Lesson 2

The purpose of this warm-up is to elicit the idea that many different questions could be asked about a situation, which will be useful when students solve problems in a later activity. 

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

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

• If not mentioned in students’ responses, ask: “¿Qué preguntas matemáticas podemos hacer sobre esta imagen?” // “What mathematical questions could we ask about this picture?” (How many apples are in each box? Are there more apples in the boxes than on the trees? How many apples are in the boxes altogether?)

The purpose of this activity is for students to represent and solve “how many in each group?” problems using whatever strategy and visual representation make sense to them. Students create a poster of their solution to the first problem with a partner. In the next activity, they participate in a gallery walk of the posters.

Monitor for students who represent the situation with:

• concrete objects: putting 20 cubes into 4 groups one by one
• drawings of objects: drawing 20 apples and then splitting them into 4 groups
• arrays: drawing 4 rows with one apple in each row to reach 20

• Groups of 2
• Give students access to connecting cubes and counters.
• “Hablen con su compañero sobre cómo podrían resolver estos problemas” // “Turn and talk to your partner about how you might solve these problems.”
• 1–2 minutes: partner discussion

• “Resuelvan estos problemas. Usen objetos, un dibujo o un diagrama para mostrar cómo pensaron” // “Solve these problems and show your thinking using objects, a drawing, or a diagram.”
• 5–7 minutes: independent work time
• As student work, consider asking:
  • “¿Cómo pueden representar lo que están pensando?” // “How can you represent what you are thinking?”
  • “¿En qué parte de su trabajo pueden ver las cajas?” // “Where can you see the boxes in your work?”
  • “¿En qué parte de su trabajo pueden ver cuántas manzanas hay en cada caja?” // “Where can you see how many apples are in each box in your work?”
• Monitor for students who solve the first problem in the same way. Arrange them into groups of 2 to create a poster together.
• “Ahora van a hacer un póster para mostrar cómo pensaron en el primer problema” // “Now you are going to create a poster to show your thinking on the first problem.”
• “Van a trabajar con un compañero que haya resuelto el problema de la misma forma que ustedes” // “You are going to work with a partner who solved the problem in the same way you did.”
• Give each group tools for creating a visual display.
• 5–7 minutes: partner work time

If students don’t find a solution to the problems, consider asking: “¿De qué se trata este problema?” // “What is this problem about?” and “¿Cómo podrías representar el problema?” // “How could you represent the problem?”

• Display posters around the room.

The purpose of this activity is for students to consider what is the same and what is different about the ways that they solved a “how many in each group?” problem in the previous activity. As students visit the posters, identify 2–3 students who show particularly well that this problem is about finding how many there are in each group. Select them to share in the next activity.

• Groups of 2

• “Cuando estén viendo los pósteres con su compañero, discutan en qué se parecen y en qué se diferencian las ideas que se muestran en los pósteres” // “As you visit the posters with your partner, discuss what is the same and what is different about the thinking shown on each poster.”
• 5–7 minutes: gallery walk

• Give students a chance to ask questions they have about any posters.
• “¿En qué se parecen las ideas que se muestran en los pósteres?” // “What is the same about the thinking shown on the posters?”
• “¿En qué se diferencian las ideas que se muestran en los pósteres?” // “What is different about the thinking shown on the posters?”

The purpose of this activity is for students to consider what is the same and what is different about the “how many groups?” and “how many in each group?” problems they solved in a previous lesson and in this lesson. The discussion should highlight that in “how many groups?” problems we know the size of each group and in “how many in each group?” problems we know how many groups there are. In order to describe how the problems are the same and how they are different, students attend to the structure of the problems, that is what is given in each situation and what is unknown (MP7).

• Gather the 2–3 posters  from the previous lesson and this lesson that highlight counting the groups in a “how many groups?” problem and finding how many in each group in a “how many in each group?” problem.

• Groups of 2
• Display the problems.
• Display the 2-3 previously selected posters for each problem.

• “Estos son dos problemas en los que trabajamos. Ayer hicimos pósteres para el primero y hoy hicimos pósteres para el segundo” // “Here are two problems we’ve worked on. Yesterday we made posters for the first one and today we made posters for the second one.”
• “Estos son algunos pósteres para cada problema” // “Here are a few posters for each problem.”
• “Discutan con su compañero en qué se parecen estos problemas y en qué se diferencian. También hablen sobre en qué se parecen y en qué se diferencian las formas de representar y resolver estos problemas” // “Talk to your partner about how these problems are alike and how they are different. Also talk about what is alike and what is different about how the problems are represented and solved.”
• 3-5 minutes: partner discussion

• “¿Qué observaron ustedes y su compañero que era parecido?” // “What did you and your partner notice was alike?”
• “¿Qué observaron ustedes y su compañero que era diferente?” // “What did you and your partner notice was different?”
• Share and record responses.
• As students share, encourage them to use the posters to show examples of what they notice.