# Lesson 11

Expresiones de multiplicación

## Warm-up: Conteo grupal: De a dos y de a cinco (10 minutes)

### Narrative

The purpose of this Choral Count is for students to practice counting by 5 and 2 and notice patterns in the count. These understandings help students begin to develop fluency and will be helpful later in this lesson when students write multiplication expressions.

When students notice patterns in the count, such as in the count by 5 that the ones place alternates between 0 and 5, they look for and express regularity in repeated reasoning (MP8).

### Launch

• “Cuenten de 5 en 5, empezando en 0” // “Count by 5, starting at 0.”
• Record as students count. See Student Responses for recording structure.
• Stop counting and recording at 50.

### Activity

• “¿Qué patrones ven?” // “What patterns do you see?”
• 1-2 minutes: quiet think time
• Record responses.
• Repeat activity. Count by 2, start at 0 and stop at 20.

### Activity Synthesis

• “¿Cómo les ayudaron algunos patrones a contar a saltos (de 2 en 2 y de 5 en 5)?” // “How could some of the patterns help you with counting by these numbers?” (I know that the next count by 5 should end in 5. I know that the next count by 2 should have a 2 in the ones place.)
• “¿Quién puede describir el patrón con otras palabras?” // “Who can restate the pattern in different words?”
• “¿Alguien quiere compartir otra observación sobre por qué ese patrón ocurre aquí?” // “Does anyone want to add an observation on why that pattern is happening here?”
• “¿Están de acuerdo o en desacuerdo? ¿Por qué?” // “Do you agree or disagree? Why?”

## Activity 1: ¿A cuál expresión de multiplicación corresponde? (10 minutes)

### Narrative

The purpose of this activity is for students to match drawings, tape diagrams, and situations to multiplication expressions (MP2). Students build on their understanding of how the structure of drawings, tape diagrams, and multiplication situations show equal groups and connect this to the structure of a multiplication expression (MP7). This will be helpful later in the lesson when students create drawings or diagrams to match expressions and write expressions that represent drawings, diagrams, and situations.

### Required Materials

Materials to Gather

### Required Preparation

• Each group of 2 needs 1 card from the card sort in the previous lesson.
• Post these expressions around the room:
• $$3\times5$$
• $$4\times3$$
• $$3\times2$$
• $$2\times10$$
• $$3\times10$$

### Launch

• Groups of 2
• Give each group of 2 students 1 card from the blackline master.

### Activity

• “En parejas, encuentren la expresión que corresponde a su tarjeta. Después, discutan cómo supieron que esa expresión correspondía a su tarjeta” // “Work with your partner to find the expression that matches your card. Then discuss how you know the expression matches your card.”
• 2 minutes: partner work time

### Student Facing

Tu profesor te va a entregar una tarjeta con un dibujo, un diagrama o una situación.

Asóciala a una de las expresiones que están pegadas alrededor del salón. Prepárate para explicar tu razonamiento.

### Activity Synthesis

• Have students standing near each expression share how they know their card matches the expression.
• “En su tarjeta, ¿dónde ven cada número de la expresión?” // “Where do you see each number in the expression on your card?”

## Activity 2: De expresiones a dibujos y a diagramas (15 minutes)

### Narrative

The purpose of this activity is for students to demonstrate a conceptual understanding of multiplication expressions by creating drawings of equal groups or tape diagrams that match expressions. Drawings of equal groups and tape diagrams are familiar representations to students from previous lessons and support students as they make sense of multiplication expressions.

Three expressions are given, but the focus of the synthesis is the second expression, $$3\times4$$. This provides an opportunity to support students on the first problem as you monitor and then let them try the second and third expressions on their own. To keep things simple and allow ideas about commutativity to develop over time, in this activity we suggest you display student responses that follow the convention of groups as the first factor and the size of the groups as the second factor.

If there is time, and you want to include more movement, this activity could be done as a gallery walk.

