Lesson 4

The purpose of this Number Talk is to elicit strategies and understandings students have for subtracting within 1,000, particularly around adding up to find differences. These understandings help students develop fluency for subtracting within 1,000.

• 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.

• “¿Por qué el valor de \(512 - 475\) es mayor que el valor de \(504 - 475\)?” // ”Why is the value of \(512 - 475\) greater than the value of \(504 - 475\)?” (Since the 475 doesn’t change, but 512 is larger than 504, the difference between the numbers is greater.)
• 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 match division expressions to division situations. Students should justify their matches by articulating how the numbers in the expression connect to what is happening in the situation (MP2).

• Groups of 2
• Display the image.
• “Estos juguetes se llaman trompos. En muchas culturas se juega con ellos. ¿Qué otros juguetes conocen?” // “These are toys called spinning tops, or sometimes just called tops. They are played with in many cultures. What are some other toys that you know about?”
• 30 seconds: quiet think time
• Share responses.
• “Ahora vamos a trabajar con algunas situaciones que incluyen trompos. Vamos a ver situaciones sobre otros juguetes en próximas actividades” // “Now we’re going to work with some situations that involve spinning tops. We’ll see situations about other toys in upcoming activities.”

• “Con su compañero, emparejen cada situación con una expresión de división” // “Work with your partner to match each situation to a division expression.”
• 3–5 minutes: partner work time
• Monitor for students who can justify their matches by explaining how the numbers in the expression represent the situation.

• Select previously identified students to share.
• Consider asking: “¿Cómo representan los números de la expresión lo que hay en la situación?” // “How do the numbers in the expression represent what is in the situation?”

The purpose of this activity is for students to understand that the same division expression can be used to represent both types of division situations. Students are given two situations and asked to match a division expression to one of the situations, but the expression matches both situations given. It is okay if students do not recognize that the expression matches both situations in the activity, because it will be discussed in the activity synthesis. Students learn that the number we are dividing by is called the divisor and understand that the divisor can represent the size of the groups or the number of groups. When students explain that a divisor can be interpreted differently based on the situation it represents, they reason abstractly and quantitatively (MP2).

• Groups of 2
• “Examinemos un poco más de cerca las expresiones de división. Tómense un minuto para leer estas dos situaciones” // “Let’s look a bit closer at division expressions. Take a minute to read these two situations.”
• 1 minute: quiet think time

• “Con su compañero, decidan cuál situación es representada por la expresión” // “Work with your partner to decide which situation the expression represents.”
• 2–3 minutes: partner work time

• Invite students to share their responses and reasoning.
• “¿Cómo puede la misma expresión representar dos situaciones diferentes?” // “How can the same expression represent two different situations?” (Both situations involve the same numbers, 21 and 3. Both situations involve putting 21 objects into equal groups. In one case, the 3 is the number of objects in the group, but in the other, it is the number of groups. Both situations are talking about 21 divided by 3, just in different ways.)
• “Observamos que el número entre el que estamos dividiendo, 3, puede tener dos significados diferentes. Puede significar 3 grupos o 3 objetos en cada grupo” // “We noticed that the number that we are dividing by, 3, can have two different meanings. It can mean 3 groups or 3 objects in each group.”
• “Cuando dividimos, el número entre el que dividimos se llama el divisor. En la expresión \(27 \div 3\), el divisor es 3” // “When we divide, the number we divide by is called the divisor. In the expression \(27 \div 3\), the divisor is 3.”

The purpose of this activity is for students to apply what they have learned about representations of division to match drawings and expressions to division situations (MP2). In doing so, they solidify their understanding that the same division expression can represent both types of division situations. The given drawings enable students to see the number of groups and how many objects are in each group. The work here helps students make connections across the three representations before they write their own division expressions and solve division problems in a subsequent lesson. When students describe how one equation can represent different stories they attend to precision in the language they use and the correspondence that they establish between the equation and the stories (MP6).

• Groups of 2
• “Ahora que hemos representado situaciones de división con dibujos y con expresiones, vamos a asociar algunas situaciones con ambas representaciones” // “Now that we’ve represented division situations with both drawings and expressions, we’re going to match some situations with both representations.”
• “Lean estas situaciones” // “Read these situations.”
• 1–2 minutes: quiet think time
• “Discutan con su compañero en qué se parecen y en qué se diferencian estas situaciones” // “Talk to your partner about what is the same and what is different about these situations.”
• 2–3 minutes: partner discussion
• Share responses.

• “Ahora, con su compañero, asocien cada situación con un dibujo y con una expresión que representan la situación” // “Now work with your partner to match each situation to a drawing and an expression that represents the situation.”
• 3–5 minutes: partner work time

• “Consideremos las primeras dos situaciones sobre Kiran y Han. ¿Por qué podemos usar la misma expresión para representar estas situaciones, pero tenemos que usar dibujos diferentes?” // “Let’s consider the first two situations about Kiran and Han. Why can we use the same expression to represent these situations but different drawings?” (Both situations are represented by 6 divided by 2, but in the first situation the 2, or the divisor, is how many blocks are in each stack. In the second situation the 2 is the number of stacks.)
• “Ahora examinemos las situaciones de Han y Jada. ¿Por qué podemos usar el mismo dibujo para representar estas situaciones, pero no la misma expresión?” // “Now let’s look at Han and Jada’s situations. Why can we use the same drawing to represent these situations but not the same expression?” (Both of these situations describe 2 groups of 3, so they match the same drawing. The first situation is 6 blocks divided between 2 stacks and the second situation is 6 blocks divided into groups of 3.)