Lesson 8

Más de una manera

Warm-up: Conversación numérica: Expresiones (10 minutes)

Narrative

The purpose of this Number Talk is to elicit strategies and understandings students have for adding and subtracting 1. These understandings help students develop fluency with the count sequence and adding and subtracting within 5. When students use their knowledge of the count sequence when they add or subtract 1, they are looking for 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 problems and work displayed.
  • Repeat with each expression.

Student Facing

Encuentra el valor de cada expresión.

  • \(3 + 1\)
  • \(1 + 3\)
  • \(4 - 1\)
  • \(4 +1\)

Student Response

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Activity Synthesis

  • Display or draw 1 red counter and 4 yellow counters:
Counters.
  • Display the expressions.
  • “¿Cuál expresión va con estas fichas? ¿Por qué piensan eso?” // “Which expression goes with these counters? Why do you think that?” (\(4 + 1\) because there are 4 yellow and 1 red.)

Activity 1: Jugo de cítricos (10 minutes)

Narrative

The purpose of this activity is for students to connect representations to story problems. Students look at two drawings and determine whether they both show solutions to a Put Together/Take Apart, Both Addends Unknown story problem. In the activity synthesis, students work with their partner to find another possible solution to the given story problem, which will be useful when they find more than one way to solve a Put Together/Take Apart, Both Addends Unknown story problem in the next activity.

When students describe how the diagrams represent the story problem, they reason abstractly and quantitatively (MP2).

MLR8 Discussion Supports. Invite students to take turns explaining their drawings to their partner, including reading the numbers to show how many satsumas and how many grapefruits were used. Listen for and clarify any questions about the numbers or drawings.
Advances: Listening, Speaking

Required Materials

Launch

  • Groups of 2
  • Give students access to connecting cubes or two-color counters.
  • Read the task statement.
  • Display the images.
  • “Clare y Diego hicieron un dibujo para mostrar lo que pasó en la historia. ¿Qué observan? ¿Qué se preguntan?” // “Clare and Diego both drew a picture to show what happened in the story. What do you notice? What do you wonder?” (They both drew 9 circles. One used color and one didn’t. One has numbers and letters and one just has numbers. I wonder why Clare didn’t use different colors. I wonder why one shows 3 and 6 and one shows 7 and 2.)
  • 30 seconds: quiet think time
  • 1 minute: partner discussion
  • Share and record responses.

Activity

  • “¿Cuál dibujo muestra la historia?” // “Which drawing shows the story?”
  • 1 minute: quiet think time
  • 2 minutes: partner discussion
  • Share responses.

Student Facing

Han exprimió 9 frutas para hacer jugo.

Algunas de las frutas eran satsumas.

El resto de las frutas eran toronjas.

¿Cuántas frutas eran satsumas?

¿Entonces cuántas frutas eran toronjas?

Grapefruit.

Clare:

2 groups of circles. 3 circles labeled S. 6 circles labeled T.

Diego:

7 orange circles labeled 7 S. 2 red circles labeled 2 T.

Han exprimió 9 frutas para hacer jugo.

Algunas de las frutas eran satsumas.

El resto de las frutas eran toronjas.

¿Cuántas frutas eran satsumas?

¿Entonces cuántas frutas eran toronjas?

Muestra cómo pensaste. Usa objetos, dibujos, números o palabras.

Expresión: ____________________________________

Student Response

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Advancing Student Thinking

If students identify either Clare or Diego’s drawings as showing the story but not both, consider rereading the story problem and asking: 
  • “¿Qué sabemos sobre las frutas que Han exprimió? ¿Qué estamos tratando de descifrar?” // “What do we know about the fruit that Han squeezed? What are we trying to figure out?”
  • “¿En qué se parecen y en qué son diferentes los dibujos de Clare y de Diego?” // “What is the same and what is different about Clare and Diego’s drawings?”

