Lesson 3

The purpose of this warm-up is for students to make sense of the structure of a story problem, which will be useful when students solve story problems and write equations in a later activity. The problem does not have numbers, so that students can focus on the action of the problem. 

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

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

• “¿Dónde se podrían incluir números en este problema-historia?” // “Where might numbers fit into this story problem?” (To tell the number of books Kiran has and the number of books he gets from his friend. To tell how many books Kiran has in all.)

The purpose of this activity is for students to solve a new type of story problem, Add To, Change Unknown. Students may solve in any way that makes sense to them. Monitor for students who show six connecting cubes or two-color counters and add two more to make eight. Students may also draw pictures, and use words or numbers, including mental math and expressions, to represent the problem. Some students may show eight, then remove the six. This is an appropriate method for solving, but the emphasis for this lesson is on addition. Students may write an equation that matches the story problem but not be able to determine which number in the equation tells the answer. Students will practice completing equations in the next activity.

The teacher selects and sequences student work as suggested in the activity. In the activity synthesis, this work is displayed and students look at how the answer to the question is shown in different representations, including the equation. When students connect different representations and explain the connections, they model with mathematics (MP4).

• Groups of 2
• Give students access to 10-frames and connecting cubes or two-color counters.
• Display and read the problem.
• “Este es el mismo problema de nuestro calentamiento. ¿Qué información nueva descubrieron? ¿Qué se preguntan todavía?” // “This is the problem from our warm-up. What new information did you learn? What do you still wonder?” (I learned how many books Kiran had in the beginning and how many he has at the end. I still wonder how many his friend gave him.)
• 1 minute: quiet think time
• Share and record answers.

• “Ahora resuelvan el problema de alguna forma que tenga sentido para ustedes” // "Now solve the problem in a way that makes sense to you."
• 2 minutes: independent work time
• “Compartan con su pareja cómo pensaron” // “Share your thinking with your partner.”
• 2 minutes: partner discussion
• Monitor and select students with the following methods to share in the synthesis: 
  • show six objects, add two more, counting up to 8
  • draw six marks, draw two more, counting up to 8
  • start at 6 and count up mentally
  • write an addition expression

If students add the six and eight instead of finding the difference, consider asking:

• “¿Puedes explicar cómo resolviste el problema?” // "Can you explain how you solved the problem?"
• “¿Cómo podrías usar los cubos encajables para mostrar que Kiran tenía seis libros al principio y terminó con ocho libros?” //  "How could you use connecting cubes to show that Kiran started with six books and ended up with eight books?"

• Invite previously identified students to share in the given order.
• “En cada método, ¿dónde ven la respuesta a la pregunta?” // “Where do you see the answer to the question in each method?”
• If needed, display \(6 + 2 = 8\).
• “¿Cómo corresponde esta ecuación a este método?” // “How does this equation match this method?” (\(6 + 2\) shows the number of books Kiran has plus the number he gets from his friend. 8 is the total number of books he has.)
• “¿Dónde debemos poner el cuadro en esta ecuación? ¿Por qué lo debemos poner ahí?” // "Where should we put the box in this equation? Why should we put it there?" (Put a box around the 2 because it is the answer to the problem.)

The purpose of this activity is for students to make sense of an Add To, Change Unknown story problem and identify the answer within an equation. Students are presented with a drawn representation and an equation to interpret. Students consider what each number in the equation means in relation to the story problem and drawn representation (MP2). They determine that the written equation is incorrect, and explain why using their own thinking. When students practice explaining their thinking, they begin to develop and refine their mathematical communication skills, and attend to precision (MP6). Students identify that even though Mai's equation has the correct numbers she identified the wrong number as the solution to the problem (MP3).

Students keep their books closed for the launch of the activity, as the teacher displays and reads the problem.

• Groups of 2
• Give students access to 10-frames and connecting cubes or two-color counters.
• “Voy a leer otro problema-historia. Piensen qué observan y qué se preguntan mientras lo leo en voz alta” // "I am going to read another story problem. Think about what you notice and wonder about the problem as I read aloud."
• Display and read the problem with missing information. 
• 30 seconds: quiet think time
• Share and record answers.

• “Ahora nos van a dar más información y veremos cómo Lin resolvió el problema” // "Now we will get more information and see how Lin solved the problem."
• Read the problem aloud.
• “Observen el dibujo de Lin y su ecuación. Piensen cómo resolvió el problema” // "Look at Lin's drawing and her equation. Think about how she solved the problem."
• 1 minute: quiet think time
• “Compartan con su pareja cómo pensaron. Después, muestren si piensan que la ecuación de Lin es correcta o no” // “Share your thinking with your partner. Then show whether or not you think Lin's equation is correct.”
• 4 minutes: partner work time

• “¿Cómo muestra el dibujo de Lin el problema-historia?” // “How does Lin’s drawing show the story problem?” (She shows the three books Andre starts with, and the six books she needs to get to nine.)
•  “¿La ecuación de Lin corresponde a la historia? ¿Por qué sí o por qué no?” // "Does Lin's equation match the story? Why or why not?" (No. The answer to the problem is how many books Mai gives Andre. That answer is 6, so the equation should be \(3 + \boxed{6} = 9\) .)
• If needed ask, “¿Cómo corresponde esta ecuación al problema-historia?” // “How does this equation match the story problem?” (Andre has three books. Mai gives him six, which is the answer, so that he has nine total.)

The purpose of this activity is for students to choose from activities that offer practice adding and subtracting within 10 or organizing and representing data. Students choose from any stage of previously introduced centers.

• Sort and Display
• Check it Off
• What’s Behind My Back

• Gather materials from previous centers: 
  • Sort and Display, Stage 1
  • Check it Off, Stages 1 and 2
  • What's Behind My Back, Stage 2

• Groups of 2
• “Ahora van a escoger un centro de los que ya conocemos” // “Now you are going to choose from centers we have already learned.”
• Display the center choices in the student book.
• “Piensen qué les gustaría hacer” // “Think about what you would like to do.”
• 30 seconds: quiet think time

• Invite students to work at the center of their choice. 
• 10 minutes: center work time

• “A Jada le gusta jugar 'Qué hay a mis espaldas'. Ella usas sus dedos para averiguar cuántos cubos hay a espaldas de su compañero. ¿Cómo creen que ella usa sus dedos?” // “Jada likes to play What’s Behind My Back. She uses her fingers to figure out how many cubes are behind her partner’s back. How do you think she uses her fingers?” (She can count the cubes that her partner shows her and hold up that many fingers. Then she can see how many fingers are down and that is how many are behind her partner’s back.)
• “¿Por qué creen que a Jada le gusta usar sus dedos en vez de cubos?” // “Why do you think Jada likes to use her fingers instead of cubes?” (With cubes you have to count out 10 first. We already know we have 10 fingers.)