Lesson 13

The purpose of this Number Talk is to elicit strategies and understandings students have for adding 2 two-digit numbers. When students add ones and ones and tens and tens and describe how they compose a new ten, they look for and make sense of the base-ten structure of numbers (MP7).

• 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 strategies.
• Keep expressions and work displayed.
• Repeat with each expression.

• “Ya sabían \(15 + 15\). ¿Cómo les ayudó eso a encontrar el valor de \(25 + 25\)?” // “How did knowing \(15 + 15\) help you solve \(25 + 25\)?” (I already knew \(15 + 15\) was 30. Then I added the 20 more to 30 since each 25 is 10 more than 15.)
• “Ya sabían \(25 + 25\). ¿Cómo les ayudó eso a encontrar el valor de \(25 + 28\)?” // “How did knowing \(25 + 25\) help you solve \(25 + 28\)?” (I knew \(25 + 25\) is 50, and 28 is 3 more than 25, so \(50 + 3 = 53\).)

The purpose of this activity is for students to make sense of and solve a new type of story problem, Take From, Start Unknown, using the Three Reads routine. As students discuss, represent, and solve the problem, they see that even though the actions in the story can be represented with subtraction, they solve it using addition. The Three Reads routine encourages students to make sense of the quantities in the story and their relationship before mapping out a strategy to solve the problem (MP2).

This activity uses MLR6 Three Reads. Advances: Reading, Listening, Representing.

• Groups of 2
• Give students access to connecting cubes in towers of 10 and singles.
• “Hay distintas artes y manualidades que las personas disfrutan hacer. Hacer pulseras de la amistad, como las de las historias que resolvimos, es una manualidad que a muchos estudiantes les gusta. ¿Qué artes y manualidades les gustan a ustedes? ¿Qué otras artes y manualidades conocen que las personas disfruten?” // “There are many different arts and crafts that people enjoy doing. Making friendship bracelets, like the ones in the stories we solved, is one craft that lots of students like. What arts and crafts do you like? What arts and crafts do you know that other people enjoy?” (painting, knitting, scrapbooking)
• 30 seconds: quiet think time
• Share responses.
• “Vamos a seguir resolviendo problemas sobre manualidades que las personas disfrutan” // “We are going to continue to solve problems about crafts that people enjoy.”

MLR6 Three Reads 

• Display only the problem stem, without revealing the question.
• “Vamos a leer este problema tres veces” // “We are going to read this problem three times.”
• 1st Read: “Elena compró una bolsa de chaquiras para hacer pulseras. Ella sacó 9 chaquiras para hacer una pulsera. Quedan 11 chaquiras en la bolsa” // “Elena bought a bag of beads to make bracelets. She takes out 9 beads to make a bracelet. There are 11 beads left in the bag.”
• “¿De qué se trata esta historia?” // “What is this story about?”
• 1 minute: partner discussion
• Listen for and clarify any questions about the context.
• 2nd Read: “Elena compró una bolsa de chaquiras para hacer pulseras. Ella sacó 9 chaquiras para hacer una pulsera. Quedan 11 chaquiras en la bolsa” // “Elena bought a bag of beads to make bracelets. She takes out 9 beads to make a bracelet. There are 11 beads left in the bag.”
• “¿Qué cosas se pueden contar?” // “What can be counted?” (number of beads she took out, number of beads are left in the bag, number of beads there are altogether).
• 30 seconds: quiet think time
• 1 minute: partner discussion
• Share and record all quantities.
• 3rd Read: Read the entire problem, including the question, aloud.
• “¿De qué formas diferentes podemos resolver este problema?” // “What are different ways we can solve this problem?” (use connecting cubes to show the beads, draw a picture, write an equation using a fact we know)
• 30 seconds: quiet think time
• 1–2 minutes: partner discussion

• “Con su compañero, representen y resuelvan el problema. Muestren cómo pensaron. Usen dibujos, números o palabras” // “Work with your partner to represent and solve the problem. Show your thinking using drawings, numbers, or words.”
• 5 minutes: partner work time
• Monitor for students who:
  • use cubes to show 9 beads out of the bag and 11 beads in the bag
  • draw bag and write 11 in it, write or draw 9 next to it
  • write \(9 + 11 = 20\)

If students subtract 9 beads from 11 beads, consider asking:

• “¿Qué ocurre en la historia” // “What is happening in the story?”
• “¿Qué es lo que el problema-historia te pide encontrar? ¿Crees que al comienzo pudo haber 2 chaquiras en la bolsa? ¿Por qué sí o por qué no?” // “What does the story problem ask you to find? Do you think there could have been 2 beads in the bag to start? Why or why not?”
• “¿Cómo podrías usar cubos encajables o dibujos para mostrar la historia?” // “How could you use connecting cubes or drawings to act out the story?”

• Invite previously identified students to share in the sequence above.
• Record student thinking with drawings and equations.

• “¿En qué se parecen estos métodos?” // “How are these methods the same?” (They all added 11 and 9.)

The purpose of this activity is for students to make sense of Take From story problems with unknowns in different positions. Students analyze one drawing and describe how it matches each story problem (MP2). As students describe how the drawing matches each problem, the teacher labels the drawing and includes a question mark for the unknown in the story. This allows students to see that although the same drawing represents three different problems, the unknown number is not in the same place in the drawing. They understand that the drawing is used differently to solve each problem. 

• Create a poster of the unlabeled diagram shown three times: 

  

  

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

• Read the task statement.
• 5 minutes: partner discussion
• Monitor for students who can explain how the diagram matches each story.

• Invite previously identified students to share.
• Record student explanations by labeling each diagram with the known quantities and a question mark for the unknown.
• Record an equation with a question mark for the unknown to match student explanations.
• “¿En qué se parecen estas historias y sus representaciones? ¿En qué son diferentes?” // “How are these stories and their representations the same? How are they different?” (They’re all about beads. Each drawing shows 15 boxes for the beads and 5 of them are shaded. The question mark is in different places. It means the total amount before any were taken away in one story, the amount that was taken away in another story, and the amount that was left in another story.)