# Lesson 6

Compongamos y descompongamos 10 con fichas geométricas

## Warm-up: Conteo grupal: Practiquemos cómo contar de 10 en 10 (10 minutes)

### Narrative

The purpose of this warm-up is for students to count by 10 to 100. Although students see the written sequence of numbers, they are not required to identify numbers beyond 20 until Grade 1.

### Launch

• “Contemos hasta 100 de 10 en 10” // “Let’s count to 100 by 10.”
• Record as students count.
• Count to 100 by 10 2-3 times.

### Activity

• “¿Qué patrones ven?” // “What patterns do you see?”
• 1-2 minutes: quiet think time
• Record responses.

### Activity Synthesis

• “Por turnos, con su compañero, cuenten hasta 100 de 10 en 10” // “Take turns counting to 100 by 10 with your partner.”
• “Vamos a seguir practicando cómo contar hasta 100 de 10 en 10” // “We will keep practicing counting to 100 by 10.”

## Activity 1: La figura de Diego (10 minutes)

### Narrative

The purpose of this lesson is for students to solve a Put Together/Take Apart, Both Addends Unknown story problem in the context of putting together pattern blocks (MP2). If students finish early, invite them to find multiple solutions to the story problem.

MLR8 Discussion Supports. Synthesis: For each decomposition that is shared, invite students to turn to a partner and restate the recorded equation.

### Required Materials

Materials to Gather

### Launch

• Groups of 2
• Give students access to connecting cubes or two-color counters, 10-frames, and pattern blocks.
• “Cuéntenle a su compañero lo que ocurrió en la historia” // “Tell your partner what happened in the story.”
• 30 seconds: quiet think time
• 1 minute: partner discussion
• Monitor for students who accurately retell the story. Choose at least one student to share with the class.
• “Muestren cómo pensaron. Usen dibujos, números, palabras u objetos” // “Show your thinking using drawings, numbers, words, or objects.”

### Activity

• 2 minutes: independent work time
• 2 minutes: partner discussion
• “Si aún no lo han hecho, escriban una expresión que muestre cuántas fichas en forma de cuadrado y cuántas fichas en forma de triángulo usó Diego” // “If you haven’t already, write an expression to show how many square pattern blocks and triangle pattern blocks Diego used.”
• 2 minutes: independent work time

### Student Facing

Diego construyó una figura usando 10 fichas geométricas.

¿Entonces cuántas fichas en forma de triángulo usó Diego?

Expresión: _________________________________

### Activity Synthesis

• Invite students who found different decompositions of 10 to share.
• As students share, record each solution with an equation, such as $$10 = 7 + 3$$.
• “¿_____ y _____ mostraron lo que ocurrió en la historia? ¿Cómo lo saben?” // “Did _____ and _____ both show what happened in the story? How do you know?” (Yes. They both have 10 pattern blocks, with some triangles and some squares.)
• “En la siguiente actividad, vamos a encontrar otras maneras en las que podemos armar figuras usando 10 fichas geométricas” // “In the next activity, we will find more ways that we can make shapes with 10 pattern blocks.”

## Activity 2: Muchas maneras de formar 10 (20 minutes)

### Narrative

The purpose of this activity is for students to compose and decompose 10 in multiple ways in the context of putting together pattern blocks. In order to draw the shapes they created with pattern blocks, students may draw or trace each shape. Using different colored crayons (red for the red trapezoids, blue for the blue rhombuses) may help students differentiate between the shapes. Students are not expected to draw precise or accurate shapes. Students may use a combination of words, numbers, and colors to label and record how many of each pattern block they used in their book. In the activity synthesis, students look for patterns in equations and try to determine if all of the decompositions of 10 have been found (MP7).

