Lesson 2

Problemas-historia y ecuaciones

Warm-up: Conversación numérica: Sumemos 1 más (10 minutes)

Narrative

The purpose of this Number Talk is to elicit strategies and understandings students have for related expressions where an addend is 1 more than in the previous expression. These understandings help students develop fluency and will be helpful later in this lesson when students add within 10. When students notice how adding 1 to an addend increases the sum by 1 they are noticing a pattern and making use of structure (MP7).

Launch

  • 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

Activity

  • Record answers and strategy.
  • Keep expressions and work displayed.
  • Repeat with each expression.

Student Facing

Encuentra mentalmente el valor de cada expresión.

  • \(5 + 1\)
  • \(5 + 2\)
  • \(6 + 2\)
  • \(7 + 3\)

Student Response

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Activity Synthesis

  • “¿En qué se parece la segunda expresión a la primera? ¿En qué es diferente?” // “How is the second expression the same as the first expression? How is it different?” (The first addend is 5, but the second addend adds 1.)
  • “¿En qué es diferente la suma de la segunda expresión?” // “How is the sum of the second expression different?” (The sum is 1 more than the first.)

Activity 1: Escribamos ecuaciones (15 minutes)

Narrative

The purpose of this activity is for students to write equations that match the story problems. The story problems are written with all three quantities revealed so students can focus on making sense of the problem, determine the operation, and write a matching equation. When students connect the quantities in a story problem to an equation, they reason abstractly and quantitatively (MP2).

Representation: Internalize Comprehension. Synthesis: Invite students to identify which details were the most important to solve the problems. Display the sentence frame, “La próxima vez que resuelva un problema-historia, voy a prestar atención a . . .” // “The next time I solve a story problem, I will pay attention to . . .“
Supports accessibility for: Attention, Conceptual Processing

Required Materials

Launch

  • Groups of 2
  • Give students access to 10-frames and connecting cubes or two-color counters. 
  • Display images of libraries, including any taken of your school or community library.
  • “¿Qué cosas pueden hacer en una biblioteca?” // “What are some things you can do in a library?”
  • 30 seconds: quiet think time
  • 1 minutes: partner discussion
  • Share and record responses.
  • “Hoy vamos a trabajar con más historias sobre la biblioteca” // “We are going to work with more stories about the library today.”

Activity

  • “Escuchen cada historia y escriban una ecuación que le corresponda” // “Listen to each story and write an equation to match.”
  • Read each problem aloud. 
  • 3 minutes: independent work time
  • “Compartan sus ecuaciones con su pareja. Asegúrense de discutir la forma en que cada ecuación corresponde a la historia” // “Share your equations with your partner. Be sure to discuss how each equation matches the story.”
  • 3 minutes: partner discussion

Student Facing

  1. Había 7 personas trabajando en las computadoras.
    3 personas más llegaron a trabajar en las computadoras.
    Ahora hay 10 personas trabajando en las computadoras.

    Ecuación: ________________________________

    Library with computers.
  2. Un grupo de niños estaba usando 10 títeres para actuar una historia.
    Ellos guardaron 5 de los títeres.
    Ahora les quedan 5 títeres.

    Ecuación: ________________________________

  3. 5 personas vinieron a la hora del cuento.
    Después llegaron 4 personas más.
    Ahora hay 9 personas en la hora del cuento.

    Ecuación: ________________________________

    Children in a library.
  4. 8 estudiantes estaban haciendo tareas en una mesa.
    3 de los estudiantes terminaron sus tareas y se fueron de la mesa.
    Ahora hay 5 estudiantes en la mesa.

    Ecuación: ________________________________

Student Response

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Advancing Student Thinking

If students write an equation with an operation that does not match the story, consider asking:

  • “¿Cómo decidiste si escribir una ecuación de suma o una ecuación de resta?” // "How did you decide whether to write an addition or subtraction equation?"
  • “¿Cómo puedes contar esta historia usando cubos encajables? ¿Qué ecuación corresponde a lo que hiciste con los cubos?” // “How can you act out this story with connecting cubes? What equation matches what you did with the cubes?"

Activity Synthesis

  • Display the equation that matches the first story problem.
  • “¿Cómo corresponde esta ecuación a la historia?” // “How does this equation match the story?”
  • Repeat for each problem as time allows.
  • Explain that none of the numbers in these equations have a box around them because there was no question to answer in these stories.