MLR2 Collect and Display. Collect the language students use to describe the diagrams for each of the expressions. Display words and phrases such as: “5 grupos de 2” // “5 groups of 2”, “hay 5 grupos y hay 2 en cada grupo” // “there are 5 groups, and 2 in each group”, and “hay 5 grupos iguales” // “there are 5 equal groups”. During the synthesis, invite students to suggest ways to update the display and to borrow language from the display as needed.
Action and Expression: Develop Expression and Communication. Provide access to a variety of tools: mini-whiteboards and counters.
Supports accessibility for: Conceptual Processing, Visual-Spatial Processing

### Launch

• Groups of 2
• Review key understandings of multiplication:
• “La multiplicación es la forma de expresar que hay grupos iguales” // “Multiplication is how we express equal groups.”
• “Usamos el signo de multiplicación para escribir una expresión como $$5\times10$$. Esta representa el número total de objetos en ‘5 grupos de 10’ o ‘5 dieces’” // “We use the multiplication symbol to create an expression like $$5\times10$$ which represents the total number of objects in ‘5 groups of 10’ or ‘5 tens.’”
• Display expressions.
• “Piensen en los dibujos o diagramas que podrían hacer para estas expresiones” // “Think about the drawings or diagrams you could make for these expressions.”
• 30 seconds: quiet think time

### Activity

• “En parejas, hagan un dibujo o un diagrama para cada expresión. Después, escriban su propia expresión y hagan un diagrama que le corresponda. Expliquen su razonamiento” // “Work with your partner to create a drawing or diagram for each expression. Then, write your own expression and matching diagram. Explain your reasoning.”
• 5–7 minutes: partner work time
• Monitor for student-created drawings and tape diagrams to share during synthesis.

### Student Facing

1. Haz un dibujo o un diagrama para cada expresión. Explica tu razonamiento.

1. $$5\times2$$
2. $$3\times4$$
3. $$3\times10$$
2. Escribe tu propia expresión y haz un diagrama que le corresponda. Explica tu razonamiento.

### Activity Synthesis

• For the expression $$3\times4$$, display 2 different representations side by side (one drawing of equal groups and one tape diagram).
• “¿En qué se parecen? ¿En qué son diferentes” // “How are they the same? How are they different?”
• “¿Cómo cambiaría el diagrama si la expresión fuera $$5\times4$$?” // “How would the diagram change if the expression was $$5\times4$$?” (There would be 5 sections instead of 3.)
• “¿Cómo cambiaría el diagrama si la expresión fuera $$3\times5$$?” // “How would the diagram change if the expression was $$3\times5$$?” (Each section would be 5 instead of 4.)

## Activity 3: Escribamos expresiones de multiplicación (10 minutes)

### Narrative

The purpose of this activity is for students to write expressions to represent drawings of equal groups, tape diagrams, and multiplication situations. As students work, continually ask where each number in the expression is in the drawing, diagram, or situation.

If students finish early, ask them to find something in the room they can represent with a multiplication expression. Have them record what they represented and their expression.

### Launch

• Groups of 2
• “Ahora van a escribir expresiones de multiplicación para representar un dibujo, un diagrama y una situación. Obsérvenlas durante un minuto antes de empezar a trabajar” // “Now you are going to write multiplication expressions to represent a drawing, a diagram, and a situation. Take a minute to look them over before you begin working.”
• 1 minute: quiet think time

### Activity

• “Trabajen en parejas. Para cada representación, escriban una expresión de multiplicación que le corresponda. Expliquen su razonamiento” // “Work with your partner to write a multiplication expression to match each representation. Explain your reasoning.”
• 3–5 minutes: partner work

### Student Facing

En cada caso, escribe una expresión de multiplicación que corresponda a la representación. Explica tu razonamiento.

1.

2.

3. Había 2 paquetes de botellas de agua. Cada paquete tenía 6 botellas de agua.

### Student Response

If a student writes a multiplication expression that doesn’t match the given representation, consider asking:

• “¿Cómo puedes describir los grupos iguales en este dibujo/diagrama/situación?” // “How could you describe the equal groups in this drawing/diagram/situation?”
• “¿Cómo puedes convertir tu afirmación en una expresión de multiplicación?” // “How could you turn your statement into a multiplication expression?”

### Activity Synthesis

• Share responses.
• “¿Por qué en cada representación se muestra una multiplicación?” // “Why does each of the representations show multiplication?” (They all show groups where there is the same number of things in each group.)

## Lesson Synthesis

### Lesson Synthesis

Display the drawing of equal groups, tape diagram, situation, and expression from Activity 2.

“Hemos aprendido cómo representar la multiplicación de varias maneras. Compartan con su compañero algo que aprendieron hoy” // “We’ve learned about different ways to represent multiplication. Share something that you learned today about multiplication with your partner.” (Multiplication can be shown with drawings of equal groups or with diagrams. Multiplication can be real-world situations that involve equal groups. Multiplication can be expressed using the multiplication symbol ($$\times$$). An expression like $$4\times5$$ means the total number of objects in 4 groups of 5.)