Engagement: Internalize Self-Regulation. Provide students an opportunity to self-assess and reflect on the shapes they made for the number 10. For example, students should be able to recognize that their shape only consists of blue and red pattern blocks and that they should have the total number of blocks used for each color listed in each drawing.
Supports accessibility for: Organization, Memory, Conceptual Processing

### Required Materials

Materials to Gather

Materials to Copy

• Book of 10, Spanish

### Required Preparation

• Create a book for each student from the blackline master.
• Create a chart labeled with “trapezoids” and “rhombuses” as pictured:

### Launch

• Groups of 2
• “Con su compañero, junten 10 fichas geométricas para armar una figura. Usen únicamente rombos azules y trapecios rojos” // “Work with your partner to put together 10 pattern blocks to make a shape. Use only blue rhombuses and red trapezoids.”
• 2 minutes: partner work time
• “En la primera página de su libro, dibujen la figura que crearon” //  “Draw the shape that you created on the first page on your book.”
• 2 minutes: independent work time
• “¿Qué números o palabras pueden usar para describir la figura que crearon?” // “What numbers or words can you use to describe the shape that you created?” (10 for the 10 pattern blocks. 6 for the 6 blue pattern blocks. 4 for the 4 red pattern blocks.)
• 30 seconds: quiet think time
• 1 minute: partner discussion
• Share responses.
• “En la parte de arriba de la página, escriban un número para mostrar cuántas fichas geométricas usaron en total” // “At the top of the page, write a number to show how many pattern blocks you used altogether.”
• 30 seconds: independent work time
• “En la parte de abajo de la página, escriban números o palabras para mostrar cuántos trapecios rojos y cuántos rombos azules usaron” // “At the bottom of the page, write numbers or words to show how many red trapezoids and how many blue rhombuses you used.”
• 1 minute: independent work time

### Activity

• “Ahora van a crear distintas figuras con 10 fichas geométricas. Usen únicamente trapecios rojos y rombos azules. Cada vez que hagan una nueva figura, cambien el número de trapecios rojos y de rombos azules. Usen una página diferente de su libro para cada nueva figura que armen” //  “Now, you are going to create different shapes with 10 pattern blocks. Use only red trapezoids and blue rhombuses. Change the number of red trapezoids and blue rhombuses you use each time you make a new shape. Fill in a new page in your book for each new shape you create.”
• 15 minutes: partner work time

### Activity Synthesis

• Display the chart paper labelled with “trapecios” // “trapezoids” and “rombos” // “rhombuses”.
• “Escojan su página favorita de su libro. ¿Cuántas fichas azules en forma de rombo y cuántas fichas rojas en forma de trapecio usaron para crear la figura que está en su página favorita?” // “Pick your favorite page in your book. How many blue rhombus pattern blocks and how many red trapezoid pattern blocks did you use to create the shape on your favorite page?”
• Share and record all student responses as equations on a chart. Record the responses systematically, as in:
• $$10 = 1 + 9$$
• $$10 = 2 + 8$$
• $$10 = 3 + 7$$
• $$10 = 4 + 6$$
• $$10 = 5 + 5$$
• $$10 = 6 + 4$$
• $$10 = 7 + 3$$
• $$10 = 8 + 2$$
• $$10 = 9 + 1$$
• If a student shares a decomposition that was previously shared, point to the decomposition that was already listed.
• “¿Qué observan?” // “What do you notice?” (Sample responses: The numbers in one column go up. The other numbers go down. We didn’t write an equation with 4 trapezoids.)
• If not all decompositions of 10 are listed, ask “¿Hay otras maneras de formar 10 que faltan en nuestra lista? ¿Qué los hace pensar eso?” // “Are there any ways to make 10 that are missing from our list? What makes you think that?” (There’s no 4 under the trapezoid. If we did 6 trapezoids and 4 rhombuses, maybe we could do 4 trapezoids and 6 rhombuses instead.)

## Activity 3: Conozcamos “Revuelve y saca: Cubre (hasta 10)” (15 minutes)

### Narrative

The purpose of this activity is for students to learn stage 4 of the Shake and Spill center. Students use 3, 4, or 5 counters. They see some of the counters and determine how many more counters are under the cup. Students fill in expressions to represent each decomposition. Although determining the missing part of a total is not required by the standards, this activity helps students build fluency with addition and subtraction within 5. In a future variation of this center, students will play with up to 10 counters.