Activity 2: Resolvamos y escribamos ecuaciones (20 minutes)

Narrative

The purpose of this activity is for students to solve and write equations to match Add To and Take From, Result Unknown story problems. Students make sense of and represent each story problem in a way that makes sense to them (MP1). Students should have access to connecting cubes or two-color counters. They may use objects or drawings to represent and solve the problems. They may use known addition or subtraction facts to solve the problems. Students write an addition or subtraction equation to match each story problem and explain how it matches. Each equation should include a box around the answer to the problem. The most important thing is for students to be able to relate the numbers in the equation to the different parts of the story (MP2).

MLR6 Three Reads. Keep books or devices closed. To launch this activity, display only the first problem stem, without revealing the question. “Vamos a leer este problema-historia tres veces” // “We are going to read this story problem three times.” After the 1st Read: “Díganle a su pareja lo que ocurrió en la historia” // “Tell your partner what happened in the story.” After the 2nd Read: “En la historia, ¿cuáles son todas las cosas u objetos que podemos contar?” // “What are all the things we can count in this story?” Reveal the question. After the 3rd Read: “¿De qué formas distintas podemos resolver este problema?” // “What are different ways we can solve this problem?” Repeat with the other three problems.
Advances: Reading, Representing

Required Materials

Launch

  • Groups of 2
  • Give students access to 10-frames and connecting cubes or two-color counters.

Activity

  • “Ahora van a resolver los problemas y a escribir ecuaciones que les correspondan. Pueden resolver los problemas de cualquier forma que tenga sentido para ustedes” // "Now you will solve the problems and write equations to match. You can solve the problems in any way that makes sense to you."
  • Read problems aloud.
  • 5 minutes: partner work time
  • “Busquen otra pareja y discutan cada problema. Compartan la ecuación que escribieron y digan cómo corresponde a la historia” // “Find another group and discuss each problem. Share the equation you wrote and how it matches the story."
  • 5 minutes: small-group discussion
  • Monitor for students who wrote equations that match the stories and can explain how they match.

Student Facing

  1. Había una pila de 6 libros sobre la mesa.
    Alguien puso 4 libros más en la pila.
    ¿Cuántos libros hay ahora en la pila?
    Muestra cómo pensaste. Usa dibujos, números o palabras.

    Ecuación: ________________________________

  2. Había 9 libros en un carrito.
    El bibliotecario tomó 2 de los libros y los puso en la repisa.
    ¿Cuántos libros quedan en el carrito?
    Muestra cómo pensaste. Usa dibujos, números o palabras.

    Ecuación: ________________________________

  3. 2 niños estaban trabajando en un proyecto de arte.
    7 niños se unieron al proyecto.
    ¿Cuántos niños están trabajando ahora en el proyecto?
    Muestra cómo pensaste. Usa dibujos, números o palabras.

    Ecuación: ________________________________

  4. El bibliotecario tenía 8 marcapáginas.
    Él le dio 5 marcapáginas a unos niños que estaban en la biblioteca.
    ¿Cuántos marcapáginas tiene él ahora?
    Muestra cómo pensaste. Usa dibujos, números o palabras.

    Ecuación: ________________________________

Student Response

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Activity Synthesis

  • Invite previously identified students to share the equation for each story problem. 

Lesson Synthesis

Lesson Synthesis

Display the problem about bookmarks and \(8 - 5 = \boxed{\phantom{3}}\).

“Hoy resolvimos problemas-historia y escribimos ecuaciones que correspondían a los problemas. Pusimos un cuadro alrededor de la respuesta del problema en nuestra ecuación. Miren este problema y esta ecuación. ¿Qué observan? ¿Qué se preguntan?” // “Today we solved story problems and wrote equations to match the problems. We put a box around the answer to the problem in our equation. Look at this problem and this equation. What do you notice? What do you wonder?” (I notice the expression \(8 - 5\) which is 3. I notice the expression matches the story problem. I see a blank box. I wonder if 3 goes in the blank box.)

If needed, ask “¿Cómo se relaciona este problema-historia con la ecuación \(8 - 5 = \boxed{\phantom{3}}\)?” // “How does this story problem connect to the equation \(8 - 5 = \boxed{\phantom{3}}\)?” (\(8 - 5\) represents the 8 bookmarks the librarian had and the 5 he gives to the kids. The blank box is where the 3 goes since that is the answer to the question.)

Cool-down: Libros en la repisa (5 minutes)

Cool-Down

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