Activity Synthesis

  • “Hay más de una forma de resolver este problema” // “There is more than 1 way to solve the story problem.”
  • “¿Cuál dibujo hace que sea más fácil decir cuántas satsumas y cuántas toronjas hay?” // “Which drawing makes it easier to tell how many satsumas and how many grapefruits there are?” (It is easier to see in Diego’s drawing because he wrote numbers.)
  • “Diego escribió números para mostrar cuántas satsumas y cuántas toronjas exprimió Han” // “Diego wrote numbers to show how many satsumas and how many grapefruits Han squeezed.”
  • “Con su pareja, muestren otra solución al problema-historia. Asegúrense de incluir números para mostrar cuántas satsumas y cuántas toronjas hay” // “Work with your partner to show another solution for the story problem. Be sure to include numbers to show how many satsumas and how many grapefruits.”
  • Reread the task statement.
  • “Muestren cómo pensaron. Usen dibujos, números, palabras u objetos” // “Show your thinking using drawings, numbers, words, or objects.”
  • 3 minutes: partner work time
  • “Escriban una expresión para mostrar cuántas satsumas y cuántas toronjas hay” // “Write an expression to show how many satsumas and how many grapefruits there are.”
  • 1 minute: independent work time

Activity 2: Dátiles para rellenar (15 minutes)

Narrative

The purpose of this activity is for students to solve a Put Together/Take Apart, Both Addends Unknown story problem about dates stuffed with cheese or almonds in more than one way. In the activity synthesis, students share their solutions. As students share, record their drawings and solutions systematically, as shown:

  • 1 cheese, 7 almond
  • 2 cheese, 6 almond
  • 3 cheese, 5 almond
  • 4 cheese, 4 almond
  • 5 cheese, 3 almond
  • 6 cheese, 2 almond
  • 7 cheese, 1 almond

Only record solutions that students find for the problem. Leave an empty space if a combination isn’t shared.

In the lesson synthesis, students discuss whether a solution of 3 dates stuffed with cheese and 5 dates stuffed with almonds is the same solution as 5 dates stuffed with cheese and 3 dates stuffed with almonds. The purpose of the question is for students to think about and discuss what decompositions of numbers mean in context (MP2, MP6). There is no correct answer to the question. Some students may determine that both solutions are the same because they both showed 5 and 3 while other students may determine that the solutions are different because there are different numbers of dates stuffed with cheese and dates stuffed with almonds (MP3).

Representation: Internalize Comprehension. Synthesis: Reiterate the fact that in this problem there is more than one answer. Make a connection between the solutions that were found and that they all add up to the same total number of dates.
Supports accessibility for: Conceptual Processing

Required Materials

Launch

  • Groups of 2
  • Give students access to connecting cubes or two-color counters.
  • Read and display the task statement.
  • “Cuéntenle a su pareja lo que pasó en la historia” // “Tell your partner what happened in the story.”
  • 30 seconds: quiet think time
  • 1 minute: partner discussion
  • “¿Qué estamos tratando de descifrar?” // “What are we trying to figure out?” (How many of the dates were stuffed with cheese and how many of the dates were stuffed with almonds?)
  • 30 seconds: quiet think time
  • 1 minute: partner discussion
  • “Muestren cómo pensaron. Usen dibujos, números, palabras u objetos” // “Show your thinking using drawings, numbers, words, or objects.”

Activity

  • 2 minutes: quiet work time
  • 2 minutes: partner discussion
  • “Escriban una expresión para mostrar cuántos dátiles estaban rellenos con queso y cuántos estaban rellenos con almendras” // “Write an expression to show how many of the dates were stuffed with cheese and how many were stuffed with almonds.”
  • 1 minute: independent work time
  • “Mientras caminan por el salón, piensen si pueden encontrar otras formas de resolver el problema-historia” // “As you walk around, look to see if you can find other ways to solve the story problem.”
  • 5 minutes: gallery walk

Student Facing

Andre y su hermano mayor tenían 8 dátiles.

Rellenaron algunos de los dátiles con queso.

Rellenaron el resto de los dátiles con almendras.

¿Cuántos dátiles rellenaron con queso?

