# Lesson 6

Compongamos y descompongamos figuras

## Warm-up: Observa y pregúntate: Una imagen de figuras (10 minutes)

### Narrative

The purpose of this warm-up is to elicit the idea that shapes can be used to compose other shapes, which will be useful when students compose shapes from equal-size shapes in a later activity. While students may notice and wonder many things about this image, identifying the shapes within the picture and noticing how they work together to compose something larger are the important discussion points.

Consider recording the shapes students name as they describe the image on chart paper for students to reference during the lesson. In addition to the vocabulary students used in the previous section (triangle, quadrilateral, hexagon), it may be helpful to review trapezoid and rhombus or add these terms to the chart. It is not necessary to provide a mathematical definition for these terms.

### Launch

• Groups of 2
• Display the image.
• “¿Qué observan? ¿Qué se preguntan?” // “What do you notice? What do you wonder?”
• 1 minute: quiet think time

### Activity

• “Discutan con su compañero lo que pensaron” // “Discuss your thinking with your partner.”
• 1 minute: partner discussion
• Share and record responses.

### Student Facing

¿Qué observas? ¿Qué te preguntas?

### Activity Synthesis

• Review the shape names that were recorded.
• “¿Qué otras figuras ven en esta imagen? ¿Qué otros nombres conocen para estas fichas geométricas?” // “What other shapes do you see in this picture? What other names do you know for these pattern blocks?”
• “Algunos de ustedes dijeron que se ve como una persona montando en patineta” // “Some of you said this looks like a person riding a skateboard.”
• “¿Qué figuras forman la cabeza y el cuerpo de la persona?” // “What shapes make up the head and body of the person?”
• “¿Qué figuras forman los brazos de la persona?” // “What shapes make up the person's arms?”
• “¿Qué figuras forman la patineta?” // “What shapes make up the skateboard?”

## Activity 1: Muchas maneras de componer figuras (15 minutes)

### Narrative

The purpose of this activity is for students to compose the same shape in different ways. Students create a butterfly by composing hexagons using different pattern blocks. By composing hexagons with different combinations of shapes, students have the opportunity to see the shape composed of equal-size shapes and combinations of different shapes. Students are encouraged to explain how they composed their hexagons using the geometric language they’ve learned in previous lessons (MP6). For example, “I used 1 trapezoid and 3 triangles to make a hexagon.” Throughout the activity, listen for the ways students notice describe how they can compose a shape from or decompose shape into smaller shapes (MP6).

In the lesson synthesis, students may share many different ways to compose the hexagon, but the focus shifts to hexagons that are composed of equal-size pieces.

MLR8 Discussion Supports. Before students begin composing hexagons, remind students to use the name of each shape rather than the color of the pattern block. Invite students to chorally repeat the shape of each block.
Representation: Develop Language and Symbols. Provide students with access to the definitions of the shapes they will be using, so they can have conversations using the correct vocabulary terms.
Supports accessibility for: Language, Memory

### Required Materials

Materials to Gather

Materials to Copy

• Compose a Butterfly, Spanish

### Launch

• Groups of 2
• Give students pattern blocks and a copy of the blackline master.
• Display the pattern block butterfly image.

### Activity

• “Mai usó fichas geométricas para hacer este diseño. Con su compañero, hagan el mismo diseño sin usar ningún hexágono amarillo” // “Mai used pattern blocks to make this design. Work with a partner to make the same design without using any yellow hexagons.”
• “Intenten usar tantas combinaciones distintas de figuras como puedan para formar cada hexágono” // “Try to use as many different shape combinations as you can to make each hexagon.”
• “Dentro de cada hexágono, dibujen las líneas para mostrar cómo lo compusieron” // “For each hexagon, draw the lines inside the shape to show how you composed it.”
• “Escojan uno de sus hexágonos. Usen palabras y números para explicar cómo lo compusieron” // “Pick one of your hexagons. Use words and numbers to explain how you composed it.”
• 10 minutes: partner work time
• Monitor for students who:
• compose a hexagon using equal-size shapes: 2 trapezoids, 6 triangles, or 3 blue rhombuses
• compose hexagons using different shapes

### Student Facing

Mai usó fichas geométricas para hacer este diseño. Con tu compañero, haz el mismo diseño sin usar ningún hexágono amarillo.

