Lesson 10

This Number Talk encourages students to think about the relationship between addends in an expression and to rely on what they know about making the next ten or next hundred to mentally solve problems. These understandings help students develop fluency and will be helpful later in this lesson when students are asked to choose methods that make sense to them and explain their choices. As students share their thinking, consider recording on an open number line.

• 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.

• “Cuando encontramos el valor de \(199 + 23\), podemos pensar en sumar de acuerdo al valor posicional y en componer una decena y una centena” // “When finding \(199 + 23\), we could think about adding by place and composing a ten and a hundred.”
• “Algunas personas pensaron en contar hacia adelante para llegar a la siguiente centena y después sumaron lo que quedaba. ¿Por qué es útil ese método?” // “Some people thought about counting on to get to the next hundred and then added what was left. Why is that a useful method?” (199 is really close to a new hundred. It’s easier for me to add \(200 + 22\) in my head than try to add by place in my head.)

The purpose of this activity is for students to sort addition expressions based on their perceived difficulty. They find the values of expressions they feel are less challenging and expressions they feel are more challenging. Then they compare the methods they use for the expressions they solve with their peers. When sharing, students have opportunities to ask questions about the methods and representations their peers use and suggest methods or representations for expressions that peers may feel are difficult to solve (MP3).

When students sort the expressions they look for place value structure to see how they would find the sums (MP7).

• Create a set of cards from the blackline master for each group of 2. 

• Groups of 2
• Give each group a set of cards.
• Give students access to base-ten blocks.

• “Este grupo de tarjetas incluye diferentes expresiones. Clasifiquen las tarjetas pensando si sería menos retador o más retador encontrar el valor de la suma” // “This set of cards includes different expressions. Sort the cards by thinking about whether it would be less challenging or more challenging to find the value of the sum.”
• “Pónganse de acuerdo en un grupo de sumas para las cuales no es tan retador encontrar el valor. Pónganse de acuerdo en otro grupo de sumas para las cuales es más retador encontrar el valor” // “Make 1 group of sums that you both agree would be less challenging. Make another group of sums that you agree would be more challenging.”
• “Si no están de acuerdo en dónde ubicar una tarjeta, manténganla separada de los otros grupos” // “If you cannot agree on where to place a card, keep it separate from the other groups.”

MLR8 Discussion Supports

• Display sentence frames to support students when they share their reasoning:
  • “Yo pienso que este valor es menos difícil de encontrar porque...” // “I think this value is less difficult to find because …”
  • “Yo pienso que este valor es más difícil de encontrar porque...” // “I think this value is more difficult to find because …”
  • “Estoy de acuerdo porque...” // “I agree because …”
  • “Estoy en desacuerdo porque...” // “I disagree because …”
• “Escojan una expresión de cada categoría y encuentren el valor de la suma. Muestren cómo pensaron. Usen diagramas, símbolos u otras representaciones” // “Choose one expression from each category and find the value of the sum. Show your thinking using diagrams, symbols, or other representations.”
• 6 minutes: partner work time
• “Si no han empezado a encontrar el valor de las sumas, por favor, háganlo” // “If you have not started finding the value of the sums, please do so.”
• 5 minutes: independent work
• 4 minutes: partner discussion
• Monitor for students who choose sums that are:
  • less difficult because they do not involve making new units
  • less difficult because they can use the relationships between the numbers to find the sum mentally
  • more difficult based on the number of compositions required
  • more difficult based on the size of the numbers or digits

If students sort most or all of their cards into the “more challenging” group, consider asking:

• “Piensa en lo que sabes sobre sumas de 10. ¿Cómo te puede ayudar eso a clasificar estas expresiones?” // “How could using what you know about sums of 10 help you sort these expressions?”
• “¿Cómo puedes organizar tus expresiones en orden de ‘menos retadora’ a ‘más retadora’?” // “How could you arrange your expressions in order of ‘least challenging’ to ‘most challenging’?”

• Invite a previously identified student to share how they found the value they felt was less challenging to find.
• “¿Qué preguntas tienes para _____ sobre su método?” // “What questions do you have for _____ about their method?”

MLR8 Discussion Supports

• Display question starters:
  • “¿Por qué tú ...?” // “Why did you …?”
  • “¿Puedes decir más sobre ...?” // “Can you say more about …?”
  • “¿Pensaste en ensayar ...?” // “Did you think about trying …?”
• 1 minute: quiet think time
• Invite 2–3 students to ask questions.
• Repeat with a previously identified student to share a value they felt was more challenging to find.
• If time, continue to select students to share strategies for expressions that they felt were less or more challenging.

The purpose of this activity is for students find an unknown addend in sums that have a value of 1,000. They may use what they know about counting by 5, 10, and 100 or use what they know about composing larger units. Although students do not need to know that a thousand is a unit made up of 10 hundreds in grade 2, listen for students who generalize their understanding of place value to make this conjecture to share in the synthesis.

• Groups of 2.
• Give students access to base-ten blocks.
• Display the image that shows 900 + __0 = 1,000.
• “¡Oh, no! Diego derramó pintura en su hoja y ahora no puede ver el número completo. ¿Cuál número de tres dígitos piensan que está cubierto? ¿Como lo saben?” // “Oh no! Diego spilled paint on his paper and now he can’t see the whole number. What three-digit number do you think is covered up? How do you know?” (100. Because it's like counting to 1,000 by 100. It would be 900, 1,000.)
• 30 seconds: quiet think time
• 1 minute: partner discussion
• Share responses.

• “Ahora van a darle sentido a algunas ecuaciones más en las que Diego derramó pintura. Cada ecuación tiene una parte del número de tres dígitos que está cubierta con pintura. Al principio, van a trabajar solos y después van a tener tiempo para compartir con un compañero” // “Now you are going to make sense of a couple more equations where Diego made a mess. Each equation has a part of the three-digit number that is covered up by paint. You’ll work on your own at first, and then have time to share with a partner.”
• 5 minutes: independent work time
• 5 minutes: partner work time
• Monitor for students who added \(615 + 85\) to find the unknown value for _85 + 615 = 1,000.

• Invite previously identified students to share their work.
• “¿Cómo encontró _____ el valor desconocido?” // “How did _____ find the unknown number?” (They started by adding the 85 to the 615 to get 700. Then they knew they needed 3 more hundreds to get to 1,000.)
• Share responses and record with equations and on an open number line.