Lesson 5

The purpose of this Number Talk is to elicit strategies and understandings students have for subtracting within 1,000, particularly with expressions with a constant difference. These understandings help to develop fluency for subtracting within 1,000. Consider drawing number lines as students share their strategies to emphasize that the difference of the two numbers in each expression is not changing.

• 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 observan acerca de estas expresiones?” // ”What do you notice about these expressions?” (They all have the same value.)
• “¿Por qué todas tienen el mismo valor?” // “Why do they all have the same value?” (Since the same number is added or subtracted to both numbers from the original expression, the difference does not change.)
• 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 determine whether a situation is about an unknown number of groups or an unknown number of objects in each group. After sorting the situations, students write a division expression to represent each situation. The fact that the structure of the expressions is the same for representing an unknown number of groups or an unknown number of objects in each group further emphasizes that division expressions can be interpreted two ways. As students discuss and justify their decisions, they share a mathematical claim and the thinking behind it (MP3).

As students explain their reasoning around the unknown in the situation, encourage students to describe how they would start to solve the problem to make it clear what is unknown in the situation. 

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

• Groups of 2
• Display the image.
• “Vamos a trabajar en algunas situaciones que incluyen insectos. Los insectos son un tipo de bicho. Todos estos son insectos” // “We are going to work with some situations involving insects. Insects are a type of bug. These are all insects.”
• “¿Qué partes de los insectos podemos contar?” // “What are some parts of the insects we could count?” (legs, eyes, wings, antennae, body segments)
• If needed, clarify what antennae are.
• Distribute one set of pre-cut cards to each group of students.

• “En esta actividad, van a clasificar algunas tarjetas en las categorías que ustedes quieran. Cuando clasifiquen las situaciones, deben inventarse las categorías con su compañero” // “In this activity, you will sort some cards into categories of your choosing. When you sort the situations, you should work with your partner to come up with categories.”
• 5 minutes: partner work time
• Select groups to share their categories and how they sorted their cards.
• Choose as many different types of categories as time allows, but ensure that one set of categories distinguishes between “how many groups?” and “how many in each group?” problems.
• If no students sorted the cards by type of division situation, give them a minute to do so, and then discuss how they know which type of division each situation represents.
• “Ahora, con su compañero, clasifiquen sus tarjetas en problemas de ‘¿cuántos grupos?’ y problemas de ‘¿cuántos hay en cada grupo?’?” // “Now work with your partner to sort your cards by ‘how many groups?’ and ‘how many in each group?’ problems.”
• “Una vez que hayan clasificado sus tarjetas, escriban una expresión de división para representar cada situación” // “Once you have sorted your cards, write a division expression to represent each situation.”
• 5 minutes: partner work time

• Invite students to share the expression for each situation.
• Consider asking:
  • “¿Qué representa cada número de la expresión?” // “What does each number represent in the expression?”
  • “¿En qué parte de la expresión ven el número de grupos?” // “Where do you see the number of groups in the expression?”
  • “¿En qué parte de la expresión ven el número de objetos en cada grupo?” // “Where do you see the number of objects in each group in the expression?”

In this activity, students consolidate their understanding of the types of division situations and their representations to solve division problems.

During the synthesis, arrange and display students‘ posters by type, as sorted in the previous activity.

This activity uses MLR7 Compare and Connect. Advances: representing, conversing

• Groups of 2
• Assign each group one of the problems from the previous activity to solve.
• Give each group tools for creating a visual display.

• “Hagan una presentación visual que muestre cómo pensaron en el problema que se les asignó. Incluyan detalles, como notas, diagramas, dibujos, etc., para ayudar a los demás a entender sus ideas” //  “Create a visual display that shows your thinking about the problem you were assigned. You may want to include details such as notes, diagrams, drawings, etc. to help others understand your thinking.”
• 5 minutes: partner work time
• 8–10 minutes: gallery walk

• “¿En qué se parecen los dos tipos de problemas de división?” // “What is the same about the two types of division problems?” (They both involve putting things into equal groups.)
• “¿En qué se diferencian?” // “What is different about them?” (Sometimes we know how many things are in each group and we need to find how many groups we can make. Sometimes we know how many groups there are, but we need to find how many things are in each group.)