Lesson 17

The purpose of this warm-up is to elicit the idea that adding 1 results in the next number in the count sequence, which will be useful when students find the value of expressions with \(+ 1\) in a later activity. While students may notice and wonder many things about these towers, 1 more being added to each tower and how that affects the total number of cubes are the important discussion points.

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

• Point to the tower with 2 cubes and then to the tower with 3 cubes while saying “¿Qué cambió de esta torre a esta otra torre?” // “What changed from this tower to this tower?” (There are still 2 blue cubes, but 1 more yellow cube was put on top.)
• Point to the tower with 2 cubes and then to the tower with 3 cubes while saying “¿Qué expresión podemos escribir para mostrar lo que cambió de esta torre a esta otra torre?” // “What expression can we write to show what changed from this tower to this tower?” (\(2 + 1\))
• “¿Cuántos cubos piensan que hay en la última torre? ¿Cómo lo saben?” // “How many cubes do you think are in the last tower? How do you know?” (5. I counted them. I know that there is 1 more than the last tower, and 5 is one more than 4.)

The purpose of this activity is to find the value of addition expressions with \(+ 0\) and \(+ 1\). Students may connect adding 1 to getting the next number in the counting sequence and will likely observe that adding 0 does not change the number (MP7). These connections will be highlighted in the next activity. 

• Each group of 2 needs 1 connecting cube.

• Groups of 2
• Display a tower of 3 connecting cubes:

• “Mai tiene una torre de 3 cubos. Mai quiere agregarle 0 cubos a la torre. ¿Qué debe hacer Mai?” // “Mai has a tower with 3 cubes. Mai wants to add 0 cubes to the tower. What should Mai do?” (Nothing. When you add 0, you don’t add anything.)
• 30 seconds: quiet think time
• Share responses.
• Give each group of students a copy of the blackline master and a connecting cube. Give students access to connecting cubes and two-color counters.
• “Tomen turnos con su compañero. Lancen el cubo para descubrir si necesitan sumar 0 o 1. Completen la expresión” // “Take turns with your partner. Roll the cube to figure out if you need to add 0 or 1. Fill in the expression.”
• “Encuentren el valor de la expresión y escriban el número sobre la línea. Si les ayuda, usen objetos o dibujos” // “Find the value of the expression and write the number on the line. You can use objects or drawings if they are helpful.”

• 5 minutes: partner work time

• “En la siguiente actividad, vamos a examinar las expresiones que escribió un grupo para ver si podemos reconocer algunos patrones” // “In the next activity we will look at the expressions that one group wrote to see if we can notice any patterns.”

The purpose of this activity is to notice the pattern that when 0 is added to a number, the number stays the same and the pattern that when 1 is added to a number, the total is the next number in the count sequence, or 1 more (MP7).

• Groups of 2
• Display student book
• “Diego y Mai escribieron sus expresiones de suma y los valores de las expresiones en esta página. ¿Qué observan? ¿Qué se preguntan?” // “Diego and Mai recorded their addition expressions and their values on this page. What do you notice? What do you wonder?” (They always added 1 or 0. Sometimes the first and last number are the same.)
• 30 seconds: quiet think time
• 1 minute: partner discussion
• Share and record responses.

• “¿Cuáles expresiones muestran que sumaron 0?” // “Which expressions show that 0 were added?” (\(4 + 0\), \(2 + 0\), and \(8 + 0\))
• 30 seconds: quiet think time
• Share responses. Highlight or circle the expressions that show \(+ 0\).
• “Cuando jugaron el juego, ¿qué hicieron cuando tenían que sumar 0?” // “When you played the game, what did you do when you had to add 0?” (Nothing. Zero means none so none were added.)
• 30 seconds: quiet think time
• 1 minute: partner discussion
• Share responses.
• “¿Qué observan en el valor de las expresiones cuando suman 0?” // “What do you notice about the value of the expressions when 0 are added?” (It stays the same.)
• 1 minute: quiet think time
• 1 minute: partner discussion
• Share responses.
• “Cuando sumamos 0, el total es el mismo número con el que empezamos porque nada se agregó” // “When we add 0, the total is the same number that we started with, because nothing was added.”
• Repeat the steps above with \(+ 1\).

• “¿\(3 + 0\) es cuánto?” // “\(3 + 0\) is how many?” (\(3 + 0\) is 3.)
• “¿\(2 + 0\) es cuánto?” // “\(2 + 0\) is how many?” (\(2 + 0\) is 2.)
• “¿Cómo saben que \(2 + 0\) es 2?” // “How do you know that \(2 + 0\) is 2?” (Because we didn’t add any more, so the 2 stayed the same.)
• Repeat with \(2 + 1\).

The purpose of this activity is for students to learn stage 1 of the Find the Value of Expressions center. Students take turns choosing an expression card and finding the value of the expression. Students may use their fingers, connecting cubes, two-color counters, or draw a picture to find the value of the expression. After they participate in the center, students choose from any stage of previously introduced centers.

• Roll and Add
• Shake and Spill
• Number Race
• Math Stories

• Gather materials from: 
  • Roll and Add, Stages 1 and 2
  • Shake and Spill, Stages 1-3
  • Number Race, Stage 1
  • Math Stories, Stages 1 and 2

• Groups of 2
• Give each group of students a set of expression cards and access to connecting cubes and two-color counters. Give each student a recording sheet.
• “Vamos a conocer un centro llamado ‘Encuentra el valor de expresiones’. Un compañero va a escoger una tarjeta de expresión. El otro compañero va a encontrar el valor de la expresión. Cuando estén de acuerdo, coloreen el número en la hoja de registro. Tomen turnos para escoger una tarjeta de expresión” // “We are going to learn a center called Find the Value of Expressions. One partner will choose an expression card. The other partner will find the value of the expression. When you agree, color in the number on the recording sheet. Take turns choosing an expression card.”

• 8 minutes: partner work time
• “Ahora pueden escoger otro centro. También pueden seguir jugando ‘Encuentra el valor de expresiones’” // “Now you can choose another center. You can also continue playing Find the Value of Expressions.”
• Display the center choices in the student book.
• Invite students to work at the center of their choice. 
• 10 minutes: center work time
• If time, invite students to choose another center.

• Write the number 4.
• “Elena coloreó el número 4. ¿Qué expresión piensan que estaba en su tarjeta?” // “Elena colored in the number 4. What expression do you think was on her card?” (\(2 + 2\), \(5 - 1\), \(3 + 1\))