:

• “¿Cuántas partes estás tratando de crear?” // “How many pieces are you trying to create?”
• “¿Cómo puedes asegurarte de que todas las partes tienen el mismo tamaño?” // “How can you make sure they are the same size?”
• “¿Cómo doblarías esta figura para obtener __ partes iguales?” // “How would you fold this shape to make __ equal pieces?”
• “¿Cómo te puede ayudar la tabla de figuras que vimos antes a planear cómo obtener __ partes iguales?” // “How can you use the table of shapes we looked at earlier to help plan how to make __ equal pieces?”

### Activity Synthesis

• Invite previously identified students to share.
• “¿Todas estas figuras muestran cuartos? ¿Cómo lo saben?” // “Do all of these shapes show fourths? How do you know?” (Yes, each of the shapes have 4 equal pieces. Each of the pieces are the same size.)
• “Cuando partimos una figura en cuatro partes de igual tamaño, la figura queda partida en cuartos. También podemos decir que la figura está partida en cuartas partes” // “When we split a shape into four equal-sized pieces, the shape is split into fourths. We can also say the shape is split into quarters.”

## Lesson Synthesis

### Lesson Synthesis

Display the two circles from activity 1.

“Tyler dice que ambos círculos están partidos en cuartos. ¿Están de acuerdo? ¿Por qué sí o por qué no?” //  “Tyler says both circles are split into fourths. Do you agree? Why or why not?” (Fourths are four equal pieces. The first circle is split into fourths because the four pieces are all the same size. The second circle has four pieces but they are not the same size, so it is not split into fourths.)

“¿De qué otra manera se puede describir cómo está partido el primer círculo?” //  What is another way to describe how the first circle is split?” (It is split into quarters.)