Lesson 6

The purpose of this Number Talk is to elicit strategies and understandings students have for adding within 1,000. These understandings help students develop fluency and will be helpful later in this lesson when students decide whether to use an algorithm or another strategy to add.

When students notice that a number is close to a multiple of 100 and use this to add, they are looking for and making use of structure (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 strategy.
• Keep expressions and work displayed.
• Repeat with each expression.

• “¿Qué hizo que fuera más fácil sumar mentalmente estos números?” // “What is it that made these numbers easier to add mentally?” (The first 3 were really close to 300 so we were able to add 300 and make little adjustments. In the last problem, the first number was really close to 200 which made it easy to subtract mentally.)
• Consider asking:
  • “¿Alguien puede expresar el razonamiento de _______ de otra forma?” // “Who can restate _______ 's reasoning in a different way?”
  • “¿Alguien usó la misma estrategia, pero la explicaría de otra forma?” // “Did anyone have the same strategy but would explain it differently?”
  • “¿Alguien pensó en el problema de otra forma?” // “Did anyone approach the problem in a different way?”
  • “¿Alguien quiere agregar algo a la estrategia de ____?” // “Does anyone want to add on to____’s strategy?”

The purpose of this activity is for students to compare two methods to record newly composed tens and hundreds when using the same algorithm. The first method, which students saw in a previous lesson, records the newly composed tens and hundreds as a 10 or 100 at the top of the problem. The second method records the newly composed tens and hundreds as a single digit of 1 at the top of the tens and hundreds column. It is important that students understand that an additional 1 in the tens column represents a newly composed ten and an additional 1 in the hundreds column represents a newly composed hundred. Students interpret the work and thinking shown in the different methods, and discuss the similarities and differences (MP3).

• Groups of 2
• “Estos son dos métodos para registrar la suma de 657 y 286. Piensen por un minuto en qué se diferencia la manera en la que se registra la suma en cada ejemplo” // “Here are two methods of recording the sum of 657 and 286. Take a minute and think about how the addition is recorded differently in each example.”
• 1 minute: quiet think time

• “Discutan con su pareja cómo se registraron de manera diferente las nuevas decenas y centenas que se compusieron en los dos métodos” // “Discuss with your partner how the newly composed ten and hundred were recorded differently in the two methods.”
• 2-3 minutes: partner discussion
• Share student responses.
• “Ahora prueben con su pareja el segundo método de registrar sumas. Úsenlo para encontrar el valor de cada suma en el segundo grupo de problemas” // “Now work with your partner to try the second method of recording to find each sum in the second set of problems.”
• 5-7 minutes: partner work time
• Monitor for student work where the second method of recording is used to share during the synthesis.

• Display student work for each problem.
• Consider asking:
  • “¿Por qué tuvimos que poner un 1 en la columna de las decenas (o centenas)?” // “Why did we need to put a 1 in the tens (or hundreds) column?”
  • “¿Qué representa el 1 de la columna de las decenas (o centenas)?” // “What does the 1 in the tens (or hundreds) column represent?”
• “Una nueva unidad en base diez que se compuso puede registrarse con un solo dígito. ¿Qué representa ese dígito?” // ”A newly composed unit can be recorded with a single digit. What does the single digit represent?” (If it’s in the tens place it stands for 10. If it’s in the hundreds place it stands for 100.)
• “¿Cómo nos ayuda el valor posicional a recordar lo que representa cada 1 adicional?” // ”How does place value help us remember what the additional ones represent?” (If the 1 is in the tens column, it represents 10. If it is in the hundreds column it represents 100.)

The purpose of this activity is for students to choose an algorithm or other strategy to add within 1,000. Students should attend to the details of numbers in the problems that could indicate whether a particular strategy or algorithm is most useful. The important thing is that students choose an algorithm or strategy that they can use efficiently and accurately for the given problem.

• Groups of 2
• “Hemos estado aprendiendo sobre algoritmos de suma en las últimas lecciones. Recuerden que un algoritmo es una serie de pasos que, si se siguen correctamente, siempre funciona. Pero ustedes saben muchas maneras de sumar números y muchas representaciones para mostrar su trabajo, como diagramas en base diez, rectas numéricas, palabras escritas o ecuaciones. Si su trabajo no es una serie de pasos que funciona siempre, lo llamamos una estrategia” // “We’ve been learning about addition algorithms for the last few lessons. Recall that an algorithm is a set of steps that works every time as long as the steps are carried out correctly. But, you know lots of ways to add numbers and lots of representations for showing your work like base-ten diagrams, number lines, and writing words or equations. If it’s not a set of steps that would work every time, we call it a strategy.”
• “En esta actividad, van a tener la oportunidad de encontrar el valor de cada una de estas sumas usando un algoritmo u otra estrategia que prefieran” // “In this activity, you’re going to have an opportunity to find the value of each of these sums using an algorithm or other strategy of your choice.”

• “Encuentren el valor de cada suma. Después, tendrán la oportunidad de compartir su trabajo” // Find the value of each sum. Later, you’ll have a chance to share your work.”
• 7-10 minutes: independent work time
• Identify students who used the same strategy to add and those who used different strategies.
• Choose a few problems for students to discuss. Consider selecting \(264 +359\) (the second expression) and \(399 + 499\) (the last expression), which lend themselves to be evaluated with an algorithm and another strategy, respectively.
• “Encuentren un compañero que haya sumado de la misma manera que ustedes. Discutan su razonamiento” // “Find a partner that added the same way you did. Discuss your reasoning.”
• 1-2 minutes: partner discussion
• “Ahora encuentren un compañero que haya encontrado la suma de una manera diferente a la de ustedes. Discutan su razonamiento” // “Now find a partner who found the sum in a different way from you. Discuss your reasoning.”
• 2-3 minutes: partner discussion
• Repeat the discussion with 1-2 expressions or as many as time permits.

• Invite 4-5 students to share a strategy or algorithm that someone they talked to used.
• “¿Qué estrategias o algoritmos quieren seguir practicando?” // “What strategies or algorithms do you want to practice more?”