Lesson 2

The purpose of this Number Talk is to elicit strategies and understandings students have for multiplying single-digit numbers. These understandings help students develop fluency and will be helpful later in this lesson when students find factor pairs of numbers.

As students use earlier problems to find the new products, they look for and make use of structure (MP7) and use repeated reasoning (MP8).

• Display one expression.
• “Hagan una señal cuando tengan una respuesta y puedan explicar cómo la obtuvieron” // “Give me a signal when you have an answer and can explain how you got it.”
• 1 minute: quiet think time

• Record answers and strategy.
• Keep expressions and work displayed.
• Repeat with each expression.

• “¿Cómo les ayudaron las primeras tres expresiones a encontrar \(7 \times 7\)?” // “How did the first three expressions help you find \(7 \times 7\)?” (The 7 breaks apart into 3 and 4, so I could multiply in parts and add them.)
• Consider asking:
  • “¿Alguien puede expresar el razonamiento de _____ de otra forma?” // “Who can restate _____’s reasoning in a different way?”
  • “¿Alguien usó la misma estrategia, pero la explicaría de otra forma?” // “Did anyone have the same strategy but would explain it differently?”
  • “¿Alguien pensó en la expresión de otra forma?” // “Did anyone approach the expression in a different way?”
  • “¿Alguien quiere agregar algo a la estrategia de ______?” // “Does anyone want to add on to _____’s strategy?”

The purpose of this activity is for students to find all the possible pairs of whole-number side lengths given the area of a rectangle. Each group is assigned 2 areas for which they find all the possible rectangles. They draw and cut out the possible rectangles with that area. In the next activity, they will display the rectangles in a gallery walk. To find all possible rectangles with a given area, students may use tiles but they may also start to observe patterns such as if there are an even number of rows then the number of tiles in the rectangle is an even number (MP7).

Areas to assign (in square units):

This activity uses MLR7 Compare and Connect. Advances: representing, conversing.

• Each of the 8 groups needs tools for creating a visual display.

• 8 groups
• Give each group access to inch tiles, grid paper, poster paper, scissors, and glue.

MLR7 Compare and Connect

• “Van a recibir 2 números. Cada número representa el área de un rectángulo. Para cada área asignada, dibujen en grupo todos los rectángulos posibles que tengan esa área y hagan un póster. Hay fichas de pulgada disponibles si piensan que les pueden ayudar” // “You are going to be given 2 numbers. Each number represents the area of a rectangle. With your group, draw all the possible rectangles with that area and create a poster for each area. Inch tiles are available if you find them helpful.”
• “Su póster debe mostrar los rectángulos para cada una de las áreas asignadas. Incluyan detalles, como el área y las longitudes de los lados, para ayudarles a otros a entender cómo pensaron” // “Your poster should show the rectangles with each of your assigned areas. Include details such as area and side lengths to help others understand your thinking.”
• Assign each group 2 area values.
• 15 minutes: small-group work time

Students may list only some of the factor pairs for a given number. Consider asking: “¿Hay otros rectángulos que puedas dibujar?” // “Are there any other rectangles you can draw?” or “¿Cómo puedes asegurarte de que dibujaste todos los rectángulos posibles?” // “How can you be sure that you have drawn all of the possible rectangles?”

• “Antes de que caminemos y veamos todos los pósteres, tómense un minuto para reflexionar sobre los números con los que trabajaron. ¿Qué observaron y qué se preguntaron mientras trabajaban en esta actividad?” // “Before we walk around and look at all the posters, take a minute to reflect on the numbers you worked with. What did you notice and wonder as you worked on this activity?”
• 1–2 minutes: quiet think time

In this activity, students examine the rectangles drawn by their classmates and learn the term factor pairs. Students recognize the side lengths of each rectangle as a factor pair of its area.

This activity uses MLR7 Compare and Connect. Advances: representing, conversing

• Groups of 2

• 5–7 minutes: gallery walk
• Monitor for different explanations students offer for how they know whether all possible rectangles with a given area have been found. 

MLR7 Compare and Connect

• “¿En qué se parecen y en qué son diferentes los rectángulos en los pósteres?” // “What is the same and what is different between the rectangles on the posters?”
• 30 seconds: quiet think time
• 1 minute: partner discussion
• “¿Cómo saben que encontraron todos los rectángulos posibles para cada área asignada?” // “How do you know that all possible rectangles have been found for the given area?” (We could not find any other numbers that multiply together to make the area.)
• Display the rectangles for 21: 1 by 21 and 3 by 7.
• “¿Podemos dibujar más rectángulos? ¿Por qué sí o por qué no?” // “Are there any more rectangles we can draw? Why or why not?” (No, there are no more whole-number factors of 21. Or, no, because to get 21 we can multiply only 1 and 21, 3 and 7, 7 and 3, and 21 and 1.)
• “1 y 21 se llama un pareja de factores de 21 porque cada uno de ellos es un factor de 21 y al multiplicarlos nos da 21. Otra pareja de factores de 21 es 3 y 7” //“We call 1 and 21 a factor pair of 21 because each of them is a factor of 21 and multiplying them gives 21. Another factor pair of 21 is 3 and 7.”
• “Con su compañero, escriban las parejas de factores de las áreas que les asigné” // “Work with your partner to write down the factor pairs for the areas you were assigned.”
• 2 minutes: partner work time