### Student Response

If students make a hexagon using the same shapes multiple times, consider asking:

• “¿Cómo sabes que estas figuras forman un hexágono?” // “How do you know these shapes make a hexagon?”
• “¿Cómo podrías usar otras fichas para formar la misma figura?” // “How could you use different blocks to make the same shape?”

### Activity Synthesis

• Invite previously identified students to display their hexagons. Begin with the examples of hexagons composed of the same shape. Then select students to share other examples of hexagons composed of different shapes.
• If possible, display student hexagons as they share. Keep the hexagons displayed into two groups like the following:

• “Encontraron muchas maneras de componer un diseño de mariposa sin usar hexágonos. ¿Qué observan acerca de estos dos grupos de hexágonos?” // “You found a lot of different ways to compose a butterfly design without using hexagons. What do you notice about these two groups of hexagons?” (In the first group, they are made using the same shape. 6 triangles, 2 trapezoids, or 3 rhombuses. Each hexagon in the second group is made using more than 1 shape.)

## Activity 2: Usemos figuras pequeñas de igual tamaño para componer otras figuras (20 minutes)

### Narrative

The purpose of this activity is for students to compose shapes with 2, 3, or 4 equal-size shapes. The work of this activity lays the foundation for partitioning shapes into halves, thirds, or fourths.

Students make three different shapes using 2, 3, or 4 pattern blocks of the same shape. They record their compositions on either the triangle or square grid paper. The structure of the grids helps students make sure that each of the parts of their shapes are equal.

### Required Materials

Materials to Gather

Materials to Copy

• Centimeter Dot Paper - Standard
• Isometric Dot Paper - Standard

### Launch

• Give each student pattern blocks.
• Display the 3 shape images.
• “¿En qué se parecen? ¿En qué son diferentes?” // “What is the same? What is different?”
• 30 seconds: quiet think time
• Share responses.

### Activity

• “En esta actividad, van a hacer figuras en las que solamente se usa la misma figura de igual tamaño, como en la primera y la tercera figura” // “In this activity, you are going to make shapes that only use the same equal-size shape, like the first and third shapes.”
• “Usen 2, 3 o 4 figuras iguales y del mismo tamaño para componer tres figuras distintas. Muestren el contorno de cada ficha en el papel cuadriculado. Nombren cada figura y expliquen cómo la compusieron” // “Compose three different shapes using 2, 3, or 4 of the same equal-size shape. Show the outline of each block on the grid paper. Name each shape and explain how you composed it.”
• “Pueden usar papel de puntos con patrón triangular o cuadrado como ayuda” // “You can use the triangle or square grid paper to help you record.”
• As needed, demonstrate drawing the outline and naming the hexagon formed from 6 triangles from the launch on dot or grid paper.
• 8 minutes: independent work time
• Monitor for a student who composes a shape out of 2 blocks and one who composes a shape out of 4 blocks.

### Student Facing

¿En qué se parecen? ¿En qué son diferentes?

• Usa 2, 3 o 4 figuras iguales y del mismo tamaño para componer 3 figuras distintas.
• Nombra cada figura y explica cómo la compusiste.
1. Usé ________________________________

para componer un _____________________________.

2. Usé ________________________________

para componer un _____________________________.

3. Usé ________________________________

para componer un _____________________________.

### Activity Synthesis

• Display selected students’ shapes.
• “Describan cómo están compuestas estas figuras” // “Describe how these shapes are composed.” (They used 2 trapezoids to compose a hexagon. They used 4 small squares to compose a larger square.)

## Lesson Synthesis

### Lesson Synthesis

“Hoy pensamos en cómo se pueden hacer figuras usando otras figuras. A partir de figuras pequeñas del mismo tamaño, compusimos otras figuras” // “Today we thought about how shapes could be made using other shapes. We composed shapes from equal-size smaller shapes.”

“Díganle a su compañero 2 figuras distintas que hayan hecho hoy. Describan qué figuras usaron para componerlas” // “Tell your partner 2 different shapes you made today. Describe what shapes you used to compose your shapes.” (I made a larger square out of 4 smaller squares. I made a hexagon with 2 trapezoids. I composed a pentagon with a square and a triangle.)

Share and record responses.