### Required Materials

Materials to Gather

Materials to Copy

• Shake and Spill Stage 4 Recording Sheet Kindergarten, Spanish

### Launch

• Groups of 2
• Give each group of students a cup, 5 two-color counters, and 2 copies of the blackline master.
• “Vamos a aprender una nueva forma de trabajar en el centro ‘Revuelve y saca’. Se llama ‘Revuelve y saca: Cubre’. Juguemos una ronda juntos” // “We are going to learn a new way to do the Shake and Spill center. It is called Shake and Spill, Cover. Let’s play a round together.”
• “Voy a poner 3 fichas en el vaso y las voy a revolver. Antes de sacar las fichas, van a cerrar sus ojos para que yo pueda cubrir todas las fichas amarillas con el vaso. Después, van a abrir los ojos y van a averiguar cuántas fichas hay debajo del vaso” // “I am going to put 3 counters in the cup and shake them up. Before I spill the counters, you will close your eyes so I can cover all the yellow counters with the cup. Then you will open your eyes and figure out how many counters are under the cup.”
• Put 3 counters in a cup and shake them up.
• “Cierren sus ojos” // “Close your eyes.”
• Spill the counters and cover 1 yellow counter. Leave 2 red counters on the table.
• “Abran sus ojos. Miren las fichas que hay en la mesa. ¿Cuántas fichas hay debajo del vaso? ¿Cómo lo saben?” // “Open your eyes. Look at the counters on the table. How many counters are under the cup? How do you know?” (One because there are 2 on the table and 2 and 1 more makes 3.)
• 30 seconds: partner discussion
• Share responses.
• Pick up the cup showing the 1 counter that was covered.
• “Ahora vamos a completar la hoja de registro. Teníamos 3 fichas en total. Luego, completamos la expresión que corresponde a las partes en las que separamos al 3. Había 2 fichas por fuera del vaso y 1 ficha debajo del vaso” // “Now we fill in the recording sheet. We had 3 counters total. Then we fill in the expression that matches the parts we broke 3 into. There were 2 counters outside the cup and 1 counter in the cup.”
• Demonstrate completing the recording sheet.
• “Por turnos, con su compañero, saquen y cubran las fichas amarillas. En cada turno, pueden decidir si usan 3, 4 o 5 fichas. Asegúrense de que ustedes y su compañero estén de acuerdo en cuántas fichas van a usar en total antes de revolver, sacar y cubrir” // “Take turns with your partner spilling and covering the yellow counters. On each turn you can decide to use 3, 4, or 5 counters. Make sure you and your partner agree on how many total counters you are using before you shake, spill, and cover.”

### Activity

• 10 minutes: partner work time

### Activity Synthesis

• Display $$1 + 3$$.
• “Mai estaba jugando ‘Revuelve y saca: Cubre’. Ella escribió esta expresión. ¿Cuáles podrían ser sus fichas?” // “Mai was playing Shake and Spill, Cover. She wrote this expression. What could her counters look like?” (1 yellow and 3 red or 3 red and 1 yellow.)
• If needed, ask “¿Cuántas fichas estaban debajo del vaso? ¿Cuántas fichas estaban afuera, sobre la mesa?” // “How many counters were under the cup? How many counters were out on the table?”

## Lesson Synthesis

### Lesson Synthesis

“Tyler hizo una figura con 10 fichas geométricas. Usó algunos rombos azules y algunos trapecios rojos. Si usó 4 trapecios, ¿cuántos rombos usó?” // “Tyler made a shape with 10 pattern blocks, some blue rhombuses and some red trapezoids. If he used 4 trapezoids, how many rhombuses did he use?” (He used 6 blue rhombuses. 4 and 6 make 10.)

## Student Section Summary

### Student Facing

En esta sección, juntamos fichas geométricas para completar rompecabezas y armar figuras. Escribimos números para mostrar cuántas fichas geométricas usamos y averiguamos de cuáles fichas geométricas usamos más.

Hay más

que

hexágonos amarillos

trapecios rojos.

Hay menos

que

trapecios rojos

hexágonos amarillos.

Asociamos ecuaciones con figuras de fichas geométricas y con problemas-historia.

$$5 + 2 = 7$$

Kiran juntó 5 fichas geométricas para armar una figura.
Jada puso 2 fichas geométricas más en la figura de Kiran.

¿Cuántas fichas geométricas hay en la figura de Kiran y Jada?

Usamos diferentes tipos de fichas geométricas para mostrar distintas maneras de formar 10.

$$4 + 6 = 10$$

$$10 = 6 + 4$$

$$2 + 8 = 10$$

$$10 = 8 + 2$$