¿Entonces cuántos dátiles rellenaron con almendras?

Expresión: _______________________________

Dates stuffed with cheese.
Dates stuffed with almonds.

Student Response

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Activity Synthesis

  • Invite students to share their solution or solutions they found during the gallery walk. Record student solutions as explained in the activity narrative.
  • “¿Qué observan? ¿Qué se preguntan?” // “What do you notice? What do you wonder?” (2 and 6 is there but not 6 and 2. When it’s 4 and 4, there are the same number of cheese dates and almond dates. The first numbers are getting bigger and the second numbers are getting smaller.)
  • “¿Hay otras formas en las que podamos resolver este problema? ¿Qué los hace pensar eso?” // “Are there any other ways that we can solve the problem? What makes you think that?”
  • Record each student solution with an equation.

Activity 3: Centros: Momento de escoger (15 minutes)

Narrative

The purpose of this activity is for students to choose from activities that offer practice composing, decomposing, adding, and subtracting numbers.

Students choose from any stage of previously introduced centers.

  • What’s Behind My Back?
  • 5-frames
  • Make or Break Apart Numbers
  • Math Stories

Required Materials

Materials to Gather

Required Preparation

  • Gather materials from from: 
    • What’s Behind My Back, Stage 1
    • 5-frames, Stages 1 and 2
    • Make or Break Apart Numbers, Stage 1
    • Math Stories, Stages 1-3

Launch

  • “Hoy vamos a escoger centros de los que ya conocemos” // “Today we are going to choose from centers we have already learned.”
  • Display the center choices in the student book.
  • “Piensen qué les gustaría hacer primero” // “Think about what you would like to do.”

Activity

  • Invite students to work at the center of their choice. 
  • 10 minutes: center work time

Student Facing

Escoge un centro.

¿Qué hay a mis espaldas?

Center. What's Behind My Back.

Tableros de 5

Center. 5 frame.

Formar o separar números

Center. Make or break apart numbers.

Historias matemáticas

Center. Math Stories.

Activity Synthesis

  • “Cuando trabajamos en los centros, es divertido compartir nuestras ideas. Pero también tenemos que escuchar las ideas de nuestros compañeros. ¿Qué les gustó más: contar su historia o escuchar la historia de su pareja?” // “When we work in centers, it is fun to share our ideas but we also need to listen to our partner’s ideas. Which did you like better: telling your own story or listening to your partner’s story?”
  • “Cuando juegan en los centros, ¿qué pueden hacer para asegurarse de que saben escuchar a sus compañeros?” // “What can you do to make sure that you are a good listener when playing in centers?”

Lesson Synthesis

Lesson Synthesis

Read the task statement.

Andre and his older brother have 8 dates.
They stuff some of the dates with cheese.
They stuff the rest of the dates with almonds.
How many of the dates did they stuff with cheese?
Then how many of the dates did they stuff with almonds?

Draw 2 representations with 3 and 5 and 5 and 3, with labels and numbers, as pictured:

Diego:

Labeled circles.

Priya:

Labeled circles.

“Diego y Priya hicieron estos dibujos para mostrar lo que pasó en la historia. Priya dice que encontraron la misma respuesta al problema-historia. ¿Ustedes qué piensan?” // “Diego and Priya drew these pictures to show what happened in the story. Priya says that they found the same answer to the story problem. What do you think?” (They did find the same answer because they both showed 5 and 3. They did not find the same answer because one showed more dates with cheese and one showed more dates with almonds.)

Write an equation for both Diego and Priya’s solutions. For example:

  • Write \(8 = 3 + 5\).
  • “Andre y su hermano tenían 8 dátiles. Rellenaron 3 con queso y 5 con almendras. Podemos escribir eso así: 8 es 3 más 5” // “Andre and his brother have 8 dates. They stuff 3 of them with cheese and 5 of them with almonds. We can write that as 8 is 3 plus 5.”

Cool-down: Ambos sumandos desconocidos (5 minutes)

Cool-Down

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