Lesson 13

This warm-up prompts students to carefully analyze and compare features of expressions and equations. When students compare the drawing, expression, and equations, they must use language precisely to describe how each is the same or different (MP6). Listen to the language students use to describe the different characteristics of each expression and equation and connect students' language to the new terms, factor and product, that are introduced in the synthesis.

• Groups of 2
• Display the image, expression, and equations.
• “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

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

• “¿En qué se diferencia C de las otras formas en las que hemos representado grupos iguales antes?” // “How is C different from the other ways we’ve represented equal groups before?” (It has an equal sign. It’s an equation.)
• “C es una ecuación de multiplicación porque tiene un signo de multiplicación y el signo igual” // “C is a multiplication equation because it contains a multiplication symbol and the equal sign.”
• “Hay palabras que nos ayudan a hablar sobre las diferentes partes de una ecuación de multiplicación. Los factores son los números que se multiplican. El producto es el resultado de multiplicar esos números. En la ecuación que vimos en C, los números 2 y 5 son los factores. El producto es 10. Recuerden esas palabras hoy mientras trabajamos con otras ecuaciones de multiplicación” // “There are words that help us talk about different parts of the multiplication equation. The factors are the numbers being multiplied. The product is the result of multiplying some numbers. In the equation in C, the numbers 2 and 5 are the factors. The product is 10. Keep these words in mind today as we work with other multiplication equations.”

The purpose of this activity is for students to match multiplication equations to situations and representations. Students make explicit connections between the factors and the number of groups or the number of objects in each group and between the product and the total number of objects. These connections are brought out explicitly during the synthesis. When students make explicit connections between multiplication situations and equations, they are reasoning abstractly and quantitatively (MP2).

• Groups of 2 and 4
• “Piensen cómo pueden emparejar cada ecuación con una situación o un diagrama” // “Think about how you might match these equations to a situation or diagram.”
• 1 minute: quiet think time

• “Por turnos, encuentren una situación o un diagrama que corresponda a cada ecuación. Explíquenle a su compañero cómo pensaron” // “Take turns finding a situation or diagram that matches each equation. Explain your reasoning to your partner.”
• 5–7 minutes: partner discussion
• Monitor for students who make direct connections between each factor representing the number in each group or the number of groups and the product representing the total number of objects to share during the synthesis.
• “Reúnanse con otro grupo para discutir sobre las parejas que armaron” // “Get together with another group to discuss the matches you made.”
• 3-5 minutes: small-group discussion

• “¿Hubo parejas con las que no estuvieron de acuerdo? ¿Cómo llegaron a un acuerdo?” // “Were there any matches you disagreed on? How did you come to an agreement?” (We went back and recounted the dots together.)
• For the first, fourth, and seventh pairs that match ask, “¿De qué forma la ecuación representa la situación (o el diagrama)?” // “How does the equation represent the situation (or diagram)?” (The 2 represents the 2 parts in the diagram. The 5 represents the 5 fingers on each hand. The 50 represents how many dots were in the groups altogether.)

The purpose of this activity is for students to write equations that match situations and diagrams. Students use what they learned in the last activity to use multiplication equations to represent situations and diagrams. In the lesson synthesis, use the words factor and product to help students connect the vocabulary to the concepts.

• Groups of 2

• “Con su pareja, escriban una ecuación que represente cada situación o diagrama” // “Work with your partner to write an equation that represents each situation and diagram.”
• 5-7 minutes: partner work time
• Monitor for students who can justify the equations they wrote by explaining the meaning of the factors and products in their equations.

• For each problem have a student share their equation. Consider asking:
  • “¿Cómo saben que esta ecuación tiene sentido para esta situación, dibujo o diagrama?” // “How does this equation make sense for this situation, drawing, or diagram?”
  • “¿Qué partes de la situación, del dibujo o del diagrama fueron las que más les ayudaron mientras escribían la ecuación?” // “What parts of the situation, drawing, or diagram were especially helpful as you wrote the equation?”