Lesson 1

The purpose of this How Many Do You See is for students to subitize or use grouping strategies to describe the images they see.

• Groups of 2
• “¿Cuántas ven? ¿Cómo lo saben?, ¿qué ven?” // “How many do you see? How do you see them?”
• Flash the image.
• 30 seconds: quiet think time

• Display the image.
• “Discutan con su compañero cómo pensaron” // “Discuss your thinking with your partner.”
• 1 minute: partner discussion
• Record responses.

• “¿Cómo los ayudó la forma en la que estaban organizadas las manzanas a ver cuántas había?” // “How did the organization of the apples help you see how many there were?” (I saw 2 rows of 4 which I knew was 8, then I doubled that to find how many apples were in the crate. I saw groups of 4 so I multiplied \(4 \times 4\) then added the other apples.)
• Consider asking:
  • “¿Alguien puede expresar con otras palabras la forma en la que ___ vio las manzanas?” // “Who can restate the way ___ saw the apples in different words?”
  • “¿Alguien vio las manzanas de la misma forma, pero lo explicaría de otra manera?” // “Did anyone see the apples the same way but would explain it differently?”
  • “¿Alguien quiere compartir otra observación sobre la forma en la que ____ vio las manzanas?” // “Does anyone want to add an observation to the way ____ saw the apples?”

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

Monitor for students who represent the situation with:

• concrete objects: putting 24 cubes into groups of 8
• drawings of objects: drawing 24 apples and then splitting them into groups of 8 or circling groups of 8
• arrays: drawing 3 rows of 8 apples in each to reach 24

When students represent the situation with objects, concrete drawings, or abstract drawings they are reasoning abstractly and quantitatively (MP2).

• Groups of 2
• Give students access to connecting cubes or counters.

• “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.”
• 6–8 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 podemos ver las manzanas?” // “Where can we see the apples in your work?”
  • “¿En qué parte de su trabajo podemos ver cuántas cajas hay?” //  “Where can we see how many boxes there are 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 making a visual display.
• 6–8 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 groups?” 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 groups are made. Select them to share their explanations in the next lesson.

• Groups of 2

• “Cuando vayan a ver 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.”
• 8–10 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?”